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®±ª¢ , 2006
¤¤¨²¨¢ ¿ ¥¤¨¨¶ Additative identity ¥ ¤¤¨²¨¢ ¿ ´³ª¶¨¿ ¬®¦¥±²¢ If c is a complex number, it is customary to write : : : Additive set function rather than : : : ¤¬¨²² ±»© ¬¥²®¤ §¥ Admittance technique Aasen Admittance method ¡¡¥ ¤º¾ª²( ) ®¯°¥¤¥«¨²¥«¿ Abbe Adjoint of a determinant ¡¥«¥¢ ²¥®°¥¬ ©¢®°¨ Abelian theorem Ivory ¡¥«¼ ©¢½¨ Abel Iwany ¡° ¬®¢¨¶ ©§¥ª± Abramowitz Isaaks ¡±®«¾² ¿ ¥¯°¥°»¢®±²¼ ¬¥° ©§¥¸² ² Absolute continuity of measures Eisenstat ¡±®«¾²® ¥¯°¥°»¢®¥ ° ±¯°¥¤¥«¥¨¥ ©²ª¥ Absolutely continuous distribution Aitken ¡±®«¾²® ²¢¥°¤®¥ ²¥«® ª ¨ª¥ Rigid body Akaike ¡±®«¾²® ³¯°³£®£® ³¤ ° § ª® ªª¥°¥² The law of perfectly elastic impact Ackeret ¡±®«¾²®¥ § ·¥¨¥ (¬®¤³«¼) ª±¨®¬ ®²¤¥«¨¬®±²¨
By A we denote the maximum of the moduli (of the absolute values) of the eigenvalues of this matrix
Separation axiom Axiom of separation
Additive problem of the number theory
Farthest neighbor algorithm
¡±®«¾²®¥ ° ±¯°¥¤¥«¥¨¥ ¶¥¯¨ °ª®¢ Absolute distribution of a Markov chain ¢¨ £®°¨§®² Arti cial horizon ¡±²° £¨°®¢ ²¼±¿ ®²
ª±¨®¬ ° ±±²®¿¨¿ Distance axiom ª±¨®¬ ±·¥²®±²¨ Axiom of denumerability ª²¨¢ ¿ ¯¥°¥¬¥ ¿ We show how the idea of number separated itself from the Active variable objects counted ª²®¬¨®§¨®¢»© ¬®²®° ¢¨ ¶¨® ¿ £° ¢¨¬¥²°¨¿ Actomyosin motor Airborne gravimetry ª²³ «¼ ¿ ª®´¨£³° ¶¨¿ ¢®£ ¤°® Actual con guration Avogadro ª³±²¨·¥±ª¨© ²¥§®° ¢²®¬®¤¥«¼®¥ °¥¸¥¨¥ Acoustic tensor Self-similar solution «£¥¡° ª®¬¯«¥ª±»µ ·¨±¥« ¢²®¬®¤¥«¼®±²¼ Algebra of complex numbers Self-similarity «£¥¡° ¶¨«¨¤°¨·¥±ª¨µ ¬®¦¥±²¢ ¢²®°¥£°¥±±¨®®¥ ¨²¥£°¨°®¢ ®¥ ±ª®«¼- Algebra of cylinder sets §¿¹¥¥ ±°¥¤¥¥ Algebra of cylinders Autoregressive integrated moving average «£¥¡° ¨·¥±ª ¿ ±²¥¯¥¼ ²®·®±²¨ ª¢ ¤° ²³°» ¢²®²° ±¯®°²»© ¯®²®ª Polynomial degree of quadrature Trac ow «£¥¡° ¨·¥±ª¨© ¯®°¿¤®ª ²®·®±²¨ ª¢ ¤° ²³°» Polynomial order of quadrature £°¥ ²¨°®¢ ¨¥ Aggregation «£¥¡° ¨·¥±ª®¥ ¤®¯®«¥¨¥ ¤ ¬ ° Cofactor Hadamard Algebraic cofactor ¤ ¬± «£¥¡° ¨·¥±ª®¥ ±«³· ©®¥ ³° ¢¥¨¥ Algebraic random equation Adams «£®°¨²¬ ¤ ¯² ¶¨¨ ¤ ¯²¨¢ ¿ ®¶¥ª Adaptive estimate Adaptation algorithm ¤ ¯²¨¢ ¿ ¯°®¶¥¤³° «£®°¨²¬ \¡«¨¦ ©¸¥£® ±®±¥¤ " Nearest neighbor algorithm Adaptive procedure «£®°¨²¬ ¢¥²¢¥© ¨ £° ¨¶ ¤ ¯²¨¢»© «£®°¨²¬ Branch-and-bound algorithm Adaptive algorithm ¤ ¯²¨°®¢ »© ±«³· ©»© ¯°®¶¥±± «£®°¨²¬ ¢«®¦¥®£® ° §¡¨¥¨¿ (° ±±¥·¥¨¿) Nested dissection algorithm Adapted random process «£®°¨²¬ \¤ «¼¥£® ±®±¥¤ " ¤¤¨²¨¢ ¿ § ¤ · ²¥®°¨¨ ·¨±¥« 1
¬¯¥° Ampere ¬¯«¨²³¤ ¢®§¡³¦¤¥¨¿ Excitation amplitude ¬¯«¨²³¤ ¯³«¼± ¶¨© Pulsation amplitude ¬¯«¨²³¤®-¬®¤³«¨°®¢ »© ¨¬¯³«¼±»© ¯°®¶¥±± Amplitude-modulated pulse process ¬¯«¨²³¤»© ª®½´´¨¶¨¥² ®²° ¦¥¨¿ Amplitude re ection coecient ¬¯«¨²³¤»© ª®½´´¨¶¨¥² ¯°®¯³±ª ¨¿
«£®°¨²¬
¢ª«¨¤ Euclidean algorithm «£®°¨²¬ ¨¤¥²¨´¨ª ¶¨¨ Identi cation algorithm «£®°¨²¬ ¬ °¸°³²¨§ ¶¨¨ Routing algorithm «£®°¨²¬ ¬¨¨¬ «¼®© ±²¥¯¥¨ Minimum degree algorithm «£®°¨²¬ ¬®¤¨´¨ª ¶¨¨ Update algorithm Modi cation algorithm
«£®°¨²¬ ¥·¥²ª¨µ c-±°¥¤¨µ Fuzzy c-means algorithm Amplitude transmittance Amplitude transmission coecient «£®°¨²¬ ¯®¨±ª ± ¢®§¢° ²®¬ Backtrack algorithm «¨§ ¡«¨§®±²¨ Proximity analysis «£®°¨²¬ \° §¤¥«¿© ¨ ¢« ±²¢³©" «¨§ ¢»¦¨¢ ¥¬®±²¨ Divide-and-conquer algorithm Survival analysis «£®°¨²¬ ±² ¡¨«¨§ ¶¨¨ «¨§ ¤®¯³±²¨¬»µ ²° ¥ª²®°¨© Stabilization algorithm Feasible path analysis «£®°¨²¬ ³¯° ¢«¥¨¿ ¤¢¨¦¥¨¥¬ «¨§ ª ®¨·¥±ª¨µ ª®°°¥«¿¶¨© Motion control algorithm Canonical correlation analysis «£®°¨²¬¨·¥±ª ¿ ½²°®¯¨¿ Algorithmic entropy «¨§ ®±² ²ª®¢ Residual analysis «£®°¨²¬» ¬¨¨¬ «¼®© ±²¥¯¥¨ «¨§ ®¸¨¡®ª Minimum degree algorithms Error analysis «¤®³± «¨§ ®¸¨¡®ª ®ª°³£«¥¨¿ Aldous «¥ª± ¤¥° Roundo error analysis Rounding error analysis Alexander «¨§ ®¸¨¡®ª ®ª°³£«¥¨¿ ¯°¨ ®¡° ²®© ¯®¤««½ ±² ®¢ª¥ Allais Backward rounding-error analysis ««¾° «¨§ ¯®°¿¤ª ¢¥«¨·¨ Pace An order-of-magnitude analysis «´ ¢¨²»© ³ª § ²¥«¼ «¨§ ¯°¥¤¯®·²¥¨© Alphabetical subject index Preference analysis «¼¬ §¨ Almansi «¨§ ± ¯¥°¥¬¥»¬ ° §°¥¸¥¨¥¬ Multiresolution analysis «¼¬ ±¨ «¨§ ±¬¥°²®±²¨ Almansi Mortality analysis «¼´ -¯®²¥¶¨ « «¨§¨°®¢ ²¼ Alpha-potential All compounds are analyzed for nitrogen «¼´ -½ª±¶¥±±¨¢ ¿ ´³ª¶¨¿ Alpha-excessive function «¨²¨·¥±ª ¿ ¬¥µ ¨ª Analytical mechanics «¼´¢¥ «¨²¨·¥±ª ¿ µ ° ª²¥°¨±²¨·¥±ª ¿ ´³ª¶¨¿ Alfven Analytic characteristic function ¬ «¼¤¨ Amaldi «¨²¨·¥±ª¨ ¯°®¤®«¦¨²¼ ¯«®±ª®±²¼ Analytically continue on the plane ¬¤ « «®£¨·® Amdahl Analogously, by analogy with, likewise, similarly ¬¤ «¼ Amdahl Similarly to (® ¥ similarly as in) Section 1 In much the same way as in Section 1 ¬¨·¨ As (Just as) in Section 1 Amici As is the case in Section 1 ¬®²® «®£®-·¨±«®¢®© ¯°¥®¡° §®¢ ²¥«¼ Amonton Analog-to-digital convertor ¬®°²¨§ ²®° ª¥°»© ¡®«² Dashpot ( ¯°¨¬¥°, ¢ ²¥«¥ ²¨¯ ¥«¢¨ {®©µ² ) Anchor bolt ¬®°²¨§ ²®° ª®«¥±®© ¯ °» ®² ¶¨¿ ±² ²¼¨ Wheelset damper ¬®°²¨§ ¶¨®»© ¨ ¯°³¦¨»© ½«¥¬¥²» ¢ Abstract of the paper (article) ³«¨°®¢ ¨¿ ±µ¥¬ ²¥«¥ ¥«¼¢¨ {®©£² Annihilation scheme
Dashpot and spring elements in a Kelvin{Voigt type body
2
°¨´¬¥²¨ª ± ´¨ª±¨°®¢ ®© ²®·ª®© Fixed-point arithmetic °¨´¬¥²¨·¥±ª ¿ ¯°®£°¥±±¨¿ Arithmetic progression °¨´¬¥²¨·¥±ª ¿ ´³ª¶¨¿ Arithmetic function °¨´¬¥²¨·¥±ª®¥ ±°¥¤¥¥
³«¿²®° ¿¤°
Annihilator of the kernel
®¬ «¨¿ £° ¢¨² ¶¨® ¿ Gravity disturbance
®¬ «¼ ¿ ±®±² ¢«¿¾¹ ¿ Anomalous component
®±®¢
Arithmetic mean Arithmetical mean
Anosov
± ¬¡«¼, ´° ª¶¨¿
°ª£¨¯¥°¡®«¨·¥±ª ¿ ´³ª¶¨¿ Inverse hyperbolic function ± °¨ °¬ ²³° Ansari Reinforcement ²¥ ° ¤¨®¯¥«¥£ ²®° °¬ ²³° ¡¥²® Direction- nding loop Concrete reinforcement ²¥ ± ¥¯®±°¥¤±²¢¥»¬ ¯¨² ¨¥¬ °¬¨°®¢ ¿ ¸¨ Directly fed antenna Reinforced tire ²¨¡«®ª¨°®¢®· ¿ ²®°¬®§ ¿ ±¨±²¥¬ °¬¨°®¢ »© ¡ ¤ ¦ ¢²®¬®¡¨«¼®£® ª®«¥± Antilock braking (brake) system Reinforced tread ²¨ª®¬¬³² ²¨¢®¥ ±®®²®¸¥¨¥ °¬¨°®¢ ²¼ Anticommutative relation Reinforce ²¨¬ ²°®¨¤ °¬±²°®£ Antimatroid Armstrong ²¨¯®¤ «¼®¥ ¯®ª°»²¨¥ °®«¼¤¨ Antipodal cover (covering) Arnoldi ²¨²¥²¨· ¿ ±«³· © ¿ ¯¥°¥¬¥ ¿ °°¥¨³± Antithetic variate Arrhenius ¼¥§¨ °°¥¨³±®¢±ª ¿ § ¢¨±¨¬®±²¼ Agnesi Arrhenius plot ¯®´¥¬ ¯° ¢¨«¼®£® ¬®£®³£®«¼¨ª The perpendicular from center to a side of a regular poly- °²¨ª«¨ 1. °¨¬¥°» ¯°¥¤«®¦¥¨© ¡¥§ °²¨ª«¿ gon 1.1. ²±³²±²¢¨¥ °²¨ª«¥© ¯¥°¥¤ ±³¹¥±²¢¨²¥«¼¯®´¥¬ ¯° ¢¨«¼®© ¯¨° ¬¨¤» ª®²®°»¥ ®¡®§ · ¾² ¤¥©±²¢¨¿ (¢ ª®The perpendicular from vertex to base of a right pyramid »¬¨, ±²°³ª¶¨¿µ ± of ¬®¦¥² ¡»²¼ ¨±¯®«¼§®¢ the) ¯¯¥«¼ Group
(The) application (use) of De nition 1 yields (gives) (2) (The) repeated application (use) of (1) shows that : : : The last formula can be derived by direct consideration of the estimate (1) This set is the smallest possible extension in which di erentiation is always possible Using integration by parts, we obtain I = I1 If we apply induction to (1), we get A = B (The) addition of (1) and (2) gives (yields) (3) This reduces the solution to division by Ax (The) comparison of (1) and (2) shows that : : : Multiplying the rst relation in (1) by x and the second one by y, followed by summation, we come to the concise form of the above equations Therefore, we omit consideration of how to obtain this solution This specimen is subjected to uniaxial active tension Consider the invariant points of the compound transformation T R , where R denotes k-fold rotation through the angle 2
Appell
¯¯°®ª±¨¬ ¶¨¿ ¤ »µ Data tting
¯¯°®ª±¨¬ ¶¨¿ ¯® x Approximation in x
¯°¨®° ¿ ¨´®°¬ ¶¨¿ Information given a priory
¯°®¡¨°®¢ ²¼
To test (® ¥ approve)
¯¼¥§® Apiezon
° £® Arago
°£
Argand
°¥ -´³ª¶¨¿
Inverse hyperbolic function
°¨´¬¥²¨ª ° ±¯°¥¤¥«¥¨© ¢¥°®¿²®±²¥©
n
Arithmetic of probability distributions
°¨´¬¥²¨ª ± ®ª°³£«¥¨¥¬
k
k
1.2. ²±³²±²¢¨¥ °²¨ª«¥© ¯¥°¥¤ ±³¹¥±²¢¨²¥«¼»¬¨, ª®²®°»¥ ®¡®§ · ¾² ±¢®©±²¢ (¥±«¨ ½²¨ ±¢®©±²¢ ¥ ®²®±¿²±¿ ª ª®ª°¥²®¬³ ®¡º¥ª²³)
Rounded arithmetic
°¨´¬¥²¨ª ± ®²¡° ±»¢ ¨¥¬ ° §°¿¤®¢ Chopped arithmetic
In questions of uniqueness one usually has to consider : : : By continuity, (1) also holds when x = 1 By duality, we easily obtain the following equality In the above reasoning, we do not require translation invariance
°¨´¬¥²¨ª ± ¯« ¢ ¾¹¥© ²®·ª®© Floating-point arithmetic
°¨´¬¥²¨ª ± ³¤¢®¥®© ²®·®±²¼¾ Double-precision arithmetic
3
1.3. ²±³²±²¢¨¥ °²¨ª«¥© ¯¥°¥¤ ±³¹¥±²¢¨²¥«¼»¬¨ ¯®±«¥ of, ª®²®°»¥ ¿¢«¿¾²±¿ ²°¨¡³² ¬¨ ®±®¢®£® ±³¹¥±²¢¨²¥«¼®£® (¯®¿²¨¿)
The point x with coordinates (1; 1) A solution in explicit (implicit, coordinate) form ¤ ª®: let B be a Banach space with a weak sympletic form w ¤ ª®: (the) two random variables with a common distribution ¤ ª®: this representation of A is well de ned as the integral of f over the domain D Then the matrix A has the simple eigenvalue = 1 with eigenvectors x = (1; 0) and y = (1; 100)
A function of class C 1 We call C a module of ellipticity The natural de nition of addition and multiplication A type of convergence A problem of uniqueness The condition of ellipticity The hypothesis of positivity The method of proof The point of increase (decrease) A polynomial of degree n A circle of radius n A matrix of order n An algebraic equation of degree n (of rst (second, third) degree) A di erential equation of order n (of rst (second, third) order; ® an integral equation of the rst (second) kind) A manifold of dimension n A function of bounded variation The (an) equation of motion The (a) velocity of propagation An element of nite order A solution of polynomial growth A ball of radius r A function of norm p A matrix of full rank ¤ ª®: (the) elements of the form a = b + c (of the form (1))
1.5. ²±³²±²¢¨¥ °²¨ª«¥© ¢ ±«³· ¿µ ¨±¯®«¼§®¢ ¨¿ ¥±ª®«¼ª¨µ ¯°¨« £ ²¥«¼»µ ¨«¨ ¯°¨ ¯¥°¥·¨±«¥¨¿µ
The order and symbol of a distribution The associativity and commutativity of this operation The inner and outer factors (radii) of f The direct sum and direct product of these elements ¤ ª®: a de cit or an excess of electrons
1.6. ²±³²±²¢¨¥ °²¨ª«¥© ¯¥°¥¤ ±³¹¥±²¢¨²¥«¼»¬¨, ¨±¯®«¼§³¥¬»µ ¯®±«¥ to have ¡¥§ ¯®±«¥¤³¾¹¥£® ³²®·¥¨¿ ½²®£® ±³¹¥±²¢¨²¥«¼®£®
The (a) matrix A has nite norm (® has a nite norm not exceeding n) This function has compact support (® has a compact support contained in R) This matrix has rank n F has cardinality c This variable has absolute value 1 This matrix has determinant zero It is assumed that the matrix A has full rank This function has zero (® has a zero of order at least n at the origin of coordinates) This distribution has density g (¥±«¨ ±¨¬¢®« g ³¯®¬¨ «±¿ ° ¥¥; ¥±«¨ ¥², ²® has a density g) The number associated with a point on the plane has geometric signi cance
1.4. ²±³²±²¢¨¥ °²¨ª«¥© ¢ ¢»° ¦¥¨¿µ, ¨±¯®«¼§³¥¬»µ ¯®±«¥ with, without, in, as ¨ at ¤«¿ ³²®·¥¨¿ ±¢®©±²¢ ®±®¢®£® ±³¹¥±²¢¨²¥«¼®£®
We shall be concerned with real n-space This program package can be installed without much dif culty Then D becomes a locally convex space with dual space
1.7. ²±³²±²¢¨¥ °²¨ª«¥© ¯¥°¥¤ ±³¹¥±²¢¨²¥«¼»¬¨, ª®²®°»¥ ®¡®§ · ¾² ³±²®¿¢¸¨¥±¿ ®¡¹¨¥ ²¥®°¨¨ ¨ ° §¤¥«» ³ª¨
D0
The set of points with distance 1 from K The set of all functions with compact support The compact set of all points at distance 1 from K An algebra with unit e An operator with domain H 2 A solution with vanishing Cauchy data A cube with sides parallel to the axes of coordinates A domain with smooth boundary An equation with constant coecients A function with compact support Random variables with zero expectation (zero mean) Any random variable can be taken as coordinate variable on X Here t is interpreted as area and volume We show that G is a group with composition as group operation It is assumed that the matrix A is given in diagonal (triangular, upper (lower) triangular, Hessenberg) form Then A is deformed into B by pushing it at constant speed along the integral curves of X G is now viewed as a set, without group structure The (a) function in coordinate representation The idea of a vector in real n-dimensional space
This idea comes from numerical analysis (homological algebra, linear algebra) These theorems are proved in Morse theory (game theory, potential theory, distribution theory; ® in the theory of games, in the theory of potential, in the theory of distribution)
1.8. ²±³²±²¢¨¥ °²¨ª«¥© ¯¥°¥¤ ¨¬¥ ¬¨ ±®¡±²¢¥»¬¨ ¢ ¯°¨²¿¦ ²¥«¼®¬ ¯ ¤¥¦¥
Minkowski's inequality (® the Minkowski inequality) Cauchy (¨«¨ Schwarz) and Bunyakovski's famous inequality («³·¸¥ the famous Cauchy{Bunyakovski inequality, ¨«¨ the famous Schwarz{Bunyakovski inequality, ¨«¨ the famous Schwarz inequality) Newton's laws (¨«¨ the Newtonian laws, ® ¥ the Newton laws) Newton's rst (second) law (® ¥ the Newton rst (second) law) ¤ ª®: the Earth's surface («³·¸¥, ·¥¬ the surface of (the) Earth), the Moon's gravity («³·¸¥, ·¥¬ the gravity of (the) Moon)
1.9. ²±³²±²¢¨¥ °²¨ª«¥© ¯¥°¥¤ ±³¹¥±²¢¨²¥«¼»¬¨, ª®²®°»¥ ± ¡¦¥» ±±»«ª ¬¨ It follows from Theorem 1 that x = 1 4
(can) conclude that Ax = 0
Section 2 of this paper gives (contains) a concise presentation of the notation to be used below Property 1 is called (known as) the triangle inequality This assertion (statement, proposition) has been proved in part 1 (part (a)) of the (our) proof Algorithm 1 (± ¡®«¼¸®© ¡³ª¢») de nes elementary permutations and elementary triangle matrices of index 2 Equation (1) ((the) inequality (1)) can thus be written in the ( °²¨ª«¼ ®¡¿§ ²¥«¥) form (2) In the language of our notation, algorithm (1) (± ¬ «¥¼ª®© ¡³ª¢») is a stable way of computing the inner product The only place where the algorithm can break down is in statement 3 (in Statement 3) We combine Exercises 1 and 2 to construct an algorithm for nding an approximate eigenvector This case is illustrated in (® ¥ on ) Figure 1 The asymptotic formula (1) was proved in Example 1 Corollary 1 can be used to estimate the error in the inverse of a perturbed matrix By property 1 (by Theorem 1), this function is positive except at the zero vector A less trivial example is given in Appendix 3 Step 1 in Example 1 and steps 2 and 3 in Example 2 The idea of a norm will be introduced in Chapter 4 Now from statements 2 and 3 of (1), we have : : : All the drivers for solving linear systems are listed in Table 1 (are illustrated in Figure 1) If Algorithm 1 in four-digit arithmetic is applied to re ne x, then we obtain : : : Assertion (ii) is nothing but the statement that one natural way of extending these ideas to R is to generalize formula (1) to obtain a Euclidean length of a vector By property 1, this function is positive except at the zero vector We have seen on page 3 that set of matrices is a vector space which is essentially identical with : : : Equation (1) e ectively gives an algorithm for using the output of Algorithm 1 to solve : : :
2.3. ¯°¥¤¥«¥»¥ °²¨ª«¨ ¯¥°¥¤ ±³¹¥±²¢¨²¥«¼»¬¨, ª®²®°»¥ ¯°¨ ¯®¬®¹¨ of µ ° ª²¥°¨§³¾² ¤°³£®¥ ±³¹¥±²¢¨²¥«¼®¥ ¨«¨ ®¤®§ ·® ¯°¨ ½²®¬ ®¯°¥¤¥«¿¾²±¿
The continuity of f follows from the continuity of g The existence of bounded functions requires to be proved This representation of A is well de ned as the integral of f over the domain D There is (exists) a xed compact set containing the support of all the functions f Then x is the center of an open ball B The intersection of a decreasing family of such sets is convex ¤ ª®: every nonempty open set in X is a union of disjoint sets (§¤¥±¼ ¥² ®¤®§ ·®±²¨) i
2.4. ¯°¥¤¥«¥»¥ °²¨ª«¨ ¯¥°¥¤ ª®«¨·¥±²¢¥»¬¨ ·¨±«¨²¥«¼»¬¨
Recall that only the two groups have been shown to have the same number of generators Each of the three terms in the right-hand side of (1) satis es equation (2) (¥±«¨ ¢ (1) ¨¬¥¥²±¿ ²®«¼ª® ²°¨ terms)
2.5. ¯°¥¤¥«¥»¥ °²¨ª«¨ ¯¥°¥¤ ¯®°¿¤ª®¢»¬¨ ·¨±«¨²¥«¼»¬¨ The rst Poisson integral in (1) converges to g The second statement follows immediately from the rst
2.6. ¯°¥¤¥«¥»¥ °²¨ª«¨ ¯¥°¥¤ ¨¬¥ ¬¨ ±®¡±²¢¥»¬¨, ¨±¯®«¼§³¥¬»¬¨ ª ª ¯°¨« £ ²¥«¼»¥
The Dirichlet problem, the Taylor expansion, the Gauss theorem ¤ ª®: Newton's rst law ¨«¨ Taylor's formula ¤ ª®: a Banach space ¨«¨ a Chebyshev polynomial ¤ ª®: Gaussian (Gauss) elimination
n
2.7. ¯°¥¤¥«¥»¥ °²¨ª«¨ ¯¥°¥¤ ±³¹¥±²¢¨²¥«¼»¬¨ ¢® ¬®¦¥±²¢¥®¬ ·¨±«¥, ª®²®°»¥ ®¯°¥¤¥«¿¾² ª« ±± ®¡º¥ª²®¢ (¢±¥ ®¡º¥ª²» ±° §³), ¥ ª ª®©-«¨¡® ®¤¨ ®¡º¥ª²
2. °¨¬¥°» ¯°¥¤«®¦¥¨© ± ®¯°¥¤¥«¥»¬ °²¨ª«¥¬ 2.1. ¯°¥¤¥«¥»¥ °²¨ª«¨ ¯¥°¥¤ ±³¹¥±²¢¨²¥«¼»¬¨, ª®²®°»¥ ¡»«¨ ° ¥¥ ³¯®¬¿³²» ¢ ²¥ª±²¥ Let A 2 R. For every set B intersecting the set A we have :::
P
The real measures form a subclass of the complex ones The solutions to equation (1) are everywhere positive This class includes the Borel sets ° ¢¨²¥: let us assume that this class includes a Borel set
2.8. ¯°¥¤¥«¥»¥ °²¨ª«¨ ¯¥°¥¤ ±³¹¥±²¢¨²¥«¼»¬¨, ª®²®°»¥ ± ¡¦¥» ±±»«ª ¬¨
Let us represent exp x = x =i!. The (this) series can easily be proved to converge
The di erential problem (1) can be reduced to the form (2) The asymptotic formula (1) follows from the above lemma The di erential equation (1) can be solved numerically What is needed in the nal result is a simple bound on quantities of the form (1) The inequality (1) ( °²¨ª«¼ ¬®¦® ®¯³±²¨²¼) shows that
i
2.2. ¯°¥¤¥«¥»¥ °²¨ª«¨ ¯¥°¥¤ ±³¹¥±²¢¨²¥«¼»¬¨, ª®²®°»¥ ®¤®§ ·® ®¯°¥¤¥«¥» ª®²¥ª±²®¬ ¢ ¬®¬¥² ¨±¯®«¼§®¢ ¨¿ Let us consider the equation y = ax + b Let x be the root of equation (1) (¥±«¨ (1) ¨¬¥¥² ¥¤¨±²¢¥»© ª®°¥¼) Let T be the linear transformation de ned by (1) (¥±«¨ ®® ¥¤¨±²¢¥®) We see that x = 1 in the compact set X of all points at distance 1 from A Let B be the Banach space of all linear operators in X Let A = B under the usual boundary conditions This notation is introduced with the natural de nitions of addition and multiplication Using the standard inner (scalar, dot) product, we may
a>b
The bound (estimate) (2) is not quite as good as the bound (estimate) (1) If the norm of A satis es the restriction (1), then by the estimate (2) this term is less than unity Since the spectral radius of A belongs to the region (1), this iterative method converges for any initial guesses The array (1) is called the matrix representing the linear transformation of f It should be noted that the approximate inequality (1) 5
bounds only the absolute error in x The inequality (1) shows that : : : The second step in our analysis is to substitute the forms (1) and (2) into this equation and simplify it by dropping higher-order terms For small " the approximation (1) is very good indeed A matrix of the form (1), in which some eigenvalue appears in more than one block, is called a derogatory matrix The relation between limits and norms is suggested by the equivalence (1) For this reason the matrix norm (1) is seldom encountered in the literature To establish the inequality (1) from the de nition (2) Our conclusion agrees with the estimate (1) The characterization is established in almost the same way as the results of Theorem 1, except that the relations (1) and (2) take place in the eigenvalue-eigenvector relation
tion with suitable constants : : :, where D and D0 are di erential operators
3.4. ¥®¯°¥¤¥«¥»¥ °²¨ª«¨ ¯°¨ ®¯°¥¤¥«¥¨¨ ª« ±±®¢ ®¡º¥ª²®¢, ².¥. ¢ ²¥µ ±«³· ¿µ, ª®£¤ ±³¹¥±²¢³¥² ¬®£® ®¡º¥ª²®¢ ± § ¤ ®© µ ° ª²¥°¨±²¨ª®© A fundamental solution is a function satisfying the above equality We call E a module of ellipticity We try to nd a solution to equation (1) which is of the form : : :
3.5. ¥®¯°¥¤¥«¥»¥ °²¨ª«¨ ¢ ±«³· ¥ 3.4 ®¯³±ª ¾²±¿, ¥±«¨ ±®®²¢¥²±²¢³¾¹¨¥ ±³¹¥±²¢¨²¥«¼»¥ ¨±¯®«¼§³¾²±¿ ¢® ¬®¦¥±²¢¥®¬ ·¨±«¥
These integrals can (may) be approximated by sums of the form : : : Taking in (1) functions f which vanish in X , we come to the conclusion that : : : The elements of A are often call test functions The set of points with distance 1 from L The set of all functions with compact support
:::
This vector satis es the di erential equation (1) The Euclidean vector norm (2) satis es the properties (1) The bound (1) ensures only that these elements are small compared with the largest element of A There is some terminology associated with the system (1) and the matrix equation (2) A unique solution expressible in the form (1) restricts the dimensions of A The factorization (1) is called the LU -factorization It is very uncommon for the condition (1) to be violated The relation (1) guarantees that the computed solution gives very small residual This conclusion follows from the assumptions (1) and (2) The factor (1) introduced in relation (2) is now equal to 2 The inequalities (1) are still adequate We use this result without explicitly referring to the restriction (1) 3. °¨¬¥°» ¯°¥¤«®¦¥¨© ± ¥®¯°¥-
3.6. ¥®¯°¥¤¥«¥»¥ °²¨ª«¨ ®¯³±ª ¾²±¿, ¥±«¨ ±³¹¥±²¢¨²¥«¼»¥, ¨±¯®«¼§³¥¬»¥ ¢® ¬®¦¥±²¢¥®¬ ·¨±«¥, ¯®¤° §³¬¥¢ ¾² ¥ ¢±¥ ®¡º¥ª²» ¨§ § ¤ ®£® ª« ±± , ª ¦¤»© ¨§ ¨µ ¢ ®²¤¥«¼®±²¨
Direct sums exist in this category of abelian (Abelian) groups Closed sets are Borel sets Borel measurable functions are often called Borel mappings This makes it possible to apply these results to functions in C1 ¤ ª®: the real measures form a subclass of the complex ones (§¤¥±¼ ¯®¤° §³¬¥¢ ¥²±¿ ¢±¥ ®¡º¥ª²» ¨§ § ¤ »µ ª« ±±®¢)
¤¥«¥»¬ °²¨ª«¥¬ 3.1. ¥®¯°¥¤¥«¥»¥ °²¨ª«¨ ¢ ²¥µ ±«³· ¿µ, ª®£¤ ®¨ § ¬¥¿¾² ·¨±«® one
3.7. ¥®¯°¥¤¥«¥»¥ °²¨ª«¨ ¯¥°¥¤ ¯°¨« £ ²¥«¼»¬¨, ª®²®°»¥ ¢»¤¥«¿¾² ª ª³¾-«¨¡® ¨§ µ ° ª²¥°¨±²¨ª ±³¹¥±²¢¨²¥«¼®£®
The four centers lie in a plane For this, we introduce an auxiliary variable x A chapter of this book is devoted to the study of di erential equations
This map can (may) be extended to all of X in an obvious fashion (way, manner) A remarkable feature of this solution should be mentioned Theorem 1 describes in a uni ed manner the above approach A simple calculation (computation) yields (gives) x = y Let us consider two random variables with a common distribution The matrix A has a nite norm not exceeding 1 The function f has a compact support contained in F Now we can rewrite (1) with a new constant C A more general theory follows from this reasoning This equation has a unique solution for every (each) righthand side ¤ ª®: this equation has the unique solution x = 1
3.2. ¥®¯°¥¤¥«¥»¥ °²¨ª«¨ ¢ ²¥µ ±«³· ¿µ, ª®£¤ ®¨ ¢»¤¥«¿¾² ª ª®©-²® ®¡º¥ª² ¨§ ¥ª®²®°£® ª« ±± ¨«¨ ¨¬¥¾² ±¬»±« some ¨«¨ one of Hence, D becomes a locally convex space with dual space
D0
The right-hand side of (1) is then a bounded function This relation is easily seen to be an equivalence relation Theorem 1 can be extended to a class of boundary value problems The transitivity is a consequence of the equality x = y This is a corollary of Lebesgue's theorem for the above case After a change of variable in this integral we obtain a = b We thus come to the estimate jI j C with a constant C °²¨ 3.3. ¥®¯°¥¤¥«¥»¥ °²¨ª«¨ ¢ ±«³· ¥ 3.2 ®¯³±- Artin
ª ¾²±¿, ¥±«¨ ±®®²¢¥²±²¢³¾¹¨¥ ±³¹¥±²¢¨²¥«¼- °µ¨¬¥¤ »¥ ¨±¯®«¼§³¾²±¿ ¢® ¬®¦¥±²¢¥®¬ ·¨±«¥ Archimedes The existence of partitions of unity may be proved by ap- °µ¨¬¥¤®¢ ¯®¤º¥¬ ¿ ±¨«
plying the above theorem Buoyancy The de nition of distributions allows us to write this equa- ±¨¬¯²®²¨·¥±ª ¿ ®²®±¨²¥«¼ ¿ 6
½´´¥ª²¨¢-
ª«¨ Buckley « ± ¬ ±±» Mass balance « ± ¬®¬¥²®¢
®±²¼ Asymptotic relative eciency (ARE) ±¬ Assmann ±±®¶¨¨°®¢ ¿ ²¥®°¨¿ ²¥·¥¨¿ Associated ow theory ±±®¶¨¨°®¢ »© § ª®
Moment balance Balance of moments
« ± ±¨«
Associated law Associated rule
Force balance Balance of forces
±±®¶¨¨°®¢ »© § ª® ¯« ±²¨·¥±ª®£® ²¥·¥¨¿ Associated plastic ow rule ±±®¶¨¨°®¢ »© ±¯¥ª²° Associated spectrum ±²® Aston ²¢³¤ Atwood ²®¬®-£« ¤ª¨©, ²®¬®-£°³¡»© (-¸¥°®µ®¢ ²»©) Atomically smooth, atomically rough ²®¬®-£« ¤ª¨© ´°®² Facetted front ²¼¿ Atiyah ³¬ Auman ³½°¡ µ Auerbach ´´¨®° ¤¥´®°¬ ¶¨© Deformation gradient ¶¨ª«¨·¥±ª¨© ®°£° ´ Acyclic digraph ·¥±® Acheson ½°®£° ¢¨¬¥²°¨·¥±ª ¿ ±¨±²¥¬ Airborne gravimetry system ½°®¤¨ ¬¨·¥±ª¨ ¥§ ¢¨±¨¬® Independently in the aerodynamic sense ½°®¤¨ ¬¨·¥±ª®¥ ±®¯°®²¨¢«¥¨¥ Aerodynamic drag ½°®§®«¼ ¿ ¢§¢¥±¼ Aerosol ½°®±º¥¬ª
«¼¬¥° Balmer ¬¥ Baume µ Banach ¤ ¦ ¢²®¬®¡¨«¼®£® ª®«¥± Tread · Bunch ° Bar °¥¡« ²² Barenblatt °ª£ ³§¥ Barkhausen °«®³ Barlow °¥²² Burnett °±«¥© Barnsley °±
Porpoising (¢ ½°®¬¥µ ¨ª¥ | ¯®¤¯°»£¨¢ ¨¥ ¯°¨ ¢§«¥²¥)
°²¥«¼± Bartels ±±¥ Basset ³½° Bauer µ¢ «®¢ Bakhvalov ¸¥ Bachet ¸´®°² Bashforth ¥¡¡¨¤¦ Babbage ¥£³®ª «®£ °¨´¬¨·¥±ª®© «¨¥©ª¨ Cursor of a sliding rule ¥§
Airborne survey
¡¨½ Babinet ¡® Babo §®¢ ¿ «¨¨¿ Base line §®¢®¥ § ·¥¨¥ ¤ ¢«¥¨¿ Basis pressure value ©¥° Bayer ©¥± Bayes ©¥²² Baillette ª«¥©
Without increasing the speed : : : Without using this method : : :
¥§ ¢»¡®° ¢¥¤³¹¥£® ½«¥¬¥²
This subroutine computes an LU -factorization of a general tridiagonal matrix with no pivoting
¥§ ¤®ª § ²¥«¼±²¢
An axiom is a statement generally accepted as true without proof
¥§ ¤®¯®«¨²¥«¼®£® ³¯®¬¨ ¨¿ Without further mention
Buckley
7
¥§ ¯°¿¦¥¨© ¯®¢¥°µ®±²¼ Stress-free surface ¥§ ®£° ¨·¥¨¿ Without restriction ¥§ ®£° ¨·¥¨¿ ®¡¹®±²¨ Without loss of generality ¥§ ¯°®±ª «¼§»¢ ¨¿ Without slip ¥§ ±®¢¬¥±²®£® ¨±¯®«¼§®¢ ¨¿ °¥±³°±®¢
¥§° §¬¥°®¥ ¢°¥¬¿
¥§ ²°³¤
¥§° §¬¥°»© ¯ ° ¬¥²°
Dimensionless time
¥§° §¬¥°®¥ (®¡¥§° §¬¥°¥®¥) ³° ¢¥¨¥ Nondimensionalized equation
¥§° §¬¥°»© ¢¥°²¨ª «¼»© ¬ ±¸² ¡ (¡¥°¿ ° ¢»¬ 1) The dimensionless vertical scale (as 1)
¥§° §¬¥°»© ¢¨¤ (´®°¬ )
Dimensionless form Dynamic load balancing strategies for parallel shared- ¥§° §¬¥°»© ®¡º¥¬ nothing database systems Dimensionless volume
This program package can be installed without much dif- Dimensionless (nondimensional) parameter culty ¥§° §¬¥°»© ° ±µ®¤ ¯®²®ª ¥§ ³·¥² Dimensionless rate of ow This method is applied without due regard to the actual Dimensionless ow rate concentration of materials ¥§³ ¥§ ¢ °¨©»© Bezout Accident-free ¥§³¤ ° ¿ ¤¥´®°¬ ¶¨¿ ¥§¢¨µ°¥¢®¥ ¯®«¥ ±ª®°®±²¥© No-impact deformation Irrotational velocity eld ¥§³¤ °®¥ ¤¢¨¦¥¨¥ ¥§¨ª®¢¨· No-impact motion Besikovitsch Non-impact motion ¥§ª ¢¨² ¶¨®®¥ ²¥·¥¨¥ Impactless motion Cavitation-free ow ¥§³±«®¢® ¥§®¯ ±® In this case, Gaussian elimination is unconditionally staIn safety ble ¥§®¯ ±»© ¨²¥°¢ « ¥§³±«®¢»© ¡ §¨± All drivers should maintain a safe interval between vehi- Unconditional basis cles ¥§¼¥ ¥§®²°»¢®¥ ¤¢¨¦¥¨¥ Bezier Continuous motion
¥§®²°»¢®¥ ¤¢¨¦¥¨¥ (½««¨¯±®¨¤ ¯® ®¯®°®© ¥¥° Beer ¯«®±ª®±²¨) ¥©¥± The motion when the ellipsoid is in contact with the sup-
Bayes
porting plane
¥§®²°»¢®¥ ®¡²¥ª ¨¥ ²¥«
¥©¥±®¢±ª¨© ª°¨²¥°¨©
¥§®¸¨¡®·»© Error-free ¥§° §«¨·® It makes no di erence ¥§° §¬¥° ¿ ª®±² ² (ª®½´´¨¶¨¥²) Dimensionless constant (coecient) ¥§° §¬¥° ¿ ª®¶¥²° ¶¨¿ Dimensionless concentration ¥§° §¬¥° ¿ ª®®°¤¨ ² Dimensionless coordinate ¥§° §¬¥° ¿ (®¡¥§° §¬¥°¥ ¿) ²¥¬¯¥° ²³° Nondimensional (nondimensionalized) temperature ¥§° §¬¥° ¿ ¯¥°¥¬¥ ¿ Dimensionless variable ¥§° §¬¥° ¿ ¯®±² ®¢ª (§ ¤ ·¨) Nondimensional formulation ¥§° §¬¥° ¿ ´³ª¶¨¿
¥ªª¥°
Unseparated (separation-free, continuous) ow around a Bayes test ¥©ª¥° body Baker ¥§®²°»¢®¥ ²¥·¥¨¥ ¥©²¬¥ Unseparated ow Bateman Separation-free ow ¥ª ¥§®²°»¢»© ¯®£° ¨·»© ±«®© Beck Unseparated boundary layer Becker
¥ªª¥°¥«¼ Becquerel
¥«« Bell
¥««¬ Bellman
¥«¼²° ¬¨ Beltrami
¥°
Baire
¥°£¥° Berger
¥°£¬
Bergmann
¥°¥£ ²°¥¹¨» Crack face
Dimensionless function
8
¥°¥£ ¬ ª°®° §°»¢
¥²²¨
¥°¥£®¢ ¿ ¡ ² °¥¿
¥°± ©¤
¥°¥±
¨ ª¨
¥°«¨£
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Betti
Zones of macrofracture
Burnside
Coast battery
Bianchi
Behrens
Beurling
Binary di usion coecient Bingham
Bernard
Bernside
Binet
Bernoulli
Bisection
Bernstein
Biot
Berry
Birkho
Bers
A bisector (bisectrix) of a (the) triangle is the segment of the corresponding angle bisector (bisectrix) from the vertex to the point of intersection with the opposite side
¥°²«®
Berthelot
¥°²°
¨±±¥ª²°¨± ³£«
¥°¶¥«¨³±
¨²²¥°
¥±ª ¢¨² ¶¨®®¥ ®¡²¥ª ¨¥
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¥±ª®¥·® ¯°®²¿¦¥®¥ ²¥«®
« £®¤ °®±²¼
Angle bisector (bisectrix)
Bertrand
Bitter
Berzelius
Bifurcations
Cavitation-free ow
The author is grateful to : : : for the problem statement ((the) formulation of the problem) and for (constant) attention to this work (and for useful discussions)
In nite body
¥±ª®¥· ¿ ²®ª ¿ ¯« ±²¨ª ±® ±¢®¡®¤»¬ ª°³£®¢»¬ ®²¢¥°±²¨¥¬ Thin in nite plate with a (the) free circular hole
« §¨³±
In nitely remote At in nity
«¨¦ ©¸¨¥ ±®±¥¤¨
¥±ª®¥·® ³¤ «¥»©
Blasius
Nearest neighbors
¥±ª®¥·® ¬¥¿¾¹¨©±¿
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¥±ª®¥·® ° ±¸¨°¿¾¹¨©±¿
«¨§ª ¿ ±¢¿§¼
¥±ª®¥·® ³¤ «¥»©
«¨§ª¨© ª
Short-range order
Chemistry is a ever-changing science This in turn produces stresses in ever widening circles
Close connection
In nitely distant
Catalytic properties of quartz are similar to those of glassy coatings We consider this manifold as the set of matrices close to the matrix X
¥±ª®¥·®«¨±²»©
: : : of in nitely many sheets
¥±ª®¥·®¬¥°»©
: : : of in nite dimensions
«¨§ª¨© ª ª³¡³ (²¥«®, ¡«¨§ª®¥ ª ª³¡³ ¯® ´®°¬¥)
In nite discontinuity
«¨§ª® ° ±¯®«®¦¥»©
Turbulent (random, chaotic) motion
«®ª-±²®«¡¥¶
Without jumps
«®ª-±²°®ª
Bessel
«®²²®
Tracer-free
«®µ
Concrete structure Concrete construction
«®· ¿ ±²°³ª²³° ¤ »µ
¥±ª®¥·»© ° §°»¢ ¥¯°¥°»¢®±²¨
Near cube-shaped body
¥±¯®°¿¤®·®¥ ¤¢¨¦¥¨¥
Closely-spaced
¥±±ª ·ª®¢»©
Block column
¥±±¥«¼
Block row
¥±²° ±±¥°»©
Blotto
¥²® ¿ ª®±²°³ª¶¨¿
Bloch
Block data structure
«®· ¿ ±µ¥¬ µ° ¥¨¿ ¤ »µ
¥²®®¥ ®±®¢ ¨¥
Block storage
Concrete base
9
«®· ¿ ²°¥µ¤¨ £® «¼ ¿ ¬ ²°¨¶ Block tridiagonal matrix «®· ¿ ¶¨ª«¨·¥±ª ¿ °¥¤³ª¶¨¿ Block cyclic reduction «®·®¥ ¢¥¸¥¥ ¯°®¨§¢¥¤¥¨¥ Block outer product «®·®¥ ¤¨ £® «¼®¥ ¤®¬¨¨°®¢ ¨¥ Block diagonal dominance «®·®¥ ¯°¥¤®¡³±«®¢«¨¢ ¨¥ Block preconditioning «®·®¥ ¯°®¨§¢¥¤¥¨¥ Block product «®·®¥ ±ª «¿°®¥ ¯°®¨§¢¥¤¥¨¥ Block inner (dot) product «®·»© «£®°¨²¬ Block algorithm «³¦¤ ¨¿ ±«³· ©»¥ ¯® £° ¨¶¥ Random walks on boundary «¿¸ª¥ Blaschke ®£ ²»© Ores abundant in iron ®¤¥ Bode ®¤® Baudot ®¥ª ° §®£ »© Accelerated striker (impactor) ®§¥ Bose ®© ¨ Bolyai ®©«¼ Boyle ®ª®¢ ¿ £° ¨¶
®«¥¥ ¯®¤°®¡»© Our proof is more detailed than that given in [1] ®«¥¥ ±²°®£® More strictly ®«¥¥ ·¥¬ ¢¥°®¿²® It is more likely that : : : ®«¥¥ ¸¨°®ª¨© ª« ±±
®ª®¢ ¿ ª°®¬ª ª°»« Wing side edge ®ª®¢ ¿ £°³§ª Lateral load ®ª®¢ ¿ ¯¥°¥£°³§ª Side overload ®ª®¢ ¿ ¯®¢¥°µ®±²¼ ¸¨» Tire sidewall ®ª®¢ ¿ ±¢¿§¼ Lateral link ®ª®¢ ¿ ±²®°® ²°¥³£®«¼¨ª Lateral side of a (the) triangle ®ª®¢®¥ ¯° ¢«¥¨¥ Lateral direction ®ª®¢®¥ ®²¢¥°±²¨¥
®«¼¸¥¡ §®¢»© Large-base ®«¼¸¥ ¥¤¨¨¶» Greater than unity ®«¼¸¥ ¨«¨ ° ¢® n is greater than or equal to k (® ¥ greater or equal to) ®«¼¸¥ (¬¥¼¸¥) ·¥¬
Lateral boundary Side boundary
Lateral ori ce Lateral opening Lateral hole Lateral outlet
®ª®¢®¥ ³±ª®°¥¨¥ Side acceleration ®«¥§¼ ¤¢¨¦¥¨¿ ¢ ª®±¬®±¥ Space motion sickness ®«¥¥ ª®ª°¥²®
Due to its simplicity, the class of problems to which collocation is easily applied is greater than for the Galerkin method
®«¥¥ ° ¿¿ ²¥®°¥¬ ©«¥° An earlier theorem of Euler ®«¼¶ ® Bolzano ®«¼¶¬ Boltzmann ®«¼¸ ¿ ¬ ±± Large mass ®«¼¸ ¿ (¬ « ¿) ¯®«³®±¼ ²¥«
The semimajor (semiminor) axis («³·¸¥, ·¥¬ major (minor) semiaxis)
®«¼¸ ¿ ®¡¹®±²¼ Great generality ®«¼¸ ¿ ° §°¥¦¥ ¿ ±¨±²¥¬ Large sparse system of linear algebraic equations ®«¼¸ ¿ · ±²¼
Most of the material in Sections 1 { 3 is classical and may be found in standard references
®«¼¸¥
n is greater than K
Within this interval, the function f varies by greater than k
®«¼¸¥ ¥ ³¦¥ These data are no longer needed ®«¼¸¥ ¥² ¥®¡µ®¤¨¬®±²¨
There is no longer need in text les for this type of computers
Discretizations with order of accuracy greater (less) than three
®«¼¸¥ ¥ This question is no longer regarded ®«¼¸¥ ¥² ¥®¡µ®¤¨¬®±²¨ No longer need ®«¼¸¥© · ±²¼¾
The proofs are, for the most part, only sketched The Siberian coasts are for the most part covered with ice
®«¼¸¨¥ ®¡º¥¬» ¨´®°¬ ¶¨¨ Large amounts of information ®«¼¸¨© ·¥¬ All points at a distance greater than K from A ®«¼¸¨±²¢®
Most of the theorems presented here are (® ¥ is) original Most of them are (® ¥ is) zero elements A matrix is said to be sparse if most entries (elements) in the matrix are zero
More speci cally
10
®«¼¸¨±²¢® ¨§
° ³½°
®«¼¸®© For n large (® ¥ big) enough ®«¼¸®© ¤¨ ¬¥²° Large diameter ®«¼¸®© ®¡º¥¬ ¨±±«¥¤®¢ ¨© The large amount of research was accomplished ®«¼¸®© ±¨«» ²®ª Large current ®«¼¸®© ²¥¯«®¢®© ¯®²®ª Large heat ux ®«¼¸³¾ · ±²¼ ¢°¥¬¥¨ Most of the time ®«¼¿© Bolyai ®¬¡¼¥°¨ Bombieri ®¬½ Baume ®¤ Bond ®¤¨ Bondi ®¥ Bonnet ®° Bohr ®°¤ Borda ®°¥«¥¢±ª ¿ «£¥¡° Borel algebra ®°¥«¼ Borel ®°²®¢®© ¢»·¨±«¨²¥«¼ Aircraft-mounted computing device ®´®°² Beaufort ®µ¥° Bochner ° ¢¥ Bravais ° ³
°®¤µ³
Most of these two-letter codes apply (are applied) to both Brouwer, Brauer real and complex matrices °¥¬¥° ®«¼¸®¥ (¡®«¼¸¥¥) ª®«¨·¥±²¢® Bremer Most of the iterations were required at rst (starting) °¥² steps, since the initial and boundary conditions were un- Brent balanced °¥¾¹¨© ¯®«¥² ®«¼¸®¥ ª®«¨·¥±²¢® Low- ying The abundance of iron in the Sun °¨¤¦¬½ ®«¼¸®¥ ª®«¨·¥±²¢® ¯³¡«¨ª ¶¨© Bridgman A signi cant number of publications (works) are (® ¥ °¨ª± is) devoted to the analysis of mechanisms for wave prop- Brix agation of chemical transformations °¨««³½ ®«¼¸®¥ ° §®®¡° §¨¥ Brillouin A wide range of °¨««¾½ ®«¼¸®¥ ° ±±²®¿¨¥ Brillouin Long distance °¨¥«¼ ®«¼¸®¥ ·¨±«® Brinell It is required (it takes) a large number of iterations to °¨®±ª¨ ensure convergence Brioschi Brodhun
°®¥¢®©
Pertaining to armour
°®¨°®¢ ¿ ¬ ¸¨ Armored vehicle
°®± ²¼ ²¥¼ ¢ ¢¨¤¥ ª®³± To cast a cone of shadow
°®³
Brown
°³²²®-±µ¥¬ °¥ ª¶¨¨ Brutto-reaction scheme
°½££
Bragg
°½¤«¨
Bradley
°½ª¥²
Brackett
°¾
Bruhat
°¾±²® Bruceton
°¾±²¥° Brewster
³¤¥¬ £®¢®°¨²¼ ®
We shall speak of n-tuples as n-vectors
³¤¥²
It was calculated that the body would move if : : :
³¤³·¨
Being inversely proportional, these relations : : :
³¤³·¨ ¢ ¯°®±²° ±²¢¥
Once in space, the spacecraft requires no further propulsion to stay aloft (in ight)
³¤¼ ²® ¤¥¼ ¨«¨ ®·¼ Whether day or night
³§¥¬
Busemann
³«¼
Boole
³¿ª®¢±ª¨©
Bunyakovsky, Bunyakovskii
Brown, Braun
11
³°¡ ª¨ Bourbaki ³°¤® Bourdon ³°»© ¯®²®ª Turbulent ow ³±±¨¥±ª Boussinesq ³² Booth ³³± Booth ³·¥° Bucher » (· ±²¨¶ )
»±²°®¥ ³¢¥«¨·¥¨¥ ¢¿§ª®±²¨ Rapid increase in viscosity »±²°»©
For combustion to be rapid, the fuel and oxidant must be quickly mixed The most swift molecules possess sucient energy to escape from the atmosphere
»±²°»© «£®°¨²¬ Fast algorithm »±²°»© ¬¥²®¤
A number of very fast direct methods have been developed for this special case
»²¼ ¡¥±¯®«¥§»¬ To be of no use »²¼ ¢ ¥¢»£®¤®¬ ¯®«®¦¥¨¨ At that time, any geometrical system not in absolute To be at a disadvantage agreement with that of Euclid's would have been consid- »²¼ ¥¨§¢¥±²»¬ § ° ¥¥
To be unknown beforehand ered as obvious nonsense In order to produce such an amount of energy, this ther- To be unknown in advance mal power plant would require as much as 100 tons of coal »²¼ ³«¿¬¨ (±³²¼ ³«¨) Without the friction between our shoes and the oor we Are zero(e)s »²¼ ®¡¹¥¨§¢¥±²»¬ could not walk To be a matter of common knowledge »«® ¡» The transfer of liquid hydrogen from the Earth's surface »²¼ ¯°¨£®¤»¬ To be suitable for, to be suited ( t) for to orbit would be more dicult than : : : It is not essential that the stages in a step rocket be of To be adequate »²¼ ¯°¨·¨®© increasing size This causes a wave to arise : : : »«® ¡», ¥±«¨ ¡» It would be much easier to compute satellite orbits if the ¼¥¥¬¥ Bienaime Earth were perfectly spherical and had no atmosphere
¼¥°«¨£ Beurling ¼¥°ª¥ Bjorken ¼¾ª¨ Bucy ¼¿ª¨ Bianchi ½¡¡¨¤¦ Babbage ½©«¼¡¨ Beilby ½ª« ¤ Becklund ½ª³± Backus ½° A compromise between the shape preservation properties Baire of the Cesaro transformation and eciency for rapidly ½·¥«®° Batchelor converging sequences ¾°£¥°± »±²°®¤¥©±²¢¨¥ Burgers Speed-in-action ¾µ¥° »±²°®¤¥©±²¢¨¿ § ¤ ·
»±²° ¿ ¢»¡®°ª Quick access »±²° ¿ ¤¨´´³§¨¿ Fast di usion »±²° ¿ ª®®°¤¨ ² Fast coordinate »±²° ¿ ¯¥°¥¬¥ ¿ Fast variable »±²° ¿ ¯®±«¥¤®¢ ²¥«¼®±²¼ One scene followed the other in rapid succession »±²° ¿ ±¢¿§¼ Quick connection »±²°® ¢° ¹ ²¼±¿ Rotate rapidly »±²°® ¤¢¨£ ¾¹¨©±¿ Rapidly moving »±²°® ±µ®¤¿¹¨©±¿
Buchner, Buechner
The speed-in-action problem
»±²°®¥ ¢° ¹¥¨¥ Fast rotation (revolution) »±²°®¥ ¢° ¹¥¨¥ ¨¢¥± Fast Givens rotation »±²°®¥ ¯°¥®¡° §®¢ ¨¥ ¨¢¥± Fast Givens transformation »±²°®¥ ° ±¸¨°¥¨¥ Rapid expansion
B
: : : ¤¥±¿²¨·®¬ § ª¥ ¯®±«¥ § ¯¿²®© In the 18th decimal ¡«¨¦ ©¸¨¥ £®¤» In years to come ¡®«¥¥ ³§ª®¬ ±¬»±«¥ ±«®¢ In a narrower sense
12
¡®«¼¸¨±²¢¥ ±«³· ¥¢ In most cases it turns out that ¢¥ª®¢®¬ ±¬»±«¥ In the secular sense ¢¨¤¥ Any polynomial may be written in the form (1) ¢»¸¥¯°¨¢¥¤¥®¬ ¯°¨¬¥°¥ In the example above £ §¥ ° §®±²¼ ¯®²¥¶¨ «®¢ The potential di erence across the gas is high enough £®¤ ¤¢ ¦¤» Twice a year : : : £®¤³ In 1993 he showed (® ¥ has shown) : : : £®¤» The foundation of this theory was laid in the 1930{1950s ¤ «¼¥©¸¥¬ From now on, in what follows, in the sequel ¤ ®¥ ¢°¥¬¿
ª ·¥±²¢¥
Let us take x in place of y
ª ·¥±²¢¥ f ¢®§¼¬¥¬ : : : For f , we take : : :
ª¢ ¤° ²³° µ
: : : in quadratures
ª®¥·®¬ ¨²®£¥ As the nal result In total
ª®¥·®¬ ±·¥²¥
The maser may eventually prove to be the best coherent detector
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At (® ¥ in) the end of Section 1
ª®¶¥ ª®¶®¢
In the long run there appeared a conviction that the unending failure in the search for a proof of the parallel postulate : : : After all, a nonmetal may possess one or more characteristics typical of metal
For the time being, this phenomenon can be considered as catastrophic ª®®°¤¨ ²®¬ ¯°¥¤±² ¢«¥¨¨ ¤¢ ° § ¡®«¼¸¥ The function in coordinate representation An SSOR iteration requires twice the work of an SOR « ¡®° ²®°¨¨ (° ¡®² ²¼) iteration At the laboratory The force of gravity between the Earth and the Moon « ¡®° ²®°¨¨ (·²®-²® ¨¬¥¥²±¿) would be twice as great as it is if the Moon were twice as In the laboratory massive as it is : : : «¥² The distance from a vertex of a triangle to its centroid is The of the Earth's substance is estimated at 5000{ twice the distance from the centroid to the opposite side 7000 age million years of the triangle «¾¡®¥ ¢°¥¬¿ ¤¢ ° § ¬¥¼¸¥ ·¥¬ At all times Two times less than
«¾¡®¬ ¨§
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In any of the (cases)
A slight change in the proof actually shows that : : : In fact, a slight change in the proof shows that : : : Note that we did not really have to use : : :
¬ ±¸² ¡ µ
It is possible now to study the Earth's surface on a scale never before possible
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The energies required by the various studies of nuclei are ¬¥²°¨ª¥ In the metric in the 1 to 20 MeV range ¬¨³²³ The best results were obtained in a range up to 15 nautical Per minute ( ¯°¨¬¥°, revolutions per minute) miles ¬¨°¥ ¤®±² ²®·®¬ ª®«¨·¥±²¢¥ The two-word verbs occur in sucient number to permit It is just interesting to know what is the shortest (longest) river in the world the formation of certain rules of word order
¤°³£ ¤°³£ Mass and energy can be transformed into each other ¥¤¨¨¶ µ To measure in terms of weight § ¢¨±¨¬®±²¨ ®² ²®£®, ¿¢«¿¥²±¿ «¨ : : : According as the energy barrier is greater or less § ª«¾·¥¨¥ In conclusion § ·¨²¥«¼®© ¬¥°¥ To a considerable extent ¨§¢¥±²®© ¬¥°¥ To a certain extent ¨±²¨²³²¥ (° ¡®² ²¼) At the institute ¨²¥°¢ «¥ In the interval ª ¦¤®© ²®·ª¥ At each point of space
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The rotation of the Earth is in a clockwise direction if looking down above the South Pole
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The disk rotates at a constant angular velocity in the (a) counter-clockwise direction
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At the beginning of a sentence For the moment, we take P = 1
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In the early 1940s Early in the 1960s This principle was rst formulated in the early fties of the 20th century
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Under zero gravity
¥ª®²®°®¬ ±¬»±«¥ In some sense
13
¥ª®²®°»µ ¨¡®«¥¥ ±«®¦»µ ±«³· ¿µ
¯®°¿¤ª¥ ¢®§° ±² ¨¿ n
¥¬®£¨µ (¥±ª®«¼ª¨µ) ±«³· ¿µ
¯®±«¥¤¨¥ : : : «¥² (£®¤»)
In some of the most complicated cases
: : : only in few cases one succeeded in integrating : : :
¥¯®±°¥¤±²¢¥®© ¡«¨§®±²¨
In the order of increasing n
Much research activity in the past (last) 30 years has been directed at improving numerical methods
In close proximity to
¯°¥¤¥« µ
In descending order
¯°¥¤¥« µ ¤®±²¨£ ¥¬®±²¨
¨±µ®¤¿¹¥¬ ¯®°¿¤ª¥ ®¡° ²®¬ ¯®°¿¤ª¥
Obviously, this coecient varies over the range (0; 1)
Within the reach (grasp) of This expression can be understood by reading it back- ¯°¥¤¥« µ «¨¨¨ (®¡« ±²¨) wards Within the con nes of the line (domain)
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When we wish to refer to a LINPACK routine generically, In nature regardless of data type, we replace the second letter (sym- ¯°®±²° ±²¢¥ bol) by : : : The idea of a vector in real n-dimensional space is a natu ®¡¹¥¬ ¨±¯®«¼§®¢ ¨¨ ral generalization of the representation of points in a plane This notation is in general use today ¯°®²¨¢®¬ ±«³· ¥ ®¡¹¨µ ·¥°² µ This equation involves at most ve unknowns when b = 0 In general terms (nine otherwise) In the contrary case ®¤® ¬£®¢¥¨¥ Instantly ¯°®¶¥±±¥ The fact that nonzeros are generated in the course of ®¤®¬¥°®© ¯®±² ®¢ª¥ The inverse problem of frequency sounding in one dimen- Gauss (Gaussian) elimination is a complicating factor sion ¯°®¶¥±±¥ ¤¢¨¦¥¨¿ ®ª°¥±²®±²¨ In the course of motion In the (a) neighborhood of : : : ¯°®¶¥±±¥ ±®²°³¤¨·¥±²¢ ®±² ¢¸¥©±¿ · ±²¨ In the course of collaboration In the remainder of this chapter we require (assume) this : : : ° § function to be continuous How many times as great In the rest of this paper Twice (ten times, one third) as long as ®±² «¼®¬ Half as big as For the rest The longest edge is at most 10 times as long as the shortest one ®²¢¥² A has four times the radius of B In response to The diameter of L is 1=k times (twice) that of M ®²®¸¥¨¨ ²®£®, ª ª There exist many theories as to how gravitational force The number of sides increases in nitely (four times as many each time) may be overcome With the result that
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Individual cracks are usually rectilinear in plan A building rectangular in plan This object has an in-plane periodic structure
In its turn
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The only isomorphisms of the topological group T into itself are the identity map and the symmetry
The four centers lie in a (the) plane
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In the mid and late 1960's
To the full extent
In case of
We give the proof only for the case n = 3; the other cases are left to the reader In the case where (when) A is symmetric In case the matrix A is symmetric In the case of smooth norms Equality (1) holds only in case n 6= 1
The problem was presented in (a most) complete (® ¥ completed) form
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The arithmetic of numbers in decimal form is in full agreement with the arithmetic of numbers in fractional form
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±«³· ¥ ¥±«¨ (£°³¯¯®¢®© ¯°¥¤«®£)
In favor of
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In the event of The electrons are accelerated in the direction transverse ±«³· ¥ ª° ©¥© ¥®¡µ®¤¨¬®±²¨ In case of emergency to their propagation 14
±«³· ¥ ®¡¹¥£® ¯®«®¦¥¨¿ In the case of general position ±¬»±«¥
closed (explicit, implicit) form Equations written in this way are said to be in (¡¥§ °²¨ª«¿) self-adjoint (divergence, conservation) form
´®°¬¥ ¸ ° Sphere-shaped · ± ¯¨ª In the rush hour ¶¥«®¬
In the sense of Cauchy In the least-squares sense The contrasts in meaning of these two statements
±¬»±«¥ £« ¢®£® § ·¥¨¿ ®¸¨ In the sense of the Cauchy principal value ±¬»±«¥ ¨¬¥¼¸¨µ ª¢ ¤° ²®¢ In the least-squared sense ±®±²®¿¨¨ · «¼®¬ In the initial state ±¯¨±ª¥ On the list ±°¥¤¥¬ On the average ±°¥¤¥¬ ª¢ ¤° ²¨·¥±ª®¬ In mean square ²¥°¬¨ µ ¬ ²°¨·»µ ®¯¥° ¶¨© In terms of matrix operations ²¥·¥¨¥
In order to solve the problem on the whole, this condition should be met It takes n operations in total Overall, however, this approximation is still not very good
The editor could ensure that the edited material is returned to the author within a period of six weeks For a long time the internal combustion engine was the only type used for aircraft The sun provides us with light during the day
²¥·¥¨¥ 20 «¥² To study for 20 years ²¥·¥¨¥ «¾¡®£® ª®«¨·¥±²¢ ¢°¥¬¥¨ For any length of time ²® ¢°¥¬¿
Enough energy should be delivered to a (the) satellite at the time it is launched
²® ¢°¥¬¿, ª ª
While Newton studied the motion of bodies, he discovered : : :
²® ± ¬®¥ ¢°¥¬¿ ª ª At the point of At the moment that
²®¬ ±¬»±«¥ ª ª : : : In the sense of how waves are re ected in the uid ²®¬ ±¬»±«¥, ·²®
The proof of the theorem is constructive in that it actually suggests an algorithm for computing the factorization This method has the advantage over capacitance methods in that it does not require di erentiation to obtain : : : The computer is only automatic in the sense that it can deal with explicit instructions
²®¬, ·²®
The internal combustion engine di ers from the steam engine in that the fuel is burned directly in the cylinder
²°¥¡³¥¬®¬ ª®«¨·¥±²¢¥ (®¡º¥¬¥)
No other method seems to be available for producing tritium in the amount required
³¨¢¥°±¨²¥²¥ At (Moscow) university ³±«®¢¨¿µ ®²±³²±²¢¨¿ £° ¢¨² ¶¨¨ Under no-gravity conditions ³±«®¢¨¿µ ¯®¬¥µ Under noise conditions ´®°¬¥
The function f (x) cannot be written in (¡¥§ °²¨ª«¿)
½ª±¯«³ ² ¶¨¨ In service ½²® ¢°¥¬¿ At this time ½²®¬ ª°³£¥ ¯°®¡«¥¬ Within this range of problems £® (¦¥«¥§®¤®°®¦»©) Vehicle (¢ ¬®¦¥² ¡»²¼ ¨ car) ª®®¬ ¿ ¤¨ ¬¨ª Vakonomic dynamics ª®®¬ ¿ ¬¥µ ¨ª Vakonomic mechanics ª®®¬»© ¯®¤µ®¤ Vakonomic approach ª³³¬»© ¯³§»°¥ª Vacuum bubble ««¥ ³±±¥ Valee-Poussin de la ««¨± Wallis «¼¤ Wald «¼µ¥° Walchner ««¥ van Allen ¥¥° van Leer ®¢ van Hove - ©ª van Daik -¤¥-° ´ van de Graa -¤¥°- «¼± van der Waals -¤¥°- °¤¥ van der Waerden ¤¥°¬®¤ Vandermonde ¤¥°¯®« van der Pol «¨ Vanlinn ²-®´´ Van't Ho ¼¥-² °ª Wannier-Stark °£ Varga
15
°¨ ¶¨®® ¤®¯®«¨²¥«¼»© Complementary variational °¨ ¶¨¿ ¬ ±±» Mass variation °¨£ Waring °¨¼® Varignon ² °¨ Watari ²±® Watson ¡«¨§¨
¥¤³¹¨© ª®½´´¨¶¨¥² Leading coecient
¥§¤¥ ¢ ±² ²¼¥
Throughout the paper we shall use this subscript to denote : : :
¥§¤¥ ¨¦¥
From here on Throughout the following discussions
¥©¡³«« Weibull
¥©¥°¸²° ±± Weierstrass
¥©« ¤°½
The function f behaves in a special way near the corner Weil point of the domain D ¥©« ¥°¬ Oscillation of a layer near the state of rest Weyl
¢¥¤¥¬ ±«¥¤³¾¹¨¥ ®¡®§ ·¥¨¿ Let us introduce the following notation ¢¥¤¥¨¥ ¢ Introduction to matrix computations ¢¥°µ ¯® ¯®²®ª³ In the upward direction along the ow ¢¥°µ³ ² ¡«¨¶» At the top of the table ¢¥±²¨ ¯®¿²¨¥ To introduce the concept of a strain tensor ¢¨¤³ (£°³¯¯®¢®© ¯°¥¤«®£) In view of ¢®¤¨²¼ ¢ ¤¥©±²¢¨¥ To put into action (operation, use, practice) ¢®¤»© ³·¥¡¨ª An introductory textbook £¨¡ ²¼ To bend in ¤ ¢ ²¼±¿ ¢ ¯®¤°®¡®±²¨ To go into particulars (details) ¤ ¢«¨¢ ¾¹ ¿ ±¨« Pressing force ¤¢®¥ «³·¸¥ Twice as good ¤¢®¥ ¬¥¼¸¥ The error estimate is only half as large ¤³¢ Injection ¤³¢ ± ¯®¢¥°µ®±²¨ Another gas is injected at the surface of the sphere ¥¡¥° Weber ¥¡«¥ Veblen ¥¤¤¥°¡¥° Wedderburn ¥¤³¹ ¿ L-§ · ¿ ¬¥° Driving L-valued measure ¥¤³¹ ¿ £« ¢ ¿ ¯®¤¬ ²°¨¶ Leading principal submatrix ¥¤³¹ ¿ ¯®¤¬ ²°¨¶ Leading submatrix ¥¤³¹¨¥ ³·»¥ ¸ª®«» Leading scienti c schools ¥¤³¹¨© ¢ «
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Weiss
¥ª²®° ¡±®«¾²®© ±ª®°®±²¨ ¢° ¹¥¨¿
Vector of absolute rotational velocity (of the frame)
¥ª²®° ª²¨¢»µ ±¨« Active force vector
¥ª²®° ¢¨µ°¿
Vortex vector Vorticity vector
¥ª²®° ¢¥¸¥© (¢³²°¥¥©) ®°¬ «¨ Outward(inward)-pointing normal vector
¥ª²®° ¨§¬¥°¥¨¿ Measurement vector
¥ª²®° ª ± ²¥«¼®© Tangent vector
¥ª²®° ª¨¥²¨·¥±ª®£® ¬®¬¥² (¢ ¥¡¥±®© ¬¥µ ¨ª¥) Vector of kinetic moment
¥ª²®° ª®®°¤¨ ² Coordinate vector
¥ª²®° ¬ «®£® ¯®¢®°®² Small rotation vector
¥ª²®° ¬ ±±®¢»µ ¬®¬¥²®¢ Mass moment vector
¥ª²®° ¬®¬¥² Moment vector
¥ª²®° ¡«¾¤¥¨© Observation vector
¥ª²®° ®°¬ «¨ ª ¯®¢¥°µ®±²¨ Normal vector to the surface
¥ª²®° ®¡®¡¹¥»µ ±¨« Vector of generalized forces
¥ª²®° ¯ ° ¬¥²°®¢ Parameter vector
¥ª²®° ±ª®°®±²¨ ¯®²®ª Flow velocity vector Flux velocity vector
¥ª²®°, ²° ±¯®¨°®¢ »© ª ¢¥ª²®°³ v The transpose of the vector v
¥ª²®° ³° Schur vector
¥ª²®°¨ «¼ ¿ «¨¨¿ Line of greatest slope
¥ª²®° ¿ ®¯¥° ¶¨¿ Vector operation
Driving shaft
16
¥ª²®° ¿ ¯«®²®±²¼ Vector density
¥ª²®° ¿ ¯°®£®ª (¬¥²®¤) Vector sweep method
¥ª²®°®-ª®¢¥©¥°»¥ ¢»·¨±«¥¨¿ Vector pipeline computing
¥ª²®°®-ª®¢¥©¥°»© ª®¬¯¼¾²¥° Vector pipeline computer
¥ª²®°®¥ ±«®¦¥¨¥ Vector addition
¥ª²®°»¥ ¢»·¨±«¥¨¿ Vector computing Vector computation
¥ª²®°»© § ª® Vector law
¥«¨·¨ ±°¥¤¥£® ª¢ ¤° ² The mean square value ¥«¨·¨ ²¥¯«®¢®£® ¨¬¯³«¼± The intensity of heat impulse ¥«¨·¨ ²¥¯«®¢®£® ¯®²®ª Heat ux magnitude ¥«¨·¨ ²°¥¨¿ Friction magnitude ¥«¨·¨ ³£«®¢®© ±ª®°®±²¨
The value of angular velocity depends on the direction of the axis of rotation and the rate of rotation
¥«¨·¨ ³ª«® Downward gradient ¥«¨·¨»
Many of the quantities to be measured in the upper atmosphere are highly variable in time and space
¥ª²®°»© ¬¥²®¤
¥¤² Wendt ¥ ¥ª²®°»© ³£®« Venn Vectorial angle ¥²¨«¼ °¥£³«¨°®¢®·»© Vector angle Control valve ¥«¨ª ¿ ²¥®°¥¬ ¥°¬ ¥²¨«¿²®° ±¤¢®¥»© ± ¨§¬¥¿¥¬»¬ ¸ £®¬ «®Fermat's last theorem (FLT) ¯ ±²¥© Fermat's great theorem Twin controllable pitch fans ¥«¨·¨ To determine the magnitude of anything, it is necessary ¥²³°¨ Venturi to make a measurement ¥°¤¥ ¥«¨·¨ ¢¥ª²®° ¿ Verdet Vector quantity ¥° ¿ ¶¨´° (° §°¿¤) ¥«¨·¨ ¢¿§ª®±²¨ Correct digit Value of viscosity ¥°® ¨ ¤«¿ Magnitude of viscosity This is also true of decimal numerals ¥«¨·¨ £° ¤¨¥² ¥°³²¼±¿ (¢®§¢° ¹ ²¼±¿) Magnitude of a (the) gradient Now we return to the above problem ¥«¨·¨ § ¤ ¿ To return to the atmosphere Given quantity ¥°³²¼±¿ ª ¥«¨·¨ §¢¥§¤» Vectorial method Vector method
Magnitude of a star
¥«¨·¨ ¨²¥±¨¢®±²¨ Intensity magnitude
¥«¨·¨ (ª®«¨·¥±²¢®) ±¨«» ¯°¨«®¦¥®© The amount of force applied
¥«¨·¨ ª°¨²¨·¥±ª®© £°³§ª¨ Value of the critical load
¥«¨·¨ ¨·²®¦ ¿ Negligible quantity
¥«¨·¨ , ®¡° ² ¿ ª Quantity inverse to
¥«¨·¨ ¯®¤º¥¬
We now turn to the case when A is symmetric After this preliminary step, we can now return to : : :
¥°³²¼±¿ § ¤ Turn back ¥°®¥§¥ Veronese ¥°®¿²®
This approach is likely (very probable) to produce good results
¥°± «¼ ¿ ¤¥´®°¬ ¶¨¿ Versal deformation ¥°²¨ª «¼® ¢¢¥°µ
Upward vertically The 0z -axis (the axis 0z ) is directed along the upward vertical
Upward gradient
¥«¨·¨ ¯®¢®°®²
Measure of an angle is a value of a turn around its vertex ¥°²¨ª «¼®¥ ¢° ¹¥¨¥ Vertical rotation Constant quantity ¥°µ¥© °¥« ª± ¶¨¨ ¯®±«¥¤®¢ ²¥«¼®© ¬¥²®¤ ¥«¨·¨ ±¨«» Successive over-relaxation method Magnitude of a (the) force ¥°µ¥²°¥³£®«¼ ¿ ¬ ²°¨¶ ¥«¨·¨ ±ª®°®±²¨ Upper triangular matrix The magnitude of (a, the) velocity is known as the speed ¥°µ¨¥ (¨¦¨¥) ±«®¨ of a moving body Upper (lower) layers
¥«¨·¨ ¯®±²®¿ ¿
¥«¨·¨ ±®«¥·®© ° ¤¨ ¶¨¨ The quantity of solar radiation
¥°µ¨© «¥¢»© (¯° ¢»©) ³£®«
Upper left-hand (right-hand) corner
17
¥°µ¨© ¯° ¢»© («¥¢»©) ³£®« Upper right-hand (left-hand) corner ¥°µ¨© ¯°¥¤¥« ¨²¥£° « Upper limit of an integral ¥°µ¿¿ £° ¼ Upper bound Supremum
¥°µ¿¿ ¤¢³µ¤¨ £® «¼ ¿ ¬ ²°¨¶ Upper bidiagonal matrix ¥°µ¿¿ ª°®¬ª Upper edge ¥°µ¿¿ (¨¦¿¿) ±²®°® Upper (lower) side ¥°µ¿¿ (¨¦¿¿) ²°¥³£®«¼ ¿ ¬ ²°¨¶ Upper (lower) triangular matrix ¥°µ¿¿ (¨¦¿¿) ¯®·²¨ ²°¥³£®«¼ ¿ ¬ ²°¨¶ Upper (lower) Hessenberg matrix Almost upper (lower) triangular matrix
¥°µ¿¿ ¯®¢¥°µ®±²¼ ¯« ±²¨» Top (upper) surface of a (the) plate ¥°µ¿¿ ¸¨°¨ «¥²» Upper bandwidth ¥°µ³¸¥· ¿ ±¢¿§¼ Tip link ¥°µ³¸ª ¢®«®±ª®¢®£® ¯³·ª Hair bundle tip ¥°¸¨ ª®¨·¥±ª®© ¯®¢¥°µ®±²¨ Vertex of a conical surface ¥°¸¨ ª°¨¢®© Point of stationary curvature on a curve ¥°¸¨ ¯ ° ¡®«» Parabola vertex ¥°¸¨ ¤°¥§ (¤¥°¥¢ ) Cut tip ¥°¸¨ ¯°¿¬®£® ³£« The vertex at the right angle ¥°¸¨ ²°¥¹¨» Tip of the (a) crack Crack tip
¥± ±®±² ¢«¿¥² The total weight roughly amounts to 1 kg ¥± ª¢ ¤° ²³°» Quadrature weights ¥±®¢»¥ ¨±¯»² ¨¿ Weight tests ¥±®¬ ¿ ¦¨¤ª®±²¼ Fluid (liquid) under gravity ¥±±¥«¼ Wessel ¥±²¨¡³«®®ª³«®¬®²®°»© Vestibular oculomotor ¥±²¨¡³«¿°»© ª « Vestibular canal ¥±²´ «¼ Westphal ¥±¼ ¨«¨ · ±²¼
circle, in other words, as the measure of the entire path formed by the circle
¥²¢«¥¨¥ Bifurcation of solutions to (of) linear elliptic equations ¥²¢«¥¨¥ ª°¨¢®© Branching of a curve ¥²¢«¥¨¥ ±®¡±²¢¥»µ °¥¸¥¨© Bifurcation of eigensolutions ¥²¢«¥¨¥ ²¥·¥¨¿ Flow branching ¥²¢¿¹ ¿±¿ ¬®¤ Bifurcating mode ¥²°¿®© ¤¢¨£ ²¥«¼ Windmill ¥· ¿ ³±²®©·¨¢®±²¼ Eternal (everlasting, perpetual) stability ¥¹¥±²¢¥®¥ ° §«®¦¥¨¥ ³° Real Schur decomposition § ¨¬ ¿ § ¤ · The dual problem § ¨¬ ¿ ®°¨¥² ¶¨¿ Relative orientation § ¨¬®¯¥°¯¥¤¨ª³«¿°»© Mutually perpendicular § ¨¬® £° ¢¨²¨°³¾¹¨¥ ²¥« Mutually gravitating bodies § ¨¬® ¨±ª«¾· ¾¹¨¥±¿ ±®¡»²¨¿ Mutually exclusive events § ¨¬® ¯°®±²»¥ ·¨±« Relatively prime numbers Co-primes
§ ¨¬® ±®¯°¿¦¥»© Mutually conjugate § ¨¬®¥ ¢«¨¿¨¥ Mutual in uence of relative motion and mass transport § ¨¬®®¡° ²»¥ ²®·ª¨ Inverse points § ¨¬®-®¤®§ ·® In a one-to-one manner § ¨¬® ¯°®¨ª ¾¹¨µ ª®²¨³³¬®¢ ¯°¨¶¨¯ The principle of interpenetrating continua § ¨¬®¤¥©±²¢¨¥ Our approach to the study of interaction of the mediums § ¨¬®¤¥©±²¢¨¥ ¨§£¨¡ ¨ ° ±²¿¦¥¨¿ Bending-extension coupling § ¨¬®¤¥©±²¢¨¥ ´ § Phase interaction § ¨¬®¤¥©±²¢³¾¹ ¿ ¨£° Cooperative game § ¨¬®¤®¯®«¿¾¹¨©
These two aspects are to be regarded as complementary rather than antagonistic
§¢¥¸¥ ¿ § ¤ · ¨¬¥¼¸¨µ ª¢ ¤° ²®¢ Weighted least squares problem §¢¥¸¨¢ ¨¥ ¯® ±²®«¡¶ ¬ Column weighting This subroutine generates all or part of the orthogonal §¢¥¸¨¢ ¨¥ ¯® ±²°®ª ¬ Row weighting matrix Q §«¥² ± ³±ª®°¨²¥«¥¬ ¥±¼ ¨²¥°¢ « (ª« ±±, ¯°®¶¥±±) Assisted take-o (takeo ) The whole interval (class, process) §®° ¥±¼ ¯³²¼ To x gaze on a target
We shall de ne the circumference as the perimeter of the
18
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Winckler, Winkler
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Archimedean screw
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The integral is taken around the unit circle The integral is taken along the contour C
¨¡° ¶¨®»© £¨°®±ª®¯ Vibratory gyroscope Vibrating gyroscope
¨¡°®£¨°®±ª®¯ Vibratory gyroscope ¨¡°®¤ ²·¨ª ³£«®¢®© ±ª®°®±²¨ Vibrating angular-rate sensor ¨¡°®¯°®±¢¥·¨¢ ¨¥ ¥¬«¨ Vibrosounding of the Earth ¨¡°®±²®©ª®±²¼ Vibration resistance ¨£¥° Wigner ¨¤ There are two kinds of exception ¨¤ ¤¢¨¦¥¨¿ A sort of motion ¨¤ ±¡®ª³ Side elevation (view) ¨¤ ±§ ¤¨ Back (rear) elevation (view) ¨¤ ±¯¥°¥¤¨ Front elevation (view) ¨¤
Screw dislocation
¨²®¢ ¿ «¨¨¿ Spiral
¨²®¢ ¿ °¥§ª Screw thread
¨²®¢ ¿ ®±¼
Axis of rotation Central axis Screw axis
¨²®¢®¥ ¯¥°¥¬¥¹¥¨¥ Twist, torque
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Pertaining to screw
¨²° Vintr
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¨°²³ «¼ ¿ ¢ °¨ ¶¨¿ Virtual variation
¨°²³ «¼»¥ ¯¥°¥¬¥¹¥¨¿ Virtual displacements
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Witt de
¢¿§ª®±²¼ The boundary conditions are either periodic or of the form ¨µ°¥¢ ¿ Eddy viscosity (3) with p and q constant along each side of a rectangular domain
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Vortex viscosity
¨µ°¥¢ ¿ ®¡« ±²¼ Vortex region
¨µ°¥¢ ¿ ¯ ° Vortex pair
¨µ°¥¢ ¿ ²¥®°¨¿ The vortex theory
¨µ°¥¢®£® ¤¢¨¦¥¨¿ £¥®¬¥²°¨¿ Geometry of vortex motion
¨µ°¥¢®¥ ¢®§¬³¹¥¨¥ Vortex disturbance Vortex perturbation
¨µ°¥¢®¥ °¥¸¥¨¥ Vortex solution
¨µ°¥¢®© ¦£³² Vortex core Rotating core
¨µ°¥¢®© ±«¥¤ Vortex wake
¨µ°¼ ¢¥ª²®° Curl of a vector
¨µ°¼ °¬ Karman's vortex
¨µ°¼ ¯®¢¥°µ®±²»© Surface vorticity
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Wiener-Hopf
19
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Vorticity vector
Inclusion in a set
Outer contour External ow
With an accuracy up to the terms of second order of small- Outer layer ness inclusive ¥¸¨© ±²¨¬³« External stimulus ª«¾·¨²¥«¼® ¤® : : : : : : to develop up to and including the rst e ect of ¥¸¿¿ (¢³²°¥¿¿) £°³§ª nonzero M0 External (internal) load Scale e ect
Exterior Neumann boundary value problem
Nested grids (meshes) Exterior boundary value problem A nested dissection ordering can lead to sparse Gauss ¥¸¿¿ £°³§ª (Gaussian) elimination External load To study (1) along with (2) This lecture hall has capacity for audience of 200 The variable y is taken in place of x
Frozen coordinates
Exterior Dirichlet boundary value problem Outer (outside) surface of a (the) cylinder External ratio
External work
It is important, however, to realize at the outset (from the At the bottom of the gure very outset) that the term : : : ®¢¼ ®¡° §®¢ »© ¥ §®» ®¡±«³¦¨¢ ¨¿ ²¥«¥´®®© ±¥²¨ The formation of nuclei in newly formed galaxies Out of the coverage ³²°¥¥ ª ± ²¼±¿ ¥ ±° ¢¥¨¿ This surface is inward tangent to the sphere S at the Beyond comparison point x ¥¤¨ £® «¼»© ½«¥¬¥² The circles internally (inwardly) tangent to the unit circle O -diagonal element These circles are internally tangent to the unit circle Extraterrestrial intelligence Extracellular substance Externally
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Internal boundary value Internal motion Inner product Dot product
This circle is externally tangent to the unit circle
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External action
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External rotation
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External heating
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Outer product Vector product
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¥¸¥¥ ¢®§¤¥©±²¢¨¥ ¥¸¥¥ ¢° ¹¥¨¥ ¥¸¥¥ £°¥¢ ¨¥
¥¸¥¥ ¯°®¨§¢¥¤¥¨¥ ¥¸¥¥ ° §«®¦¥¨¥ Outer expansion
¥¸¥¥ ²¥¯«®§ ¹¨²®¥ ¯®ª°»²¨¥ External heat-shielding coating External heat protection coating
¥¸¨¥ ·«¥»
Inner expansion
Interior eigenvalue
Interior relation(ship)
Internal (inside) heat-shielding coating Internal (inside) heat protection coating Internal friction Inner friction
³²°¥¥¥ ¿¤°® ¥¬«¨ The Earth's inner core
³²°¥¨¥ ¯¥°¥¬¥»¥ ±®±²®¿¨¿ Internal state variables
Extreme terms
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The exterior of the (an) engine
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Internal degrees of freedom Inside diameter Internal diameter
External diameter
20
³²°¥¨© ª®²³° Inner contour
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®¤®-¢®¤¿®© ¿¤¥°»© °¥ ª²®° Pressurized water reactor (PWR) Pressurized water nuclear reactor
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®§¢¥¤¥¨¥ ¢ ±²¥¯¥¼ n
® ¢±¥µ ®²®¸¥¨¿µ
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Internal angular momentum
Internal ow
Interior extremum
Interior Neumann boundary value problem
Rectangular (trapezoidal, triangular) weir Sharp-edged weir Over ow edge Water gauge
Interior injectivity
Watery
Inner (inward) normal
Voevodin
Interior boundary value problem
Exciting force
Interior Dirichlet boundary value problem
Excitation amplitude
Internal ratio
The temperature t satis es this equation in the interior of Raising to the nth power ®§¢¥¤¥¨¥ ¢ ±²¥¯¥¼ «¨¨¨ the region (domain) R Involution on a line ³²°¥¿¿ £°³§ª ¤¨ ¬¨·¥±ª ¿ ®§¢¥¤¥¨¥ ¢ ²°¥²¼¾ ±²¥¯¥¼ Internal dynamic load Cubing ³²°¥¿¿ ¯¥°¥¬¥ ¿ ®§¢¥±²¨ ¢ ±²¥¯¥¼ n Inner variable To raise to the nth power ³²°¥¿¿ ¯«®²®±²¼ (¤ ¢«¥¨¥) ®§¢° ² ¤¥¥£ Inner density (pressure) Money back ³²°¥¿¿ ° ¡®² ®§¢° ² ¿ ¢®« Internal work Re ected wave ³²°¥¿¿ ±ª®°®±²¼ £°¥¢ ¨¿ ®§¢° ² ¿ ±²°³¿ Internal heating rate Reverse jet ³²°¥¿¿ ²¥¬¯¥° ²³° The inside temperature of the Sun is estimated to be : : : ®§¢° ²®¥ ¤¢¨¦¥¨¥ Recurrent motion ³²°¨ There is some concern whether a strain pulse measured ®§¢° ²®¥ ²¥·¥¨¥ by a gauge on the surface of a bar (rod) is representative Reverse ow of the wave travelling down its interior ®§¢° ²®±²¼ ´ §®¢»µ ²° ¥ª²®°¨© Recurrence of phase trajectories ³²°¨ ª ¬¥°» ±£®° ¨¿ Inside the combustion chamber ®§¢° ¹ ¥¬®±²¼ The property to be returnable is absent ³²°¨ª«¥²®· ¿ ¬¨¸¥¼ Intracellular target ®§¢° ¹¥¨¥ Return to the old theory ³²°¨¯®°®¢®¥ ¤ ¢«¥¨¥ The possibility of a successful reentry of the rocket was Intrapore pressure demonstrated ³²°¨´ §»© ®§¬®¦ ¿ ° ¡®² Intraphase Virtual work ® ¢°¥¬¿ ¨±¯®«¥¨¿ ¯°®£° ¬¬» Two implementations of the library selectable at program ®§¬®¦® It is possible for a function to be continuous execution time (runtime) allow optimized use of : : : In all respects
® ¨§¡¥¦ ¨¥ § ²°³¤¥¨©
It is possible for such a system to be used as carriers of energy
To avoid diculties
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These methods are much like those considered above
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By all means, at any cost
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Possible (® ¥ feasible) global chill Feasible motion
Possible deviation Secondly, we have not yet commented on the speed (rate) ®§¬®¦»¥ ¯¥°¥¬¥¹¥¨¿ Virtual (possible) displacements of convergence 21
®«®®¡° §®¢ ¨¥ Rise of (the) waves ®«®ª® ¤¥°¥¢ Theorem 1 shows that the active Jordan form is robust Wood grain ®«®±ª®¢ ¿ ª«¥²ª under small perturbations to the problem Hair cell ®§¬³¹¥¨¥ ¬ ¿²¨ª ®«®±ª®¢ ¿ ²°¥¹¨ Excitation of a pendulum Hair-line crack ®§¬³¹¥¨¥ ¯®±²®¿®© · ±²®²» Hair crack Constant-frequency disturbance (perturbation) ®«®±ª®¢»© ¯³·®ª ®§¨ª ²¼ Boundary conditions of this form arise in a number of Hair bundle di erent settings ®«¼² ®§¨ª ²¼ ¢ ±¢¿§¨ ± Volta In designing the engine, special problems may emerge ®«¼²¥°° from fuel consumption Volterra ®«¼´®¢¨¶ ®§¨ª®¢¥¨¥ ª®¢¥ª¶¨¨ The onset of convection Wolfowitz ®§° ±²»¥ ° §«¨·¨¿ ®«¼´±® Age distinctions Wolfson ®§¼¬¥¬ ®®¡¹¥ When we wish to refer to a LINPACK routine generically, We shall take ®© ¯°®²¨¢ regardless of data type, we replace the second letter (symThe war on (against) bol) by : : : ®© ± ®®¡¹¥ ¥ Gamma rays have no charge at all The war against (with, on) ®-¯¥°¢»µ ®« °®¢¨· Volarovich First (® ¥ at rst) we note that : : : ®«« ±²® In the rst place, this algorithm may loop inde nitely if A is too ill conditioned for the iteration to converge Wollaston ®¯°®± ¢°¥¬¥¨ ®««¬½ A matter of time Wallman ®« £®°¥¨¿ ®¯°®± ® ²®¬, ª ª : : : The question of how to obtain the sought-for solution for Combustion wave the problem formulated in terms of stresses ®« ª°³²¨«¼ ¿ (° ±²¿£¨¢ ¾¹ ¿) ®°®ª®®¡° §»© ¢¨µ°¼ Torsional (tensile) wave Funnel vortex ®« £°³¦¥¨¿ Load wave ®±¯°¨¿²¨¥ ¯°®±²° ±²¢ Space perception ®« ¥³±²®©·¨¢®±²¨ Space cognition Instability wave ®±¯°®¨§¢®¤¿¹¥¥ ¿¤¥°®¥ ¯°®±²° ±²¢® ®« -¯°¥¤¢¥±²¨ª Reproducing kernel space Precursor wave ®« ° §°³¸¥¨¿ ®±±² ¢¨²¼ ¯¥°¯¥¤¨ª³«¿° To erect a perpendicular Destruction wave ®±±² ®¢¨²¼ ¯¥°¯¥¤¨ª³«¿° ®« ±¬¥¹¥¨© To draw a perpendicular Displacement wave ®±±² ®¢«¥¨¥ °µ¨²¥ª²³°» ®« ²®°¬®¦¥¨¿ (³±ª®°¥¨¿) Deceleration (acceleration) wave Architecture recovering ®« ½¥°£¨¨ ®±µ®¤¿¹ ¿ (¨±µ®¤¿¹ ¿) ¢¥°²¨ª «¼ Upward (downward) vertical Energy wave ®±¼¬ ¿ · ±²¼ ®«®¢ ¿ ¤¨ ¬¨ª Wave dynamics (wavedynamics) One eighth part ®«®¢ ¿ ª °²¨ ®±¼¬¨£° »© Wave pattern Eight-faced ®«®¢®¤ ®¯®°»© (¯¥°¥¤ ¾¹¨©) ¯¥°¥¤¨ There are closed streamlines in front of the blu bodies Supporting (transmitting) waveguide ®«®¢®¥ ¯°¨¡«¨¦¥¨¥ Flow separation from the body surface well ahead of the Wave approximation rear stagnation point ®«®¢®¥ °¥¸¥¨¥ ¯«®²¼ ¤® Some people can hear sounds as high as 20000 cycles Wave solution The voltage dropped to as low as 25 volts ®«®®¡° §®¥ ¤¢¨¦¥¨¥ ®§¬³¹ ¾¹ ¿ ´³ª¶¨¿ Perturbation function ®§¬³¹¥¨¥
Flights at speeds up to Mach 3 Operations at temperatures down to 5 C
Wave-like motion Wavy motion
22
°¥¬¿ ±³¹¥±²¢®¢ ¨¿
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Existence time Lifetime
Completely additive measure
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Completely continuous operator
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This property will be used in the sequel
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Rotary derivative
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Rotational Couette ow
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Collapse time
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The time it takes for a body to fall along this curve
Relaxation time for the self-similar solution
° ¹ ²¥«¼ ¿ ¯°®¨§¢®¤ ¿
Wronski
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The close agreement of these data is unlikely (is probably not) to be a coincidence
° ¹ ¾¹¨©±¿ £¨°®±ª®¯ Spinning gyroscope
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Thus, this subroutine name refers to any or all of the routines
Spinning detonation
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Rotating liquid ( uid)
All we can do in this regard (at present) is to compare these results
° ¹ ¾¹ ¿±¿ ¯®¬¯ Rotating pump
° ¹ ¾¹ ¿±¿ ±´¥° (¢®ª°³£ ±¢®¥© £¥®¬¥²°¨·¥- ±¥£¤ This equation is always self-adjoint ±ª®© ®±¨) ±¥£¤ ª®£¤ Spinning sphere The integral S is equal to zero whenever n is odd ° ¹ ¾¹¨¥±¿ ¶¨«¨¤°» ±¥£® (¢ ±®¢®ª³¯®±²¨) Rotating cylinders
There are nine circles in all
° ¹¥¨¥ ¢¥ª²®° ±ª®°®±²¨ Rotation of the velocity vector
±¥£® «¨¸¼
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Rotation about an (the) axis through an angle of 2
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° ¹¥¨¥ £« §
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° ¹¥¨¥ ª°¨¢®© ¢®ª°³£ ®±¨
±¥¶¥«® ±¬¥¸ ¿ ¨£°
The wave properties are found to be merely two di erent aspects of the same thing
° ¹¥¨¥ ¢®ª°³£ ®±¨
Newton created his theory of universal gravitation being only 24 years old
Givens rotation Eye rolling Ocular rolling
Universal quanti er
Completely mixed game
Revolution of a curve about an axis
±¥ £®¢®°¨² ® ²®¬, ·²® : : :
° ¹¥¨¥ ³£®«
It is every indication that : : :
Rotation of the gure F through (about) an angle of
±¥ ¥¹¥
° ¹¥¨¥ ®ª®«®
Rotation of the gure F about the origin of coordinates
A (¨«¨ One) question still unanswered is whether : : : What is still lacking is an explicit description of : : : This application is still useful in the banking industry This method is still used (up) to this (present) day The phase that is not yet destroyed As yet we have not considered the speeds of spacecrafts
° ¹¥¨¥ ± ¬®«¥² ®²®±¨²¥«¼® ¯®¯¥°¥·®© ®±¨ Pitch
°¥¬¿ ¢»¯®«¥¨¿ ¯°®£° ¬¬» Program running time
±¥ ¦¥
Displacement time
±¥ ¯°®±²° ±²¢®
Execution time
±¥ ° ±±²®¿¨¥ (¯®«®¥ ° ±±²®¿¨¥)
Final time
±¥ ²¥«®
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This problem is still more dicult than the previous one The whole space Total distance
Body as a whole The mass of a whole body is the sum of the masses of its parts
A control that ensures a precise lower estimate for disengagement time is proposed
°¥¬¿ ¯®¤£®²®¢ª¨ ¤ »µ
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°¥¬¿ °¥« ª± ¶¨¨ (¯®«§³·¥±²¨)
±ª®°¥ ¯®±«¥
Data ready time
Residence time of droplets in the (a) reactor
Ever larger nite sets
If all this seems complicated, remember that : : : Shortly after
Relaxation (creep) time
23
±«¥¤ Immediately after ±«¥¤ § ½²¨¬
²¥ª ¾¹ ¿ ±²°³¿
±«¥¤±²¢¨¥ (£°³¯¯®¢®© ¯°¥¤«®£) In consequence of ±«¥¤±²¢¨¥ ·¥£® In consequence of which ±¯«»¢ ¾¹¨© ª« ±²¥° Up oating cluster ±¯«»¢ ¿ ±¨« Force of buoyancy ±¯«»²¨¥ ¯³§»°¼ª Bubble oating-up ±¯®¬®£ ²¥«¼»¥ ±°¥¤±²¢ Auxiliary means ±¯®¬®£ ²¥«¼»© ª®¬¯¼¾²¥° Satellite computer ±¯»¸ª ®«¶¥ A solar are ±² ¢¨²¼
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Inward jet In owing jet
In this experiment, the speed increases and thereafter de- ²¥ª ¾¹¨¥ ª ¯«¨ creases steadily In owing droplets
Interior Neumann boundary value problem
²®° ¿ ª° ¥¢ ¿ § ¤ ·
The Neumann boundary value problem
²®° ¿ ®°¬ ¬ ²°¨¶» The matrix 2-norm The 2-norm
²®°®© ·«¥ ¯°®¯®°¶¨¨ Consequent in a proportion
²®°®±²¥¯¥®¥ ¢«¨¿¨¥ Minor in uence
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Wood
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Entry of the rocket into the lower atmosphere
µ®¤ ¢ ²¬®±´¥°³ °±
Martian atmospheric entry To interpose a screen grid between the cathode and the µ®¤ ¢ ª « plate Channel inlet ±² ¢«¥»¥ ¯°®¬¥¦³²ª¨ µ®¤ ¥² Nested intervals Exit only
±²°¥· ²¼±¿ Uranium occurs in three isotopic forms ±²°¥· ²¼±¿ ¢ «¨²¥° ²³°¥ : : : is seldom encountered in the literature ±²°¥· ¿ ¢®« Oncoming wave ±²°¥· ¿ ±²°³¿ Counterjet ±²°¥·»¥ ²¥·¥¨¿ Secondary ows ±²³¯ ²¼ ¢ ¤¥©±²¢¨¥
µ®¤¨²¼ ¢ ¢¥°µ¨¥ ±«®¨ ²¬®±´¥°» To enter the upper atmosphere
µ®¤®¥ ³±²°®©±²¢® ¯°¿¬®²®·®£® ¤¢¨£ ²¥«¿ Inlet of a (the) ramjet
µ®¤®© ¯®²®ª ¦¨¤ª®±²¨ Fluid in ow Input uid ow Inlet uid ow
µ®¤®© ³£®«
Reentrant angle
To come (put) into action (operation, service, use, prac- µ®¤¿¹ ¿ ¯®·² Incoming mail (email) tice) µ®¤¿¹¨© ±²³¯ ²¼ ¢ ±²°®©
Reentrant polygon clipping
To go into service
µ®¤¿¹¨© ¢
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Let us calculate the perturbations of all quantities entering into the above equation
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Here and subsequently Throughout the paper In the sequel From now on
±¿ § ¤ · The whole problem ±¿ £° ¨¶
Entry air
µ®¤¿¹¨© ¯®²®ª Incoming ux
µ®¤¿¹¨© ³£®« Reentrant angle
These boundary conditions specify the solution along the entire boundary
±¿ ®¡« ±²¼ (±¨±²¥¬ ) The whole domain ±¿ ¯®±«¥¤®¢ ²¥«¼®±²¼ Entire sequence ±¿ ½¥°£¨¿
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A diagonally dominant (dominant-like) matrix is one for which it is known a priori that (¡¥§ °²¨ª«¿) pivoting for stability is not required
»¡®° £« ¢®£® ½«¥¬¥² ¬ ²°¨¶» Pivoting
»¡®° ®¯²¨¬ «¼»µ ¯ ° ¬¥²°®¢
Optimal parameter choice All the energy available to us comes ultimately from the »¡®° ¯®¤¬®¦¥±²¢ Subset selection Sun
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We can conclude that jf (x) Lj < " whenever jx aj <
»¡®° ° §¬¥° ¸ £ Step size selection
24
»¡®° °¥¦¨¬ Mode selection »¡®° ¸ £ ( ¯°¨¬¥°, ¨²¥£°¨°®¢ ¨¿) Step size control »¡®°ª ¨§ § ¯®¬¨ ¾¹¥£® ³±²°®©±²¢ Storage access »¡®°®· ¿ ®°²®£® «¨§ ¶¨¿ Selective orthogonalization »¡®°®· ¿ ¯®£°¥¸®±²¼ (®¸¨¡ª ¢»¡®°®·»µ ¡«¾¤¥¨©) Sampling error »¡°®± ½¥°£¨¨
»³¦¤¥®¥ °¥¸¥¨¥ Forced solution Forced decision
»¯«¥±³²¼ °¥¡¥ª ¢¬¥±²¥ ± £°¿§®© ¢®¤®© (¢®¤®© ¨§ ¢ ») To throw the baby out with the bath water
»¯®«¨²¼ ¢»·¨±«¥¨¥
To accomplish the evaluation
»¯®«¨²¼ ¨²¥° ¶¨¾
The solution is transferred to the next coarser grid where more iterations are performed
»¯®«¨²¼ ²¥±²¨°®¢ ¨¥
Fission of the nucleous would result in a tremendous out- To perform testing burst of energy »¯°¿¬«¿¾¹ ¿ ¯«®±ª®±²¼ »¡° ±»¢ ²¼ (§ ¡®°²) Rectifying plane To jettison the bomb load »¯³ª« ¿ ¢¢¥°µ ´³ª¶¨¿ »¢ « «¥± Upward-convex function Forest fall »¯³ª« ¿ ¢¨§ ´³ª¶¨¿ »¢®¤®¥ ®²¢¥°±²¨¥ Downward-convex function Outlet hole »¯³ª«®±²¼ ¯® ° £³ 1 Outlet ori ce Rank-one convexity »¢®° ·¨¢ ¨¥ ¨§ ª³ »¯³·¨¢ ¨¥ ¯« ±²¨» (®¡®«®·ª¨) Everting Buckling of a plate (shell) Eversion »° ¡®²ª »¤ ¢ ²¼ ¯°®¯³±ª Mine opening To issue a pass »° ¢¨¢ ¨¥ ¤ »µ »¤¢¨³²¼ Data tting To give rise to new problems
»° ¢¨¢ ¨¥ ¬¥²®¤®¬ ¨¬¥¼¸¨µ ª¢ ¤° ²®¢ »¤¥«¥¨¥ ¬ ²°¨ª± Least-squares tting Matrix secretion »° ¢¨¢ ²¼ ± ¬®«¥² »¤¥«¥»© ª®¬¯¼¾²¥° ¤«¿ ±¯¥¶¨ «¼»µ § ¤ · To even o (to level) an aircraft Dedicated computer »° ¦ ²¼ »¤¥«¿²¼ «¨¥©»¥ ·«¥» To isolate the linear terms in the left-hand side of equa- The equation of motion of a sphere, which re ects Newton's law
tion (1)
»¤¥°¦¨¢ ²¼ ¤ ¢«¥¨¥
»° ¦¥¨¥ ¤«¿
»§»¢ ²¼ § ²°³¤¥¨¿
»° ¦ ²¼ ·¥°¥§
»¨£°»¢ ²¼ ¢°¥¬¿ To gain time »©²¨ § ¯°¥¤¥«» ¬®¦¥±²¢ To fall outside the limits of a (the) set »©²¨ ¨§ ±²°®¿ The pump failed »¥±¥¨¥ § § ª ª®°¿ Taking from under the root sign »®± ª°»«¼¥¢ (ª°»« ) ¢¯¥°¥¤ (¯®«®¦¨²¥«¼»©) Forward (positive) stagger »®± ª°»«¼¥¢ (ª°»« ) ®¡° ²»© ( § ¤, ®²°¨¶ ²¥«¼»©) Back (negative) stagger »³¦¤¥®¥ ª®«¥¡ ¨¥
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We can endure the pressure at the bottom of our ocean of Expression for »° §¨²¼ ·¥°¥§ air To express in terms of : : : »§¢ »© »° ¦ ¥¬»© Strati cation induced by strong heating The tangential projection is de ned by this third-order »§¢ »© ¯®«¿°»¬ ±¨¿¨¥¬ tensor being expressed in terms of strains The auroral phenomena should be : : : This tensor can be expressed through the electromagnetic transition amplitude
To give rise to some diculties (to a really serious diculty)
This surface degenerates into a paraboloid
»°®¦¤ ¾¹ ¿±¿ ª®³± ¿ ¯®¢¥°µ®±²¼ Degenerate conical surface
»°®¦¤¥®±²¼ ¬ ²°¨¶» Matrix singularity
»±®ª ¿ ®°¡¨² Elevated orbit
»±®ª ¿ ²° ¢
The tall grass is harder to walk through
»±®ª®£® ¯®°¿¤ª ³° ¢¥¨¥ Higher-order equation Equation of higher order
»±®ª®¯°®¨§¢®¤¨²¥«¼»¥ ¢»·¨±«¥¨¿ High performance computing
»±®² ¡ °®¬¥²°¨·¥±ª®¥ ¨§¬¥°¥¨¥
Forced oscillation Forced vibration
Barometric measurement of altitude
25
»²¿³²»© ½««¨¯±®¨¤ ¢° ¹¥¨¿
»±®² ¤ ¢«¥¨¿ Pressure head »±®² ¯®° Head »±®² ®¤®°®¤®© ²¬®±´¥°» Scale height »±®² ¯®«¥² Flight altitude, ying height »±®² ¯°®´¨«¿ Pro le thickness »±®² ¯°¿¬®³£®«¼¨ª Rectangle of height h and width (base) l »±®² ° §°³¸¥¨¿
Prolate ellipsoid of revolution Oblong ellipsoid of revolution
»µ«®¯ ±¦ ²®£® ¢®§¤³µ ¥¯®±°¥¤±²¢¥»© Direct discharge of compressed air
»µ®¤ ¬®±² (¬®±²®¢®© ±µ¥¬») Bridge output
»µ®¤ °¥¦¨¬
The onset of a propagation regime close to a steady-state one
»µ®¤ ° ª¥²» ¢ ª®±¬¨·¥±ª®¥ ¯°®±²° ±²¢® The escape of a rocket out into space
»µ®¤¨²¼ § ¯°¥¤¥«»
Breakup altitude Fragmentation altitude Altitude at which breakup occurs
To be (go, fall) beyond (outside) the scope (limits) of
»µ®¤¨²¼ ¨§
When the gases leave the combustion chamber : : :
»±®² ±¡«¨¦¥¨¿ Engagement altitude »±®² ²°¥³£®«¼¨ª
»µ®¤¨²¼ °¥¦¨¬
»±®²»© High-altitude »±®²®© ¢ : : :
»·¨±«¥¨¥
The process reaches the regime of stabilization
»µ®¤®¥ ±¥·¥¨¥ ª «
We have drawn a triangle, the measure of its altitude being Channel outlet section three times the measure of its base »µ®¤¿¹¨© ¨§ An altitude of a triangle is a line drawn through a vertex Angle is a gure formed by two rays going out of the same perpendicular to the side of the triangle opposite to the point vertex »µ®¤¿¹¨© ¯®²®ª Triangle of height h and width (base) l Outgoing ux »±®² ³ª«® »·¥°ª¨¢ ²¼, ®¯³±ª ²¼ Slant height All terms not linear in the small quantities are deleted Evaluation of integral (polynomial, determinant, function)
A building 50 m high A tree about 10 m high
»·¨±«¥¨¥ ¯®«¨®¬ Polynomial evaluation
»±²³¯ ²¼ ¯°®²¨¢ To raise an objection to »²¥ª ¨¥ Out ow »²¥ª ²¼ ·¥°¥§ The uid ows across the lter »²¥±¥¨¥ ¦¨¤ª®±²¨ Displacement of the liquid ( uid) »²¥±¥¨¿ ±ª®°®±²¼ ¦¨¤ª®±²¨ Displacement rate of a liquid ( uid) »²¥±¥ ¿ ¦¨¤ª®±²¼ Displaced liquid ( uid) »²¥±¿²¼
To force out from To displace a liquid ( uid) by another liquid ( uid)
»·¨±«¥¨¥ ´³ª¶¨¨ Function evaluation
»·¨±«¥®¥ °¥¸¥¨¥
The computed solution is an exact solution of a problem in which T is perturbed slightly
»·¨±«¨²¥«¼ ¿ ±µ¥¬ Computational scheme
»·¨±«¨²¥«¼»¥ § ²° ²»
There are a number of techniques for extending this problem class at the expense of an increase in computing cost
»·¨±«¨²¼ ¨²¥£° « (´³ª¶¨¾)
All integrals (functions) are evaluated at the point (x; y) in this case
»²¥±¿¾¹¨© ¯®²®ª Displacing ow »²¿£¨¢ ¥¬»© ¨§ Film drawn out of a liquid volume »²¿£¨¢ ²¼ Film entrained by a ber »²¿¦ª «¨±² Stretching (drawing) of a sheet »²¿¦ª ¯« ±²¨» £«³¡®ª ¿ Deep drawing of a plate »²¿³² The ellipsoidal cavity is prolate along its axis of symmetry »²¿³²»© ½««¨¯±®¨¤ Prolate ellipsoid Oblong ellipsoid
»·¨² ¨¥ ·¨±¥«
Subtraction of numbers
»·¨² ²¼ ¨§
To subtract a from b
»¸¥ (¨¦¥) ¯°¨¢¥¤¥»©
The rst term above (below) represents : : :
»¸¥¤®ª § »© Proved above
¼¥²
Viete
¼¥²®°¨± Vietoris
¾°¶
Wurtz
¿§ª ¿ ¤¥´®°¬ ¶¨¿
Viscous deformation (strain)
26
°¬®¨·¥±ª®¥ ±°¥¤¥¥
¿§ª¨© °®±² ²°¥¹¨» Ductile crack growth ¿§ª¨© ±«¥¤ Viscous wake ¿§ª®¥ ° §°³¸¥¨¥ (¨§«®¬) Ductile fracture ¿§ª®-¥¢¿§ª®¥ ¢§ ¨¬®¤¥©±²¢¨¥ Viscous-inviscid interaction ¿§ª®¯« ±²¨·¥±ª ¿ ¤¥´®°¬ ¶¨¿
Harmonic mean
° ª
Harnack
°±¨ Garcia
°²®£± Hartogs
²®
Viscoplastic strain Viscoplastic deformation
Gateaux
³±±
¿§ª®±²¼ ¯® ®¡º¥¬®¬³ ±¦ ²¨¾ Bulk viscosity ¿§ª®±²¼ ¯°¨ ±¤¢¨£¥ Shear viscosity Viscosity under shear
¿§ª®³¯°³£®¯« ±²¨·¥±ª¨© Viscoelastoplastic ¿§ª®±²¼ ° §°³¸¥¨¿ Fracture toughness
£¥ Hagen § -¤¥°- «¼± Van der Waals gas §®¢ ¿ ¯®«®±²¼ (¸ °) Gaseous cavity §®¢§¢¥±¼ (¢ µ¨¬¨·¥±ª¨µ °¥ ª²®° µ) Air-dispersed mixture §®¢»¥ ¤¥²® ¶¨¨ Gaseous detonations §®ª ¯¥«¼»© Gas-droplet «¨«¥© Galilei, Galileo ««¥© Halley «±¨ Halsey «³ Galois «¼¢ ¨ Galvani «¼²® Galton ¬¥«¼ Hamel ¬¨«¼²® Hamilton ¬¨«¼²®-½««¨ Hamilton-Cayley ¬®¢ Gamow §¥ Hansen ª¥«¼ Hankel °¢¨ Garwin °¤¥° Gardner
Gauss
³±±®¢ ª°¨¢¨§ Gaussian curvature
³±±®¢® ¨±ª«¾·¥¨¥
Gaussian elimination (³¯®²°¥¡«¿¥²±¿ ¡¥§ °²¨ª«¿)
¸¥¨¥ ª®«¥¡ ¨©
Suppressing (the) oscillations (vibrations) Suppression of oscillations (vibrations)
¤¥ ¡» ¨
X-rays radiate from the place of impact wherever that may be To disclose the presence of hydrogen wherever it occurs Solids maintain their sizes and shapes no matter where they are placed
¥£¥¡ ³½° Gegenbauer
¥¤¥
Gaede
¥©£¥° Geiger
¥©¤®
Gaydon
¥©§¥¡¥°£ Heisenberg
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Heyn
¥©¥
Heine
¥©°¨£¥° Geiringer
¥©±«¥° Geissler
¥©²¨£ Heyting
¥«¼¬£®«¼¶ Helmholtz
¥«¼¬¥°² Gelmert
¥§¥«¼ Hensel
¥ª¨
Hencky
¥°¨
Henry
¥²¶¥ Gentzen
¥¶¥
Gentzen
¥®£° ´¨·¥±ª ¿ ¯ ° ««¥«¼ Parallel of latitude
27
Geographical parallel Geographic parallel
¥®¬¥²°¨·¥±ª ¿ ° §®±²¼ Geometrical di erence Geometric di erence
¥®¬¥²°¨·¥±ª ¿ ²¥®°¥¬ ³ ª °¥ The geometric theorem of Poincare Poincare's geometric theorem
¥®¬¥²°¨·¥±ª¨© ¨²¥£° « Geometric integral
¥®¬¥²°¨·¥±ª®¥ ¬¥±²® Locus
¥®¬¥²°¨·¥±ª®¥ ®£° ¨·¥¨¥ Geometrical constraint
¥®¬¥²°¨·¥±ª®¥ ¯®±²°®¥¨¥ Geometric construction
¥®¬¥²°¨·¥±ª®¥ ±°¥¤¥¥ Geometric mean
¥®¬¥²°¨¿ ±´¥°¥
Geometry on the sphere
¥°ª¥
Gehreke
¥°«
Hurle
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Hermann
¥°®
Heron
¥°¶
Hertz
¥°¶ (±®ª° ¹¥ ¿ § ¯¨±¼) Hz
¥°¸£®°¨ Gershgorin
¥±±¥
Hesse
¨«¼¡¥°² Hilbert ¨¯®²¥§ ¥¤¨®© ®°¬ «¨ (¢ ²¥®°¨¨ ±«®¨±²»µ ¯« ±²¨) Hypothesis of a linear variation of strain through the thickness
¨° Gear ¨°®±¨«®¢®© Gyroforce ¨°®±ª®¯¨·¥±ª¨ ¥±¢¿§ ¿ ±¨±²¥¬ Gyroscopically disconnected system ¨°®±² ²¨·¥±ª¨© ¬®¬¥² Gyrostatic moment ¨²²®°´ Hittorf « ¢ ¿ ¢¥²¢¼ Principal branch « ¢ ¿ ¯«®¹ ¤ª Basic area (element) « ¢®¥ § ·¥¨¥ °£³¬¥² ª®¬¯«¥ª±®£® ·¨±« Principal value of the argument of a complex number « ¢®¥ § ·¥¨¥ ®¸¨ Cauchy principal value « ¢®¥ ³¤«¨¥¨¥ Principal elongation « ¢»¥ ° ¤¨³±» ª°¨¢¨§» Principal radii of curvature « ¢»© ¢¥ª²®° ¬¥¦¤³ ¯®¤¯°®±²° ±²¢ ¬¨ Principal vector between two subspaces « ¢»© ±¤¢¨£ Principal shear « ¢»© ³£®« ¬¥¦¤³ ¯®¤¯°®±²° ±²¢ ¬¨ Principal angle between two subspaces « ¢»¬ ®¡° §®¬ For the most part Largely
¥´¥°
« §¥¡°³ª Glazebrook « §®¤¢¨£ ²¥«¼»¥ ¬»¸¶» Oculomotor muscles « Glan « ³½°² Glauert «¨±® Gleason «®¡ «¼®¥ ¢°¥¬¿ Global time «³¡®ª®³¢ ¦ ¥¬»© Greatly esteemed ®¢®°¨²¼ ® : : : (ª ª ®)
Hefner
¥¤¥«¼ Godel
¥«¼¤¥° Holder
¥°²«¥° Gortler
¨¢¥± Givens
¨¡¡±
Gibbs
¨¡¥«¼ ª«¥²®ª Death of cells
¨¡°¨¤ ¿ ±µ¥¬ Hybrid scheme
We may speak of families of matrix norms We speak of a set (kit) of programming tools as a set of : : :
¨¤°®¤¨ ¬¨ª ¡®«¼¸¨µ ±ª®°®±²¥©
®¢®°¿² A body is said to be in motion ®¤¨²¼±¿ ¤«¿ ·¥£®-«¨¡® To be t ®¤®¢®¥ ª®«¼¶® (¤¥°¥¢ ) Annual ring ®«®¢ª ´®°±³ª¨
High-speed hydrodynamics
¨¤°®¤¨ ¬¨·¥±ª ¿ ±¯¨° «¼®±²¼ Hydrodynamic helicity
¨¤°®³¤ °
Hydraulic impact Hydraulic shock
¨«±
Nozzle head
Giles 28
®«³¡
Golub
®«¼¤¡ µ Goldbach
®«¼¤¸²¥© Goldstein
®¬¥®¨¤»© Homeoidal
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Homeomorphism of : : : onto : : :
®¬®²¥²¨¨ ¶¥²° Center of similitude
®®°
Gonor
®®·»© ± ¬®«¥² Racing aircraft
®¯ª¨±® Hopkinson
®° §¤®
° ¤¨¥²®¥ § ¯®«¥¨¥ Gradient lling ° ¤¨¥²®¬¥²°¨¿ (£° ¤¨¥²®¬¥²°¨·¥±ª¨©) Gradiometry (gradiometric) ° ©§ Gries ° ¬ Gram ° ¨¶ ¡±®«¾²®© (®²®±¨²¥«¼®©) ¯®£°¥¸®±²¨ Bound of absolute (relative) error ° ¨¶ ¤¨±¯¥°±¨¨ Variance bound ° ¨¶ §¢¥§¤®®¡° §®±²¨ Boundary of a star domain ° ¨¶ ª®² ª² Contact boundary ° ¨¶ ¬®¦¥±²¢ Boundary of a (the) set Set boundary
Convergence much faster than the Jacobi method can be ° ¨¶ ¤¥ obtained in this way Bottom boundary ®°¤ ° ¨¶ ®¤®±²®°®¨µ ±¢¿§¥© Gordan Unilateral constraint boundary ®°¥¨¿ ¯°®¶¥±± ° ¨¶ ®¸¨¡ª¨ Combustion process ®°¨§®² «¼® ¯¥°¥¬¥ ¿ (¨§¬¥¿¾¹ ¿±¿) ²³°- Error bound
° ¨¶ ° §¤¥« ( ¯°¨¬¥°, ¬¥¦¤³ ¯®¢¥°µ®±²¿¬¨ ¨«¨ ®¡« ±²¿¬¨) Horizontally variable eddy viscosity Interface ®°¥° ° ¨¶ ±¢¿§¨ Horner Constraint boundary ®°»© ¬ ±±¨¢ ° ¨¶» ¨§¬¥¥¨¿ ¯¥°¥¬¥®© Rock massif Bounds (ranges) of a variable ®°¿·¥¥ §¥°ª «® ° ¨· ¿ ª ± ²¥«¼ ¿ Hot mirror Boundary tangent ®±±¥² ° ¨· ¿ £°³§ª Gosset Boundary load ®±³¤ °±²¢¥»© ª®¬¨²¥² ¯® ¤¥« ¬ ¨§®¡°¥²¥- ° ¨·»© °¥¦¨¬ ¨© ¨ ®²ª°»²¨© Boundary regime State Committee on Inventions and Discoveries ° ³«¨°®¢ ¿ ±°¥¤ ®²® Granular medium Goto ° ¼ ¢®¤®±«¨¢ ®³«¤±² © Over ow edge Goldstine ° ¼ ª«¨ ° ¢¨² ¶¨®®¥ ¢®§¤¥©±²¢¨¥ The face of a wedge ¡³«¥² ¿ ¢¿§ª®±²¼
Gravitational action
° ¢¨² ¶¨®»© £° ¤¨¥² Gravity gradient
° ¢¨² ¶¨®»© £° ¤¨¥²®¬¥²° Gravity gradiometer
° ¢¨²®¨¥°¶¨ «¼»© Gravitoinertial
° ¤¨¥² ¢¥ª²®°®£® ¯®«¿ Gradient of a (the) vector eld
° ¤¨¥² ¯°¿¦¥¨¿ Stress gradient
° ¤¨¥² ¯¥°¥¬¥¹¥¨© Displacement gradient
° ¤¨¥² ¯®¢¥°µ®±²®£® ²¿¦¥¨¿ Surface-tension gradient
° ¤¨¥² ·³¢±²¢¨²¥«¼®±²¨ Sensitivity gradient
Wedge face
° ¼ ¯®«®±» Side of a (the) strip ° ±£®´´ Grashof ° ±±¬ Grassman ° ´ n-¢¥°¸¨»© Graph on n vertices ° ´ ¯®²®ª ¤ »µ Data ow graph ° ´ ¯°¥¤¸¥±²¢®¢ ¨¿ Precedence graph ° ´ °¥£³«¿°»© ±²¥¯¥¨ k k-regular graph on n vertices °¥¡¥¼ ¢®¤®±«¨¢»© Over ow edge
29
³¯¥° Hooper ³°¢¨¶ Hurwitz ³°¢¨· Gurwitsch ³°¥¢¨· Hurewicz ³°± Goursat ¾£®¨® Hugoniot ¾£®¼® Hugoniot ¾©£¥± Huygens ¾«¼¤¥
°¥¡®© ¢ « Paddle (propeller, propulsion) shaft °¥£®°¨ Gregory °¥¥ Grenet °¥´´¥ Gra e °¥²¸ Grotzsch °¥· Grotzsch °¨ Green °¨¢¨· Greenwich °¨´´¨²± Griths °®¬®§¤ª®±²¼
Guldin
The rest of the proof is omitted because of the awkwardness of the required mathematical operations ¢ ²¼ °®²¥¤¨ª Such an approach does not readily yield information Grothendieck about : : : °³¡ ¿ ®¶¥ª The application of Theorem 5 yields : : : Rough estimate ¢ ²¼ ¢ °¥§³«¼² ²¥ °³¡ ¿ ±¥²ª To result in Coarse grid ¢ ²¼ ¢®§¬®¦®±²¼ °³¡® £®¢®°¿ A more profound analysis enables us to prove that : : : Roughly speaking ¢¥¯®°² °³¡»¥ ¯°¥¤±² ¢«¥¨¿ ® Davenport Rough ideas on ¢«¥¨¥ ª±¨ «¼®¥ (®±¥¢®¥) °³¡»© ¬ ±¸² ¡ End thrust Coarse scale ¢«¥¨¥ ¡®ª®¢®¥ (¯®¯¥°¥·®¥) °³²®¢»µ ¢®¤ ¤¢¨¦¥¨¥ Lateral thrust (pressure) Motion of ground water ¢«¥¨¥ ±²®ª¥ °³¯¯ ª°¨±² ««®¢ Outlet pressure Cluster of crystals ¢«¥¨¥ ®² ³±ª®°¥¨¿ °³¯¯ ¯® ³¬®¦¥¨¾ Acceleration pressure Group under multiplication Pressure due to acceleration
°³¯¯ ±®²°³¤¨ª®¢ A team of sta members °³¯¯¨°®¢ ²¼ ¤°³£ ¯®¤ ¤°³£®¬ 2
¢® This theory was abandoned long ago ¢® ¯°¨§ ®, ·²® The vector X is the vector in C obtained by stacking It has long been an accepted fact that : : : ¢® ±² «® ¯°¥¤¬¥²®¬ ¨±±«¥¤®¢ ¨© the columns of the matrix X °³¯¯¨°®¢ª¨ ¬¥²®¤ ¤«¿ ° §«®¦¥¨¿ ¬®¦¨- The phenomenon of laminar ame propagation in reactive ²¥«¨ mediums is the subject of long-term scienti c studies Method of grouping for resolution into factors (for factor- ©ª ization) Dyke °½¢®«« ¦¥ ¢ ½²®¬ ±«³· ¥ Even so, a layer of lava 1 km thick is required to produce Granwall ³¤¥°¬ the 250 m di erence in depth Gudermann « ¬¡¥° d'Alembert ³¤¼¥° «¥¥ Goodier ³¨ In the following, we restrict ourselves to the symmetric Guinan case «¥ª® ¨¤³¹¥¥ § ª«¾·¥¨¥ ³ª Hooke Far-reaching conclusion «¥ª® ¥ ³ª®¢±ª¨© ½«¥¬¥² Not by a long way Hookean element «¥ª® ®² ³«¤ n
The Stokes approximation is not correct far from the body
Gould
30
«²® Dalton
«¼ª¢¨±² Dahlquist
«¼¨© ¯®°¿¤®ª Long-range order
«¼¨© ±¨£ « Remote signal
¢¨£ ²¥«¼ (°¥ ª²¨¢»©) ª®¶¥ «®¯ ±²¨ ¥±³¹¥£® ¢¨² Rotor tip-drive unit ¢¨£ ²¼±¿ ®² To move away from the origin of coordinates ¢¨£ ²¼±¿ ®²®±¨²¥«¼® ¤°³£ ¤°³£
The missile and the target are in relative motion to each other
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¢¨£ ²¼±¿ ¯® ¨¥°¶¨¨ To move by inertia ¢¨£ ²¼±¿ ¯® ª°³£³ To circulate ¢¨¦¥¨¥ : : : ®²®±¨²¥«¼® Motion : : : relative to ¢¨¦¥¨¥ ¢ ®²±³²±²¢¨¥ ±¢¿§¥© Unconstrained motion ¢¨¦¥¨¥ ¢®«» Wave motion ¢¨¦¥¨¥ £« §
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¢¨¦¥¨¥ £®«®¢»
«¼¨© ±«¥¤ Far wake
«¼®±²¼ ¢¨¤¨¬®±²¨ Range of visibility
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The range of this airplane is about 1000 km
«¼®±²¼ ¯®°¿¤ª n Distance of order n
«¼²® Dalton
Damkeler Dandelin
¦³ Denjoy
¨¥«¼ Daniell
»¥ ®
Eye movement Eye motion
Head motion Head movement
¢¨¦¥¨¥ ¦¨¤ª®±²¨ Fluid motion Liquid motion
²·¨ª ³£«®¢®£® ³±ª®°¥¨¿
¢¨¦¥¨¥ ¯®¤ ¤¥©±²¢¨¥¬ ±¨«» ²¿¦¥±²¨ Gravity-forced motion ¢¨¦¥¨¥ °¥ «¼»µ ¦¨¤ª®±²¥© Movement (motion) of real liquids ( uids) ¢¨¦¥¨¥, ±¨¬¬¥²°¨·®¥ ®²®±¨²¥«¼® ®±¨ Axisymmetric(al) ow ¢¨¦¥¨¥ ±® ±ª®°®±²¼¾ Motion with (at) the (a) velocity ¢¨¦¥¨¥ ¶¥²° ¬ ±± Center-of-mass motion ¢¨¦¥¨¿ (¬®¦¥±²¢¥®¥ ·¨±«® ¨¬¥¥²±¿) The problem on (of) investigating the motions of mixtures ¢¨¦³¹ ¿±¿ £° ¨¶ ° §¤¥« Moving interface ¢¨¦³¹¥¥±¿ ²¥«®
²·¨ª ³£«®¢®© ±ª®°®±²¨
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Data on
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°¡¨ Durbin
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Darboux
°±¨ Darcy
²·¨ª (¨§¬¥°¨²¥«¼»©) Actuator, sensor, transducer
²·¨ª ¬ £¨²»© ¨ ®¯²¨·¥±ª¨© Magnetic and optic sensors
Angular acceleration sensor Angular velocity sensor
²·¨ª ³¤¥«¼®© ±¨«»
Moving body Body in motion
Moving object Object in motion
Speci c force sensor
¢¨¦³¹¨©±¿ ´°®² Advancing front The rst two (® ¥ two rst) equations are simpler than ¢®¨·®¥ ¢®§¢¥¤¥¨¥ ¢ ±²¥¯¥¼ the third Binary powering ¢ ¦¤» ¢ £®¤ ¢®© ¿ ®°¬ «¼ Twice a year Binormal ¢ ¦¤» ¯°®µ®¤¨¬»© «³· ¢®© ¿ ®±®¡ ¿ ²®·ª Twice passable ray Singular double point ¢¥ ²°¥²¨ ¢®© ¿ ¯°¿¬ ¿ Two-thirds of its diameter is equal to : : : Double line Two-thirds of the gamblers are ruined ¢®© ¿ ° §®±²¼ ( ¯°¨¬¥°, ¢ § ¤ · µ ¢¨£ ¢¥ ¤¶ ²¨°¨· ¿ ±¨±²¥¬ ±·¨±«¥¨¿ ¶¨¨) Duodecimal system of numbers Double di erence ¢®©¨ª®¢®¥ ±° ±² ¨¥ ª°¨±² ««®¢ ¢¨£ ²¥«¼ ¢¨²®¢®© ¢ ¯¥°¢»µ
Crystal twinning
Screw propeller
31
¢®©®© ( ¯°¨¬¥°, ¤¢®©®¥ ³¯° ¢«¥¨¥) Double (control) ¢®©®© ¯®«¾± Dipole ¢®©®© ±¤¢¨£ (¯°¨ ¯®¨±ª¥ ±®¡±²¢¥»µ § ·¥¨©) Double shift ¢®©±²¢¥»© «£®°¨²¬ Dual algorithm ¢³±¥°¨ «¼»© ª®½´´¨¶¨¥² ª®°°¥«¿¶¨¨ Biserial correlation coecient ¢³±²®°®¥¥ ®£° ¨·¥¨¥
¥ §
¢³±²®°®¨© ª®¥ª Bilateral Chaplygin sleigh (skate) ¢³±²®°®¨© ®²°¥§®ª Two-sided segment ¢³±²®°®¿¿ ®¶¥ª Estimate of a lower and an upper bound ¢³±²®°®¿¿ ¯®¢¥°µ®±²¼ Two-sided surface ¢³µ¤¨ £® «¨§ ¶¨¿ Bidiagonalization ¢³µ¤¨ £® «¼ ¿ ±¨±²¥¬ Bidiagonal system ¢³µ¤¨´´³§¨® ¿ ª®¢¥ª¶¨¿ Double-di usive convection ¢³µ§¢¥»© ¬¥µ ¨§¬ Two-link mechanism ¢³µª®¬¯®¥² ¿ ¬®¤¥«¼ Two-compartment model ¢³µ¬®²®°»© ± ¬®«¥² Twin-engine (air)plane ¢³µ®± ¿ ¤¥´®°¬ ¶¨¿ Biaxial deformation ¢³µ¯ ° ¬¥²°¨·¥±ª®¥ ° §«®¦¥¨¥ Two-parameter expansion ¢³µ¯®«®±»© ²° ±¯®°²»© ¯®²®ª Two-lane trac ow ¢³µ±«®© ¿ ±²°³ª²³° Two-layer structure ¢³µ±«®©»© ¬¥²®¤ Two-layer method ¢³µ±²¥¯¥»© £¨°®±ª®¯ Restrained gyroscope ¢³µ³°®¢¥¢»© ¬¥²®¤ Two-level method ¢³µ´ §®¢»© ±«¥¤ Two-phase wake ¢³·«¥»¥ ª®½´´¨¶¨¥²» Two-term coecients ¢³·«¥»© Consisting of two terms ¤¥ °®©«¼ de Broglie ¥ ³° de Boor ¥ ¥³¢ De Leeuw ¥ ¾
¥¢¨±
Bilateral constraint Two-sided constraint
De Leeuw
de Haas
¥¡ ©
Debye
¥¡¥°¥©¥° Dobereiner
¥¢¨ ²®° ±ª®°®±²¥© ¤¥´®°¬ ¶¨¨ Strain-rate deviator
¥¢¨ ²®° ±ª®°®±²¨ ¯« ±²¨·¥±ª®© ¤¥´®°¬ ¶¨¨ Plastic-strain rate deviator
¥¢¨ ²®° ²¥§®° ¯®¢°¥¦¤¥®±²¨ Damage tensor deviator
¥¢¨ ²®° ¿ ±®±² ¢«¿¾¹ ¿ ²¥§®° ¯°¿¦¥¨© Deviatoric part of the stress tensor Devis
¥¤¥ª¨¤ Dedekind
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Desargues
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Day
¥©«¨ Daily
¥©±²¢¨¥ ¨£°» Play of a game
¥©±²¢¨¥ ° ±±²®¿¨¨
The action at a distance Experiments on the action-at-a-distance
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Sparse matrix solvers have even greater potential savings by storing and operating only on nonzero elements
¥©±²¢¨¥ £°³§ª¨, ¤¥©±²¢¨¥ £°³§®·®¥ Load action
¥©±²¢¨¥ ±¨«» Force action
¥©±²¢¨²¥«¼®
Venus and Mercury are the only known planets that do travel closer to the Sun than the Earth does The orbits of both planets do lie inside the Sun's orbit
¥©±²¢®¢ ²¼ ¡»±²°® (¡¥§ ¯°®¬¥¤«¥¨¿) To act promptly
¥©±²¢³¾¹ ¿ ¢¥«¨·¨ ¯°¿¦¥¨¿ A virtual voltage
¥©±²¢³¾¹ ¿ ¯®¢¥°µ®±²¼ Active surface
¥ª °²
Descartes
¥ª®¬¯®§¨¶¨¿ ®¡« ±²¨ Domain decomposition
¥« ²¼ ¢®§¬®¦»¬ (¥¢®§¬®¦»¬)
The existing conditions make it (im)possible to speed up the process This condition enables the computer to carry out (the) operations This makes it (im)possible for the computer to solve a given problem
¥« ²¼ ¢»¢®¤»
We draw certain conclusions from this (the) experiment
¥« ²¼ ¢»¥¬ª¨ To notch
32
¥« ²¼ ¯¥²«¾ ¥±²¥°®¢ To loop the loop ¥«¥¨¥ ¢ ª° ©¥¬ ¨ ±°¥¤¥¬ ®²®¸¥¨¨ Golden section ¥«¥¨¥ ª«¥²®ª Division of cells ¥«¥¨¥
¥´¥ª² ¿ ¬ ²°¨¶ Defective matrix
¥´¥ª²®¥ ·¨±«® De cient number Defective number
¥´®°¬ ¶¨® ¿ ¨§®²°®¯¨¿ Strain-induced anisotropy
: : : is obtained by (sub)dividing the interval along X into n ¥´®°¬ ¶¨®®¥ ±¢®©±²¢®
equal parts and then taking the limit
Strain property
¥«¥¨¥ ®²°¥§ª ¢ ¤ ®¬ ®²®¸¥¨¨ Division of a segment in a given ratio ¥«¥¨¿ ²®·ª Point of division ¥«¥®¥ ¯°®±²° ±²¢® (´ ª²®°-¯°®±²° ±²¢®) Quotient space ¥«¨¼ Deligne ¥«® ®¡±²®¨² The situation is ¥«® Delon ¥«®¥ Delaunay ¥«¨²¥«¼ ³«¿
¥´®°¬ ¶¨¿ ¡¥§ ¨§¬¥¥¨¿ ®¡º¥¬
¥«¨²¼ ¢ ®²®¸¥¨¨
¥´®°¬ ¶¨¿ ³¯°³£®£® ±¤¢¨£
¥¬¯´¨°®¢ ¨¿ ª®½´´¨¶¨¥² Damping coecient ¥ Dehn ¥¥¦»© ¯¥°¥¢®¤ Money transfer ¥°¥¢¼¿ ¡¥§ ®¡¹¨µ ¤³£ Arc-disjoint trees ¥°¦ ²¼ £« § ®²ª°»²»¬¨ To keep the eyes open ¥°¦ ²¼ ¯®¤ ª®²°®«¥¬ To keep under control ¥±¿²¨· ¿ ±¨±²¥¬ ³¬¥° ¶¨¨ Decimal system of numeration ¥±¿²¨·»© § ª Decimal place (digit) ¥±¿²ª¨ ²»±¿·
¥´®°¬¨°®¢ ®¥ ±®±²®¿¨¥
Deformation without change of volume Deformation without dilatation
¥´®°¬ ¶¨¿ ¢° ¹¥¨¿ Rotational deformation Rotational strain Rotation deformation Rotation strain
¥´®°¬ ¶¨¿ ¤¥¢¨ ²®° ¿ Deviator deformation
¥´®°¬ ¶¨¿ ª°¨²¨·¥±ª ¿ Ultimate (critical) strain
¥´®°¬ ¶¨¿ ®¡º¥¬ , ®¡º¥¬ ¿ ¤¥´®°¬ ¶¨¿ Irrotational deformation
¥´®°¬ ¶¨¿ ¯°¨ ±¤¢¨£¥
Divisor of zero Zero divisor
Shearing (shear) strain
Elastic shear strain The center of gravity of a (the) triangle divides each me- Elastic shear deformation dian by ratio 2:1, considering from a vertex ¥´®°¬ ¶¨¿ ´®°¬» ¥«¿¹ ¿±¿ ª«¥²ª Shape deformation Dividing cell ¥´®°¬¨°®¢ ¿ ª®´¨£³° ¶¨¿ ¥¬¯±²¥° Deformed con guration Dempster Strain state
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¥´®°¬¨°³¥¬ ¿ ±°¥¤ Deformable medium
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¥±¿²¼ ¢ ª³¡¥ Ten cubed ¥² «¼ (·¥£®-²®) Part ¥´ §§¨´¨ª ¶¨¿ Defuzzi cation ¥´¥ª² ¯«®²®±²¨ Density defect ¥´¥ª² ±ª®°®±²¨ Velocity defect
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33
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Dissipative moment
Diagonally sparse matrix Diagonal dominance Diagonal pivoting
Dissipation factor
Volume fracture dissipation
Full dissipation
Loading diagram Diagram of loading
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Divergence of vortex lines
Dyck
Dickson
Dynamics of saturation
Dynamic loss of stability Dynamical system
Dynamic deformation
Shear fracture dissipation Teaching branch of study
Di erential on a surface
Algebraic-di erential equation Impulse di erential equation Substance separation Gravity separation
Di erentiation in the sense of distributions Di erentiation of vectors
Di erentiation of an integral with respect to a parameter Di erentiation with respect to a parameter Di erentiation by parts Di erentiation
Diocles
Diophantus
Diophantine approximation
Di erintegral
Di usion-viscous ow Di usion number
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Di usion term
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¨±¯¥°±¨®®¥ ³° ¢¥¨¥ (¢ ¯°¨¿²® ¨±- Permittivity ¯®«¼§®¢ ²¼ ¯®¿²¨¥ \¤¨±¯¥°±¨®®¥ ®²®¸¥- Dielectric constant ¨¥") «¨ ¢¥ª²®° Dispersion relation Length (magnitude) of a vector Vector length ¨±¯¥°±¨®®¥ ·¨±«® Dispersion number «¨ ®ª°³¦®±²¨ Length of circumference of a circle ¨±¯¥°±¨®»© ¯®²®ª Dispersion ux ( ow) «¨ ¯³²¨ ¯¥°¥¬¥¸¨¢ ¨¿ ¦¨¤ª®±²¨ (£¨¯®²¥§ ¨±¯¥°±¨¿ ®°¬ «¼®£® § ª® ° ±¯°¥¤¥«¥¨¿ ° ¤²«¿) The mixing length of a liquid
Dispersion in a normal distribution
34
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For a function f to be continuous it is necessary that : : : A necessary and sucient condition for a matrix to be nonsingular is that its determinant be nonzero In order that this process have (® ¥ has) meaning, it is necessary that it give (® ¥ gives) a unique result Formula (1) is applied to study the above case (to derive the theorem below, to obtain an x with norm not exceeding 1) Let us consider some examples to show how this function decreases at in nity This approach is too complicated to be used in the above case This particular case is important enough to be considered separately We now apply (use) Theorem 1 to obtain x = y Insert (1) into (2) (substitute (1) into (2)) to nd that : : : We partially order Z by declaring X < Y to mean that
A period of 5 years A plank 5 m in length A plank 5 m long A mean free path one hundred light years long
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For this to happen (in order that this happens), this set must be compact For the second estimate to hold, it is enough to assume that : : : Then for such a map to exist, we should assume that : : : One must use basis functions of degree at least two in order for x to be nonzero
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Without the pipelining, the vector computation would ap- «¿ ²®£® ·²®¡» : : : ¥ For deactivation not to occur before decomposition, it is proximately require time n for completion necessary that the pressure be low «¿ ¨´®°¬ ¶¨¨ «¿ ²®£®, ·²®¡» ¯®²®ª ¨¬¥« ¬¥±²® ¯°¨ t > 0 For information In order for a ow to take place for t > 0, : : : «¿ ª° ²ª®±²¨ «¿ ³¤®¡±²¢ ®¡®§ ·¥¨© We denote the product brie y (® ¥ shortly) by : : : For notational convenience We write it f for brevity (for short) «¿ ½²®© ¶¥«¨ For abbreviation, let f stand for : : : For conciseness, this may simply be called the normalized To this end; for this purpose; to do this (® ¥ for this aim) transmittance We omit the direct indication of this dependence for con- ¥¢ ¿ ¯®¢¥°µ®±²¼ (²¥°¬¨, ¨±¯®«¼§³¥¬»© ¢ £¥®«®£¨¨) ciseness Day (® ¥ diurnal | ±³²®·»©) surface «¿ ®¡¥±¯¥·¥¨¿ The rotation of a spacecraft is one of the cheapest methods Daylight surface for providing the required orientation of the spacecraft ¥¢®¥ ¢°¥¬¿ Daylight time axis in space
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The system for (the) determination of the next discretiza- DNA-microarray ® tion step Before this discovery, it was thought that : : : The system for determining the next discretization step Some people can hear sounds as high as 20000 cycles The problem to determine x The problem of determining the steady-state distribution The voltage dropped to as low as 25 volts Several experiments were performed prior to and during «¿ ®¯°¥¤¥«¥®±²¨ the launch of Apollo To be de nite, for de niteness
Mars seems to be the most comfortable place for life to exist beyond the Earth
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This element was discovered in the Sun before it was dis- Fraction of the free surface ®¬¨¨°³¾¹¥¥ ¨¢ °¨ ²®¥ ¯®¤¯°®±²° ±²¢® covered on the Earth Dominant invariant subspace ® ½²¨µ ¯®° ® «¤±® Thus far, till now, hitherto Donaldson ®¡ ¢«¥¨¥ ±²®«¡¶ ®£ °° Column addition Dongarra ®¡ ¢«¥¨¥ ±²°®ª¨ ® Row addition Donnan Additional force
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36
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®¯³±ª ²¼ ¨²¥£° «» To admit (the) integrals ®¯³±²¨¬ ¿ ¤¥´®°¬ ¶¨¿ Admissible deformation ®¯³±²¨¬ ¿ £°³§ª Admissible (allowable) load ®¯³±²¨¬ ¿ ®¡« ±²¼ Feasible region ®¯³±²¨¬ ¿ ®¸¨¡ª (¯®£°¥¸®±²¼) Tolerable (tolerate) error ®¯³±²¨¬ ¿ ±¨« Allowable force ®¯³±²¨¬ ¿ ²° ¥ª²®°¨¿ Feasible path ®¯³±²¨¬®¥ § ·¥¨¥ Admissible value ®¯³±²¨¬®¥ ¯°¿¦¥¨¥ Permissible voltage ®¯³±²¨¬®¥ ®²ª«®¥¨¥ Admissible deviation ®¯³±²¨¬®¥ ¯¥°¥¬¥¹¥¨¥ Admissible displacement Feasible displacement
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Attainable speed (velocity)
®±²¨¦¨¬ ¿ ²®·®±²¼ Attainable accuracy
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37
°®¡®-«¨¥©®¥ ¯°¥®¡° §®¢ ¨¥ Linear fractional transformation Fractional linear transformation
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Mass and energy can be transformed into each other
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From one another It is hardly surprising that this problem has not been From each other solved yet Independently of one another (of each other)
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¤¨¨¶ £°³¯¯» °³£ ± ¤°³£®¬ Group unit element This collision causes the formation of numerous smaller Identity element of a group particles, which may collide with each other, producing
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Du Bois-Reymond 38
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The life on other planets, if it exists at all, is not like ours Sti characteristic These particles, if present at all, comprise 0.5 per cent of Rigid characteristic the primary radiation ¥±²ª¨© ª«¨ (±²¥°¦¥¼) The question now is what energy, if any, is required to Rigid wedge (rod) bring about such a rotation ¥±²ª¨© ±«®©
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The quantity of solar radiation received : : : on a unit of surface in a unit of time is called the solar constant
Rigid plastic ow
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§ ¤¥© ª°®¬ª®© § ¢¨µ°¥¨¥ Lateral sti ness of a (the) wheelset ¥±²ª®±²¼ ¢§ ¨¬®¤¥©±²¢¨¿ ¨§£¨¡ ¨ ° ±²¿¦¥- Vorticity at the trailing edge : : : «¥² ¨¿
An actual collision between two stars can occur on the average only once in 600 billion years
Bending-extension coupling sti ness
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Rigidity of the Winkler foundation
An algorithm for constructing the union of arbitrary polygons on the basis of triangulation with linear-time complexity on average
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Flexural (bending) rigidity (sti ness)
¥±²ª®±²¼ ª®±²°³ª¶¨¨ Sti ness of the (a) structure
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Torsional rigidity
¥±ª®«¼ª® ±²®«¥²¨© ¤® Some centuries before ®¤¨ ¤¥¼ In one day : : : ®¯¥° ¶¨© In O(n ) operation ®¤¨ ° § At the time ¯¥°¨®¤ In (over) a period ¯°¥¤¥« ¬¨ «¨¨¨ (®¡« ±²¨) Beyond the con nes of the line (domain) ³¢¥«¨·¥¨¥¬ The rise in bacterial numbers is followed by a sudden drop ´°®²®¬ ³¤ °®© ¢®«» Behind the shock wave (shock-wave, shockwave) front : : : ¸ £®¢ (½² ¯®¢) The theorem is proved in three steps ¡¨¢ª Driving in ¢¥¤®¬® Known to be ¢¥°¸¥® °¥¸¥¨¥ § ¤ ·¨
¥±²ª®±²¼ ª°³·¥¨¿ ¥±²ª®±²¼ ¨§£¨¡ Bending sti ness
¥±²ª®±²¼ ° ±²¿¦¥¨¥ ¨ ¨§£¨¡ Tensile and bending sti ness
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Sti ness of the (a) membrane
¥±²ª®±²¼ ¯°³¦¨» Spring constant
¥±²ª®±²¼ ±² ¶¨® °»µ ¤¢¨¦¥¨© Rigidity of steady motions
¥±²ª®-³±²®©·¨¢»¥ ¬¥²®¤» (´®°¬³«») Sti y stable methods (formulas)
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Kinetic energy (vis viva)
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¨¤ª ¿ ¬ ±± Liquid mass
¨¤ª¨© ¬®±² Liquid bridge
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In a maximum (minimum) of time In maximal (minimal) time
2
Solution (the consideration) of the problem is completed When solving the dual problem is nished, we conclude that : : :
Liquid ( uid) state
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To conclude the proof of the theorem, it remains to note that the above expression is negative The above equality completes the proof of Lemma 1
Hydraulic fracturing uid
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To be printed in bold face
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®°¤ ( ¬¨«¼) Jordan
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¢¥°¸¨²¼ ®¯°¥¤¥«¥¨¥ To complete the de nition ¢¨±¥²¼ ®¤¨ ®² ¤°³£®£® To depend on one another ¢¨±¨¬®±²¼ ¬¥¦¤³ ¯°¿¦¥¨¿¬¨ ¨ ¤¥´®°¬ ¶¨¿¬¨ Stress-strain dependence
40
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Balloon problem
Time (density, pressure)-dependent
The billiard ball problem
Vorticity at the trailing edge Flow vorticity
Sunspot problem Flutter problem
To wind the watch
To turn round (up, down)
Four-color problem Ball problem
To turn about (up) Title of a book
Identi cation problem The problem of identi cation
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Figure title
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The problem of determining the trajectory of optimal evasion : : :
Relative contraction ratio of ow Relative cross-section area reduction ratio of ow
Mapping problem
Roll-in
Path-following problem
Prescribe
Plane stress state (stress-state) problem
The region of interest is prescribed by this condition
Plane plasticity problem
Prescribed error (accuracy)
Plane elasticity problem
To set oneself an aim
The objective (aim, ® ¥ problem, ¥±«¨ °¥·¼ ¨¤¥² ® ª®- The problem in identi cation ª°¥²®¬, · ±²®¬ ¤¥©±²¢¨¨) of optimization is to mini- ¤ · ¯®«®£® ° £ mize : : : Full rank problem Problem in terms of stresses
Procrustes problem
The di usion{convection problem
Recognition problem
Identi cation problem The problem of identi cation
Quantum scattering problem
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¤ · ±®¡±²¢¥»¥ § ·¥¨¿ Eigenproblem
Problem with inequality constraints Inequality constrained problem Inequality constraint problem
Nonsymmetric eigenproblem Unsymmetric eigenproblem
Problem with equality constraints Equality constrained problem Equality constraint problem
Screen problem
The problem consists in the high-precision determination of the gravity disturbance
¤ · ±®¡±²¢¥»¥ § ·¥¨¿ ¤«¿ ¥±¨¬¬¥²°¨·»µ ¬ ²°¨¶ ¤ · ± ®£° ¨·¥¨¿¬¨ ²¨¯ ° ¢¥±²¢ ¤ · ±®¡±²¢¥»¥ § ·¥¨¿ ¤«¿ ±¨¬¬¥²°¨·»µ ¬ ²°¨¶ ¤ · ± ±¥¤«®¢»¬¨ ²®·ª ¬¨ Symmetric eigenproblem Saddle point problem ¤ · ½ª° ¥ ¤ · ±®±²®¨² ¢ ¢»±®ª®²®·®¬ ®¯°¥¤¥«¥¨¨ : : : ¤ · ½ª±²°¥¬³¬
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Rank-de cient problem
41
¤ · ³±²®©·¨¢®±²¨ Stability problem ¤ · ½«¥ª²°®¤¨ ¬¨ª¨
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Locality law
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Normal distribution law The large amounts of power required constituted a serious ª® ¯ ° ««¥«®£° ¬¬ drawback to the development of multichannel receivers Parallelogram law
¤¥°¦ª ¤°®¡«¥¨¿ ª® ¯°®¯®°¶¨® «¼®£® ¢¥¤¥¨¿ Fragmentation delay The proportional navigation law ¤¿¿ ª°®¬ª ª® ±®µ° ¥¨¿ £¥®¬¥²°¨¨ Trailing edge Geometric conservation law ¤¿¿ ®£ ª® ±®µ° ¥¨¿ ¨ ¯°¥¢° ¹¥¨¿ ½¥°£¨¨ Hind leg The law of conservation and transformation of energy ¤¿¿ ²®·ª § ±²®¿ (¯®«®£® ²®°¬®¦¥¨¿ ¯®- ª® ±®µ° ¥¨¿ ¨¬¯³«¼±®¢ ²®ª ) The law of conservation of momentum Rear stagnation point ª® ±®µ° ¥¨¿ ®¡º¥¬ ¤¿¿ ¯®¢¥°µ®±²¼ ²¥« Volume conservation law Rear (back, posterior) surface of a body Law of volume conservation ¤¨° ¨¥ ± ¬®«¥² (±¢ «¨¢ ¨¥ µ¢®±²) ª® ²°¥¨¿ Tail heaviness Friction law ¤¨© ´°®² ¨¬¯³«¼± ª°³£«¥ ¿ ®±®¢ ¿ · ±²¼ ´¾§¥«¿¦ Trailing edge of a pulse Rounded fuselage nose ¤®«£® ¤® ª°³²ª ª°»« ½°®¤¨ ¬¨·¥±ª ¿ Long before the internal structure of atoms was studied, Aerodynamic twist of a wing
chemists had learned much about the elements
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ª «¥ ¿ ±² «¼ Hardened steel ª ·¨¢ ¾¹¨©±¿ ing (ed) Ending in ing (ed) ª ·¨¢ ¥¬ ¿ ¦¨¤ª®±²¼ Injected uid ª«¾· ²¼ ¢ ±ª®¡ª¨ To put within brackets ª«¾·¥»© ±²°®£® ¢³²°¨ Strictly contained in ª® °ª±¨³± Arcsine law ª® °ª² £¥± Arctangent law ª® ¢³²°¥¥£® ²°¥¨¿ ¢ ¦¨¤ª®±²¿µ Law of internal friction in uids ª® ¢±¥¬¨°®£® ²¿£®²¥¨¿
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Swirl, swirling Some methods were applied long before they were under- ª°³·¥ ¿ ±¯³² ¿ ±²°³¿ ¢¨² stood Rotating slipstream §®° Swirling slipstream There are no gaps between (the) adjacent sheets ª°³·¥®¥ The gap between these eigenvalues is not suciently wide Swirling ow ²¥·¥¨¥ Swirling ow
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Flap of an aerofoil (airfoil)
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Gravity law The law of gravitation
Slowly reversible Slow-reversible Slow reversible
The law of mass variation
Remarkable lines and points of a triangle
¬¥ ¡ §¨± (¯°¥¤±² ¢«¥¨¿) ª® ¤¢®©±²¢¥®±²¨ Change of basis (representation) Principle of duality ¬¥ ª °²°¨¤¦¥© ª® ¦¨¢»µ ±¨« Replacing cartridges Principle of kinetic energy (of vis viva) ª® ¨§¬¥¥¨¿ ª¨¥²¨·¥±ª®£® (³£«®¢®£®) ¬®- Replacement of cartridges ¬¥² »© ¬¥² Here V is the volume swept by the moving object The law of variation of angular momentum ¬¥· ¨¥ ª ª® ¨§¬¥¥¨¿ ª®«¨·¥±²¢ ¤¢¨¦¥¨¿ This remark on the last lemma is very valuable The law of variation of momentum ¬¥· ²¥«¼»¥ «¨¨¨ ¨ ²®·ª¨ ²°¥³£®«¼¨ª ª® ¨§¬¥¥¨¿ ¬ ±±» 42
¯®«¿²¼ ¯®°» To ll pores ¬ª³²®¥ ¬®¦¥±²¢® ®²®±¨²¥«¼® ®¯¥° ¶¨¨ ¯®«¿²¼ ¯°®¡¥« This paper lls a much needed gap in the literature ±«®¦¥¨¿ ¯®¬¨ ¨¥ ¬ ²°¨¶ ¢ ¯ ¬¿²¨ This set is closed under the operation of addition Storage of matrices ¬ª³²®¥ °¥¸¥¨¥ ¯®¬¨ ²¼ ¢ ¯ ¬¿²¨ Closed solution Envelope solvers only store elements from the rst nonzero ¬ª³²®±²¼ to the last nonzero, thus reducing storage costs The property of being closed ¯° ¢«¿²¼±¿ ²®¯«¨¢®¬ (£®°¾·¨¬) ¬ª³²»© ¢¨¤ ¬¥¹¥¨© ¯®±«¥¤®¢ ²¥«¼»µ ¬¥²®¤ Successive displacement method
Under these conditions, a rocket could fuel up again and continue its ight
These invariants do not exist in closed form for real gases
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All -algebras are closed under countable intersections
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¬ª³²»© ±¨§³ Closed from below
¯°¥¤¥«¼»© Superlimiting behavior of solids ¯³±ª Triggering ° ¥¥ ¨§¢¥±²»© Known beforehand Known in advance
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Closure of the space R
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Cavity closure on the (a) conical forebody
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The calculations must be done all over again
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ETNA is registered with the library of Congress and has ISSN 1068 { 9613
There are a number of techniques for extending this problem class at the expense of an increase in computing cost
The systems with delay
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²°³¤¿²¼ Little information makes it dicult to continue research ¯ ± ±² ²¨·¥±ª®© ³±²®©·¨¢®±²¨ ²³¯«¥®¥ ²¥«® Static stability margin Blunt body ¯ ± ²®¯«¨¢ ²³µ ¨¿ «®£ °¨´¬¨·¥±ª¨© ¤¥ª°¥¬¥² Fuel supply will last for two months Logarithmic decrement of damping ¯¨¸¥²±¿ ²³µ ¾¹ ¿ ¯ ¬¿²¼ ¬ ²¥°¨ « (It) will be written (down) Fading memory of a material ¯®«¥¨¥ ³½° Completing the triangle by points Sauer Occupation of the levels by electrons ´¨ª±¨°®¢ ¢ ¯®«¥¨¥ ¯®¢¥°µ®±²¨ Having xed x, we can nd y such that : : : The process of occupation of the surface by adsorbed par- µ¢ ² ticles is steady A gain of negative electrons ¯®«¥¨¿ ·¨±«® (¢ ª¢ ²®¢®© ¬¥µ ¨ª¥) µ¢ ² ¬¥¤«¥»µ ¥©²°®®¢ Occupation number The capture of slow neutrons µ®¤ ¯®± ¤ª³ ¯®«¨²¼ ² ¡«¨¶³ ·¥¬-«¨¡® Delayed feedback
Approach for landing
To complete the table with something
43
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It was necessary to provide an adequate protection against ª¨ ³£«®¢ thermal failure Signs of angles ¹¨² ®² ¿¤¥°®© ° ¤¨ ¶¨¨ ª®®¯°¥¤¥«¥ ¿ ´³ª¶¨¿ Nuclear radiation shielding Function of xed sign ¹¨² ¯® ¯ °®«¾ ª®®¯°¥¤¥«¥»© Password protection Sign-de nite ¹¨² ¿ ±²°³ª²³° ª®¯¥°¥¬¥»© Protective structure Alternating in sign ¹¨²®¥ ±¢®©±²¢® ¬¥ ²¥«¼ £¥®¬¥²°¨·¥±ª®© ¯°®£°¥±±¨¨ Protective property Common ratio of a geometric progression ¢¥§¤ : : :-²®·¥· ¿ ¨¥ (¬®¦¥² ³¯®²°¥¡«¿²¼±¿ ± ¥®¯°¥¤¥«¥»¬ This formula is known as the ve(seven)-point star °²¨ª«¥¬) ¢¥® ¬ ¿²¨ª Particular solutions of this system may be obtained from Pendulum link a knowledge of the eigenvalues and eigenvectors of A Link of the (a) pendulum ²¼, ®²¤ ¢ ²¼ ®²·¥² ®, ±®§ ¢ ²¼ ¥£¥° To be aware of Seger
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Transparency (nontransparency) zone
Siegbahn
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Tethered atmospheric probe
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44
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£®«¼· ² ¿ ®¯²¨¬¨§ ¶¨¿ Needle optimization £° ± ³«¥¢®© ±³¬¬®© Zero-sum game ¤¥ «¼ ¿ ¯« ±²¨·®±²¼ Perfect plasticity ¤¥ «¼® ª ² «¨²¨·¥±ª ¿ ¯®¢¥°µ®±²¼ Ideal catalytic surface ¤¥ «¼® ¯« ±²¨·¥±ª¨© ±«®© Perfect plastic layer ¤¥ «¼® ¯« ±²¨·¥±ª®¥ ²¥«® Perfect plastic body ¤¥ «¼® ¯« ±²¨·¥±ª®¥ ²¥·¥¨¥ Perfect plastic ow ¤¥ «¼®¥ ±¬¥¸¥¨¥ Ideal mixing ¤¥²¨´¨ª ¶¨¿ ¯ ° ¬¥²°®¢ Parameter identi cation ¥±¥ Jensen §
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By then the results of these experiments had been known to many scientists
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In order to take the square root of a complex number, it is A collection of stamps and the like can be called a set reasonable to convert this number into trigonometric form if the contents of the collection is limited to the objects §£¨¡ ¡ «ª¨ described in the name of the collection Beam bending Bending without tension (extension, stretching)
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§£¨¡ ¾¹¥¥ ¯°¿¦¥¨¥ Bending stress
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Manufacturing Page 1 of 10 §£®²®¢«¥»© ¨§ The moments of inertia about two of the coordinate axes Things made of metal § ¢±¥µ Things made from metal sheets The most complicated problem of all A great number of verbs may be derived from each other by adding or removing a pre x
The overhead storage requirements imposed by sparse matrix methods are still substantial There is little overhead required Due to centrifugal forces, bodies at the equator weigh loss than they weigh at the poles
This theorem allows us to eliminate from consideration all §-§ ¥¤®±² ²ª ¬¥±² these parameters This section has been deleted for space reasons § : : : ±«¥¤³¥² §«¨¸¨© From the condition a = b follows c = d This package is redundant if it is used in the above situa§ ²®£®, ·²® From what has been said so far, one might think that : : : tion
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§«®¬ (¯«¥ª¨) Rupture
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Excess speci c energy
45
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These are the results of four attempts to time the motion : : :
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Variation in density and temperature Density and temperature variation
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Representative point
§¬¥¥¨¥ ¯® y
§®¡° ¦¥¨¥ ¯®²®ª £¥®¬¥²°¨·¥±ª®¥
§¬¥¥¨¥ ¯®°¿¤ª ·«¥®¢
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Change in y, changing in y
Geometrical representation of a ow
Rearrangement of the order of terms
Curved duct Curved tube
§¬¥¥¨¥ ³±ª®°¥¨¿
The variation in acceleration
§®£³²®±²¼
Alter the dynamics of the model Alter the le This changes the dynamics of behavior
§®£³²®±²¼ ª°»«
To change by something
§®ª«¨ «¼
Subject to change
§¬¥¿²¼±¿ ¢ ¸¨°®ª¨µ ¯°¥¤¥« µ
§®«¨°®¢ ¿ ²¥°¬¨·¥±ª¨ (²¥¯«®¨§®«¨°®¢ ¿) ¯®¢¥°µ®±²¼ ¯«®±ª ¿
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§®¬¥²°¨·¥±ª ¿ ±¥²¼
§¬¥¿¾¹ ¿±¿ ¢® ¢°¥¬¥¨ £° ¢¨² ¶¨¿
§®¯¼¥±²
§¬¥¿¾¹ ¿±¿ £° ¢¨² ¶¨¿
§®² µ
§¬¥¨²¼
State of having been bent Wing camber
§®£³²®±²¼ ª°»« ±°¥¤¿¿
§¬¥¨²¼±¿ ·²®-«¨¡®
Mean wing camber
§¬¥¿¥¬»©
Isoclinic line
The radiation ranges widely in intensity
Thermally insulated plane surface
To vary continuously with respect to space and time
Disturbance decoupling
To change in a stepwise fashion
Isometric net
Time-varying gravity
Isopiestic line
Altered gravity Varying gravity
Isotachic line (isotach)
§®´®²
§¬¥°¥¨¥ ¢°¥¬¥¨
Isophot curve (isophot, isophote) The timing is not so reliable as the distance measurement §®½²°®¯¨·¥±ª¨© §¬¥°¥¨¥ ¯°®±²° ±²¢¥®¥ Isentropic Boundary value problems involving three space dimen- Isoentropic (°¥¤ª®) sions are also very important §³·¥¨¥ ¢®§¬®¦®±²¨ (¢ ±¬»±«¥ ®±³¹¥±²¢¨¬®-
§¬¥°¥¨¥ ±ª®°®±²¨ ¯® ®²±«¥¦¨¢ ¨¾ ²° ¥ª²®- ±²¨) °¨© · ±²¨¶ Feasibility study on a prototype of vestibular implant Particle tracking velocimetry §³·¥¨¥ ¬ ²¥¬ ²¨ª¨ §¬¥°¥¨¥ ±ª®°®±²¨ ¯® ²° ±±¥° ¬ · ±²¨¶ Study of mathematics Particle tracking velocimetry «¨ §¬¥°¥¨¥ ³£«®¢ Eley Goniometry «¨ ®ª®«® ²®£® (½²®£®) §¬¥°¥¨© ¯®¬¥µ¨ These hundred or so elements combine in various ways to produce : : : For the last hundred years or so, the world's consumption of fuels has greatly increased
Measurement errors
§¬¥°¥¨¿ ¯®¢¥°µ®±²¨ Measurements on a surface
§¬¥°¨²¥«¼ Sensor
«¨- ©¤¨« Eley-Redeal
46
¬¥¥² ±¬»±« It makes sense to speak of matrix norms ¬¥® ¯® ½²®© ¯°¨·¨¥
¢ °¨ ² ²¥§®°
¬¯³«¼± ¦¨¤ª®±²¨ The momentum of a (the) liquid ¬¯³«¼± ª°³²¨«¼»© Torsional pulse ¬¯³«¼± ®²¤ ·¨
¥°¶¨®®¥ °¥ª³°±¨¢®¥ ¤¥«¥¨¥ ¯®¯®« ¬ Recursive inertia bisection ¥°¶¨®®±²¼ The response rate ¥°¶¨®»© ¯ ° ¬¥²° Inertial parameter ¥°¶¨¿ ¬ ²°¨¶»
Invariant of a (the) tensor Tensor invariant
It is for this reason that the BLAS subprograms (subrou- ¢ °¨ ²®±²¼ ®²®±¨²¥«¼® ±¤¢¨£ tines, routines) are used as the communication layer of Shift invariance ¢ °¨ ²» ¯°¿¦¥¨¿ ScaLAPACK Stress invariants ¬¥²¼ ¢±¥ ®±®¢ ¨¿ To have good reason ¢®«¾²¨¢ ¿ ¬ ²°¨¶ Involuntary matrix ¬¥²¼ ¬¥±²® ¤¥ª± ¯°®´¨«¿ In some instances, gasoline vapor explosions occur Pro le index ¬¥²¼ ¬®£® ®¡¹¥£® ± : : : ¤¨¢¨¤³ «¼®¥ ¢°¥¬¿ To have much in common with : : : Individual time ¬¥¾¹¨¥±¿ ¤ »¥ (¨´®°¬ ¶¨¿) ¤¨ª ²°¨± ª°¨¢®© Available data ¬¨² ²®° Indicatrix of a curve ¤³ª¶¨¿ ¬ £¨² ¿ Simulator Magnetic induction ¬¨² ¶¨¿ Simulation ¤³ª¶¨¿ ¯® n The proof is by induction on n ¬¯³«¼± ¤ ¢«¥¨¿ The impulsive boundary motion produces a pressure im- ¥°¶¨ «¼ ¿ ª®®°¤¨ ² Inertial coordinate pulse in the uid In uence of various factors on the air pressure pulse from ¥°¶¨® ¿ ¬ ²°¨¶ passing trains Inertial matrix
Recoil impulse Recoil momentum
¬¯³«¼± ®²² «ª¨¢ ¨¿ Repulsive momentum ¬¯³«¼± ¯°¨²¿£¨¢ ¨¿ Attractive momentum ¬¯³«¼± ° ±²¿¦¥¨¿ Tensile pulse ¬¯³«¼± ¨±²®·¨ª Source impulse ¬¯³«¼± ª³¯®«®®¡° §»© Domal pulse ¬¯³«¼± ¯°®¤®«¼»© Longitudinal (im)pulse ¬¯³«¼± ²¥¯«®¢®© Heat impulse ¬¯³«¼± ¯ ° Vapor momentum ¬¯³«¼± ¯®²®ª
The inertia of a symmetric matrix is the triple whose elements are the number of positive, negative, and zero eigenvalues, counted with multiplicities
¥°¶¨¿ §°¨²¥«¼®£® ¢®±¯°¨¿²¨¿ The persistence of vision ®°® ¯®«®¦¨²¥«¼»© Inner positive ±²¨²³² ¬¥¤¨ª®-¡¨®«®£¨·¥±ª¨µ ¯°®¡«¥¬ Institute for Biomedical Problems ±²¨²³² ¬¥µ ¨ª¨ Moscow University Institute of Mechanics ±²¨²³² ´¨§¨ª¨ ¢»±®ª¨µ ½¥°£¨© Institute for High Energy Physics (IHEP)
The International Association for the Promotion of Cooperation with Scientists from the Independent States of the Former Soviet Union
The total ux of momentum is the same at each cross ²¥£° « ¥·¥²®© (·¥²®©) ±²¥¯¥¨ Integral of odd (even) degree section
¬¯³«¼± ¿ °¥ ª¶¨¿ Impulsive reaction ¬¯³«¼±®¥ ¢®§¤¥©±²¢¨¥ Impulse action Impulse force
¬¯³«¼±®¥ £°³¦¥¨¥ Impulsive loading ¬¯³«¼±»© ¯°®¶¥±± Pulse process ¬¯³«¼±»© ¶¨´°®¢®© ®±¶¨««®£° ´ Pulse digital oscilloscope ¬¯³«¼±®¢ ¤¨´´³§¨¿ Di usion of impulses
²¥£° « ¯® ¢¥¸¥¬³ (¢³²°¥¥¬³) ª®²³°³ Outer (inner) contour integral ²¥£° « ¯® ª®®°¤¨ ² ¬ Integral over coordinates ²¥£° « ¯® ±®±²®¿¨¿¬ State integral ²¥£° « ½¥°£¨¨ Energy integral Integral of energy
²¥£° «¼ ¿ ¬¨ª°®±µ¥¬ Integrated circuit ²¥£° «¼ ¿ ° ¡®² Total work
47
´ ²
²¥£° «¼»© ¯ ° ¬¥²° Integral parameter ²¥£°¨°®¢ ¨¥ ¢ ª¢ ¤° ²³° µ Integration in quadratures ²¥£°¨°®¢ ¨¥ ¢ ¯°¥¤¥« µ
Infante
´®°¬ ¶¨®®-²¥®°¥²¨·¥±ª ¿ ¬®¤¥«¼ Information-theoretical model
´®°¬ ¶¨®»© ª°¨²¥°¨©
Integration in the limits of a to b Integration in the limits from a to b Integration between a and b
Information criterion
´®°¬ ¶¨¿ ®¢ ¿ ® ¢±¥µ ±¯¥ª² µ : : : Up-to-date information about all aspects : : :
²¥£°¨°®¢ ¨¥ ¯® ®¡« ±²¨ Integration over a (the) domain (region) ²¥£°¨°®¢ ¨¥ ¯® ¨¬ ³{²¨«²¼¥±³ Riemann{Stieltjes integration ²¥£°¨°®¢ ²¼ ¢ ¯°¥¤¥« µ ®² : : : ¤® : : : To integrate between a and b ²¥£°¨°®¢ ²¼ ¯®
´®°¬ ¶¨¿ ®
²¥£°¨°®¢ ²¼ ®² : : : ¤® : : : To integrate between a and b ²¥£°¨°³¥¬ ¿ ®±®¡¥®±²¼ Integrable singularity ²¥£°¨°³¥¬ ¿ ¯® ¨¬ ³ ´³ª¶¨¿ Riemann-integrable function ²¥£°¨°³¥¬»© ¢ ±¬»±«¥ ¨¬ Riemann integrable ²¥£°¨°³¥¬»© ¯® ¥¡¥£³ Lebesgue integrable ²¥£°¨°³¥¬»© ± ª¢ ¤° ²®¬ Integrable in square (square integrable) ²¥±¨¢®±²¼ ¨¬¯³«¼± Impulse intensity ²¥±¨¢®±²¼ ¨±²®·¨ª Strength of a (the) source ²¥±¨¢®±²¼ ¯¥°¥µ®¤
® ª «¼¶¨¿
Information on
´° ª° ± ¿ ¢¨¤¥®ª ¬¥° Infrared video camera
®£ ±®
Johansson
® ª «¨¿
To integrate with respect to (in) x To integrate over the domain D
Potassium ion Calcium ion
®±¨¤
Yoshida
±ª ¦ ¥¬®±²¼
Ability to be distorted
±ª ¦ ²¼±¿
The cone shape is distorted by the Fourier transform
±ª ¦¥
This le is corrupted
±ª ¦¥¨¥ ½«¥ª²°¨·¥±ª®£® ¯®«¿ Distortion of an electric eld
±ª ²¼
We seek the matrix M in the form M = I me We seek a good estimate of the least value of the function of one variable We now search for sucient conditions for f to coincide with g on X
Transient intensity Transition intensity
±ª«¾· ²¼
Eliminating y from the last two equations, we come to the conclusion that : : :
²¥±¨¢»© ¯ ° ¬¥²° Intensive parameter ²¥°¢ « § ·¥¨© ¯®ª § ²¥«¿ Exponent range ²¥°¢ « ¨§¬¥¥¨¿ ¯® Interval (range) of changing in y ²¥°¢ « ¨²¥£°¨°®¢ ¨¿ Interval of integration Integration interval
T k
±ª«¾·¥¨¥ ³±± (³¯®²°¥¡«¿¥²±¿ ¡¥§ °²¨ª«¿) A number of direct methods based on classical Gauss elimination have been developed for the cases where the fast direct methods are inapplicable
±ª«¾·¥¨¥ (£ ³±±®¢®) ³±± ¤«¿ ° §°¥¦¥»µ ¬ ²°¨¶ (³¯®²°¥¡«¿¥²±¿ ¡¥§ °²¨ª«¿)
²¥°¢ « ®°²®£® «¼®±²¨ Orthogonality interval ²¥°¢ « ²®°¬®¦¥¨¿ Interval with (of) nonzero braking moment ²¥°¥± ¤«¿ ¯° ª²¨ª¨ Of interest in practice ²¥°¥±³¾¹¨¥ ²®·ª¨ The points of interest ²¥°¯®«¨°®¢ ²¼ ¯® To interpolate with respect to x ²¥°¯®«¿¶¨® ¿ ´®°¬³« ²¨°«¨£ Stirling's interpolation formula ²¥°¯®«¿¶¨¿ ´³ª¶¨¨ f ¯® ½²¨¬ ²®·ª ¬ (³§« ¬) Interpolation of the function f in these points (nodes) ²¥°´¥©± ¯¥°¥¤ ·¨ ±®®¡¹¥¨©
Sparse (Gaussian) Gauss elimination
±ª«¾·¥¨¥ ±²°®ª¨ Row elimination Row deletion
±ª®¬ ¿ ®¡« ±²¼
The sought-for region
±ª®¬ ¿ ´³ª¶¨¿
The sought-for function The required function
±ª®¬®¥
The sought for
±ª°®¢®© ¯¥°¥¤ ²·¨ª Spark transmitter
±¯ °¿²¼±¿ ± ¯®¢¥°µ®±²¨
Heat from the Sun causes water to evaporate from the Earth's surface
±¯®«¨²¥«¼»¥ ¬¥µ ¨§¬»
Massage passing interface (MPI)
48
Operating actuators
±µ®¤¨¬ We start from ±µ®¤ ¿ § ¤ · Original (® ¥ initial) problem ±µ®¤®¥ ¢¥¹¥±²¢® Reagent ±µ®¤®¥ ³° ¢¥¨¥ (±®®²®¸¥¨¥) By using (applying) the Fourier integral, it is possible to Basic (original, ® ¥ initial) equation (relation) ±µ®¤¿ ¨§ ¯°¥¤¯®«®¦¥¨¿ obtain : : : The above equation is obtained by making use of equa- On the assumption of (that) ±µ®¤¿ ¨§ ½²®£® tions (1) and (2) By making use of amplitudes, it is possible to determine On this basis ±µ®¤¿¹ ¿ ¯®·² all the three elastic parameters Outgoing mail (email) ±¯®°·¥ ±µ®¤¿¹¨© ¨§ This le is corrupted Angle is a gure formed by two rays going out of the same ±¯»² ¨¥ ¯°®¤®«¦¨²¥«¼®±²¼ point Endurance test ±µ®¤¿¹¨© ²®ª ±¯»² ¨¥ ±° ¢¥¨¥¬ Outward current Comparison test ±·¥§ ¾¹ ¿ ¢¿§ª®±²¼ ±¯»²»¢ ¥¬ ¿ ¬®¤¥«¼ Vanishing viscosity Model under test ±·¥§ ¾¹ ¿ ´³ª¶¨¿ ±¯»²»¢ ²¼ Vanishing function To su er alternation ±·¥§®¢¥¨¥ ¯®°¿¤ª ·¨±« (§ · ¹¨µ ° §°¿To su er a loss of stability ¤®¢) ±¯»²»¢ ²¼ Under ow To test the (an) element for alpha-emission ±·¥°¯»¢ ¨¥ (¢ «¨¥©®© «£¥¡°¥) ±¯»²»¢ ²¼ ±¥¡¥ ±¨«» A particle experiences forces in the presence of magnetic De ation ±·¨±«¥¨¥ ´ ª²®°®¢ elds Factor analysis ±¯»²»¢ ²¼ ¥¤®±² ²®ª ¢ ·¥¬-«¨¡® ±·¨±«¨¬®¥ (±·¥²®¥) ¬®¦¥±²¢® To be (to fall) short of Denumerable set ±¯»²»¢ ²¼ ¥¤®±² ²®ª ª¨±«®°®¤ ²¥° ¶¨®®¥ ³«³·¸¥¨¥ To experience lack of oxygen Iterative re nement ±¯»²»¢ ²¼ ²°³¤®±²¨ Iterative improvement The web site might be experienced technical diculties ²¥° ¶¨®®¥ ³²®·¥¨¥ ±¯»² ¨¿ ¥°³««¨
±¯®«¼§®¢ ¨¥ Use is (can be) made of the fact that : : : ±¯®«¼§®¢ ²¼ Programs make use of the instruction collection ±¯®«¼§®¢ ²¼ : : : ¢¬¥±²® : : : To use : : : for : : : ±¯®«¼§³¿
Iterative re nement Iterative improvement
Bernoulli trials
±±«¥¤®¢ ¨¥ ¥³±² ®¢¨¢¸¥£®±¿ ¤ ¢«¥¨¿ Pressure transient analysis ±²¥·¥¨¥ ¦¨¤ª®±²¨ Liquid out ow from Fluid out ow from
±²¥·¥¨¥ ¨§ ±®¯« Nozzle ow ±²¥·¥¨¥ ±²°³¨ ¨§ Jet out ow from ±²¨ ¿ ¯«®²®±²¼ True density ±²¨»¥ ¯°¿¦¥¨¿ True stresses ±²¨»© ®¡º¥¬ True volume ±²®ª®®¡° §»© Sourcewise Source-like
±²®·¨ª{±²®ª Source{sink Source{outlet
±²®·¨ª®¢ ¬¥²®¤ Method of sources ±²°¥¡¨²¥«¼ (± ¬®«¥²) Fighter plane
²¥° ¶¨®»© ¬¥²®¤ °»«®¢ Krylov subspace method ²¥° ¶¨¿ ± ¤¢®©»¬ ±¤¢¨£®¬ Double shift iteration ²¥° ¶¨¿ ± ¬®£®ª° ²»¬ ±¤¢¨£®¬ Multi-shift iteration ²¥° ¶¨¿ ± ®¤¨ °»¬ ±¤¢¨£®¬ Single shift iteration ²¥° ¶¨¿ ± ®²®¸¥¨¥¬ ¥«¥¿ Rayleigh quotient iteration ²¥° ¶¨¿ ± ¯¥°¥¬¥»¬ ±¤¢¨£®¬ Variable-shift iteration ²¥° ¶¨¿ ±® ±¤¢¨£®¬ Shifted iteration ²®£®¢ ¿ ª °²¨ Concluding picture ²®£®¢®¥ ¬®¦¥±²¢® Concluding set ¹¥¬ We seek
¥±¥ Jensen
49
¥²± Yates ® John ®°¤ ( ±ª³ «¼)
No rigorous upper bound on the error, however sharp, can satisfactorily account for the statistical nature of rounding error Our knowledge of oncology, limited as it may be, has tended to show that : : :
ª ¡»«® ³¯®¬¿³²® ¢»¸¥
Jordan
ª®¶³ : : : £®¤®¢ Towards the end of 1930s ±²®¿¹¥¬³ ¢°¥¬¥¨
As has been mentioned above, a convenient method of representing such a system is the block diagram
K
ª ¤®«¦® ¡»²¼ As should be the case ª ¥±«¨ ¡»
Each process is treated as if it were a processor He speaks about computers as if he were an expert on them In this case, the air is treated as if it had no viscosity
By now many types of these instruments have been constructed
²®¬³ ¢°¥¬¥¨
By then the results of these experiments had been known ª ¨ ¢»¸¥ to many scientists As above ¢ «¼¥°¨ ª ¨§¢¥±²® Cavalieri These results are known to be (to have been) used ¢¥¤¨¸ As is known, one of the main sources of nuclear energy is Cavendish the combustion of hydrogen ¢¥° ± ¤¢³¬¿ ¯®¤¢¨¦»¬¨ ª°»¸ª ¬¨ ª «³·¸¥ Double lid-driven cavity The question here is how best to overcome (the) random ¢¥° ± ¯®¤¢¨¦®© ª°»¸ª®© noise Lid-driven cavity
ª ¬®¦® ¡®«¥¥
¢¨² ²®° Cavitator ¢¨² ¶¨® ¿ ¯®«®±²¼
These propellants are chosen with the objective of creating as high a temperature as possible
ª ¬®¦® ¬¥¼¸¥
Cavity Cavity pocket Cavitation pocket
We choose this parameter to make this norm as small as possible
ª ¨ ±²° ®
¢¨² ¶¨®®¥ ®¡²¥ª ¨¥
Curiously (strangely) enough, the experiments did not con rm the theoretical conclusions
Cavity ow around (past) Cavitational ow around (past) Cavitation ow around (past)
ª ®¡»·® As is customary ª ®¡»·® ¡»¢ ¥² As is usually the case, there are several types of situations ª ®ª § «®±¼ It appeared that the statement was false ª ®²¬¥·¥® ¢»¸¥
¢¨² ¶¨®®¥ ²¥·¥¨¥ Cavity ow Cavitation ow Cavitational ow
¢¨² ¶¨¿ · ±²¨¶ Particle cavitation ¦¤»© For any (® ¥ every) two matrices from this class : : : ¦¤»© ¨§ Each of the real numbers x, y, and z is positive ¦¥²±¿, ·²® It is felt (it seems) that this type of treatment is suitable ¦³¹ ¿±¿ ¢¥°²¨ª «¼ Subjective vertical ¦³¹¥¥±¿ ³±ª®°¥¨¥ Apparent acceleration ¦³¹¨©±¿ ¢¥± Apparent weight ¦³¹¨©±¿ £®°¨§®² False horizon ª ¡³¤²® ¡» He behaved as if he had never seen a telescope before ª ¡»
As (was) noted above, a vector is associated with a point in the plane
ª ¯®ª § ®
As (is) shown in Figure 2, as demonstrated in Figure 2 As is shown (® ¥ as it is shown) in Figure 1 (in Section 1)
ª ¯®ª § ® ¨¦¥ As (is) shown below ª ¯®« £ ¾² The charged particles are supposed to have : : : ª ° §
The delegation arrived just in time to take part in (at) the conference
ª : : : ² ª Both : : : and ª ² ª®¢®© As such ª ²®«¼ª®
Once a program has been written, the computer : : : As soon as pressure is removed, the air springs back to its original volume
As it were It is as of : : :
ª ¡» : : : ¨ ¡»«( ,®,¨)
There are many lines through a point which do not inter- ª ³¯®¬¨ «®±¼ ¢»¸¥ sect a given line within any xed distance, however large As previously mentioned 50
ª ³¯®¬¿³²®
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ª (½²®) «¥£ª®
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ª ½²® ¬®¦® ¡»«® ¡»
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« ±¥°¢®³¯° ¢«¥¨¿
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KAM(Kolmogorov{Arnold{Moser)-theory As (was) mentioned above As was mentioned at the beginning of this paper, the no- ¬¯¡¥«« tion of limit of a sequence of matrices : : : Campbell As is known, : : :
Vortex chamber
As (¡¥§ it) is easy to check, this norm is less than unity
Outlet (inlet) channel
In this case, temperature does not decrease as might at Conductance channel rst be expected (supposed) « ± ¸¥°®µ®¢ ²»¬¨ ±²¥ª ¬¨ ª ½²® ®¡»·® (· ±²®) ¨¬¥¥² ¬¥±²® Rough channel As it is usually (often) the case Channel with rough walls Whatever the direction of propagation happened to be Servocontrol channel under the above conditions, we can observe that : : : ¨½«¼ Kaniel ª¨¬ ¡» ¨ ¡»« Whatever the method, the calculation (computation) ®¨·¥±ª¨© ¨¬¯³«¼± must be accurate (precise) Canonical momentum No matter how small, the radiation should be avoided ²¥««¨ However thin the shockwave, the air speed is reduced Cantelli No matter what the nature of such a surface, there is al- ²¨«¥¢¥°»© ways some opposition to (the) motion Of cantilever What kind (sort) of
Cantor
No matter how accurate the measuring device may be, Capelli repeated readings will not be the same ¯¥«¼ ¿ ¦¨¤ª®±²¼ ª®¢» ¡» ¨ Liquid in drops It is not dicult to show, however, that our result can be ¯¥«¼»© applied to any two points, no matter what the algebraic In the form of drops signs of their coordinates are ¯¨««¿° ª®¢» ¡» ¨ ¡»«¨ Capillary tube Our result applies to any two point, no matter what the ¯¨««¿° ¿ ±¨« algebraic signs of their coordinates are Capillary force It makes no di erence which specimen is tested
Capillary viscometer (viscosimeter)
No matter what kind of
Kapitsa
Whatever be the error, we must detect it
Caratheodory
No matter which
Carborundum
Calais
Cardan
Gauge coecient
Universal joint Hooke's joint Cardan joint Hardy{Spicer joint U-joint
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Cardano
Kahlbaum
Gimbal Gimbals Cardan (gimbal) suspension
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Calmodulin regulator Stony inclusions
Framework Carleman
51
±±¨¨ Cassini ±²¨«¼¿¨ Castiglianian ±²¨«¼¿® Castigliano ² ª Wire rod ² «¨²¨·¥±ª ¿ ¯®¢¥°µ®±²¼ Catalytic surface ² «¨²¨·¥±ª ¿ °¥ª®¬¡¨ ¶¨¿ Catalytic recombination ²¥®¨¤ Catenoid ²¥° Kater ²¥² (¯°¿¬®³£®«¼®£® ²°¥³£®«¼¨ª ) Leg of a right-angled triangle ²³¸ª ¨¬¯³«¼± ¿ Pulse-forming coil ²³¸ª ¨¤³ª¶¨® ¿ Induction coil ²¿¹¨©±¿ ª ¬¥¼ Rolling stone ³«¨£ Cowling µ Kahane µ W. Kahan µ ¥° Kahaner ¶ Kac, Katz · ¨¥ ¬ ¿²¨ª Swing of a pendulum ·¥¨¥ ¡¥§ ¯°®±ª «¼§»¢ ¨¿
°«¥±® Carleson
°«±® Carlson
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Karman Karman
°¬ ¥³±²®©·¨¢®±²¨ Instability pocket
°®
Carnot
°°¨ Curry
°±¥« Carcel
°±¥«¼ Carcel
°² ±®ª°®¢¨¹ Treasure map
°² ²¥µ®«®£¨·¥±ª®£® ¯°®¶¥±± Flow chart
°² Cartan
°²¨ «¨¨© ²®ª Streamline pattern
°²¨ ®¡²¥ª ¨¿ ²¥«
Pattern of ow around a body
± ¨¥ ¢²®°®£® ¯®°¿¤ª Second-order tangency
± ²¥«¼ ¿ Tangent Tangent line
± ²¥«¼ ¿ ¢ °¨ ¶¨¿ Tangential variation Tangent variation
± ²¥«¼ ¿ ª ¯«®±ª®© ª°¨¢®© Tangent to a plane curve
No-slip rolling Rolling without slip Rolling without slipping
± ²¥«¼ ¿ ¯®¢¥°µ®±²¼ Tangent surface
± ²¥«¼ ¿ ±®±² ¢«¿¾¹ ¿
·¥¨¥ ± ¯°®±ª «¼§»¢ ¨¥¬ Rolling with slip ·¥¨¥ ²¥« Rolling of a body ·¥±²¢® ¤°®¡«¥¨¿ Quality index of fragmentation ·¥±²¢® ±² ¡¨«¨§ ¶¨¨ Stabilization quality ·¬ ¦ Kaczmarz ¢ ¤° ² ¥¢ª«¨¤®¢ ° ±±²®¿¨¿ Squared Euclidean distance ¢ ¤° ² (ª³¡) ° ±±²®¿¨¿ (¢°¥¬¥¨)
Tangential component
± ²¥«¼®¥ ¯¥°¥¬¥¹¥¨¥ Tangential displacement Tangent displacement
± ²¥«¼®¥ ° ±±«®¥¨¥ (¢ ¬¥µ ¨ª¥) Tangent bundle
± ²¥«¼»© ¢¥ª²®° Tangent vector
± ²¥«¼»© ¢¥ª²®° ¯®¢¥°µ®±²¨ Surface tangent vector
± ²¥«¼»© ®²°¥§®ª Tangent segment Tangential segment
The cubes of the main distances of the planets from the Sun are proportional to the squares of their times of revolution
± ²¼±¿
The line l is tangent to the curve C at the point A
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Cassegrain
±ª ¤ ¿ ¬®¤¥«¼ Shell model
±±¥£°¥ Cassegrain
¢ ¤° ²¨· ¿ ¯®¯° ¢ª Quadratic correction ¢ ¤° ² ¿ °¥§ª Square thread ¢ ¤° ²®¥ ²¥«® Square body
52
¢ ¤° ²»© ª®°¥¼ ¨§
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¢ §¨®¤®¬¥°»¥
« ¯ ¯®¤ ·¨ ¦¨¤ª®±²¨ Fluid (liquid) supply valve « ¯¥©°® Clapeyron « °ª Clark « ±± ¢»·¥²®¢ Residue class « ±± § ¤ ·
The square root of (¡¥§ the) binary number 110 001 (dec- Kiefer imal 49) is : : : « © Cline The square root of a (the) matrix Quasi-one-dimensional
¢ §¨±² ¶¨® °®¥ ª®«¥¡ ¨¥ Quasistationary oscillation
¢ ²¨´¨ª ¶¨¿ ½«¥ª²°®®-§®¤®¢ ¿ Electron probe quanti cation
¢ ²®¢ ¿ § ¤ · ° ±±¥¿¨¿ Quantum scattering problem
¢ °²¨«¼®¥ ®²ª«®¥¨¥ Quartile deviation
¢¨««¥ Quillen
¥¡¥
Koebe
¥«¥°
Kahler
¥««¨
Kelley
¥«¼¢¨ Kelvin
¥¤ «« Kendall
¥¨£ Konig
¥¼¿°-¿²³°
Caignard de la Tour
¥¯«¥° Kepler
¥°° Kerr
¥²«¥
Quetelet
¥¡¥
Koebe
¥¨£
Konig, Koenig
¨ª®¨ Kikoin
¨««¨£ Killing
¨«®¤¦®³«¼ (±®ª° ¹¥ ¿ § ¯¨±¼) kJ
¨«®®¬ (±®ª° ¹¥ ¿ § ¯¨±¼) k
¨¥²¨ª ¦¨¤ª®±²¥© Hydrokinetics
¨¥²¨·¥±ª¨© ¬®¬¥² Angular momentum
¨®¶¨«¨¿
Kinocilium Kinocilia (¬. ·¨±«®)
¨¯¯ Kipp
¨°µ£®´ Kirchho
¨°¸
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There are a number of techniques for extending this problem class at the expense of an increase in computing cost
« ±±¨´¨ª ¶¨¿ ¯® Classi cation by « ±±¨·¥±ª¨¥ ³° ¢¥¨¿ Classical equations « ±±¨·¥±ª¨©
A generalization of the classical gradient concept seems indispensable
« ³§¨³± Clausius «¥¡¸ Clebsch «¥¥¢®¥ ±®¥¤¨¥¨¥ Glued joint «¥© Klein «¥¸® Clenshaw «¥°® Clairaut «¥²ª¨-¨±²®·¨ª¨ Source cells «¥²®· ¿ ª³«¼²³° (¯®¯³«¿¶¨¿) Cell culture (population) «¥²®· ¿ °¥¸¥²ª Block lattice «¨¨ Kleene «¨´´®°¤ Cli ord ¥§¥° Kneser ³¤±¥ Knudsen ³¯ Knoop ³² Knuth ½¯¯ Knapp ® ¢°¥¬¥¨ By (at) the time of publishing this book ®¢ «¥¢±ª ¿ Kowalewski [Kovalevskaya] ®¢¥ª²®° Covector ®¢¥°±¨³± Coversed sine
53
®«¥® ¢®§¤³µ®¯®¢®°®²®¥
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When visible, sunspots are the most interesting objects Air intake on the solar surface ®«¥± ¿ ¡ § ®£¤ ¡» ¨ Wheel base Whenever we see that an object suddenly begins to move, ®«¥± ¿ ¯ ° we assume at once that : : : Wheelset
®£¤ ¡» ¨ (¢±¿ª¨© ° § ª®£¤ ) ®«¥±® ¢° ¹ ¾¹¥¥±¿ We can conclude that jf (x) Lj < " whenever jx aj < Spinning wheel ®£¤ -«¨¡® ®«¨¥©®¥ (¯°®¥ª²¨¢®¥) ¯°¥®¡° §®¢ ¨¥ This is the most dicult problem ever met in our practice Collineatory transformation ®£¤ ¨ ²®«¼ª® ª®£¤ ®«¨·¥±²¢® When and only when
There are (® ¥ is) large ( nite, small, in nite, negligible) number of exceptions (sets, points) N is the number of times that this contour winds around O We consider a number of results concerning this problem There are a number of results concerning this problem A number of results concerning this problem are published This conclusion is valid for a countable number of points A = B for all n except a nite number (¨«¨ for all but nitely many n) Q contains all but a countable number of the x There are only countably many elements q of Q with : : : Quite a few of (a considerable number) of these results are now widely used Only a few of these results have been published before
®£¤ -²®
Atoms were once supposed to be indivisible units (items)
®¤ ¨° Kodaira
®¤¤¨£²® Coddington
®¤®¢»¥ ¨§¬¥°¥¨¿ Code measurements
®¥-ª²®
j
Someone or other
®¥-·²®
Something or other
®©´¬ Coifman
®ª°¥
®«¨·¥±²¢® ¤¢¨¦¥¨¿
The principle (law) of conservation of linear momentum means that in the absence of external forces the momentum remains constant
Cochran
®ª°®´² Cockroft
®«¨·¥±²¢® ¤¢¨¦¥¨¿ ®²¤ ·¨
Coxeter
®«¨·¥±²¢® ¦¨¤ª®±²¨
Coxeter
®«¨·¥±²¢® ®¡« ª®¢
Measuring ask
®«¨·¥±²¢® ° ¡®²» ¤«¿ ®²ª°»²¨¿ ²°¥¹¨»
Fluctuation of pressure
®«¨·¥±²¢® ° ¡®²» (½¥°£¨¨)
Small-amplitude oscillation Small-amplitude vibration
®«¨·¥±²¢® ³¬®¦¥¨© ¨ ±«®¦¥¨©
®ª±¥²¥° ®ª±²¥° ®«¡ ¨§¬¥°¨²¥«¼ ¿ ®«¥¡ ¨¥ ¤ ¢«¥¨¿
®«¥¡ ¨¥ ¬ «®© ¬¯«¨²³¤»
Recoil momentum
Fluid (liquid) amount Amount of clouds
The amount of work for opening the crack
Quantity of work (energy)
This algorithm requires 7 multiplications (multiples) and 18 additions (adds)
®«¥¡ ¨¥ ®ª®«® (®²®±¨²¥«¼®)
Oscillations of the pendulum about the point of suspen- ®«¨·¥±²¢® ½¥°£¨¨ The total work depends on the amount of available energy sion
®«¥¡ ¨¥ ±ª®°®±²¨ ¯»«¥¨¿
®««¥ª²®°®±²¼ 8:1
®«¥¡ ¨¥ ±²¥°¦¿
®«¬®£®°®¢
®«¥¡ ¨¥ ±²°³»
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®«¥¡ ¨¥ ²¥¬¯¥° ²³°» °¥¤ª¨¥
®«¯ ª ¢®§¤³¸»©
®«¥¡ ²¥«¼ ¿ ½¥°£¨¿
®«¼° ³¸
®«¥¡ ²¥«¼®¥ ¢®§¡³¦¤¥¨¥
®«¼¶¥¢ ¿ ¤¥´®°¬ ¶¨¿
Deposition rate uctuation Oscillation of a rod
Vibration of a string
Wide temperature extremes Oscillatory energy
Vibrational excitation
®«¥¡ ²¥«¼®¥ §¢¥®
Contraction eight to one Kolmogorov Nozzle liner
Air vessel (chamber) Kohlrausch
Ring deformation Ring strain
Oscillatory link
®«¼¶¥¢ ¿ ¯«¥ª
Oscillatory regime Oscillation regime
®«¼¶¥¢ ¿ ±¥²¼
®«¥¡ ²¥«¼»© °¥¦¨¬
Annular lm
Ring network
54
®«¼¶¥¢ ¿ ´ ª²®°¨§ ¶¨¿ Ring factorization ®«¼¶¥¢®¥ ³±¨«¨¥ Ring strength ®«¼¶¥¢®© «£®°¨²¬ Ring algorithm ®«¼¶¥¢®© ±³¬¬ ²®° Ring accumulator ®«¼¶¥¢®© ²®ª Ring current ®«¼¶® ¨±²®·¨ª®¢ Ring of sources Source ring
®«¼¶® ¯¥°¥¤ ·¨ ±®®¡¹¥¨© Message passing ring ®«¼¶® ± ¥¤¨¨¶¥© Ring with identity Ring with unit element
®«¼¶® ²®° Annulus (pl.: annuli) ®«¼¸¥° Kolscher ®¬ ¤»© ²®ª Command current ®¬¬¥²¨°®¢ ²¼ ·²®-«¨¡® Comment on ®¬¬³¨ª ¶¨® ¿ ¤«¨ Communication length ®¬¯¥± ²®°®¥ ¤¢¨¦¥¨¥ Compensatory movement ®¬¯¥±¨°®¢ ²¼
®¬¯®®¢ª ½°®¤¨ ¬¨·¥±ª®© ²°³¡» Arrangement of wind (air) tunnel
®¬¯²® Compton
®¬´®°²»© ³£®« Convenient angle
®
Cohn
®¢¥©¥°»© «£®°¨²¬ Pipelined algorithm
®¢¥©¥°»© ª®¬¯¼¾²¥° Pipelined computer Pipeline computer
®¢¥ª²¨¢»© ¯®²®ª
Convective (convection) ux Convective (convection) ow
®£°³½²®±²¼ ²°¥³£®«¼¨ª®¢
Congruence of two triangles means that both triangles have the equal sides and equal angles
®£°³½²»¥ ¬ ²°¨¶» Congruent matrices
®£°³½²»¥ ²°¥³£®«¼¨ª¨
Congruent triangles have the same shape and size
®¤®°±¥ Condorcet
®¥¶ ( ¯°¨¬¥°, ¨²¥°¢ « ) Endpoint
®¥¶ ¢¥ª²®°
Endpoint of a (the) vector End of a (the) vector
«®¯ ±²¨ To make the needed corrections to compensate for the ®¥¶ The tip of the blade inevitable errors ®¥¶ ®²°¥§ª ®¬¯«¥ª±® ±®¯°¿¦¥ ¿ ¢¥«¨·¨ Endpoint of a (the) segment Complex conjugate value ®¥¶ ¯ «¼¶ Complex conjugate quantity Finger tip ®¬¯«¥ª±® ±®¯°¿¦¥ ¿ ¬ ²°¨¶ ®¥· ¿ ¤¥±¿²¨· ¿ ¤°®¡¼ Complex conjugate matrix Terminating decimal fraction ®¬¯«¥ª±® ±®¯°¿¦¥»¥ ³«¨ ®¥· ¿ ¤¥´®°¬ ¶¨¿ Complex conjugate zeros (zeroes) ®¬¯«¥ª±® ±®¯°¿¦¥»¥ ±®¡±²¢¥»¥ § ·¥¨¿ Finite strain ®¥· ¿ ±ª®°®±²¼ Complex conjugate eigenvalues Finite velocity ®¬¯«¥ª±® ±®¯°¿¦¥»¥ ´³ª¶¨¨ ®¥· ¿ ²®·ª ª°¨¢®© Complex conjugate functions End point (endpoint) of a curve ®¬¯«¥ª±® ±®¯°¿¦¥»© The complex conjugate of a complex number is repre- ®¥·®¥ ¯®«®¦¥¨¥ Final position sented by changing the sign of its imginary part End-position ®¬¯«¥ª±® ±®¯°¿¦¥»© ª ®¥·®¥ ·¨±«® This space is complex conjugate to the space de ned above There exist a nite number of points such that : : : ®¬¯«¥ª±® ±®¯°¿¦¥»© ²¢¨±²®° ®¥·®© ¸¨°¨» Complex conjugate twistor Of nite width ®¬¯«¥ª±®¥ ³° ¢¥¨¥ ®¥·®-° §®±² ¿ ±¥²ª Complex equation Finite-di erence grid ®¬¯®§¨² Finite-di erence mesh Composite
®¥·®±²¼ (°®¡®² ) ®¬¯®¥² ¯¥°¥®± Limb Translation component ®¥·»© °¥§³«¼² ² ®¬¯®¥²»© «¨§ What is needed in the nal results is a simple bound on Component analysis ®¬¯®¥²» ®¸¨¡ª¨ ¢»±®ª® (¨§ª®) · ±²®²»¥ quantities of the form (1) Gauss{Seidel iterations quickly reduce high frequency ®¨·¥±ª ¿ £®«®¢ª (¡®«² ) To tighten from the inside by bolts with tapered heads
components of the error, but not low frequency ones
55
®ª³°¨°®¢ ²¼ ± : : : ¢ : : :
®¶¥¢®¥ ±¥·¥¨¥
®±² ² ±ª®°®±²¨ Rate constant ®±² ² ³¯°³£®±²¨ Elasticity constant ®±² ²» ¬ ²¥°¨ « Constants of the material ®±²°³¨°®¢ ¨¥ ¯°®£° ¬¬ Software design ®±²°³ª¶¨®»© Structural ®±²°³ª¶¨®»© ¯ ° ¬¥²° Design parameter ®² ª² ª ·¥¨¿ Rolling contact ®² ª² ¿ § ¤ · Contact problem ®² ª²®¥ ¯°¿¦¥¨¥ Contact stress ®²¥ª±²®-³¯° ¢«¿¥¬»© Context-driven ®²¨³ «¼»© ¯®¤µ®¤ Continual approach ®²°®«¼ ª ·¥±²¢ Quality control ®²°±²° ²¥£¨¿ Counterstrategy ®²³° ®¡° ²®© ±¢¿§¨ ¯® y The feedback loop in y ®´¥°¥¶¨¿ (±«¥¤³¾¹ ¿) ±®±²®¨²±¿ The next conference on : : : will be held in Moscow ®´¨£³° ¶¨¨ ®²±·¥² ¿ ¨ ª²³ «¼ ¿ Reference and actual con gurations ®´¨£³° ¶¨®®¥ ¯°®±²° ±²¢® Con gurational space ®´«¨ª² ¸¨¥ Bus contention ®´®°¬»© ¬®¦¨²¥«¼ Conformal multiplier ®-®±±¥ Cohn-Vossen ®´³§®° Confuser ®¶¥¢ ¿ ²®·ª
®®°¤¨ ²» ¢¥ª²®°
This engine is competitive with a turbojet in fuel con- End section (end-section) sumption ®¶¥¢®© ¢¨µ°¼ ® Trailing vortex Connes Trailing line vortex ®±®«¼ ¿ ¡ «ª Tip vortex Cantilever beam ®¶¥¢®© £° ¨·»© ½«¥¬¥² ®±®«¼ ¿ ±²®©ª End boundary element Cantilever column ®¶¥²° ²®° (²®ª¨©) ¯°¿¦¥¨© ®±®«¼®¥ ¯°¨«®¦¥¨¥ Thin concentrator of stresses in elastic bodies Console application ®· ¿ ®±®«¼»© ±²¥°¦¥¼ Until the mid-1980s (the middle 1980s, the late 1980s) Cantilever beam (bar) ®®°¤¨ ² ¶¥²° ¬ ±± ®±² ² ¯«®¹ ¤¥© Center-of-mass coordinate Area constant ®®°¤¨ ² ¿ ±´¥° ®±² ² ¯°®¯®°¶¨® «¼®±²¨ Coordinate sphere Proportionality constant ®®°¤¨ ²»© ¡ §¨± Proportionality coecient Coordinate basis
Endpoint
Components of a vector
®¯¥°¨ª
Copernicus
®° ¡¥«¼»© ± ¬®«¥² Ship-based aeroplane
®°¥¼ ª° ²®±²¨ n
Root of multiplicity n (n-fold root)
®°¥¼ µ ° ª²¥°¨±²¨·¥±ª®£® ³° ¢¥¨¿ ¬ ²°¨¶» Eigenvalue of a matrix
®°¨®«¨± Coriolis
®°¥®°¥²¨ «¼»© ¯®²¥¶¨ « Corneo-retinal potential Corneal-retinal potential
®°¾ Cornu
®°®²ª¨© ¯³²¼ Short path
®°®²ª®¥ § ¬»ª ¨¥ Short-circuit
®°®²ª®¥ ° ±±²®¿¨¥ Short distance
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In brief (to be brief), the task of a transmitter is to generate : : :
®°¯³± ( ¢²®¬®¡¨«¿) Body, frame
®°¯³± ¯ °®¢®£® ª®²« Steam boiler
®°¯³± ± ¬®«¥² Fuselage of a plane
®°¯³± ±³¤ Hull of a ship
®°°¥ª²¨°®¢ª ®£¿ Fire adjustment
®°°¥ª²¨°®¢¹¨ª-± ¬®«¥² Spotting aircraft
®°°¥ª²¨°³¥¬ ¿ ±¨±²¥¬ Aided system
®°°¥ª²¨°³¾¹ ¿ ¦¨¤ª®±²¼ Correction uid
56
®°°¥ª²¨°³¾¹¥¥ ³¯° ¢«¥¨¥ Feedback control Correcting control
®°°¥ª²¨°³¾¹¨© ª®²°®«¼ Feedback control Correcting control
®°°¥ª²® ®¯°¥¤¥«¥»© Now the matrix multiplication is well de ned ®°°¥ª²®¥ °¥¸¥¨¥ Correct solution ®°°¥ª²»© Well-de ned, well-posed ®°°¥«¿¶¨® ¿ ¤«¨ Correlation length ®°²¥¢¥£ ¥ °¨§ Korteweg de Vries ®± ¿ ¢»±®² Slant height ®± ¿ «¨¥©· ² ¿ ¯®¢¥°µ®±²¼ Skew ruled surface ®±¥ª ± ³£« Cosecant of an angle ®±¨®°- «¨§ Cosinor-analysis ®±¨³± ¬ ²°¨¶» Cosine of a (the) matrix ®±¬¨·¥±ª ¿ ¡®«¥§¼ ¤¢¨¦¥¨¿ Space motion sickness ®±®±®¯°¿¦¥»© ®¯¥° ²®° Skew-adjoint operator ®±®© «³· Slanting beam ®±®© ²°¥³£®«¼¨ª Oblique triangle ®±±¥° Cosserat ®±²¥° Koster ®±²»«¼ ± ¬®«¥² Tail-skid of an aeroplane ®±»¥ «¨¨¨ Skew lines ®²¥± Cotes ®²®°»©
®·°½ Cochran ®¸¨ Cauchy ®½ Cohen ®½°¶¨²¨¢ ¿ ª° ¥¢ ¿ § ¤ · Coercive boundary value problem ®½´´¨¶¨¥² ªª®¬®¤ ¶¨¨ ½¥°£¨¨ Energy accommodation coecient ®½´´¨¶¨¥² ¡¨ °®© ¤¨´´³§¨¨ Binary di usion coecient ®½´´¨¶¨¥² ¢«¨¿¨¿ In uence coecient ®½´´¨¶¨¥² ¢®±±² ®¢«¥¨¿ ±¨«» (¬®¬¥² ) Restoring force (moment) coecient ®½´´¨¶¨¥² ¢¿§ª®£® ±®¯°®²¨¢«¥¨¿ Viscous resistance (drag) coecient ®½´´¨¶¨¥² ¤ ¢«¥¨¿ Pressure coecient ®½´´¨¶¨¥² ¤¥¬¯´¨°®¢ ¨¿ Damping coecient ®½´´¨¶¨¥² ¤¥´®°¬ ¶¨¨ Strain coecient ®½´´¨¶¨¥² ¤¨´´³§¨¨ Di usion coecient ®½´´¨¶¨¥² ¦¥±²ª®±²¨ ¯°³¦¨» Spring constant ®½´´¨¶¨¥², § ¢¨±¿¹¨© ®² ¢°¥¬¥¨ Time factor (coecient) ®½´´¨¶¨¥² § ²³µ ¨¿ Attenuation coecient ®½´´¨¶¨¥² ¨²¥±¨¢®±²¨ ¯°¿¦¥¨© Stress intensity factor (coecient) ®½´´¨¶¨¥² «®¡®¢®£® ±®¯°®²¨¢«¥¨¿ Drag coecient ®½´´¨¶¨¥² ¬ £¨²®© ¤¨´´³§¨¨ Magnetic di usivity ®½´´¨¶¨¥² ª«® Slope coecient ®½´´¨¶¨¥² ®°¬ «¼®© ±¨«» Normal force coecient ®½´´¨¶¨¥² ®¡º¥¬®£® ° ±¸¨°¥¨¿ Coecient of volume expansion Volume-expansion coecient
®½´´¨¶¨¥² ®¡º¥¬®£® ±¦ ²¨¿ (±¦¨¬ ¥¬®±²¨) The set all of whose subsets are : : : Coecient of volume compressibility The matrix whose norm is : : : The procedure by means of which this function can be Volume compressibility coecient ®½´´¨¶¨¥² ®²° ¦¥¨¿ ¯°¿¦¥¨© computed Stress re ection coecient The condition for which this is true The point at which this function has a local minimum ®½´´¨¶¨¥² ¯¥°¥®± The operator which will be de ned later (below) Transfer coecient Transport coecient A sequence each of whose term is positive
®²®°»© ¨§
®½´´¨¶¨¥² ¯®¢¥°µ®±²®£® ¤ ¢«¥¨¿
It is yet unknown which of these factors is responsible for Surface pressure coecient such a situation ®½´´¨¶¨¥² ¯®¢¥°µ®±²®£® ²¿¦¥¨¿ ®²²°¥«« Surface tension coecient Cottrell ®½´´¨¶¨¥² ¯®¤®¡¨¿ Ratio of similitude ®³²± Similarity ratio Cotes Coecient of similarity ®´±² ¤ Similarity coecient Kofstad 57
®½´´¨¶¨¥² ¯®¤º¥¬®© ±¨«»
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Quenching coecient
Lift (force) coecient
Among (the) other viscous modes, the growth rate of mode 2 is maximal
Eciency coecient
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Flux coecient Flow coecient
Antenna gain
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° ¥¢ ¿ ª ± ²¥«¼ ¿
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The coecient at x in the polynomial p(x) of degree 2n
Wave ampli cation factor
n
Re ex gain
Sticking coecient of molecules
Filter gain
Wave transmittance
Elastic wave transmittance
Emissivity factor
Enthalpy coecient
Intensity transmission coecient
Coecients at equal powers of t
Stress transmission coecient Slip ratio Slip coecient
Edge tangent Boundary tangent
Spatial ampli cation factor
Tread edge
The Poisson ratio (Poisson's ratio)
Cramer
Piezoconductivity coecient
Cramer
Coupling coecient
Throttle
Coecient of contraction Contraction coecient
Crank
° ª-¨ª®«±®
®½´´¨¶¨¥² ±¨«»
Crank-Nicolson
Force coecient
° ±®-·¥°®¥ ³¯®°¿¤®·¥¨¥
Reaction rate coecient
° ²ª®¢°¥¬¥»© ¨¬¯³«¼± ¤ ¢«¥¨¿
Drag coecient
° ²ª®¥ ¨§«®¦¥¨¥ ¤®ª« ¤
Dry friction coecient
° ² ¿ ²®·ª ª°¨¢®©
Cohesion coecient
° ²®¥ ¤¢³µ ·¨±¥«
Temperature conductivity coecient
° ²®¥ ±®¡±²¢¥®¥ § ·¥¨¥
Thermal volume-expansion coecient
° ²®¥ ·¨±«
Thermal coecient of contraction Thermal contraction coecient
° ²»©
®½´´¨¶¨¥² ±ª®°®±²¨ °¥ ª¶¨¨
Red-black ordering
®½´´¨¶¨¥² ±®¯°®²¨¢«¥¨¿ £¨¤° ¢«¨·¥±ª®£®
Short-time pressure impulse
®½´´¨¶¨¥² ±³µ®£® ²°¥¨¿
A summary of the report
®½´´¨¶¨¥² ±¶¥¯«¥¨¿
Multiple point of a curve
®½´´¨¶¨¥² ²¥¬¯¥° ²³°®¯°®¢®¤®±²¨
Common multiple of two numbers
®½´´¨¶¨¥² ²¥¯«®¢®£® ®¡º¥¬®£® ° ±¸¨°¥¨¿
Multiple eigenvalue
®½´´¨¶¨¥² ²¥¯«®¢®£® ±¦ ²¨¿
Multiple of a numbers The k-fold integration by parts shows that : : : F covers M twofold M is bounded by a multiple of t (i.e., by a constant times t) This distance is less than a constant multiple of G acts on H as a multiple, say n, of V
®½´´¨¶¨¥² ²¥¯«®¥¬ª®±²¨ Coecient of heat capacity
®½´´¨¶¨¥² ²¥¯«®¯°®¢®¤®±²¨ Thermal conductivity coecient Heat conductivity coecient
° ²»© ª®°¥¼ ³° ¢¥¨¿
Drag coecient
° ²· ©¸ ¿
®½´´¨¶¨¥² ²®°¬®¦¥¨¿
®½´´¨¶¨¥² ²³°¡³«¥²®£® ±¬¥¸¨¢ ¨¿ Eddy-mixing coecient
®½´´¨¶¨¥² ²³°¡³«¥²®±²¨ Eddy coecient
Multiple root of an equation Shortest line (on a surface) Geodesic
° ²· ©¸¥-«¨¥©»¥ ¯ ° ««¥«¨ Geodesic parallels
58
°¨²¥°¨© ¢»¡®° Choice criterion °¨²¥°¨© ¥¤¨±²¢¥®±²¨ Criterion for (the) uniqueness °¨²¥°¨© ª ·¥¨¿ ª®«¥± ¡¥§ ¯°®±ª «¼§»¢ ¨¿ No-slip criterion for the rolling of a wheel °¨²¥°¨© ª ·¥±²¢ ³¯° ¢«¥¨¿ Performance criterion of control °¨²¥°¨© ª®¢¥ª²¨¢®© ®£° ¨·¥®±²¨ Convection boundedness criterion °¨²¥°¨© ³° ² {°¨¤°¨µ± {¥¢¨
° ³² Crout ° ³· Crauch ° ´² Kraft °¥««¼ Crelle °¥¬® Cremona °¥¥° Kroner °¥¯¥¦ ¿ ¤¥² «¼ Fastener °¥±²®¢¨¤»© In form of a cross °¥±²®®¡° § ¿ ª°¨¢ ¿ Cruciform curve °¥±²®®¡° §»© In shape of a cross °¨¢ ¿ ¼¥§¨ Witch of Agnesi °¨¢ ¿ ¢¥°®¿²®±²¨ Probability curve °¨¢ ¿ ¢®§° ±² ¨¿ Curve of growth °¨¢ ¿ ¤ ¢«¥¨¿
The Courant{Friedrichs{Levy (stability) criterion The Courant{Friedrichs{Lewy (stability) criterion The Courant stability criterion
°¨²¥°¨© ¬¨¨¬ «¼®© ° ¡®²» Minimum work criterion °¨²¥°¨© · « ¬ ª°®° §°³¸¥¨¿ Criterion of the beginning of macrofracture °¨²¥°¨© ¥¢¿§ª¨ Residual criterion °¨²¥°¨© ®¡° §®¢ ¨¿ Formation criterion °¨²¥°¨© ®±°¥¤¥¨¿ Averaging criterion °¨²¥°¨© ¯°¥¤¥«¼®© ³¤¥«¼®© ¤¨±±¨¯ ¶¨¨ Criterion of limiting speci c dissipation °¨²¥°¨© ¯°®·®±²¨ Strength criterion Line of pressure °¨²¥°¨© ° ±ª°»²¨¿ Pressure curve Opening criterion °¨¢ ¿ ¤¢®©®© ª°¨¢¨§» °¨²¥°¨© ±³¹¥±²¢®¢ ¨¿ Curve of double curvature Criterion for (the) existence Twisted curve °¨¢ ¿ § ¢¨±¨¬®±²¨ ª®½´´¨¶¨¥² ¯®¤º¥¬®© °¨²¥°¨© ²¥ª³·¥±²¨ Yield criterion ±¨«» °¨²¥°¨© ³±²®©·¨¢®±²¨ ° ¢®¢¥±¨¿ ¯« ¢ ¾¹¥£® Lift curve °¨¢ ¿ § ¢¨±¨¬®±²¨ ¯°¿¦¥¨© ®² ¤¥´®°¬ - ²¥« Criterion of stable equilibrium of a oating body ¶¨© °¨²¨·¥±ª¨© ¬ ±¸² ¡ Stress-strain curve Critical scale °¨¢ ¿ ª° ²· ©¸¥£® ±¯³±ª °¨²¨·¥±ª¨© ° §°¥§ «£®°¨²¬ Brachistochrone Critical section of the (a) algorithm °¨¢ ¿ ¯®¢®°®² (®ª°³¦®±²¼ ¯®¢®°®² ) Turning circle °¨²¨·¥±ª¨© ³£®« ² ª¨ Stalling angle of attack °¨¢ ¿ ¯®£®¨ Critical angle of attack Pursuit curve Stall angle of attack °¨¢ ¿ ¯°¨ ¢±¥±²®°®¥¬ ±¦ ²¨¨ Stall(ing) angle Volumetric compression curve °®¢®± ¡¦¥¨¥ °¨¢ ¿ ° ±¯°¥¤¥«¥¨¿ ±ª®°®±²¥© Blood supply Velocity distribution curve °®£ °¨¢ ¿ ±²¥ Krogh Curved wall °®ªª® °¨±² ««»-®²®«¨²» Crocco Otoconial crystals °®¬¥ °¨±²®´´¥«¼ Apart from Christo el °®¬ª § ¤¿¿ °¨²¥°¨ «¼ ¿ ¢¥«¨·¨ Trailing edge Criterion quantity °®¬ª ª°»« °¨²¥°¨ «¼ ¿ ´³ª¶¨¿ Wing edge Criterion function °®¬ª ¯¥°¥¤¿¿ Criterial function Leading edge °¨²¥°¨© °®¬ª ¯°®´¨«¿ Performance criterion of control Pro le edge
Criterion for (® ¥ of) the occurence of this event
59
°®¥ª¥° Kronecker
°®¥ª¥°®¢±ª ¿ ±³¬¬ Kronecker sum
°®ª ©² Cronkite
°®°®¤ Kronrod
°®±± Cross
°³£ ¤¨ ¬¥²°
Diameter of a circle
°³£« ¿ °¥§ª Round thread
°³£«®¥ ²¥«® Round body Circular body
°³£«®±³²®·»© (¤®±²³¯) Round-the-clock access
°³£«»© ª ¯¨««¿° Round capillary
°³£®¢ ¿ ±¨¬¬¥²°¨¿ ¯¥°¥¬¥»µ Cyclic symmetry of variables
°³£®¢ ¿ ²®·ª (²®·ª ®ª°³£«¥¨¿) Umbilical point
°³£®¢ ¿ ´³ª¶¨¿ Circular function
°³£®¢®¥ ¢ª«¾·¥¨¥ Circular inclusion
°³£®¢®© ¤¢³³£®«¼¨ª Crescent Lune
°³£®¢®© ¬®£®³£®«¼¨ª Polygon of circular arcs
°³¦¨²¼
To rotate in a circle
°³ª±
Crookes
°³¯ ¿ ª ¯«¿
Large-scale droplet
°³¯®£ ¡ °¨²®¥ ²¥«® Bulky body
°³¯®§¥°¨±²®±²¼ Large-scale granularity
°³²¨«¼ ¿ £°³§ª ( £°³¦¥¨¥) Torsion(al) load (loading)
°³²¨«¼ ¿ ¯°³¦¨ Torsion(al) spring
°³²®© ¬¨«¼²®¨ Steep Hamiltonian
°³²¿¹¨©±¿ £¨°®±ª®¯ Spinning gyroscope
°³·¥¨¿ ¬®¬¥²
Torsional (turning) moment Torque
°»« ² ¿ ° ª¥²
Aerodynamic missile
°¾±± ° Crussard ³ © Quine ³§¥ Cousin ³§®¢ ¬ ¸¨» Vehicle body ³¨««¥ Quillen ³©««¥ Quillen ³«¨ Cooley ³«¨¤¦ Coolidge ³«® Coulomb ³«® (±®ª° ¹¥¨¥: ª) Coulomb (abbreviation: Q) ³«®®¢±ª®¥ ²°¥¨¥ Coulomb friction ³¬¬¥° Kummer ³¬³«¿²¨¢»© § °¿¤ Jet charge ³¬³«¿¶¨¿ ½¥°£¨¨ Energy cumulation ³ Kuhn ³¤ Kundt ³¯¥° Cooper ³¯®«®®¡° §»© Domal ³¯³« Cupula ³° ² Courant ³° ²®¢±ª¨© Kuratowski ³°± ¬ ²¥¬ ²¨ª¨ A course in mathematics ³±®·®-¯ ° ¡®«¨·¥±ª¨© ¬¥²®¤ Piecewise parabolic method ³²² Kutta ³½²² Couette ½«¥° Kahler ½«¨ Cayley ¾¥² Kunneth ¾°¨ Curie
°»«®¢ Krylov
°»«¼¿ £°¥¡®£® ¢¨² Blades of a propeller
¡®° ²®° ¿ ±¨±²¥¬ ®²±·¥²
Laboratory coordinate (or reference) system
60
¥¢ ¿ · ±²¼ ³° ¢¥¨¿ Left-hand side of an (the) equation ¥¢¥°¥²² Leverett ¥¢¥°¼¥ Le Verrier ¥¢¨±® Levinson ¥¢¨ ¥¯¯® Levi ¥¢¨ . Levy ¥¢¨ ®«¼-¼¥° Levy ¥¢¨-¨¢¨² Levi-Civita ¥¢®¥ ¢° ¹¥¨¥
¡®° ²®°®¥ ¢°¥¬¿ Laboratory time ¢ «¼ Laval ¢«¥©± Lovelace ¢°¥²¼¥¢ Lavrentjev £¥°° Laguerre £° ¦ Lagrange £° ¦¥¢ ¯¥°¥¬¥ ¿ Lagrangian variable §¥° ± ®¡° ¹¥¨¥¬ ¢®«®¢®£® ´°®² Phase conjugate laser ©²µ¨«« Lighthill ª± Lax ª³ °®¥ ¯°®±²° ±²¢® Lacunary space « ¤ Lalande «¥±ª® Lalesco ¬¡ Lamb ¬¡¥°² Lambert ¬¥ Lame ¬½ Lame ¤¥ Lande ¤®«¼² Landolt ¦¥¢¥ Langevin ¶®¸ Lanczos ·¥±²¥° Lanchester ¯« ± Laplace °¬®° Larmor ³½ Laue ¥ ²¥«¼¥ Le Chatelier ¥¡¥£ Lebesgue ¥¢ ¿ ±¨±²¥¬
Left-hand rotation Left-handed rotation
¥¢®°³ª¨© Left-handed ¥£ª ¿ ¦¨¤ª®±²¼ Light liquid ( uid) ¥£ª® A readily adjustable device ¥£ª®¤¥´®°¬¨°³¥¬»© ¬ ²¥°¨ « Easy-deformable material ¥£ª®±²¼ ¨±¯®«¼§®¢ ¨¿ Ease of use ¥£ª®¢®© ¢²®¬®¡¨«¼ Passenger car ¥¦ ¤° Legendre ¥©¡¨¶ Leibnitz, Leibniz ¥ª« ¸¥ Leclanche ¥ª± ®¢ ¿ ¯« ±²¨ Lexan plate ¥ª¶¨¿ ¯® Lecture on hereditary mechanics ¥¬¬ ® ¤¨¢¥°£¥¶¨¨ ¨ °®²®°¥ Div-curl lemma ¥ °¤ Lenard ¥£ Lang ¥£¬¾° Langmuir ¥²®· ¿ ¬ ²°¨¶ Band matrix Banded matrix
¥²®· ¿ ®¡° ² ¿ ¯®¤±² ®¢ª Band backward substitution ¥²®· ¿ ¯°¿¬ ¿ ¯®¤±² ®¢ª Band forward substitution ¥²®· ¿ ±¨±²¥¬
Left-handed system Left-hand system
¥¢ ¿ ±¨±²¥¬ ª®®°¤¨ ²
Left-handed coordinate system Left-handed system of coordinates
¥¢ ¿ ²°¥³£®«¼ ¿ ¬ ²°¨¶ Left triangular matrix
This subroutine solves a symmetric positive de nite banded system of linear equations
¥²®·®¥ (£ ³±±®¢®) ¨±ª«¾·¥¨¥ ³±± (³¯®²°¥¡«¿¥²±¿ ¡¥§ °²¨ª«¿) Band (Gaussian) Gauss elimination
61
¨¥©»© ª®° ¡«¼
¥²®·®¥ ° §«®¦¥¨¥
Ship of the line
Band decomposition Band factorization
¨¥©»© ¬ ±±¨¢
¥²®·®±²¼
Linear array It is reasonable to take advantage of the bandedness of ¨¥©»© ¯® ª®®°¤¨ ² ¬ matrices This expansion is linear in coordinates
¥²®·»© «£®°¨²¬
¨¥©»© ½«¥¬¥²
¥²®·»© ¬¥²®¤ Band method
¨¨¿ (¯³ª²¨° ¿, ¸²°¨µ®¢ ¿, ¢®«¨±² ¿, ±¯«®¸ ¿)
Band width of a (the) matrix
¨¨¿ ¢¥ª²®°®£® ¯®«¿
Lenz
¨¨¿ ¢¨§¨°®¢ ¨¿
Antenna lobe
¨¨¿ ±»¹¥¨¿
Leray
¨¨¿ ®¡¹¥£® ¯° ¢«¥¨¿
Leray
¨¨¿ ° ¢®£® ¤ ¢«¥¨¿
Lesniewski
¨¨¿ ±ª®«¼¦¥¨¿
Flying boat
¨¨¿ ²®ª (²¥·¥¨¿)
Band algorithm
Line element
¥²» ¸¨°¨ ¬ ²°¨¶»
(Dotted, dashed, wavy, continuous (solid)) line
¥¶
Vector eld line
¥¯¥±²®ª ¤¨ £° ¬¬» ¯° ¢«¥®±²¨ ²¥»
Line of sight
¥°¥
Line of saturation
¥°½
Trend line
¥±¨¥¢±ª¨©
Isobaric (isopiestic) line
¥² ¾¹ ¿ «®¤ª
Sliding line
¥²¥²¼ ¢ ±¢®¡®¤®¬ ¯®«¥²¥
Streamline The rocket coasts along its orbit in space, following a bal- ¨¨¿ ²®ª ¢¿§ª ¿ Viscous streamline listic course
¥²² ³
¨ª®«¼
¥´¸¥¶
¨¼
¥µ¥°
¨®±
¥£ª®£® ®°¨¥²¨°®¢ ¨¿ ±¨±²¥¬
¨¯¸¨¶
¨
¨±± ¦³
¨¡¡¨
¨²³³±
¨¡¨µ
¨³¢¨««¼
¨§¥£ £
¨´¸¨¶
¨¤¥«¥´
¨¶¥¢ ¿ ¯®¢¥°µ®±²¼
Lincoln
Lettau
Lin
Lefschetz
Lions
Lecher
Lipschitz
Easy-orientable system
Whether the spacecraft (spaceship) will be able to leave Lissajous the Earth, depends on its speed ¨²®© ¬ ²¥°¨ « Cast material ¨ (´ ¬¨«¨¿) Lie ¨²®±² ²¨·¥±ª®¥ ¤ ¢«¥¨¥ Lithostatic pressure ¨ ¨«¨ ¥² This conclusion may be based on whether or not vacuum- ¨²®±´¥° ¥¬«¨ ²¢¥°¤ ¿ («¨²®±´¥° ¯« ¥²») tube elements are employed The Earth's crust (the planet's crust) The question whether or not this ampli er can meet spe- ¨²²«¢³¤ cial requirements will be of great importance Littlewood Libbi
Lituus
Liebig
Liouville
Liesegang
Lifshitz
Lindelof
Outer surface Face surface Face
¨¤¥¬ Lindeman
¨¥©ª
«®©¤
¨¥©® ±¢¿§ »©
®¡ ²²®
¨¥©®-³¯°³£¨© ¬ ²¥°¨ «
®¡ ·¥¢±ª¨©
Drawing ruler
Lloyd
The space X is arcwise (® ¥ linearly) connected
Lobatto
Lobachevsky, Lobachevski, Lobatchevsky
Linear elastic material
62
³·¸ ¿ µ ° ª²¥°¨±²¨ª Superior characteristic (property, performance) ³·¸¥ ³·¨²»¢ ²¼
®¡®¢®¥ ±®¯°®²¨¢«¥¨¥ Motion drag
®£ °¨´¬¨°®¢ ¨¥
The above formula should be supplemented with two terms in order to better take into account the nonuniformity of characteristics
Taking logarithms
®£ °¨´¬¨°®¢ »© In logarithmic form
®£ °¨´¬¨°®¢ ²¼
To take the logarithm of
®£¨²- «¨§ Logit-analysis
®£¨·¥±ª¨© ¢»¢®¤ ²¨¯ ¬¤ ¨ Mamdani-type inference
®¤¦
Lodge
³·¸¥ ·¥¬ ¨·¥£® Better than none ¼¾¨± Lewis ½¬¡ Lamb ¾¡®©
Thus, this subroutine name refers to any or all of the routines
®¤¥
¾¡®£® ¯®°¿¤ª Of any order ¾¤¥°± Luders ¾¨«¼¥ L'Huilier ¾ª Door ¾¬¬¥° Lummer ¿¢ Love ¿£¥°° Laguerre ¿¯³®¢
Lode
®¤ª «¥² ¾¹ ¿ Flying boat
®¤®·»© £¨¤°®± ¬®«¥² Flying boat
®¦¥ °¥ª¨
Bed of a river
®ª «¼®-¨²¥£°¨°³¥¬ ¿ ´³ª¶¨¿ Locally integrable function
®ª «¼®¥ ¯®¤®¡¨¥ Local similarity
®ª®¬®¶¨¿ Locomotion
®ª±®¤°®¬¨·¥±ª ¿ ±¯¨° «¼ Loxodromic spiral
Lyapunov, Liapunov
®£°¥
Lonngrenn
®£±² ´´ Longsta
®¯ ±²¨ ¸¨°¨ Blade width
®¯ ²¨±ª¨© Lopatinskii
®¯ ²ª ° ¡®·¥£® ª®«¥± Wheel blade Impeller vane
®¯¨² «¼
L'Hospital
®°
Laurent
®°¥¶ Lorentz
®°¨
Laurie
®¸¬¨¤²
Loschmidt, Loshmidt
³¤®«¼´ Ludolph
³ª ±¥¢¨·
Lukasiewicz
³¬¬¥°
Lummer
³·¥¢®¥ ° §«®¦¥¨¥ Ray expansion
³·¨±²»© ¯®²®ª Radioactive ux
M
± Maass £¥«« Magellan £¨±²° «¼ ¿ ²°¥¹¨ Main crack £¨² ¿ ª®¢¥ª¶¨¿ Magnetoconvection £¨²®£¨¤°®¤¨ ¬¨ª Magnetohydrodynamics £¨²®±²°¨ª¶¨®»© Magnetostrictive £¨²®±²°®´¨·¥±ª¨© Magnetostrophic £³± Magnus ¦®°¨°®¢ ²¼ To nd a majorant of §¥° Mather §³° Mazur ©¥° Mayer ©ª¥«¼±® Michelson ª-¨ McGehee
63
¤¥«¼¡°®©² Mandelbrojt ¤¥«¼¡°®² Mandelbrot ²¨±± «®£ °¨´¬ Mantissa of a logarithm ° £®¨ Marangoni °¨®²² Mariotte °ª®¢ Markov °ª®¢±ª¨© ¯ ° ¬¥²°
ª¤® «¼¤ Macdonald ªª¨ Mackey ª-« ±ª¨ McCluskey ª- ´«¨ McLaughlin ª«¥© MacLane ª-¥®¤ McLeod ª«®°¥ Maclaurin ª°®±²³¯¥¼ Macrostep ª±¢¥«« Maxwell ª±¨¬ «¼ ¿ ®°¬ Maximum norm ª±³²®¢ Maksutov ª³« ± ªª³«¾± Saccular macula « ¿ ²¥®°¥¬ ¥°¬ Fermat's small theorem (FST) «® Mahlo «® ¯® ¬ «³ Little by little «® ±¢¥² A little light «®¡ §®¢ ¿ °®§¥²ª Low-base rosette «®¢¥°®¿²® The temperature is unlikely to rise «®¢¥°®¿²®¥ ±®¡»²¨¥ Event of small probability «®¢¿§ª ¿ ¦¨¤ª®±²¼ Low-viscous uid (liquid) «®£® ° §¬¥° (¢ ¯®§¨¶¨¨¨ ¯°¨« £ ²¥«¼®£®) Small-size «®¨§®£³²»© Slightly bent (curved) «®¨¥°¶¨®»¥ · ±²¨¶» Low-inertia particles «®© ²®«¹¨» A body of small thickness relative to its length and width «®° ª³°± ¿ ²®¬®£° ´¨¿ Few view tomography «®±²¥±¥»© ¯®²®ª Low-constricted ow «®±²¨ ¯®°¿¤®ª Order of smallness «®±³¹¥±²¢¥»© Unessential «¾± Malus ¬¤ ¨ Mamdani ¬´®°¤ Mumford
Markovian parameter Markov parameter
°²¥± Martens °¸¥¢»© «£®°¨²¬
An implementation of this method known as the generalized marching algorithm is described in detail in [1]
±«®¡ ª Oil tank ±± ¬®«¿ Molar mass ±± ¯®ª®¿ · ±²¨¶» Mass of a (the) particle at rest ±±¨¢®¥ ²¥«® Massive body ±±®¢ ¿ ¤®«¿ Mass fraction ±±®¢ ¿ ±ª®°®±²¼ ´®°¬¨°®¢ ¨¿ Mass rate of formation ±±®¢®-£¥®¬¥²°¨·¥±ª¨© Mass-geometric ±±®¢®-¨¥°¶¨®»© ¯ ° ¬¥²° Mass-inertia parameter ±±®¢»© ¤¨´´³§¨®»© ¯®²®ª Mass di usion ux ±±®¢»© ¬®¬¥² Mass moment ±¸² ¡ ¢ ¯®¯¥°¥·®¬ ¯° ¢«¥¨¨ Transverse scale ±¸² ¡ ¢®§¬³¹¥®© ²¥¬¯¥° ²³°» The scale of the perturbed temperature ±¸² ¡ £«³¡¨» ¢ 25 ¬ A scale depth of 25 m ±¸² ¡ ¤«¨»
The length scales in the y- and z -coordinates The length scale is smaller than : : :
±¸² ¡ ±ª®°®±²¨ The scale of velocity ±¸² ¡¨°®¢ ¨¥ ¬ ²°¨¶ Matrix scaling ±¸² ¡¨°®¢ ¨¥ ¯® ±²°®ª ¬ ¨ ±²®«¡¶ ¬
This subroutine performs row and column scalings to equilibrate (to balance) a real general matrix
±¸² ¡¨°®¢ ¿ ±¨±²¥¬ ³° ¢¥¨© Scaled system of equations ±¸² ¡¨°³¾¹¨© ¬®¦¨²¥«¼ Scaling factor ±¸² ¡ ¿ ²¥¬¯¥° ²³° Scaling temperature
64
±¸² ¡»© «¨§
Scale analysis, scaling analysis
²¥¬ ²¨·¥±ª¨© ° §°¥§ Mathematical cut
²¥¬ ²¨·¥±ª¨© ±«®¢ °¼ Dictionary of mathematics Mathematics dictionary
²¥°¨ « ± ¢»±®ª¨¬ (¨§ª¨¬) ¯®ª § ²¥«¥¬ ¯°¥«®¬«¥¨¿
²°¨¶ ¡«¾¤¥¨© Observation matrix ²°¨¶ ¥¯®«®£® ° £ Rank-de cient matrix ²°¨¶ ®°¨¥² ¶¨¨ Orientation matrix ²°¨¶ ®°²®£® «¼®£® ¯°¥®¡° §®¢ ¨¿
This subroutine multiplies a general matrix by the orthogonal transformation matrix from a reduction to (¡¥§ °²¨ª«¿) Hessenberg form
High (low) refractive index material
²¥°¨ « ± ¨§ª¨¬ (¢»±®ª¨¬) ¯®ª § ²¥«¥¬ ¯°¥- ²°¨¶ ®²° ¦¥¨¿ Re ection matrix «®¬«¥¨¿ Re ector Low (high) refractive index material ²°¨¶ ¯®¢®°®² ²¥°¨ « ±«®¦®±²¨ 2 Rotation matrix Matrix of rotation
Material of second grade
²¥°¨ «®¢¥¤¥¨¥
Materials science (technology)
²¥°¨ «¼ ¿ ¯«®¹ ¤ª Material area element
²¥°¨ «¼ ¿ ¯°®¨§¢®¤ ¿ The material derivative The Lagrangian derivative
²¥°¨ «¼»© ¡ « ± Mass balance
²¥°¨ «¼»© ®²°¥§®ª Material segment
²°¨¶
Matrix (¢ ¬ ²¥¬ ²¨ª¥ ¨ ¡¨®«®£¨¨) Binder (¢ ª®¬¯®§¨² µ)
²°¨¶ «£¥¡° ¨·¥±ª¨µ ¤®¯®«¥¨© Cofactor matrix Matrix of cofactors
²°¨¶ ¤¥°¬®¤ Vandermonde matrix
²°¨¶ , ¢±¥ ½«¥¬¥²» ª®²®°®© ° ¢» 1 Unit matrix
²°¨¶ ¢° ¹¥¨¿ Rotation matrix Matrix of rotation
²°¨¶ ¢²®°»µ ¯°®¨§¢®¤»µ Second derivative matrix
²°¨¶ ¢¿§ª®±²¨ Viscosity matrix
²°¨¶ ¤ »µ Data matrix
²°¨¶ ¥¬ª®±²¨
²°¨¶ ¯®«®£® ° £ Full rank matrix ²°¨¶ ¯®«®£® ±²®«¡¶®¢®£® ° £ Full column rank matrix ²°¨¶ ¯®«®£® ±²°®·®£® ° £ Full row rank matrix ²°¨¶ ¯®«®¦¨²¥«¼® ®¯°¥¤¥«¥ ¿ Positive de nite matrix ²°¨¶ ¯° ¢»µ · ±²¥© ±¨±²¥¬» The right-hand-side matrix of a system ²°¨¶ ¯°¨ ¤«¥¦®±²¨ Membership matrix ²°¨¶ , ¯°¨±®¥¤¨¥ ¿ ª The matrix adjoint to A ²°¨¶ ° ±¹¥¯«¥¨¿
The classical iterative methods for solving linear systems are based on writing the matrix A as : : :, where Q, called the splitting matrix, is nonsingular
²°¨¶ ± ¤¨ £® «¼»¬ ¯°¥®¡« ¤ ¨¥¬ Diagonally dominant matrix ²°¨¶ ± ¯®±²®¿»¬¨ ¤¨ £® «¿¬¨ Diagonal-constant matrix ²°¨¶ ±¢¿§¥© Constraint matrix ²°¨¶ ±ª®°®±²¥© ¤¥´®°¬ ¶¨© Strain-rate matrix ²°¨¶ ±® ±²°®£¨¬ ¤¨ £® «¼»¬ ¯°¥®¡« ¤ ¨¥¬ Strictly diagonally dominant matrix ²°¨¶ ²®¦¤¥±²¢¥®£® ¯°¥®¡° §®¢ ¨¿
Capacitance matrix
Identity transformation matrix Identity matrix
Mass matrix
Matrix-vector multiplication
²°¨¶ ¦¥±²ª®±²¨ ¢§ ¨¬®¤¥©±²¢¨¿ ¨§£¨¡ ¨ ²°¨¶ , ²° ±¯®¨°®¢ ¿ ª ¬ ²°¨¶¥ ° ±²¿¦¥¨¿ The transpose of the matrix A Bending-extension coupling sti ness matrix ²°¨¶ ³¯° ¢«¥¨¿ (³¯° ¢«¿¥¬®±²¨) ²°¨¶ ¨§£¨¡®© ¦¥±²ª®±²¨ Controllability matrix Bending sti ness matrix ²°¨¶ ³±¨«¥¨¿ ²°¨¶ ¨¥°¶¨¨ Ampli cation matrix Matrix of inertia ²°¨¶ °¬¨² Inertia matrix Hermitian matrix ²°¨¶ ª®½´´¨¶¨¥²®¢ ¢«¨¿¨¿ ²°¨· ¿ ®¯¥° ¶¨¿ In uence coecient matrix Matrix operation ²°¨¶ «¥²®· ¿ ²°¨· ¿ ½ª±¯®¥² Band matrix Matrix exponential ²°¨·®-¢¥ª²®°®¥ ³¬®¦¥¨¥ ²°¨¶ ¬ ±± 65
²°¨·»¥ ¢»·¨±«¥¨¿ Matrix computation Matrix computing
²°¨·»© ¯®«¨®¬ Matrix polynomial
²¼¥
¥¦´ §®¥ ¢§ ¨¬®¤¥©±²¢¨¥ Phase interaction Interphase interaction Interfacial interaction
¥¦´ §»© ¬ ±±®®¡¬¥
Interphase mass exchange (transfer) Phase mass exchange (transfer) Interfacial mass exchange (transfer)
Mathieu
²¼¥
Mathieu
²¼¾
Mathew
µ
Mach
µ®¢¨· ¿ ±¨±²¥¬ Flywheel system
µ®¢®© ¬®¬¥²
Moment of gyration
¸¨ ¿ ²®·®±²¼ Machine precision
¸¨®¥ ¯°®¥ª²¨°®¢ ¨¥ Computer aided design
¸¨®¥ ½¯±¨«® Machine epsilon
¸¨»¥ ª®±² ²» Machine constants
¸«¥°
Maschler
¿²¨ª ¯«®±ª¨© (¯°®±²° ±²¢¥»©) Plane (spatial) pendulum
£®¢¥® ®¡° ²¨¬»© Instantaneously reversible
£®¢¥®¥ ¢° ¹¥¨¥
¥¦´ §»© ®¡¬¥
Interphase exchange (transfer) Interfacial exchange (transfer)
¥¦´ §»© ²¥¯«®®¡¬¥
Interphase heat exchange (transfer) Phase heat exchange (transfer) Interfacial heat exchange (transfer)
¥©¥° Meyer ¥©±±¥° Meissner ¥«¥° Mehler ¥«ª ¿ ª ¯«¿
Fine droplet Small-scale droplet
¥«ª ¿ ±¥²ª Fine grid ¥«ª¨© ¯¥±®ª Fine sand ¥«ª®§¥°¨±²®±²¼ Small-scale granularity ¥«ª®§¥°¨±²»© «£®°¨²¬ Fine-grained algorithm Fine-grain algorithm
Instantaneous rotation
¥¬¡° »© Membranous Immediate action ¥¬¡° »© ª « ¥£ £¥°¶ (±®ª° ¹¥ ¿ § ¯¨±¼) Membrane channel MHz ¥£¥° ¥£ ®¬ (±®ª° ¹¥ ¿ § ¯¨±¼) Menger M
¥¥¥ ²®·»© ¥¤¨ ¿ ²®·ª (±°¥¤¿¿ ²®·ª ) The rst formula is less accurate than the second one Median point ¥¥« © ¥¤«¥¥¥ Menelaus More slowly ¥¼¥ ¥¤«¥® ®¡° ²¨¬»© Meusnier Slowly reversible ¥¼¸ ¿ ¢¿§ª®±²¼ Slow-reversible Smaller viscosity Slow reversible ¥¼¸ ¿ ®±¼ ¥¦¤³ ±®¡®© Minor axis All perpendiculars to one and the same straight line are ¥¼¸¥ parallel between themselves This set has fewer elements than K has ¥¦¤³ ²¥¬ ª ª n is less than K £®¢¥®¥ ¤¥©±²¢¨¥
Whilst
¥¦ª¢ °²¨«¼ ¿ §®
Within this interval, the function f varies by less than k
¥¦´ § ¿ £° ¨¶
¥¼¸¥ ¥¤¨¨¶» Less than unity ¥¼¸¥ ¨«¨ ° ¢® n is less than or equal to k (® ¥ less or equal to) ¥¼¸¥ ·¥¬
¥¦´ § ¿ ¯®¢¥°µ®±²¼
¥¼¸¥ : : : ·¥¬ : : :
Interquartile range (zone)
¥¦´ § ¿ ¢®« Interfacial wave
Interface Phase boundary Phase interface
The drags of these bodies are lower than the drag of the cone is for < 2
x is smaller than y by a term of order n
66
¥²®¤ n-¸ £®¢»© (®¤®¸ £®¢»©, ¤¢³µ¸ £®¢»©) n-step method (one-step, two-step) ¥²®¤ ( ²¨¤¨´´³§¨¨) ± ª®°°¥ª¶¨¥© ¯®²®ª As a solution of the equation, we take the smaller of its Flux corrected transport method ¥²®¤ ²¨²¥²¨·»µ ¯¥°¥¬¥»µ roots Antithetic variate method (technique) To nd the density of the smaller of X and Y The smaller of the two ¥²®¤ ¯¯°®ª±¨¬ ¶¨¨ ¥¼¸¨© ·¥¬ Approximation method All points at a distance less than K from A ¥²®¤ ±¨¬¯²®²¨·¥±ª®£® ° §«®¦¥¨¿ Asymptotic-expansion method ¥¿²¼ § ª¨ ¥²®¤ ¡¨±¥ª¶¨© Alternate in signs Bisection method ¥¿²¼±¿ ¢ ¨²¥°¢ «¥ The surface temperature of Mars seems to range from 30 ¥²®¤ ¡¨±®¯°¿¦¥»µ £° ¤¨¥²®¢ Biconjugate gradient method C down to 60 C ¥¿¾¹ ¿±¿ £° ¢¨² ¶¨¿ ¥²®¤ ¡¨±®¯°¿¦¥»µ £° ¤¨¥²®¢ ± ¯°¥¤®¡³Altered gravity ±«®¢«¨¢ ¨¥¬ Varying gravity Preconditioned biconjugate gradient method ¥¿¾¹¥¥±¿ ¬¥¤«¥® °¥¸¥¨¥ ¥²®¤ ¡«³¦¤ ¨¿ ¯® £° ¨¶¥ Walk-on-the-boundary method Slowly varying solution ¥²®¤ ¢¥ª²®°®© ¯°®£®ª¨ ¥° ª°³·¥¨¿ Measure of twist Vector sweep method ¥° ®¡º¥¬®£® ¤¥´®°¬¨°®¢ ¨¿ ¥²®¤ ¢¥°µ¥© °¥« ª± ¶¨¨ Volumetric strain measure Over relaxation (overrelaxation) method Measure of volumetric strain ¥²®¤ ¢±¥µ °¥£°¥±±¨© Method of all possible regressions ¥° ³£« Measure of an angle is a value of a turn around its vertex ¥²®¤ £¨¡°¨¤»© ¥°¨¤¨ ¿ ª°¨¢ ¿ One especially promising class of hybrid methods : : : Meridian curve ¥²®¤ ®°¥° Horner's method ¥°ª ²®° ¥²®¤ £° ¤¨¥²®£® ±¯³±ª Mercator Gradient descent method ¥°»© Pertaining to measure Method of gradient descent ¥°±¥ ¥²®¤ £° ¨·»µ ½«¥¬¥²®¢ Boundary element method Mersenne ¥²®¤ ¤¥«¥¨¿ ®²°¥§ª ¯®¯®« ¬ ¥°²¢ ¿ ¯¥²«¿ Looping the loop Bisection method Loop-the-loop ¥²®¤ ¤¨±ª°¥²¨§ ¶¨¨ ¥±±¡ ³½° Discretization method Mossbauer ¥²®¤ ¤¨±ª°¥²»µ ®±®¡¥®±²¥© Method of discrete singularities ¥±²»© ¯°¥¤¥« ²¥ª³·¥±²¨ The level of ow stress ¥²®¤ ¤«¿ ¥®¯°¥¤¥«¥»µ ±¨±²¥¬ ¥±²® ¤±®°¡¶¨¨ Inde nite system method Adsorption site ¥²®¤ ¥¬ª®±²¨ ¥±²® ª®² ª² Numerical solution of Helmholtz's equation by ((the) use of) the (a) capacitance (matrix) method Place of contact ¥²®¤ ¦¨¤ª¨µ ®¡º¥¬®¢ ¥±²® ¯®¢¥°µ®±²¨ Surface site Volume-of- uid method ¥±²® °¥ ª¶¨¨ ¥²®¤ ¨£®«¼· ²®© ¢ °¨ ¶¨¨ Needle (variation) method Reaction site ¥²®¤ ¨£®«¼· ²®© ®¯²¨¬¨§ ¶¨¨ ¥±²® ±®¥¤¨¥¨¿ ¢ ²°³¡¥ A joint in a pipe (tube) Needle optimization technique (method) ¥² ««¨·¥±ª ¿ · ±²¨¶ ¥²®¤ ¨§¬¥°¥¨¿ ±ª®°®±²¨ ¯® ¨§®¡° ¦¥¨¿¬ · Metallic particle ±²¨¶ Particle image velocimetry method ¥² ²¥«¼®-¤°®¡¿¹¨© PIV method Launching-crushing ¥²¥®°®¨¤ ¥²®¤ ¨§¬¥°¥¨¿ ±ª®°®±²¨ ¯® ®²±«¥¦¨¢ ¨¾ Meteoroid ²° ¥ª²®°¨© · ±²¨¶ Particle tracking velocimetry method ¥²ª PTV method Label attached to the particle ¥²®¤ ¨§¬¥°¥¨¿ ±ª®°®±²¨ ¯® ²° ±±¥° ¬ · ±²¨¶ ¥²®¤
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The method for solving the problems in mechanics The method of describing the motion of a body
67
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Flux corrected transport scheme (FCT-scheme) ¥²®¤ ¯®±«¥¤®¢ ²¥«¼®© ¢¥°µ¥© °¥« ª± ¶¨¨ ¥²®¤ ° ³² (¤«¿ °¥ «¨§ ¶¨¨ ¨±ª«¾·¥¨¿ (¨«¨ ±¢¥°µ°¥« ª± ¶¨¨) ³±± ) Successive overrelaxation method Crout reduction ¥²®¤ ¯®±«¥®¡° §®¢ ¥²®¤ «®¦®£® ¯®«®¦¥¨¿ After-image method Regula falsi ¥²®¤ ¯®²®ª Flux method ¥²®¤ «®ª «¼®£® ¯®¤®¡¨¿ Local similarity method ¥²®¤ ¯°¨¡«¨¦¥¨¿ ¥²®¤ ¬ °ª¥°®¢ ¨ ¿·¥¥ª Approximation method Method of markers and cells ¥²®¤ ¯°¨° ¹¥¨© ¥²®¤ ¬ ²°¨·®© ´³ª¶¨¨ °¨ Incremental method Matrix Green function method ¥²®¤ ¯°®¥ª¶¨¨ ¥²®¤ ¬¨¨¬ «¼®© ¥¢¿§ª¨ Projection method Minimal residual method ¥²®¤ ¯°®±²®© ¨²¥° ¶¨¨ ¥²®¤ ¬¨¨¬ «¼®© ¯®«®© ¢ °¨ ¶¨¨ Fixed point iteration method Total variation diminishing method (TVD method) ¥²®¤ ¯°¿¬»µ ¥²®¤ ¬¨¨¬ «¼»µ ¥¢¿§®ª The method of straight lines Minimal (minimum) residual method ¥²®¤ ° §°»¢»µ ¯¥°¥¬¥¹¥¨© ¥²®¤ ¬¨¨¬¨§ ¶¨¨ Displacement discontinuity method Minimization method ¥²®¤ ° §°»¢»µ ±¬¥¹¥¨© ¥²®¤ ¬®£®ª° ²®© (¬®¦¥±²¢¥®©) ¯°¨- Displacement discontinuity method ±²°¥«ª¨ (±²°¥«¼¡») ¥²®¤ °¥£³«¿°¨§ ¶¨¨ Multiple shooting method
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sparsity structure, their overhead storage requirement are still substantial
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The Poincare section method Steepest descent method Method of steepest descent
Random-walk-on-the-boundary method
68
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The ( nite-di erence) relaxation method
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In the cyclic reduction method, half the unknowns are Milgram ¨««¨ª¥ eliminated by : : : Millikan ¥²®¤ · ±²¨¶ ¨««¨¬¥²°®¢ ¿ ¡³¬ £ Particle method Millimeter paper, squared paper ¥²®¤ ¸¥«³¸¥¨¿ ¨««¨¬¥²°®¢ª Shelling method Millimeter squared paper ¥²°¨ª ¯®¢¥°µ®±²¨ (¯°®±²° ±²¢ ) ¨««¨±¥ª³¤ (±®ª° ¹¥ ¿ § ¯¨±¼) Metric of a surface (of a space) ms ¥²°¨ª¨ ¨««± Metrics Mills ¥µ ¨§¬ ¤¨´´³§¨¨ ¨« Mechanism of di usion Milne ¥µ ¨ª ¤¥´®°¬¨°³¥¬®£® ²¢¥°¤®£® ²¥« ¨«®° Mechanics of deformable solids Milnor ¥µ ¨ª ¤¥´®°¬¨°³¥¬»µ ²¥« ¨«¼¾ Mechanics of deformable solids Milloux Mechanics of deformable solid bodies ¨¤«¨ Deformable solid body mechanics Mindlin Deformable body mechanics ¨¨¬ ª±»© ¯®¤µ®¤ Mechanics of deformable bodies Minimax approach ¥µ ¨ª ¦¨¤ª®±²¥© ¨ £ §®¢ ¨¨¬ «¼ ¿ ¥¢¿§ª Fluid mechanics Minimal residual ¥µ ¨ª ª®¬¯®§¨²®¢ Minimum residual Composite mechanics Mechanics of multiphase mediums
Minimum norm
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®£®®£¨© ¨¨¬ «¼®¥ ° ±±²®¿¨¥ Multilegged Minimum distance ¨¨¬ «¼®¥ ±®¯°®²¨¢«¥¨¥ (¯°¨ ¤¢¨¦¥¨¨ ®£®®¡° §¨¥ °¥¸¥¨© Variety of solutions ²¢¥°¤®£® ²¥« ¢ ±°¥¤¥) ®£®¯®²®·®±²¼ (¤ »µ), ¬®£®¯®²®·»© Minimum drag Multithreading, multithreaded ¨¨¬¨§ ¶¨¿ The problem of minimizing the spectral abscissa over the ®£®° §®¢»© ª®±¬¨·¥±ª¨© ¯¯ ° ² set X Re-entry space vehicle ¨¨¬¨§ ¶¨¿ (¬ ª±¨¬¨§ ¶¨¿) ¯® ¢°¥¬¥¨ ®£®±¥²®·»© ¬¥²®¤ In the multigrid method one de nes a set of nested grids Time minimization (maximization) ®£®±«®© ¿ ±²°³ª²³° ¨¨¬¨§ ¶¨¿ ¯® x Multi-layered structure Minimization in x ¨¨¬¨§¨°®¢ ²¼ ¢ (¯°®±²° ±²¢¥) R Multi-layer structure ®£®²®·¥· ¿ ª° ¥¢ ¿ § ¤ · To minimize over R ¨ª®¢±ª¨© Multipoint boundary value problem ®£®³£®«¼¨ª (¢ § ¤ · µ ²°¨ £³«¿¶¨¨) Minkowski Polypolygon ¨®° ®¯°¥¤¥«¨²¥«¿ Minor of a determinant ®£®´ § ¿ ¬ ²°¨¶ Polyphase matrix ¨®° ²»© °¿¤ Multiphase matrix Minorant series ®£®´ § ¿ ±°¥¤ ¨²² £-¥´«¥° Multiphase medium Mittag-Leer ®£®· ±²¨·»© ¨²¥£° « ¨²·¥«« Many-body integral Michell ®£®·¨±«¥»¥ ¨±±«¥¤®¢ ¨¿ ¨µ¥«¼±® Much research in di erential equations is directed toward Michelson re nement of these computer methods ®£® ¢®¤» Much research has been done (conducted) on electric A lot of water propulsion systems ®£® ° § ®£®·«¥ ®²®±¨²¥«¼® x ¨ y Over and over again Polynomial in x and y Many times ®£®·«¥ ¥¡»¸¥¢ ®£®¥ ¬®¦® ±ª § ²¼ ® : : : Chebyshev polynomial Much can be said about : : : ®£®·«¥»© ®£®§¢¥»© ¬¥µ ¨§¬ Many-termed Multilink mechanism ®¦¥±²¢¥ ¿ (¬®£®ª° ² ¿) ¯°¨±²°¥«ª ®£®§ ·»© ¨²¥£° « Multiple shooting Many-valued integral ®¦¥±²¢¥»© ³¸¨¡ ®£®§ ·»© ¬¥²®¤ Di use contusion Multi-value method ®¦¥±²¢® ¢®§¬³¹¥¨© ®£®ª®°¯³±®¥ ±³¤® Disturbance set Multi-hull ship Perturbation set ®£®ª° ²® These digits are used over and over again in various com- ®¦¥±²¢® ¤®¯³±²¨¬»µ °¥¸¥¨© Feasible solution set binations ®¦¥±²¢® ¤®¯³±²¨¬»µ ³¯° ¢«¥¨© ®£®ª° ²®¥ «®¦¥¨¥ Admissible (feasible) control set Repeated superposition ®¦¥±²¢® ¤®±²¨¦¨¬®±²¨ ®£®ª°¨²¥°¨ «¼ ¿ ´³ª¶¨¿ Attainability set Multi-criterion function ®¦¥±²¢® ¥¤¨±²¢¥®±²¨ Multi-criterial function ®£®«³·¥¢®±²¼ (¢ § ¤ · µ ±¯³²¨ª®¢®© ¢¨£ - Set of uniqueness Uniqueness set ¶¨¨) ®¦¥±²¢® ª®°°¥ª²®±²¨ Multipath Correctness set ®£®«³·¥¢»¥ ¨§¬¥°¥¨¿ ®¦¥±²¢® ¯° ¢«¥¨© Multipath measurements Direction set ®£®¬¥°®¥ ¬®¦¥±²¢® Multidimensional set ®¦¥±²¢®-° §¤¥«¨²¥«¼ Separator set ®£®¬¥°»© ±² ²¨±²¨·¥±ª¨© «¨§ ®¦¨²¥«¼ Multivariate statistical analysis The origin is a point of generalized equilibrium with mul®£®¬®¤®¢»¥ ²¥·¥¨¿ tipliers : : : Many-mode ows ®¦¨²¥«¼ £° ¦ ®£®¬®²®°»© n
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®¦¨²¥«¼ ¬®£®·«¥ Factor of a polynomial ®¦¨²¥«¼ ®°¬¨°³¾¹¨© Normalizing factor ®¦¨²¥«¼ ±µ®¤¨¬®±²¨
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In the case of linear convergence, in each step the error Compression modulus is multiplied by an almost constant convergence factor Pressure modulus whose absolute value is less than 1 ®¤³«¼ ±ª®°®±²¨ Speed is the absolute value of velocity ®¦¨²¼±¿ ®¤³«¼ ±ª°³·¨¢ ¨¿ To be multiplied by Modulus of torsion ® ¢° ®¤³«¼ ±² «¼®© °¬ ²³°» Moivre de Steel reinforcement modulus ®£³² ¡»²¼ ¯°¥¤±² ¢«¥» It is possible for two entirely di erent systems to be rep- ®¤³«¼ ³¯°³£®±²¨ resented by the same block diagram Elasticity modulus Modulus of elasticity ®¤ Among (the) other viscous modes, the growth rate of Elastic modulus mode 2 is maximal ®¤³«¼ ³¯°³£®±²¨ ¯°¨ ±¤¢¨£¥ Modulus of rigidity ®¤ ª®«¥¡ ¨© Rigidity modulus Mode of oscillations ®¤³«¼ ·¨±« Oscillation mode Modulus of a (the) number ®¤¥«¼ ¢²®°¥£°¥±±¨¨-±ª®«¼§¿¹¥£® ±°¥¤¥£® ®¦¥² ¢±²°¥²¨²¼±¿ Autoregressive-moving average model It may occur ®¤¥«¼ ª®²°®«¼»µ ®¡º¥¬®¢ We may come across Control-volume model It may be encountered ®¤¥«¼ «®ª «¼®£® ¢§ ¨¬®¤¥©±²¢¨¿ ®¦¥² ¡»²¼ Local interaction model It is possible for a function to be continuous ®¤¥«¼ ± ° ±¯°¥¤¥«¥®© ¯ ¬¿²¼¾ ®§«¨ Distributed memory model Moseley ®¤¥«¼ ²°¥¨¿ ®«¥ª³«¿°®-ª¨¥²¨·¥±ª¨¥ ° §¬¥°» Friction model Molecular-kinetic sizes ®¤¨´¨ª ¶¨¿ ®«¥ª³«¿°®¥ ¤¢¨¦¥¨¥ Update Molecular motion Modi cation Molecular collisions (¬¥¦¤³ ¬®«¥ª³« ¬¨) Molecular impact ( ¯°¨¬¥°, ® ±²¥ª³ ±®±³¤ )
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These fragments are what we observe at upper levels of At the (a) conference the atmosphere ª®°®²ª®¥ ¢°¥¬¿ ¢¥± For a short time By the weight ª°¨¢®© ¢°¥¬¿ On the curve For a while ª°³£®¢®© ®°¡¨²¥ ¢±¥ ¯°®±²° ±²¢® On a circular orbit The extension of f to the entire space «¨²°» ¢±¥¬ ¯°®²¿¦¥¨¨ By the liter The air ow in this case remains steady throughout «¾¡®© ¨§ ¤³£ ¢±¾ ¸¨°¨³ ±²° ¨¶» On any one of the arcs At full page width : : : ¬¥¼¸ ¿ ° §¬¥°®±²¼ ¢µ®¤¥ ¢ ª « One less dimension At the channel inlet ¬®£¨µ ³°®¢¿µ ¢µ®¤¥ (¯°®£° ¬¬») At many levels On entry ¬®£®®¡° §¨¨ ¢»±®² µ On the manifold The atmosphere conducting layer lies at heights above ¬®¦¥±²¢¥ ¢»¡° »µ § ° ¥¥ ² ¡«¨·»µ about 85 km Meteors glow at heights of 120 to 80 km above sea level ²®·¥ª A linear combination of the values of f (x) at a set of pre ¢»±®²¥ chosen tabular points This spacecraft can orbit at any altitude around the Earth · «¼®¬ ½² ¯¥ ¢»µ®¤¥ ¨§ °¥ ª²®° At the initial stage At outlet from the (a) reactor Except for the Sun and the Moon, Venus is the brightest object in the sky
¨¦¥© · ±²¨ ª°¨¢®© This layer lies at a depth of about 40 km beneath the On the lower part of the (a) curve continents ¨¦¥¬ ³°®¢¥ £° ¨¶¥ These fragments are what we observe at lower levels of On (at) the boundary the atmosphere £° ¨¶¥ ° §¤¥« The vertical velocity jump across (at) the interface is nu- ¨§ª®¬ ³°®¢¥ At a low level merically evaluated by the above formula ®¡« ±²¨ ¤¨ £® «¨ On the domain The elements on the (main) diagonal of the matrix A We can endure the pressure at the bottom of our ocean of air
This device may exceed the transmission rate by one or two orders of magnitude A method for determining the shapes of pulses caused by the impact of bullets at one end of a long rod
The quantity of solar radiation received : : : on a unit of (®¤³) ¨²¥° ¶¨¾ 2 The work per iteration is n operations in general surface in a unit of time is called the solar constant
At each iteration of the algorithm, this matrix is decom- The strain levels are indicated on the (left) axis ¯¥°¢»© ¢§£«¿¤ posed into two triangular matrices The number of correct decimals are doubled in (at) each At rst glance, X appears to di er from X in two major ways iteration In each iteration, we shall compute the value of the poly- ¯¥°¥±¥·¥¨¨ At the intersection nomial and its derivative ¯®«¾± µ The matrix A is positive de nite at each iteration At the poles ª ¦¤®¬ ¸ £¥ ¯® ¢°¥¬¥¨ ¯®°¿¤®ª At each time step This approach can improve the overall process by an order ª¨«®£° ¬¬» of magnitude By the kilogram 73
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for the whole day For sedimentary rock, the ultimate tensile strength is an ¸ £¥ order of magnitude less In one step, in the next step ¯°®²¿¦¥¨¨ To integrate in two steps We can follow in detail the gradual development of com- At the second step plicated structures in polymers through the various inter- In the rst step of interpolation (extrapolation) mediate stages This method minimizes the error at each step Throughout the 20th century ½ª¢ ²®°¥ ¯°®¶¥±±®° µ At the equator To operate concurrently on di erent processors ½ª±¯¥°²¨§¥ The eciency of a parallel algorithm depends on the time Your application is now under scienti c expertise required to execute the program on p processors ½² ¯¥ ° ¤¨®· ±²®²¥ In (at) the rst stage of its development : : : At radio frequency ½²®² ° § ° ±±²®¿¨¨ This time Lunnik I passed the Moon at a distance of a few thousand For the present miles only ¿§»ª¥ ° ±±²®¿¨¨ ®² This knowledge base is written in a natural language, in At a distance of 10 km from the Earth's surface a dictionary-like structure
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Induced pressure gradient One third as long as ¢¥°µ³ °¨±³ª F is greater by a third At the top of the gure The other player is one third as fast G is less than a third of the distance between these two ¢¥²°¥ ¿ ¯®¢¥°µ®±²¼ Windward surface points ¢±²°¥·³ ³°®¢¥ Coming from the opposite direction Parallelism on the programming language level ¢¼¥ : : : end occurred inside a group at level 2 Navier ³°®¢¥ ¬®°¿ £°¥¢ ¨¥ ±¢¥°µ³ At sea level Heating from above ³°®¢¥ ¨¦¥¬ (¢¥°µ¥¬) These fragments are what we observe at lower (upper) £°¥¢ ¨¥ ±¨§³ Heating from below levels of the atmosphere
Because of emergency conditions, the embassy was closed
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£°³¦¥¨¥ ¯®¢²®°®¥ Repeated loading
74
¢¥¤¥¨¥ · «¼®¬ (±°¥¤¥¬, § ¢¥°¸ ¾¹¥¬) ³· ±²ª¥ ²° ¥ª²®°¨¨ Initial (midcourse, terminal) guidance §¥¬»© ¬¥²®¤ Land-based method Very little work seems to have been performed on dynamic §®¢¥¬ We (will) call a function continuous if : : : compressive loading (up) to this day We (will) call m the product measure £°³¦¥¨¥ ±«®¦®¥ (ª®¬¡¨¨°®¢ ®¥) §»¢ ²¼ Combined loading Relation (4) may be referred to as the basic equation of Development of new combined-loading testing devices airborne gravimetry £°³¦¥¨¥ ³¤ °®¥ Studies on (of) impact loading and dynamic behavior of ¨¡®«¥¥ Most probably, this method will prove useful if : : : materials What most interests us is whether : : : £°³¦¥®¥ ²¥«® Loaded body ¨¡®«¥¥ ¡»±²°® ³¢¥«¨·¨¢ ¥²±¿ Axisymmetric perturbations increase the most if the inner £°³§ª ¢ ¯°®¶¥² µ cylinder rotates and the outer one is xed Percentage load ¨¡®«¥¥ ¢®§¬®¦»© £°³§ª ²®°¬®¦¥¨¿ This gives the most compact system possible Deceleration load ¨¡®«¥¥ : : : ¨§ : : : £°³§ª ´« ²²¥° The most famous of these almost stable atoms is radium Flutter load ¨¡®«¥¥ ¬®¹»© ¥±¬¥¹¥»© ª°¨²¥°¨© £°³§ª¨ ®°¬ «¼ ¿ ¨ ª ± ²¥«¼ ¿ Most powerful unbiased test Normal and tangential loads ¨¡®«¥¥ ³¤ «¥ ¿ ± ¬ ¿ ¢¥°µ¿¿ ²®·ª ¤ £°³¦¥¨¥ ¯°®¨§¢®«¼®¥ An arbitrary loading £°³¦¥¨¥ ° ±²¿£¨¢ ¾¹¥¥ Extension loading £°³¦¥¨¥ ±¦ ²¨¥¬
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76
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77
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78
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This theory should hold whether localized or dynamic adsorption is assumed
Irrotational vector
¥§ ¢¨±¨¬»¥ ±¨±²¥¬» Unrelated systems ¥§ ¢¨±¨¬»© ®² ¬¥²®¤ (¯ ° ¬¥²° ) ¥¢»°®¦¤¥»© ¬¨«¼²®¨ Method(parameter)-independent preconditioner Nonsingular Hamiltonian ¥§ ¢¨±¨¬»© ®² ±¨±²¥¬» ®²±·¥² ¥¢»·¥² ±²¥¯¥¨ Frame-independent Power nonresidue ¥¢¿§ª ( ¯°¨¬¥°, ¯°¨ °¥¸¥¨¨ ±¨±²¥¬ «¨¥©- ¥§ ¢¨±¿¹¨© ®² Independent of »µ «£¥¡° ¨·¥±ª¨µ ³° ¢¥¨©) ¥§ ¤®«£® ¤® ²®£®, ª ª Residual Shortly before ¥¢¿§ª ¿ ±°¥¤ ¥§ ª°³·¥»© ¯®²®ª Inviscid medium Nonswirling ow ¥¢¿§ª ¿ ²¥®°¨¿ ¥§ ·¥¬ ¡¥±¯®ª®¨²¼±¿ ® Inviscid theory No need to worry about ¥¢¿§ª¨© ¯°¥¤¥« ¥§ ·¨²¥«¼®¥ ®²ª«®¥¨¥ Inviscid limit Slight de ection ¥¢¿§ª®¥ ¢®§¬³¹¥¨¥ ¥§ ·¨²¥«¼»© Inviscid perturbation A few minor typographical errors are listed below ¥£ °¬®¨·¥±ª ¿ ¯°®¯®°¶¨¿ ¥¨§¡¥¦»¥ ²°³¤®±²¨ Nonharmonic (anharmonic) ratio Unavoidable diculties Cross ratio ¥¨§¢¥±²®¥ ª®«¨·¥±²¢® ¥£« ¤ª ¿ § ¤ · Unknown quantity Necessary conditions for nonsmooth problems in optimal ¥¨§¢¥±²»© ¤«¿ control and the calculus of variations These new concepts are entirely unknown to classical ¥¤¢¨¦³¹ ¿±¿ ²®·ª physics Stationary point ¥¨§¬¥®¥ ¢° ¹¥¨¥ ¥¤¥´®°¬¨°®¢ ®¥ ±®±²®¿¨¥ Permanent rotation Undeformed state ¥¨§¬¥¿¥¬ ¿ ±ª®°®±²¼ ¥¤®¯³±²¨¬ ¿ ®¸¨¡ª Constant speed (velocity) Intolerable error ¥¨¢ «¾²¨¢»© ¥¤®¯³±²¨¬® ¡®«¼¸®© Noninvolutive Intolerably large ¥¨¢ °¨ ² ¿ ±¨±²¥¬ ¥¤®±² ¢ ²¼ Noninvariant system This system lacks accuracy ¥¨±¯ °¿¾¹¨©±¿ ¥¤®±² ¾¹¨¥ § ·¥¨¿ Unvaporizing, nonvaporizing De cient parameter values ¥©« De cient values of variables Neil ¥¥«¼ ¥©«¼ Neel Neil ¥¦¥±²ª ¿ £° ¨¶ ¥©¬ Nonrigid boundary Neumann ¥¦¥±²ª¨© ¯®«¨¬¥° ¥©¯¨° Nonrigid polymer Napier ¥¦¥±²ª®±²¼ ¥©°®¬¥¤¨ ²®° Nonrigidity Neuromediator ¥©°®-¥·¥²ª¨© «®£¨·¥±ª¨© ¢»¢®¤ ¥§ ¢¨±¨¬® ®² . . . More generally, the sum a + a is the same, irrespectively Neuro-fuzzy inference of the order in which sums are grouped ¥©²° «¼ ¿ ª°¨¢ ¿ (®²¤¥«¿¥² ®¡« ±²¼ ³±²®©·¨To dominate over . . . , irrespective of the choice of : : : ¢®±²¨ ®² ®¡« ±²¨ ¥³±²®©·¨¢®±²¨) The sum is the same regadless of the order of the addition The neutral curve Irrespective of the number of neutrons, isotopes of an el- ¥©²° «¼»© ½«¥¬¥² £°³¯¯» ement are atoms Identity element of the (a) group Whatever the shape of the magnet, it has two poles ¥©²°®»© ¯³·®ª Neutron beam ¥§ ¢¨±¨¬® ®² ²®£® Electrical disturbances, no matter how weak, produce ra- ¥ª ² «¨²¨·¥±ª ¿ ¯®¢¥°µ®±²¼ Noncatalytic (uncatalyzed) surface dio waves No matter what modi cations were introduced in this de- ¥ª¢ ¤° ² ¿ ¬ ²°¨¶ Non-square matrix sign, it is possible to : : : A certain quantity of work is equivalent to a certain quan- ¥ª®¨·¥±ª®¥ ²¥«®
¥¢»°®¦¤¥®¥ ±² ¶¨® °®¥ § ·¥¨¥ Nonsingular stationary value
1
2
tity of heat, no matter how that work is turned into heat
79
Nonconical body
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If a function is di erentiable, then it is necessary continuous We need to consider the following two cases (situations) We need only (¡¥§ to) consider the case when A is symmetric
Nonconservative load
¥ª®±¥°¢ ²¨¢® £°³¦¥»© Nonconservatively loaded
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Some of the particles happen to approach the Earth
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One of these conditions is necessarily ful lled
Several (® ¥ some) purposes
We consider a number of results concerning this problem An adequate supply of air ¥®¡µ®¤¨¬®±²¼ ¢ This may happen in a number of cases To compensate for the losses of energy, the need for more There are a few exceptions to this rule ecient lasers should be eliminated We now describe a few of these cases Half the unknowns are eliminated by taking certain linear This step of research would still not eliminate the need for heavy electric generators combinations of equations A generalization of the classical gradient concept seems indispensable
Nonlinear viscous uid (liquid) Viscous non-Newtonian uid (liquid)
If x and y are any elements (not necessarily the same) of the set A, then : : : This steplength is not necessarily constant
Nonlinear elastic body Nonlinearly elastic body
¥¬ «®
Not a little
¥®¡¿§ ²¥«¼»©
Noninstantaneous
¥®£° ¨·¥ ¿ (±¢®¡®¤ ¿) ¤¥²® ¶¨¿
Idemfactor
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In Russian, this word order is not mandatory
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Uncon ned detonation
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Unbounded medium The above results were obtained in a period of a little over ¥®£° ¨·¥ ¿ ½¥°£¨¿ Unlimited energy four years
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The substances with permeability a little larger (smaller) Unbounded expansion ¥®£³ª®¢ than 1 are said to be paramagnetic (diamagnetic) Neo-Hookean ¥¬®£® ° ¡®² ¯®±¢¿¹¥® : : : Only a (§¤¥±¼ ¥®¡µ®¤¨¬ ¥®¯°¥¤¥«¥»© °²¨ª«¼) few ¥®¤®§ ·® ° §°¥¸¨¬»© Nonuniquely solvable studies are devoted to : : : Integer-valued phase ambiguity
A little later
Non-one-dimensional
Nilpotent
Nonuniform load
Nemytsky
Inhomogeneous shell
Unobservable
Inhomogeneous plate Nonhomogeneous plate
Un lled polymeric material Un lled polymer
Inhomogeneous slab
Nonnatural systems
Nonuniform surface
Nonzero space
Inhomogeneous permeability
Nonzero eigenvalue
Nonunique solvability
Nonhomogeneous boundary conditions
Nonhomogeneous mixture
Areas not numbered should be left white
Nonhomogeneous equation
Non-Newtonian uid (liquid)
An experiment is needed to determine : : :
Nonuniformity of a (the) eld
80
¥®¤®°®¤®±²¼ ¯°®¨¶ ¥¬®±²¨
¥¯¥°¥µ®¤®¥ ®²®¸¥¨¥ (±¢¿§¼) Intransitive relation ¥¯¥°¨®¤¨·¥±ª ¿ ´³ª¶¨¿ ¥®¤®°®¤»¥ ¢»·¨±«¨²¥«¼»¥ ±¨±²¥¬» Nonperiodic function Heterogeneous parallel computing systems with dis- ¥¯¥°¨®¤¨·¥±ª ¿ ¶¥¯¼ °ª®¢ tributed memory Aperiodic Markov chain ¥®¤®°®¤»© ¯® ²®«¹¨¥ ¥¯¥°®¢® ·¨±«® : : : thin lms with nonuniform thickness The base \e" of natural logarithms ¥®¤®°®¤»© ¯°®´¨«¼ ±ª®°®±²¨ ¥¯¥°®¢» «®£¨ Nonuniform velocity pro le Napier's analogies ¥®¤®°®¤»© ·«¥ ¥¯¥°®¢» «®£ °¨´¬» Nonhomogeneous term Napierian logarithms ¥®¤®°®¤»© ¸ ° ¥¯®¢°¥¦¤¥»© ¬ ²¥°¨ « Inhomogeneous ball Undamaged material ¥®¤®±¢¿§ ¿ ®¡« ±²¼ ¥¯®¤¢¨¦ ¿ ±¨±²¥¬ ª®®°¤¨ ² Non-simply-connected region (domain) Fixed coordinate system ¥®¯« ¢«¥ ¿ ¯®¢¥°µ®±²¼ ª®±¬¨·¥±ª®£® ¯¯ - ¥¯®¤¢¨¦»© ° ² Fixed Nonablated surface of the (a) spacecraft ¥¯®¤¢¨¦»© £ § ¥®¯®§ »¥ ±¨£ «» Quiet gas Unrecognized signals Quiescent gas ¥®¯°¥¤¥«¥ ¿ ±¨¬¬¥²°¨· ¿ ¬ ²°¨¶ ¥¯®¤®¡»¥ ·«¥» Symmetric inde nite matrix Dissimilar (unlike) terms ¥®¯°¥¤¥«¥ ¿ ±¨±²¥¬ ¥¯®« ¿ ªª®¬®¤ ¶¨¿ Inde nite system Incomplete accommodation ¥®¯°¥¤¥«¥® ¤®«£® ¥¯®« ¿ ¯« ±²¨·®±²¼ We could continue pthis process inde nitely and never get Partial plasticity the exact value of 20 ¥¯®« ¿ ´ ª²®°¨§ ¶¨¿ ¥®¯°¥¤¥«¥®¥ ³° ¢¥¨¥ Incomplete factorization Diophantine equation ¥¯®«®¥ ° §«®¦¥¨¥ ¥®¯°¥¤¥«¥»¥ ´®°¬» Incomplete decomposition Indeterminate forms ¥¯®«»© ¡«®·»© ¯°¥¤®¡³±«®¢«¨¢ ²¥«¼ ¥®¯°¥¤¥«¥»© «¨§ Incomplete block preconditioner Diophantine analysis ¥¯®«»© ° £ ¥®¯°¥¤¥«¥»© ¯ ° ¬¥²° A square matrix is rank de cient if its rank is less than Undetermined parameter its order ¥®±¥±¨¬¬¥²°¨·»¥ ¢®§¬³¹¥¨¿ ¥¯®«®¦¨²¥«¼® ®¯°¥¤¥«¥ ¿ ¬ ²°¨¶ Nonaxisymmetric perturbations (disturbances) Nonpositive de nite matrix ¥®±« ¡«¥»© Negative semi-de nite matrix Not weakened ¥¯®±«¥¤®¢ ²¥«¼»© ¥®±¶¨««¨°³¾¹¨© Inconsistent (with) Error components that are nonoscillatory with respect to ¥¯®±°¥¤±²¢¥® ±«¥¤®¢ ²¼ ¨§ Permeability inhomogeneity Inhomogeneity of permeability
a ne grid are usually oscillatory with respect to a coarse (coarser) grid
¥®²°¨¶ ²¥«¼® ®¯°¥¤¥«¥ ¿ ¬ ²°¨¶ Nonnegative de nite matrix Positive semi-de nite matrix
¥®¹³²¨¬ ¿ ¸¥°®µ®¢ ²®±²¼ Insensible roughness ¥¯ ° ¬¥²°¨·¥±ª¨© ¤¨±ª°¨¬¨ ²»© «¨§ Nonparametric discriminant analysis ¥¯¥° Napier ¥¯¥°¥ª°»¢ ¾¹¨¥±¿ ®¡« ±²¨ Nonoverlapping domains ¥¯¥°¥±¥ª ²¼±¿ ¯®¯ °® To be mutually nonintersecting To be disjoint
¥¯¥°¥±¥ª ¾¹¨¥±¿ ¯®¯ °® ¤¨±ª¨ Disjoint disks ¥¯¥°¥µ®¤ ¿ § ¢¨±¨¬®±²¼ Intransitive dependence (relation)
The proof is immediate from the de nition of limit and is left as an exercise
¥¯®±°¥¤±²¢¥»¬¨ ¢»·¨±«¥¨¿¬¨ This identity can be obtained by direct calculations ¥¯®²¥¶¨ «¼ ¿ ±¨« Nonpotential force ¥¯°¥°»¢® § ¢¨±¨² ®² " Continuous in " ¥¯°¥°»¢®±²¼ ¬ ±±» Continuity of mass ¥¯°¥°»¢»¥ ±«³· ©»¥ ¢¥«¨·¨» Continuous random quantities ¥¯°¥°»¢»© Continuous over all of the intervals ¥¯°¥°»¢»© ¯® µ Continuous in x ¥¯°¥°»¢»© ¯® ¨¯¸¨¶³ Lipschitz continuous ¥¯°¥°»¢»© ¯® ®¡¥¨¬ ¯¥°¥¬¥»¬ Continuous in both variables
81
¥¯°¨¢¥¤¥ ¿ ¬ ²°¨¶ Unreduced matrix ¥¯°¨¢®¤¨¬ ¿ ¬ ²°¨¶ Irreducible matrix ¥¯°®¨¶ ¥¬ ¿ ¯®¢¥°µ®±²¼ Impermeable surface ¥¯°®¨¶ ¥¬®±²¼ Impermeability of gas phase components ¥¯°®±ª «¼§»¢ ¨¿ ³±«®¢¨¥ No-slip condition ¥¯°®²¥ª ¥¬®±²¼ Leakproofness ¥¯°®²¥ª ¨¿ ³±«®¢¨¥ Impermeability condition ¥¯°®²¨¢®°¥·¨¢ ¿ ²¥®°¨¿ A consistent theory ¥¯°¿¬®£® ¤¥©±²¢¨¿ ¯°¨¡®° Relay-operated device ¥¯°¿¬®³£®«¼»© Nonrectangular ¥° ¢¥±²¢® ®¸¨{¢ °¶ Cauchy{Schwartz inequality ¥° ¢¥±²¢® ²°¥³£®«¼¨ª Triangle inequality ¥° ¢®¢¥±® ª¨¯¿¹ ¿ ¦¨¤ª®±²¼ Liquid boiling under nonequilibrium conditions ¥° ¢®¢¥±®¥ ±®±²®¿¨¥ Nonequilibrium state ¥° ¢®¢¥±»© ½´´¥ª² Nonequilibrium e ect ¥° ¢®¢¥±®±²¨ ª®½´´¨¶¨¥² Nonequilibrium coecient ¥° ¢®¦¥±²ª®±²¼
¥°«¾¤ Norlund ¥°±² Nernst ¥°®¢®±²¼ ¯®¢¥°µ®±²¨ Irregularity(ies) of the surface ¥°®² ²¨¢»© ¢¥ª²®° Irrotational vector ¥±¢¿§ ®¥ ³±«®¢¨¥
A condition of this type (form) is called (termed) uncoupled
¥±¢¿§ »¥ ®±¶¨««¿²®°» Disconnected oscillators ¥±¢¿§ »¥ ±¨±²¥¬» Unrelated systems ¥±¨¬¬¥²°¨· ¿ ¬ ²°¨¶ Nonsymmetric (unsymmetric) matrix ¥±¨¬¬¥²°¨· ¿ ¯°®¡«¥¬ ±®¡±²¢¥»µ § ·¥¨© Nonsymmetric eigenproblem Unsymmetric eigenproblem
¥±ª®«¼§¿¹¨© (±¢¿§ »©) ¢¥ª²®° Localized vector ¥±ª®«¼ª®
Let us consider several examples We now consider a ( °²¨ª«¼ ®¡¿§ ²¥«¥) few examples
¥±¬ ·¨¢ ¾¹ ¿±¿ ´ § Nonwetting phase ¥±¬¥¸¨¢ ¾¹¥¥±¿ ²¥·¥¨¥ Immiscible ow ¥±¬®²°¿ (£°³¯¯®¢®© ¯°¥¤«®£) In spite of, regardless of ¥±®¡±²¢¥ ¿ § ¤ · «¨¥©®£® ¯°®£° ¬¬¨°®A drift component in a vibratory gyroscope is caused by ¢ ¨¿ Improper problem of (in) linear programming the anisoelasticity of its rotor support ¥±®¢¥°¸¥»© ª°¨±² «« ¥° ¢®¬¥° ¿ ±¥²ª Imperfect crystal Unequally-spaced grid ¥±®¢¬¥±² ¿ ±¨±²¥¬ ¥° ¢®¬¥°® ®ª° ¸¥»© Inconsistent system Irregularly painted ¥±®¢¬¥±² ¿ ±¨±²¥¬ «¨¥©»µ ³° ¢¥¨© ¥° ¢®½« ±²¨·®±²¼ Inconsistent system of linear equations Anisoelasticity Inconsistent linear system ¥° ¢»© ³«¾ ²®¦¤¥±²¢¥® In general, we must have at least one of f and q not iden- ¥±®¢¬¥¹¥»¥ ¢¥²¢¨ Not superposed branches tically zero in order to guarantee a unique solution ¥° §°¥¸¥®¥ ¤¨´´¥°¥¶¨ «¼®¥ ³° ¢¥¨¥ ¥±®ª° ²¨¬ ¿ ¤°®¡¼ Fraction in lowest terms Implicit di erential equation Di erential equation not solved with respect to the highest ¥±®¬¥®, ·²® It is (quite) certain (true) that : : : derivative It is beyond (any) doubt that : : : ¥° §°¥¸¥®¥ ° §®±²®¥ ³° ¢¥¨¥ ¥±®¬¥®¥ ±¢¨¤¥²¥«¼±²¢® (¤®ª § ²¥«¼±²¢®) Implicit di erence equation Sure evidence ¥° §°³¸ ¥¬ ¿ ¯®¢¥°µ®±²¼ ¥±¯«®¸®±²¼ Indestructible surface Nonuniformity ¥° ±²¿¦¨¬ ¿ ±²°³ ¥±² ¶¨® ° ¿ ±ª®°®±²¼ ¯« ¬¥¨ Inextensible string Velocity of unsteady ame propagation ¥° ±²¿¦¨¬»© Inextensible tread band (thread, etc.) ¥±² ¶¨® °®¥ ²¥·¥¨¥ Unsteady ow ¥°¢»© ®²ª«¨ª ¥±² ¶¨® °®¥ ³° ¢¥¨¥ Neural response Unsteady-state equation ¥°¢»© ±¨£ « Time-dependent equation Neural signal ¥±² ¶¨® °»¥ ¢®«» ¥°¥ £¨°³¾¹¨© £ § Unsteady waves
Nonreacting gas
82
¥±² ¶¨® °»© ¯®²®ª Unsteady ow ( ux) Transient ow ( ux)
¥±²°³ª²³°¨°®¢ ¿ ±¥²ª
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The atom is something very di erent from the solid sphere
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The Earth itself is a sort of magnet
Unstructured grid
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Nonmatching grid
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Load-bearing area element
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¨ ¢ ª ª®¬ ®²®¸¥¨¨
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¥±³¹¨¥ ±¢®©±²¢ ¥±³¹¨© £°³§ª³ ¥±´¥°¨·¥±ª¨¥ ª®«¥¡ ¨¿ Nonspherical oscillations
¥² ¥®¡µ®¤¨¬®±²¨ ¢ ²®¬, ·²®¡»
There is no need (that) the magnetic substance be a metal
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There is not (® ¥ no) any point
¥² ¯°¨·¨», ¯®·¥¬³ ¡» : : :
Implicit assignment of a function Implicit double shift Norlund Noether
In no respect
About nothing
The upper atmosphere emits light of two kinds, but neither (of them) is visible
¨ ®¤¨ ¨§ ª®²®°»µ
Let a be a sequence of positive integers none of which is 1 less (greater) than a power of two n
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The functions X and Y are continuous, but neither is nite Neither of these two (® ¥ three, etc.) functions is nite None of these three functions is nite
There is no reason why a normal coin should fall one side up rather than the other
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Defect of image
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Level(ing) lines
Nowhere dense It is not hard to extend our approach to nonsmooth prob- ¨£¤¥ ¥ ¯«®²»© Nowhere dense lems
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The experiment ends in failure
Unilateral (one-sided) constraint Subtle (inde nable) di erence
Nonunitary similarity transformation Nonunitary decomposition Unbalanced disk
¥³±² ®¢¨¢¸¥¥±¿ ¤ ¢«¥¨¥
The theorem below
Lower triangular matrix
Lower left-hand (right-hand) corner Lower right-hand (left-hand) corner Lower limit of an (the) integral
Lower (upper) Hessenberg matrix Almost lower (upper) triangular matrix
Transient pressure
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Instability to small perturbations (disturbances)
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Lower (upper) triangular matrix Lower bound In mum
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Oil-bearing stratum Fuzzy clustering Fuzzy inference Fuzzy operator
Lower bidiagonal matrix
Bottom (lower) surface of a (the) plate Lower bandwidth Low water
Low-catalytic coating
Fuzzy singleton
83
®°¬ «¨§®¢ »© ¯® ·¨±«³ " > 0 The kinematic viscosity can be considered as constant for A number a 6= 0 is said to be normalized in " > 0 if : : : low-rate isothermic processes of deformation ®°¬ «¼ ¿ °¥ ª¶¨¿ ¨§ª®· ±²®² ¿ ¯¯°®ª±¨¬ ¶¨¿ Normal reaction Low-frequency approximation ®°¬ «¼®¥ ¢°¥¬¿ ¨§ª®· ±²®² ¿ ¢®« Standard time Low-frequency wave ®°¬ «¼®¥ ³° ¢¥¨¥ ¯«®±ª®±²¨ ¨§®¢ ¿ ¢®¤ Normal equation of a (the) plane Downstream water ®°¬ «¼®¥ ³° ¢¥¨¥ ¯°¿¬®© ¨§®¢»¥ ¢®°®² Normal equation of a (the) line Tail gate ®°¬ «¼®¥ ³±ª®°¥¨¥ ±¨«» ²¿¦¥±²¨ ¨§¸ ¿ ²®·ª Normal gravity Lowest point ®°¬ «¼®±²¼ ¬ ²°¨¶» ¨ª®£¤ ° ¥¥ Matrix normality Never before has the imagination of mankind been capti- ®°¬ «¼»© ¢¨¤ vated so much by the concept of space Standard (normal, canonical) form ¨§ª®±ª®°®±²®© ¯°®¶¥±±
¨ª®«±® Nicolson ¨ª®«¼ Nicol ¨ª®¬¥¤ Nicomedes ¨ª²® ¥ § ¥² ®²ª³¤ ¨ ª³¤
®°¬ «¼»© ¢¨¤ ¨°° ¶¨® «¼®£® ¢»° ¦¥¨¿ Normal form of an irrational expression
®°¬ «¼»© § ª® ° ±¯°¥¤¥«¥¨¿ Normal law of distribution
®°¬¨°®¢ ¿ ¯«®²®±²¼ Normalized density
®±¨ª ²°¥¹¨» A rapidly deforming mass comes from none knows where Crack tip and goes none knows where ®±¨²¥«¼ ´³ª¶¨¨ ¨«¼±¥ Nielsen
¨¯ª®¢ Nipkow ¨°¥¡¥°£ Nirenberg ¨±ª®«¼ª® ¥ This method is no worse than others ¨±µ®¤¿¹ ¿ (¢®±µ®¤¿¹ ¿) ¢¥°²¨ª «¼ Downward (upward) vertical ¨±µ®¤¿¹¨© ²¥¯«®¢®© ¯®²®ª Downward heat ux ¨²¼ ª²¨®¢ ¿ Actinic lament ¨²¼ ¨«¨ ²°®± ¢ ±¯³²¨ª®¢»µ ±¢¿§ »µ ±¨±²¥¬ µ Tether ¨·²® ¨®¥ ª ª This is nothing else but the sti ness matrix ¨·²®¦ ¿ ¢¥«¨·¨ Negligible quantity ®¢ ¶ª¨© Nowacki ®¤® Nodon ®«¨ª¨ ¨ ª°¥±²¨ª¨ Noughts and crosses ®«« Noll ®¬¨ «¼ ¿ ±®¡±²¢¥ ¿ · ±²®² Nominal natural frequency ®°¤±¨ª Nordsieck ®°¬ ²¨¯ ±ª «¿°®£® ¯°®¨§¢¥¤¥¨¿ Inner product norm ®°¬ °®¡¥¨³± Frobenius norm
Support of a function
®±¨²¥«¼ ½¥°£¨¨ Energy carrier Carrier of energy
®±ª®¢ Noskov
®±®¢ ¿ · ±²¼ ±³¤ Bow of a (the) ship
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An experiment is needed to determine : : :
³«¥¢ ¿ ¯®±«¥¤®¢ ²¥«¼®±²¼ Null sequence
³«¥¢®£® ° ¤¨³± ¯®²¥¶¨ « Zero-range potential
³«¥¢®¥ ±®¡±²¢¥®¥ § ·¥¨¥ Zero eigenvalue
³«¥¢®© ¢®§° ±² Zero age
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Homogeneous boundary conditions
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Zero element of a ring
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³«¼-¯°®±²° ±²¢® Null space Nullspace
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84
Newton
¡«¥£·¨²¼ § ¤ ·³ To ease the problem of structural design ¡¬¥ £° ¢¨² ¶¨®»¬¨ ¢®« ¬¨ Exchange by gravitational waves ¡¬¥ ¨¬¯³«¼±®¬
¼¾²®¬¥²° Accelerometer ¼¾²®®¢±ª®¥ ¯°¨²¿¦¥¨¥ Newtonian attraction ½¸ Nash
Momentum transfer (exchange) between charged and neutral particles
O
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¡ ½²®¬ ¥ ¬®¦¥² ¡»²¼ ¨ °¥·¨ It is out of the question ¡¤¨° ¨¥ ±«®¥¢ Layer-stripping ¡¤³¢ ²¼ The plate is blown over by a gaseous ow ¡¥§° §¬¥°¨¢ ¨¥ Nondimensionalization ¡¥§° §¬¥°¨¢ ²¼
The rate of energy exchange between electrons and nitrogen molecules The rapid interchange of energy between the electric elds and the metal's electrons
¡¬®²ª \±«®© § ±«®¥¬" (®¡¬®²ª ° ¢»¬¨ ±«®¿¬¨) Layer-by-layer winding ¡®¢«¥¨¥ ®¡®°³¤®¢ ¨¿ Upgrade Nondimensionalize (distance, velocity, time, temperature, ¡³«¥»© Zeroed etc.) The distance is made nondimensional with the sphere ra- ¡³«¿²¼ To zero dius or with the viscous length ¡®¡¹¥ ¿ ¦¥±²ª®±²¼ ¡¦ ²¨¥ ¯« ±²¨» Generalized sti ness Generalized rigidity
Plate compression
¡¦ ²¨¥ ¯®«®±» Strip compression ¡¦ ²¨¥ ³£« Angle compression ¡« ¤ ²¼ ¯°¥¨¬³¹¥±²¢®¬ (¥¤®±² ²ª®¬)
¡®¡¹¥ ¿ ¯°®¡«¥¬ ±®¡±²¢¥»µ § ·¥¨© Generalized eigenproblem ¡®¡¹¥®¥ ±¨£³«¿°®¥ ° §«®¦¥¨¥ Generalized singular value decomposition The binary numeration system has the advantage of hav- ¡®¡¹¥»© ¬¥²®¤ ¨¬¥¼¸¨µ ª¢ ¤° ²®¢ Generalized least-squares method Total least-squares method
ing only two digit symbols but it also has a disadvantage of using many more digits : : :
¡®§ · ²¼ (³ª §»¢ ²¼, ®²®±¨²¼ ª)
¡« ±²¼ § ¤ ¨¿ ´³ª¶¨¨ Domain of de nition of a function ¡« ±²¼ § ¬»ª ¨¿ Closure region ¡« ±²¼ § µ¢ ² Entrapment zone (region) ¡« ±²¼ § ·¥¨© ¬ ²°¨¶» Range of a (the) matrix ¡« ±²¼ ¨§¬¥¥¨¿ ¯ ° ¬¥²°®¢
To designate matrix norms This product is denoted by : : : The dot over the symbol indicates the material derivative The symbol A stands for the matrix that : : : : : :, where y stands for the height and x for the time For example, the rst noun refers to a whole class of : : :
¡®§ ·¥¨¥ The designation of parallel straight lines is as follows ¡®§ ·¥¨¥ ¡±®«¾²®© ¢¥«¨·¨» The range of the parameters x and y is found It is shown that the allowed (admissible, feasible) param- Absolute value notation ¡®§ ·¥¨¥ \ ¡®«¼¸®¥" eter range enlarges dramatically The big-O notation (big-Oh notation) is used to describe ¡« ±²¼ ¥³±²®©·¨¢®±²¨ the asymptotic behavior of functions Instability region (domain) ¡®§ ·¥¨¥ \® ¬ «®¥" ¡« ±²¼ ®¯°¥¤¥«¥¨¿ De nition domain Domain of de nition
The little-o notation (little-oh notation) is used to describe the behavior of functions under some conditions
¡« ±²¼ ®²°»¢ Separation region ¡« ±²¼ ¯°¨«¨¯ ¨¿ (±ª®«¼¦¥¨¿) Adhesion (sliding) region ¡« ±²¼ ±¢¿§®±²¨
¡®§ ·¥¨¿
¡« ±²¼ ±µ®¤¨¬®±²¨ °¿¤
¡®§ ·¨¬ Let (set, write, ® ¥ denote) a = b + c ¡®«®·¥· ¿ ®¡« ±²¼
Domain of connectivity Region of connectivity
Domain of convergence of the series Convergence domain of the series
¡« ±²¼ ³±²®©·¨¢®±²¨ Region of stability, stability domain ¡« ±²¼ · ±²®² Frequency domain
Let us introduce the following notation Let us introduce the temporary notation y for x In the notation used in [1] we have : : : With this notation, we have : : : For simplicity of notation, we use y instead of x To simplify (shorten) notation, we use y for x Shell region Shell domain
¡®«®·¥·»© ½«¥¬¥² Shell element
85
¡®«®·ª ¬®¦¥±²¢
¡° ²®
The convex hull of the set A
Conversely, let n be composite and let p be a prime factor of n
¡° ¡®²ª
¡° ²® ¨§¬¥¿²¼±¿ ¯® ²®«¹¨¥
Treatment of zero elements Signal processing
To vary inversely with the thickness of the thermal boundary layer
¡° ¡®²ª ¬¥² ««®¢ ¤ ¢«¥¨¥¬ ()
Metal working process (½ª¢¨¢ «¥², ¯°¨¬¥¿¥¬»© ¢ ¡° ²® ¯°®¯®°¶¨® «¼® Inversely proportional )
¡° §®¢ ¨¥ ¢ª«¾·¥¨©
¡° ²® ¯°®¯®°¶¨® «¼»¥ ¢¥«¨·¨» Inversely proportional quantities ¡° ²®¥
¡° §®¢ ¨¥ ¯¥²«¨
¡° ²®¥ ¨²¥°¨°®¢ ¨¥
¡° §¥¶
Sample (specimen)
Let us assume the converse The inverse of the matrix A is denoted by A
Inclusion formation
To study the process of loop formation Kinking
1
By inverse iterating (iteration), we can avoid the costly accumulation of such transformations
¡° §®¢»¢ ²¼ ¨§
¡° ²®¥ ¥° ¢¥±²¢® Reverse inequality ¡° §®¬ ¡° ²®¥ ¯°®¥¶¨°®¢ ¨¥ ± ´¨«¼²° ¶¨¥© In a (special) way (manner, fashion) Filtered back projection ¡° §³¾¹ ¿ (¢¥¸¿¿) ²°³¡» ¡° ²®¥ ±®®²®¸¥¨¥ ¤«¿ (1) Outer generating lines of the (a) tube Inverse relation of (1) ¡° §³¾¹ ¿ ¯®¢¥°µ®±²¨ ¡° ²®¥ ²¥·¥¨¥ Generator of a surface Reverse ow Surface generator ¡° ²®¥ ·¨±« ¡° §³¾¹¥¥ ¬®¦¥±²¢® Reciprocal of a number Generating set ¡° ²»¥ ¢¥«¨·¨» ¡° §¶» ¯¥±ª Reciprocal quantities Samples of sand ¡° ²»© «¨§ ®¸¨¡®ª ¡° ²¨¬®±²¨ £°³¯¯ § ª® Backward error analysis Invertibility in the group ¡° ²»© (®²°¨¶ ²¥«¼»©) ¢»®± ª°»«¼¥¢ (ª°»« ) ¡° ²¨¬®±²¼ £°³¯¯ Back (negative) stagger Invertibility of groups ¡° ²»© °¥´«¥ª± ¡° ²¨²¼ ¢¨¬ ¨¥ I would like to draw your attention to the fact that di er- Reciprocal re ex ent ISSN have to be assigned to the di erent editions of a ¡° ²»© ·¨±«³ °³¤¥ Reciprocal of the Froude number serial published on di erent media ¡° ¹ ²¼ ¢¨¬ ¨¥ ²®, ·²® ¡° ²¨²¼±¿ ª We turn now to an important process for constructing the To point to the fact that ¡° ¹ ²¼±¿ ¢ ³«¼ matrix A This function vanishes (becomes zero) at a nite number ¡° ² ¿ ¢¥«¨·¨ ®²®±¨²¥«¼® ±«®¦¥¨¿ of points The additive inverse of a is denoted by a ¡° ¹ ²¼±¿ ¢ ²®¦¤¥±²¢® ¡° ² ¿ ¢¥«¨·¨ ®²®±¨²¥«¼® ³¬®¦¥¨¿ To become identical The multiplicative inverse of a is denoted by a ¢ ¬ ¸¨»© ³«¼ ¡° ² ¿ £¨¯¥°¡®«¨·¥±ª ¿ (²°¨£®®¬¥²°¨·¥±- ¡° ¹¥¨¥ Under ow ª ¿) ´³ª¶¨¿ ¡° ¹¥¨¥ ¤³£¨ Inverse hyperbolic (trigonometric) function Arc reversal ¡° ² ¿ ¬ ²°¨¶ ª ¡° ¹¥¨¥ ª § ¯®¬¨ ¾¹¥¬³ ³±²°®©±²¢³ Let us consider the inverse of (for) the matrix A Storage access ¡° ² ¿ ®°²®£® «¼ ¿ ¨²¥° ¶¨¿ ¡° ¹¥¨¥ ª ¯ ¬¿²¨ Inverse orthogonal iteration Storage reference ¡° ² ¿ ®¯¥° ¶¨¿ ¯® ®²®¸¥¨¾ ª ¡° ¹¥¨¥ ¥ª®²®°»µ ¬ ²°¨¶ Dividing by 5 is the inverse of multiplying by 5 The reciprocation of certain matrices ¡° ² ¿ ¯®«§³·¥±²¼ ¡° ¹¥»© ±¨³± Inverse creep Versed sine ¡° ² ¿ ±²®°® ¡°¥§ ¨¥ On the reverse side of : : : Reentrant polygon clipping ¡° ² ¿ ±²°¥«®¢¨¤®±²¼ ¡°»¢ ®¡° §¶ Forward sweep The break of the (a) specimen ¡²¥ª ¥¬ ¿ ¯®¢¥°µ®±²¼ ¡° ² ¿ ²¥®°¥¬ Expressions which are made up of proposition and noun
1
Streamlined surface
Converse theorem
86
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¡³·¥¨¿ ¯«
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General-purpose
Streamlined contour
System in general position
Streamlined body
Let a catalytic surface be streamlined by a dissociated Common value mixture of carbon dioxide and nitrogen ¡¹¥¥ ¯®«®¦¥¨¥ Generic case ¡²¥ª ¾¹¨© £ § Streaming gas ¡¹¥¥ ±¥¬¥©±²¢® Generic family ¡²¥ª ¾¹¨© ¯®²®ª Streaming ow ( ux) ¡¹¥¥ ³±¨«¥¨¥ Overall gain ¡³±«®¢«¥ These di erences are often due to the variation in the kind ¡¹¥¨§¢¥±²®, ·²® and number of the built-in operations It is commonly known that the wing creates lift In other words, if is near (far from) another eigenvalue It is generally agreed that most of the fundamental proof A, then its eigenvector will be ill (possibly well) condi- cesses : : : tioned ¡¹¥¯°¨¿²»© It should not be thought that the only ill-conditioned Generally accepted eigenvectors are those corresponding to poorly separated ¡¹¥³¯®²°¥¡¨²¥«¼»© eigenvalues The most common choices for the splitting matrix Q are Some insight into the meaning of the de nition of stability based on writing the matrix A as : : : can be gained by considering what happens when a stable Two scales in common use to-day are the Fahrenheit and algorithm is used to solve a well-conditioned problem Centigrade Conditioned constraints
Generic case
Matrix condition
Greatest common divisor
Kinetic energy is energy due to motion
Total current
The necessity of this adjastment is caused (® ¥ stipu- Searcher (evader) lated ¨«¨ conditioned) by the di erence between : : : ¡º¥¬ ¢»²¥±¥®© ¦¨¤ª®±²¨ Clouds are responsible for the brightness of Venus Volume of the displaced liquid ( uid)
Teaching plan
The scalar (dot, inner) product is an O(n) operation, which means that the amount of work (arithmetic, computations) is linear in the dimension
¡µ®¤¨²±¿ ¢
Informal testing worth of at least six hours of using this (sub)routine must be done ¡º¥¬ ¯ ¬¿²¨ (ª®¬¯¼¾²¥° ) ¡µ®¤®© ª « The amount of storage By-pass channel ¡º¥¬ ° ¡®²» ¨ ¢°¥¬¥¨ ¡µ®¤»¬ ¯³²¥¬ The amount of work and time In a roundabout way ¡º¥¬ ²¥« ¡¸¨¢ª ª®±¬¨·¥±ª®£® ª®° ¡«¿ Volume of a body Spacecraft (vehicle) skin Body volume Body's volume ¡¸¨°»© ³¸¨¡ Di use contusion ¡º¥¬ ¿ ½°®¤¨ ¬¨·¥±ª ¿ ´®°¬³« Bulk aerodynamic formula ¡¹ ¿ ®¡±² ®¢ª Overall situation ¡º¥¬ ¿ ¢¿§ª®¯« ±²¨·¥±ª ¿ ¤¥´®°¬ ¶¨¿ Volumetric viscoplastic strain ¡¹ ¿ ®±¼ ±¨¬¬¥²°¨¨ ( ¯°¨¬¥°, ¤¢³µ ²¥«) Common axis of symmetry ¡º¥¬ ¿ ¤¥´®°¬ ¶¨¿ Volumetric (volume, bulk) strain (deformation) ¡¹ ¿ ¯ ¬¿²¼ Common memory ¡º¥¬ ¿ £°³§ª Shared memory Volume (volumetric) load
¡¹ ¿ ±¨«
¡º¥¬ ¿ ª®¶¥²° ¶¨¿
¡¹ ¿ ²®·ª ¯¥°¥±¥·¥¨¿
¡º¥¬ ¿ ¯®¢°¥¦¤¥®±²¼
¡¹¥£® ¢¨¤
¡º¥¬ ¿ ³¯°³£ ¿ ¤¥´®°¬ ¶¨¿
Total force
Volumetric (volume) concentration Volume (volumetric) damage
Common point of intersection
These quasilinear equations take the general form of (1) or (2), but have coecients which are also functions of x 87
Volumetric elastic strain Bulk elastic strain
¡º¥¬®¥ ¤¥´®°¬¨°®¢ ¨¥ Volume deformation Volumetric deformation Bulk deformation
¡º¥¬®¥ ¨²¥£° «¼®¥ ³° ¢¥¨¥ Volume integral equation
¡º¥¬®¥ ° §°³¸¥¨¥ Volume fracture
¡º¥¬®¥ ±¦ ²¨¥
Volume compression Bulk compression Volumetric compression
¡º¥¬®¥ ±¬¥¹¥¨¥ Volume displacement
¡º¥¬®¥ ±®¤¥°¦ ¨¥
£° ¨·¥ ±¢¥°µ³
The maximizing sequence fx g is bounded from above (majorized) by the number x n
£° ¨·¥ ±¨§³
The minimizing sequence fx g is bounded from below by the number x n
£° ¨·¥¨¥
The approximations used by discretization modules are more accurate with the constraints of machine arithmetic
£° ¨·¥¨¥
In order to prove this lemma, it is necessary to put (impose) some restrictions on f
£° ¨·¥¨¥ ¢®§¬³¹¥¨¥ Disturbance constraint Perturbation constraint
Volume content
£° ¨·¥¨¥ ®¡« ±²¼
Volume ow
£° ¨·¥¨¥ ±³¹¥±²¢®¢ ¨¥
Volume charge
£° ¨·¥¨¥ ³¯° ¢«¥¨¥
Volume integral
£° ¨·¥¨¥ ´®°¬³
¡º¥¬»© ¬®¬¥²
Volume modulus
£° ¨·¥¨¥ ²¨¯ ª¢ ¤° ²»µ ¥° ¢¥±²¢
¡º¥¬»© ¯ ° ¬¥²° ³±²®©·¨¢®±²¨
£° ¨·¥¨¥ ²¨¯ ° ¢¥±²¢
¡º¥¬®¥ ²¥·¥¨¥ ¡º¥¬»© § °¿¤ ¡º¥¬»© ¨²¥£° « ¡º¥¬»© ¬®¤³«¼ Volume moment Bulk moment
Restriction on the region Existence constraint Control constraint
Restriction (imposed) on a shape Shape restriction Quadratic inequality constraint
£° ¨·¥¨¥ ²¨¯ ¥° ¢¥±²¢ Inequality constraint
Bulk stability parameter
Equality constraint
¡º¥¬»© ¯®²®ª ¦¨¤ª®±²¨ Volume uid (liquid) ux ( ow)
¡º¿±¨²¼ ª®¬³-«¨¡®
He explained the rule to the student
¡º¿±¿²¼
£° ¨·¥¨¥ ·¥£®-«¨¡® Restriction of : : : to
£° ¨·¥¨¿ ®¡º¥¬ ¨ ¢¥± Volume and weight constraints
£° ¨·¥ ¿ ¯ ¬¿²¼ No rigorous upper bound on the error, however sharp, can Limited memory
satisfactorily account for (® ¥ of) the statistical nature Finite memory of rounding error £° ¨·¥ ¿ ¯°®¡«¥¬ ²°¥µ ²¥« ¡»ª®¢¥ ¿ ¤°®¡¼ Restricted problem of three bodies Common fraction £° ¨·¥ ¿ ´³ª¶¨¿ ¡»ª®¢¥ ¿ ²®·ª ª°¨¢®© Con ned function Regular point of a curve Bounded function
¡»ª®¢¥®¥ ¤¨´´¥°¥¶¨ «¼®¥ ³° ¢¥¨¥ ± £° ¨·¥»© ¨¬¯³«¼±®© ¯° ¢®© · ±²¼¾ An in nite straight-line bounded from one side is called a Impulse ordinary di erential equation
half-line (a ray) in one direction
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£° ¨·¥»© ±¢¥°µ³
¡»·»¬ ®¡° §®¬
£° ¨·¥»© ±«¥¢
¡»·»¬ ¯³²¥¬ (±¯®±®¡®¬)
£° ¨·¥»© ±¯° ¢
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£° ¨·¨¢ ¾¹¨© ®¡º¥¬
£¨¡ ¾¹ ¿ «¨¨¿
£° ¨·¨²¥«¼
£¨¡ ¾¹ ¿ ±¥¬¥©±²¢ ª°¨¢»µ
£° ¨·¨²¥«¼ ¯®²®ª
Common logarithms
An ordinary (conventional, common) experiment
The results (the author) obtained are of limited interest Bounded from above
The linear recurrence relation can be parallelized in a stan- Bounded from the left dard way £° ¨·¥»© ±¨§³ In a conventional manner Bounded from below In a general (standard) way Ogden
Envelope
Envelope of a family of curves
Bounded from the right Bounding volume Delimiter
Flux ( ow) limiter
88
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£° ¨·¨²¼ To restrict f to X ¤¨ ¨ ²®² ¦¥
Unicellular
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One and the same computer may be required to help in One-component vortex the design of : : : ¤®ª° ²»© ³¤ ° ¤¨ ¨§ ¤¢³µ Simple impact One of two ¤®¬®¤ «¼ ¿ ¬ ²°¨¶ ¤¨ ¨§ ¤°³£®£® ¢»·¨² ²¼ Unimodular matrix To subtract one from another ¤®¬®¤®¢»© ¤¨ ¨«¨ ¤°³£®© One-mode Most kinds of adverbs can go in both mid-position and ¤®®± ¿ ¤¥´®°¬ ¶¨¿ end-position, but there some that can only go in one or Uniaxial strain the other ¤®®± ¿ ®°¨¥² ¶¨¿ ¤¨ ®² ¤°³£®£® Uniaxial orientation The molecules are isolated one from another ¤®®±»© ª±¥«¥°®¬¥²° ¤¨ ° § Unidirectional accelerometer In a scattering medium, light that has already been scat- ¤®®±»© £¨°®±ª®¯ tered once is scattered again Single-axis gyroscope
¤¨ °»© ±¤¢¨£ (¯°¨ ¯®¨±ª¥ ±®¡±²¢¥»µ § - ¤®¯ ° ¬¥²°¨·¥±ª ¿ ¬®¤¥«¼ ·¥¨©) One-parameter model Single shift ¤®¯®«®± ¿ ¤®°®£ Single-shift QR algorithm (QR iteration) Single-lane road (highway) ¤¨®·®¥ ª°³£®¢®¥ ¢ª«¾·¥¨¥ One-lane road (highway) Single circular inclusion ¤®¯®«®±®¥ ¸®±±¥ ¤¨®·»© ¢¨µ°¼ Single-lane highway Single vortex One-lane highway ¤ ¤¥±¿²¨²»±¿· ¿ ±¥ª³¤» ¤®¯®«®±»© ²° ±¯®°²»© ¯®²®ª One tenthousandth of a second Single-lane trac
ow ¤ ¨§ ®±®¢»µ ¯°¨·¨, ®¯°¥¤¥«¿¾¹¨µ : : : One-lane trac
ow One of the main factors (® ¥ reasons) that govern (® ¤®° §®¢»© ¯°®¯³±ª (ª ª ¤®ª³¬¥²) ¥ governs) the intensity of heat exchange : : : Once-only pass ¤ ±®² ¿ · ±²¼ ·¨±« ¤®° £®¢ ¿ ¬®¤¨´¨ª ¶¨¿ One hundredth part of a number Rank-one modi cation ¤® «¨¸¼ ¤®°®¤ ¿ ²¬®±´¥° (¢®¤ , ¨²¼) The mere existence of quasars con rms that : : : Homogeneous atmosphere (water, thread) ¤®£® ¯®°¿¤ª (®¤¨ ª®¢»¥ ¯® ¯®°¿¤ª³) ¤®°®¤ ¿ ¡¥²® ¿ ¯«¨² : : : by grouping terms of the same magnitude Homogeneous concrete slab ¤®£®°¡»© ¤®°®¤ ¿ £°³§ª One-humped Uniform load ¤®¤¨ ´° £¬¥»© ¤®°®¤ ¿ ¯« ±²¨ One-diaphragm Homogeneous plate ¤®§¢¥»© ¬ ¿²¨ª ¤®°®¤ ¿ ±¢¿§¼ Simple pendulum Homogeneous constraint ¤®§ · ¿ ° §°¥¸¨¬®±²¼ ¤®°®¤ ¿ ²¥¬¯¥° ²³° Unique solvability Uniform temperature ¤®§ ·® ®¯°¥¤¥«¥ ¤®°®¤ ¿ ´³ª¶¨¿ ±²¥¯¥¨ ®¤¨ The factorization A = LU is uniquely de ned if : : :
The elements of the matrix A are uniquely determined by Homogeneous function of unit degree ¤®°®¤® ¯°®¨¶ ¥¬»© formulas (1) and (2) Homogeneously permeable ¤®§ ·® ®¯°¥¤¥«¥ ¿ ´³ª¶¨¿ ¤®°®¤®¥ ¢¨µ°¥¢®¥ ¤¢¨¦¥¨¥ Uniquely de ned function Uniform vortex motion ¤®§ ·® ° §°¥¸¨¬»© ¤®°®¤®¥ ¢¥¸¥¥ ¤ ¢«¥¨¥ Uniquely solvable Uniform external pressure ¤®§ ·® ±®¯®±² ¢«¿²¼±¿ The function H is uniquely associated to a vector eld v ¤®°®¤®¥ £° ¨·®¥ ³±«®¢¨¥ (³° ¢¥¨¥) Homogeneous boundary condition (equation) ¤®§ ·®¥ ±«¥¤±²¢¨¥ ¤®°®¤®¥ ¯°¿¦¥®¥ ±®±²®¿¨¥ Direct consequence Homogeneous stress state ¤®§ ·»© ¨²¥£° « ¤®°®¤®¥ ®¡« ª® Single-valued integral ¤®ª«¥²®·»¥ (¯°®±²¥©¸¨¥) ®°£ ¨§¬», ¯°®- Uniform cloud
²¨±²» (¬. ·¨±«®) Protista
¤®°®¤®¥ ¯®«¥ (¢ ¯°®±²° ±²¢¥) Uniform eld
89
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The crack velocity exerts an in uence on the crack tip opening rate
Uniform gravity eld Homogeneous gravity eld
¤®°®¤»¥ ¢»·¨±«¨²¥«¼»¥ ±¨±²¥¬»
Homogeneous parallel computing systems with distributed memory
¤®°®¤»© ¤¨±ª Homogeneous disk
¤®°®¤»© ¬ ²¥°¨ « (¯ ° ««¥«¥¯¨¯¥¤, ¯®²¥¶¨ «, ±¯¥ª²°, ½««¨¯±®¨¤) Homogeneous material (parallelepiped, potential, spectrum, ellipsoid)
¤®°®¤»© ¯®²®ª (²¥·¥¨¥) ¡¥±ª®¥·®±²¨ Uniform stream ( ow) at in nity
¤®°®¤»© ±²¥°¦¥¼
Uniform beam (rod, bar) Homogeneous beam (rod, bar)
¤®±ª®°®±² ¿ ¬®¤¥«¼ One-speed model One-velocity model
¤®±®«¨²®»© One-soliton
¤®±²®°®¥¥ £° ¨·®¥ ³±«®¢¨¥ Unilateral boundary condition One-sided boundary condition
¤®±²®°®¥¥ ®£° ¨·¥¨¥ Unilateral constraint One-sided constraint
¤®±²®°®¨© ª®¥ª
Unilateral Chaplygin skate (sleigh)
ª §»¢ ²¼ ¯®¤¤¥°¦ª³ To give support to ªª ¬ Occam ª®¥·®±²¼ ª°»« Wing tip ª®· ²¥«¼ ¿ ±²®¨¬®±²¼ Ultimate cost ª°¥±²®±²¼ ³«¿ Zero neighborhood ª°³£«¥¨¥ ¤® n ¤¥±¿²¨·»µ ¶¨´° Rounding to n decimals ª°³£«¥¨¥ ¤® ·¥²®£® ·¨±« Rounding to even ª°³£«¥¨¥ ®²¡° ±»¢ ¨¥¬ (³±¥·¥¨¥¬) ¬« ¤¸¨µ ¶¨´° (° §°¿¤®¢) Chopping ª°³£«¥»© ¤® The residual of the computed solution is roughly of the same size as the residual of the exact solution rounded to t gures
ª°³£«¿²¼ ¤® ¢²®°®© § · ¹¥© ¶¨´°» ¢ ±²®°®³ ³¢¥«¨·¥¨¿ To round upward to the second signi cant digit ª°³¦ ¾¹¨¥ ³±«®¢¨¿ Ambient conditions ª°³¦ ¾¹¨© £ § Ambient gas Surrounding gas
¤®±²®°®¿¿ (¥³¤¥°¦¨¢ ¾¹ ¿) ±¢¿§¼
ª°³¦ ¿ ª®¬¯®¥² Circumferential component ¤®±²®°®¿¿ ¥¯°¥°»¢®±²¼ ª°³¦®±²¼ ± ¶¥²°®¬ O ¨ ° ¤¨³± R One-sided continuity Circle of center O and radius R ¤³°¿¾¹¨© § ¯ µ ª°³¦®±²¼ ¶¨«¨¤° Stupefying odor Circumference of a cylinder ¦¥ ¬ Auger Ohm ¦¨¢ «¼ ¿ ´®°¬ § £¥° Ogive shape Onsager Ogival shape ± £¥° ¦¨¢ «¼®¥ ²¥«® Onsager Ogive body ¯¥° ²®° ¤¨¢¥°£¥¶¨¨ ¦¨¤ ²¼, ·²® : : : ¡³¤³² : : : Divergence operator We would expect computers to be used as : : : ¯¥° ²®° ¤¨´´¥°¥¶¨°®¢ ¨¿ §¥¥ Di erentiation operator Oseen ¯¥° ²®° ª®¬¯«¥ª±®£® ±®¯°¿¦¥¨¿ § ª®¬¨²¼±¿ ± Complex conjugation operator This permits us to become familiar with these methods of ¯¥° ²®° ¯®¤±² ®¢ª¨ science Substitution operator § · ²¼ ¯¥° ²®° ° ±²¿¦¥¨¿ This work signi es a new approach to the problem Stretching operator This symbol stands for the Jacobian matrix ¯¥° ²®° ±«¥¤ ª §»¢ ¥²±¿ Trace operator It appears that rst rockets were invented in the thirteenth ¯¥° ²®° ¿ § ¯¨±¼ century Writing in operator form This layer appears to be rather laminar, in contrast ¯¥° ²®°®-²¥®°¥²¨·¥±ª¨© with : : : Operator-theoretical It turns out that : : : ¯¥° ¶¨¿ ª®¬¯«¥ª±®£® ±®¯°¿¦¥¨¿ Operation of complex conjugation ª §»¢ ²¼ ¢«¨¿¨¥ Unilateral (one-sided) constraint
Complex conjugation operation
To have an e ect (in uence) on
90
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¯°¥¤¥«¨²¼
We de ne a complex number to be a + bi, where : : : This map is de ned by requiring f to be constant (by the requirement that f be (® ¥ is) constant, by imposing the following condition: : : :)
¯¥° ¶¨¿ ° ±±»«ª¨ Scatter operation
¯¥° ¶¨¿ ± ¯« ¢ ¾¹¥© ²®·ª®© Floating point operation ( op)
¯¥° ¶¨¿ ±¡®°ª¨ Gather operation
¯¥° ¶¨¿ ±¦ ²¨¿
Compression operation
¯¥° ¶¨¿ ±«¨¿¨¿ Merge operation
¯¥° ¶¨¿ ±³¬¬¨°®¢ ¨¿ The sum operation
¯¥°¥¦ ¾¹¥¥ ¢»·¨±«¥¨¥
¯°¥¤¥«¨²¼ ¶¥®±²¼ To estimate the practical value of an invention ¯°¥¤¥«¿¾¹¥¥ ¤®¯³¹¥¨¥ Constitutive assumption ¯°¥¤¥«¿¾¹¥¥ ®²®¸¥¨¥ Constitutive relation ¯°¥¤¥«¿¾¹¥¥ ±®®²®¸¥¨¥ Constitutive relation ¯°¥¤¥«¿¾¹¥¥ ³° ¢¥¨¥ Constitutive equation Governing equation
Look-ahead computation
¯¥°²»© (±¢®¡®¤® ®¯¥°² ¿ ¯« ±²¨ª )
¯°¥¤¥«¿¾¹¨¥ ¯ ° ¬¥²°» (µ ° ª²¥°¨±²¨ª¨)
¯¨° ¨¥
¯°¥¤¥«¿¾¹¨© ¯ ° ¬¥²°
Freely supported plate
Conditions of free support
Constitutive parameters (characteristics) Governing parameters (characteristics)
Governing parameter Relying upon the Pythagorean theorem for right-angled Constitutive parameter ¯°®ª¨¤»¢ ¨¿ ª®«¥¡ ¨¥ triangles : : : Upset oscillation ¯¨±»¢ ²¼±¿ ³° ¢¥¨¥¬ ¯°®ª¨¤»¢ ¾¹ ¿ ±µ¥¬ The motion of charged particles is governed (discribed) by Flip- op circuit the above equation of equilibrium ¯°®ª¨³²»© ¬ ¿²¨ª ¯®§ ¢ ¨¥ ¶¥«¨ Inverted pendulum Target identi cation
¯¨° ¿±¼
¯®§ ¢ ²¥«¼»¥ ±¨£ «» Recognition signals
¯®§ ¢ ²¼
To identify an airplane
¯®°
In practice, one chooses basis functions with small support
¯®° ¿ ª«¥²ª Supporting cell
¯®° ¿ ®£ Supporting leg
¯®° ¿ ¯«®±ª®±²¼ Support plane Supporting plane Plane of support
¯®°»© ¢®«®±®ª Supporting hair
¯®°»© ¶¨«¨¤° Supporting cylinder
¯°¥¤¥«¥¨¥
Well-posed problems of this type require the determination of a function which satis es a given equation on some domain as well as additional conditions along its boundary
¯°¥¤¥«¥¨¿ § ¤ ·
The problem of determining values of y and z at future times t
¯°¥¤¥«¥ ¿ ¢±¥¬ : : :
The function f de ned on all of the set X is continuous
¯°¥¤¥«¥»© ¢ ²®·ª¥
This function is de ned at x (at the (a) point x)
¯°¥¤¥«¨²¥«¼ °®±ª®£® Wronskian determinant
¯°¥¤¥«¨²¥«¼ ¯°¥®¡° §®¢ ¨¿
¯²¨¬ «¼®¥ ¯® ¯®°¿¤ª³ °¥¸¥¨¥ An order-of-magnitude optimal solution ¯²¨¬ «¼»© ¯® ¢°¥¬¥¨ (¡»±²°®¤¥©±²¢¨¾) Time optimal ¯²¨¬ «¼»© ¯® ²®·®±²¨ Optimal with respect to accuracy Optimal in accuracy
¯²®¢®«®ª®»© £¨°®±ª®¯ Fiber-optic gyroscope ¯³±ª ²¼ For reasons of space, the proof is omitted ¯³±ª ²¼ ·«¥» ¢»±®ª®£® ¯®°¿¤ª Dropping higher-order terms ¯³±²¨²¼ (·²®-²® ¨§ ·¥£®-²®) Leave out ¯³µ®«¼ Tumor ¯»² ¿ ª°¨¢ ¿ Empirical curve °¡¨² (¤¢¨£ ²¼±¿ ¯® ®°¡¨²¥) To move along (in) an orbit °¡¨² ( µ®¤¨²¼±¿ ª°³£®¢®© ®°¡¨²¥) On a circular orbit °£ ¨§®¢»¢ ²¼ ª®´¥°¥¶¨¾ To arrange for the conference °£° ´ Digraph °¥¬ Oresme °¥±¬ Oresme °¥« (°¥¸ª )
The probability that the coin will fall (come down) heads (tails) is 1/2
Transformation determinant
91
°¨¥² ¶¨¿ ¢ §¨¬³²¥
±®¢ ¨¥ ¯®«®±»
°¨¥² ¶¨¿ ° ¢®¢¥±¨¿
±®¢ ¿ ¬®¤
°°
±®¢ ¿ ±ª®°®±²¼
Azimuthal orientation
Equilibrium orientation Orr
°² ®±¨ ª®®°¤¨ ²
Unit vector of the coordinate axis Unit coordinate vector
Strip foundation
Primary mode
Principal velocity Main velocity
±®¢®¥ ¬®¦¥±²¢® Fundamental set
°²®£® «¼ ¿ ¨²¥° ¶¨¿
±®¢®¥ ±®¤¥°¦ ¨¥
°²®£® «¼ ¿ ±¨±²¥¬ ´³ª¶¨©
±®¢®¥ ±®±²®¿¨¥
°²®£® «¼®¥ ¯°¥®¡° §®¢ ¨¥ ¯®¤®¡¨¿
±®¢®© ¢¥ª²®°
°²®£® «¼®¥ ¯°¨¢¥¤¥¨¥
±®¢®© ¢®¯°®±
°²®£® «¼»© ¨¢ °¨ ²
Invariant under orthogonal transformations
±®¢®© § ª® (¯ ° ¬¥²°, ³° ¢¥¨¥, µ ° ª²¥°¨±²¨ª )
Orthogonal projector
±®¢®© ¬ ±¸² ¡
Orthogonal iteration
System of orthogonal functions
Orthogonal similarity transformation
Orthogonal reduction
°²®£® «¼»© ¯°®¥ª²®°
°²®£® «¼»© ®²®±¨²¥«¼® ¢¥±®¢®© ´³ª¶¨¨
The subject matter of this paper is : : : Basic state
Base vector
The subject matter of this paper is : : :
Governing law (parameter, characteristic, equation)
Main scale Orthogonal with respect to the weight function W (x) over ±®¢»¥ ¨²¥£° «» Standard integrals the domain
°²®®°¬ «¼®±²¼
±®¢»¥ ³· ±²¨ª¨
°²®®°¬ «¼»© ¡ §¨±
±®¢»
Orthonormality
Orthonormal basis
The principal participants in the project were : : : Fundamentals ( ¯°¨¬¥°, of physics) The scienti c background of space travel
°²®¯²¥° Orthopter
±®¢» £ §®¢®© ¤¨ ¬¨ª¨
Orthocenter of a (the) triangle
±®¡ ¿ ®¡« ±²¼
Sedimentary rocks
±®¡ ¿ ²° ¥ª²®°¨¿
°²®¶¥²° ²°¥³£®«¼¨ª ± ¤®·»¥ ¯®°®¤» ± ¦¤¥¨¥ · ±²¨¶
Fundamentals of gas dynamics Singular (special) domain
Special trajectory The transport process for solid particles of di erent sizes ±®¡® ²³£®¯« ¢ª¨© ¬¥² «« Super-refractory metal with deposition on the lateral surface of the channel
±¢®¡®¦¤¥¨¥ ®² ±¢¿§¨
±®¡® ²³£®¯« ¢ª¨© ½«¥¬¥²
±¥¤ ¨¥ ¡»±²°®¥
±®¡®¥ ³¯° ¢«¥¨¥
±¥¤« ¿ ¦¨§¼
±®¡»© ¨²¥£° «
±¥±¨¬¬¥²°¨·®¥ ²¥·¥¨¥
±®¡»¬ ®¡° §®¬
±ª®«®·»© ¶¨«¨¤°
±°¥¤¥¨¥ ·¨±«¥®¥
±« ¡«¥¨¥
±°¥¤¥¨¥¬ ¯®
±« ¡«¿²¼ · ±²®²³
±°¥¤¥¨¥ ¯® ¯°®±²° ±²¢³
±®¢ § ¯¨±¨ ( ¯°¥¤±² ¢«¥¨¨)
±°¥¤¥ ¿ ¬®¤¥«¼
±®¢ ¨¥ £®°»
±°¥¤¥»© ¯® ½ª±¯¥°¨¬¥² ¬
±®¢ ¨¥ «®£ °¨´¬®¢
±² ¢¨²¼ ¬¥±²®
Constraint release
Quick deposition of a uid on the wall of a tube
Super-refractory element Singular control
Singular integral
Settled life
In a special way
Axisymmetric ow
Numerical homogenization
Fission cylinder
The velocity is determined by averaging the above equation with respects to x
Attenuation depth The weakening of viscous dissipation
Spatial averaging
To attenuate the (a) frequency
The classical iterative methods for solving linear systems Averaged model are based in writing the matrices as : : : ±°¥¤¥»© ¯® ¯®¯¥°¥·®¬³ ±¥·¥¨¾ The mean velocity averaged over the cross section in±®¢ ¨¥ £¨°®±ª®¯ creases with time The gyroscope's support frame The base of a mountain Base of logarithms
Averaged over experiments To leave space
92
±¶¨««¿¶¨® ¿ ¬ ²°¨¶
±² ¢«¥ : : : are left as exercises ±² ¢«¿²¼ ¡¥§ ¢¨¬ ¨¿ To leave aside ±² ¢¸ ¿±¿ · ±²¼
Oscillation matrix Oscillatory matrix
±¼ ¯¯«¨ª ² Applicate axis The remainder of this section is devoted to the problem ±¼ ¢»²¥±¥¨¿ Displacement axis of computing least squares solutions ±² ¢¸¥¥±¿ ¢°¥¬¿ (¤® ®ª®· ¨¿ ¯°®¶¥±± ) ±¼ «¥£ª®£® ®°¨¥²¨°®¢ ¨¿ ®¶¥ª Easy-orientable axis Estimated time left ±¼, ª®²®°³¾ ± ¦¥» ¤¢ ¢¥¤³¹¨µ ª®«¥± Axle between the two driving wheels ±² ¢¸¨¥±¿ ±¼ ¯¥°¥±¥·¥¨¿ The remaining k + 1 equations Let A be the rst of the remaining A Axis of intersection ±² ¥²±¿ ¯°®¢¥°¨²¼ Intersection axis It remains to check that : : : ±¼ ¯°®¥ª¶¨¨ Projection axis ±² «¼»¥ ½«¥¬¥²» The rest of elements Axis of projection ±² ®¢ª¨ ¬®¬¥² ±¼ ° ¢®¢¥±¨¿ Stopping time Axis of equilibrium Equilibrium axis ±² ²ª¨ ²®¯«¨¢ ±¼ ·³¢±²¢¨²¥«¼®±²¨ Fuel remains, fuel remnant(s) Sensitivity axis ±² ²®ª ®² ¡¥±ª®¥·®£® °¿¤ Remainder of an in nite series ² : : : ¤® : : : ±² ²®ª ®² ¤¥«¥¨¿ To integrate (sum) from 1 to n i
j
We can obtain a solution to the original problem at the expense of ve to ten fast direct solutions
Remainder of division Remainder on dividing a by b Remainder in division
² ¢»¡®°
±² ²®ª °¿¤ Remainder of a series ±² ²®· ¿ ¯«¥ª (²®«¹¨ ) Residual lm (thickness) ±² ²®·»© ±«®© Residual layer ±² ²®·»© ·«¥ ª¢ ¤° ²³°» Remainder of quadrature ±² ²®·»© ·«¥ ° §«®¦¥¨¿ Remainder term of the Taylor series expansion ±² ²®·»© ·«¥ °¿¤ Remainder term of a series ±²®©·¨¢®±²¼ ±³¤ Stability of a ship ±²° ¿ °¥§ª
We may come to the following two conclusions, depending on the (® ¥ a) choice of the origin
² ¢»±®ª®© ª ¨§ª®© ²¥¬¯¥° ²³°¥
The tendency of heat to ow from a higher to a lower temperature makes it possible for a heat engine to transform heat into work
² · « ¤® ª®¶ From beginning to end ² ¯¥°¥¬¥»µ
The polynomial p of degree n in the variable x The function f of the variables x and y
² ²®·ª¨ ª ²®·ª¥ Dot-to-dot ²¡° ±»¢ ¨¿ ®¸¨¡ª ( ¯°¨¬¥°, ¢±«¥¤±²¢¨¥ ®²¡° ±»¢ ¨¿ ·«¥®¢ °¿¤ ) Truncation error ²¡° ±»¢ ²¼
Triangular thread V-thread
±²° ¿ ²®·ª Sharp point ±²°®£° ¤±ª¨© Ostrogradskii ±²°»© ª° © Sharp edge ±²»¢ ²¼
This allows one to discard the boundary conditions on the opposite side of the domain The rst term in this expression can easily be disposed of
²¡° ±»¢ ²¼ ·«¥»
To drop the terms of order h3 To drop the terms of order 2 and higher To drop the terms of order equal to or higher (greater) than 3 To drop the terms of order higher than linear in x To drop the terms of order greater than 3
To become cold To grow cool
±³¹¥±²¢«¿¥¬»© ¢ ¤ ®¥ ¢°¥¬¿ Under way ±³¹¥±²¢«¿²¼, ¯°¨¢®¤¨²¼ ª
²¢¥°±²¨¥ ¢ ¤¥
±³¹¥±²¢«¿²¼ ª®²°®«¼ ¤ To exercise (the) control over ±³¹¥±²¢«¿²¼±¿
²¢¥°±²¨¥ ± ®±²°»¬¨ ª°®¬ª ¬¨ (ª° ¿¬¨) Sharp-edged ori ce ²¢¥²¢«¿²¼±¿
The new method brought about a great increase of eciency
Ori ce in the bottom Hole in the bottom Outlet in the bottom
Periodic solutions bifurcate from the stationary (steady
This program is now under way
93
state) solution
²«¨· ²¼±¿ (®²)
Responsive movement Responsive motion
²«®¦¥ ¿ ¬®¤¨´¨ª ¶¨¿
²¢¥²¢«¿¾¹ ¿±¿ ¯« ±²¨ Branching plate ²¢¥²®¥ ¤¢¨¦¥¨¥
This expression di ers from : : : by a term of order n These two vectors di er by a scale factor These two expressions di er by a linear term The di erential of f is di erent from 0
²¢¥²±²¢¥»© § A researcher responsible for this work ²¢¥· ²¼ §
Delayed update Delayed modi cation
²¥±¥»© ª
Some values of L taken relative to R are presented in the table
A variation of this angle is responsible for perturbations of the principal stresses
²®±¨²¥«¼ ¿ ¤®«¿ Relative fraction ²®±¨²¥«¼®
²¢«¥·¥ ¿ ¢¥«¨·¨ Abstract quantity ²¢«¥·¥®¥ ¯®¿²¨¥ Abstract notion Abstraction
The equation is solved for y Antisymmetric function with respect to x Measurable with respect to : : : A hypercomplex system over a commutative eld The algebra of square n n matrices with respect to the multiplication of matrices A nite limit with respect to the weak topology Multiplication is distributive over addition in the set of natural numbers To be symmetric with respect to : : : The position relative to the xed axes The error in B with respect to x is equal to : : : For the above reason, this term is called the condition number of A with respect to inversion The set of natural numbers is not closed under subtraction The moment of inertia about two of the coordinate axes This is a device that provides reactive force when in motion relative to the surrounding air
²¢®¤ ²¥¯« Removal of heat, heat removal ²¤ «¥®¥ ¯°®¸«®¥ The distant past ²¤¥«¨²¼ ®²
The last equation can be split o from the system The upper left block of the matrix can be separated from (the) others
²¤¥«¿¾¹ ¿ ¯«®±ª®±²¼ Separating plane ²¤¥«¿¾¹ ¿±¿ ¬ ±± Separating mass ²¤¥«¿¾¹ ¿±¿ ª®®°¤¨ ² Separable coordinate ²ª § ±°¥¤¥¥ ¢°¥¬¿ The mean time to failure (MTTF) ²ª«®¥¨¥ ¢ ®±² ²®·®¬ ·«¥¥ Discrepancy ²ª«®¥¨¥ ¢®§¬®¦®¥ Possible deviation ²ª«®¥¨¥ ®² ®°¬ «¼®±²¨ This quantity is referred to as departure from normality ²ª«®¥¨¥ ®² ° ¢®¢¥±¨¿ Equilibrium deviation ²ª«®¥¨¥ ±²®µ ±²¨·¥±ª®¥ Stochastic deviation ²ª«®¥¨¿ ¡®ª®¢»¥ ¯®¥§¤ Lateral de ections of a (the) train ²ª«®¥ ¿ ±¯³² ¿ ±²°³¿ ¢¨² De ected slipstream ²ª«®¨²¼ ±² ²¼¾ The referee recommended that this paper be rejected ²ª®«¼®¥ ° §°³¸¥¨¥ (¨§«®¬) Spallation fracture ²ª®«¼»© ´° £¬¥² Spallation fragment ²ª°»²¨¥ ¨ § ª°»²¨¥ ª « Channel opening and closing ²ª°»²¨¥ ²°¥¹¨» Crack opening ²ª°»²»© ¦¨¤ª®±²»© ¬ ®¬¥²° Open liquid manometer ²«¨¢ Low water ²«¨· ²¼±¿ ¬¥¥¥, ·¥¬ 1 % Di er by less than 1 %
²®±¨²¥«¼® ¤°³£ ¤°³£
The case when the source and the observer are in motion with respect to each other The movement of two particles relative to one another
²®±¨²¥«¼® ¥¬«¨
To determine the position of a (the) ship relative to the Earth
²®±¨²¥«¼® ª®´®°¬»µ ¨«¨ ¯°®¥ª¶¨®»µ ¯°¥®¡° §®¢ ¨© Under conformal or projective transformations ²®±¨²¥«¼® ¬®£®®¡° §¨¿ With respect to the manifold M ²®±¨²¥«¼® ¥¤ ¢® Relatively recently ²®±¨²¥«¼® : : : ¥¨§¢¥±²»µ This a system of two second-order elliptic equations in two unknown functions System of n linear algebraic equations in the n unknowns : : :
²®±¨²¥«¼® ®°¬» With respect to the 1-norm ²®±¨²¥«¼® ®¡« ±²¨ The measure with respect to the domain D ²®±¨²¥«¼® ±¢®¡®¤ ¿ ®°¨¥² ¶¨¿ Relatively free orientation ²®±¨²¥«¼® ±ª «¿°®£® ¯°®¨§¢¥¤¥¨¿ Orthogonal with respect to the scalar product : : : ²®±¨²¥«¼® ²®¯®«®£¨¨ Relative to the topology T
94
²®¸¥¨¥ ¢¿§ª®±²¥©
Leading-edge vortices formed above wings with highly swept leading edges
Viscosity ratio
²°»¢ (®¯²¨¬ «¼»©) ®² ¯°¥±«¥¤®¢ ²¥«¿
²®¸¥¨¥ § °¿¤ ª ¬ ±±¥
Optimal disengagement of a proportional navigation pursuer
Charge-to-mass ratio
²®¸¥¨¥ · «¼®£® ¤ ¢«¥¨¿ Initial pressure ratio
²°»¢ ®²
Di erence quotient for a derivative
²°»¢ ±ª®°®±²¼
Heat capacity ratio Speci c heat ratio
²°»¢ ²°¥¹¨
²®¸¥¨¥ ° §®±²®¥ ¤«¿ ¯°®¨§¢®¤®©
Separation from
²®¸¥¨¥ ²¥¯«®¥¬ª®±²¥©
Escape velocity
Separation crack
²¾¤¼ ¥
²°»¢ ¿ ª ± ²¥«¼ ¿ «¨¨¿ ²®ª
²¤¥«¼ ¿ ²° ¥ª²®°¨¿
²°»¢ ¿ ®¡« ±²¼ ²¥·¥¨¿
²®¸¥¨¥
²°»¢®¥ ®¡²¥ª ¨¥
Tangential separation streamline
The rocket is by no means a modern development
Separate trajectory
Separated- ow region
Ratio of x to y (² ª «³·¸¥, ·¥¬ between x and y)
Separated ow past (around) a circular cylinder at large Reynolds numbers
²®¸¥¨¥ ¥«¥¿
²°»¢®¥ ®¡²¥ª ¨¥ ²¥«
The scalar r(x) is called the Rayleigh quotient
²®¡° ¦ ²¼
Separated ow past (around) a body The transformation T takes radial segments across the ²°»¢®¥ ²¥·¥¨¥ ring into curves starting at the same points of the inner Separated ow circle ²±«¥¦¨¢ ¨¥ ²° ¥ª²®°¨¨ ²®¡° ¦ ²¼ ¢ Path tracking Let the projection P take each point (x; y) to (0; 0) Trajectory tracking Path following ²®¡° ¦ ²¼±¿ The set X is mapped by the function f to the set Y ²±«¥¦¨¢ ¨¥ ²° ¥ª²®°¨¨ · ±²¨¶ Particle tracking ²®¡° ¦ ²¼±¿ ¢ ±¥¡¿ : : : is mapped into itself ²±² ¢ ²¼ Theory lags behind practice ²®¡° ¦¥¨¥ §¥°ª «¼®¥ To lag behind Mirror image
²®«¨²®¢ ¿ ¬¥¬¡°
²±²®©¨ª
²®«¨²®¢»© °¥´«¥ª±
²±³²±²¢¨¿ ¯°®±ª «¼§»¢ ¨¿ £° ¨·®¥ ³±«®¢¨¥
²®°¢ ²¼±¿ ®² ¥¬«¨
²±·¥² ¿ ª®´¨£³° ¶¨¿
²®¸¥¤¸ ¿ ³¤ ° ¿ ¢®«
²±»« ²¼ ª
²° ¦ ²¼
²±¾¤
²° ¦¥¨¥ ¨¢¥±
²±¾¤ ¢»²¥ª ¥², ·²® : : :
²° ¦¥¨¥
²µ®¤¨²¼ ®², ¨±µ®¤¨²¼ ¨§ (³¤ «¿²¼±¿ ®²)
Sink
Otolith membrane
No-slip boundary condition
Otolith re ex
Reference con guration
To leave the Earth
For more details we refer the reader to [1]
Detached shock wave
The equation of motion of a sphere, which re ects Newton's law, is : : :
It follows from here that : : : From here it follows that : : : From this it follows that : : :
Givens re ection
This domain appears in the water after the shockwave proceeds from (moves o ) the contact surface to the shell
Re ection at
²°¥§®ª ®°¬ «¨
Segment of the normal
²·¥² ¤«¿
x(y,z )-intercept
²·¥²«¨¢ ¿ «¨¨¿ ° §£° ¨·¨²¥«¼ ¿
Forward sweep
²¹¥¯«¿¥²±¿ ®² ±¨±²¥¬» (8)
²°¥§®ª, ®²±¥ª ¥¬»© ®±¨ ²°¨¶ ²¥«¼ ¿ ±²°¥«®¢¨¤®±²¼ ²°¨¶ ²¥«¼® ®¯°¥¤¥«¥ ¿ ¬ ²°¨¶
Geomechanics report to the National Science Foundation Sharp line of demarcation
: : : separates from system (8) If all the eigenvalues of a symmetric matrix are negative, ²»±ª ¨¥ ±ª®°®±²¥© Finding the velocities then this matrix is said to be negative de nite
²°¨¶ ²¥«¼® ®¯°¥¤¥«¥»©
µ¢ ²»¢ ²¼
²°¨¶ ²¥«¼® ¯®«³®¯°¥¤¥«¥ ¿ ¬ ²°¨¶
¶¥¨¢ ¨¿ ¬®¤¥«¼ ¯® ³£«®¢»¬ ¨§¬¥°¥¨¿¬
Negative de nite
Negative semide nite matrix
The contour C surrounds the origin of coordinates Bearing-only model of estimation
²°»¢ (§ ¢¨µ°¥¨¥) ¯®²®ª ± ¯¥°¥¤¥© ª°®¬ª¨ ¶¥¨¢ ²¥«¼ Estimator ª°»« ¡®«¼¸®© ±²°¥«®¢¨¤®±²¨ 95
¶¥¨¢ ²¼ ° ¡®·¨¥ µ ° ª²¥°¨±²¨ª¨
«¼¶¥®¡° §®¢ ¨¥ ¨§-§ ° §®±²¨ ¢¿§ª®±²¥©
With all the software operating in the same environment, Viscous ngering we can evaluate the performance of these methods (pro- ¬¿²¨ ¡¥§° §¬¥°»© ¯ ° ¬¥²° Nondimensional memory parameter grams, subroutines, modules) Chapter 3 of this book presents some simple examples of ¬¿²¼ ±®¢¥°¸¥ ¿ performance evaluation When = 0, the material has perfect memory; when = 1, the material has no memory ¶¥ª ®¡³±«®¢«¥®±²¨ ¬¿²¼ Condition estimate The use of external storage can slow the process down ¶¥ª ®¸¨¡ª¨ considerably Error estimate ¶¥ª ®¸¨¡®ª ®±®¢¥ ®¡° ²®£® (¯°¿¬®£®) Each of these methods requires very little extra storage We obtain a solution to the original problem at the ex «¨§ pense of ve to ten fast solutions with only a modest inBackward (forward) error estimate (bound) crease in storage ¶¥ª ²¥±²¨°®¢ ¨¿ ¯¯ Estimate of testing Pappus Testing estimate
° ¦¨¤ª®±²¨ Liquid vapor ° ¢¨µ°¥© Vortex pair ° ¨¤¥ª±®¢ Obviously («³·¸¥, ·¥¬ evidently | ½²® ±«®¢® ¥±¥² ¢ Index pair ° ¨²¶ ±¥¡¥ ½«¥¬¥² ¥³¢¥°¥®±²¨) Ritz pair ·¥¢¨¤»¬ ®¡° §®¬ ° ±¨£³«¿°»µ ¯®¤¯°®±²° ±²¢ In an obvious way Singular subspace pair ·¨±²¨²¼ ¯ ¯ª³ ° ¡®« ³±²®©·¨¢®±²¨ To empty a (the) folder Stability parabola ¸¨¡ª ¢»·¨±«¥¨© ° §¨²»¥ ª®«¥¡ ¨¿ Computation error Spurious vibrations (oscillations) ¸¨¡ª ¨§¬¥°¥¨© ° «« ª± §¢¥§¤» Measurement error Parallax of a star ¸¨¡ª ²¥±²¨°®¢ ¨¿ ° ««¥«¼ ±ª«®¥¨¿ Error of testing Parallel of declination Testing error ° ««¥«¼® ®±¿¬ ¹³¹ ²¼ ¥¤®±² ²®ª ¢ ·¥¬-«¨¡® Drawing these lines parallel to the axes : : :, we obtain : : : To be short of ° ««¥«¼®-¢¥ª²®°»© Parallel-vector ° ««¥«¼®¥ ¤¢¨¦¥¨¥ ¦¨¤ª®±²¨ ¤ ¾¹ ¿ ¢®« ±¬¥¹¥¨© Parallel ow Incident displacement wave ° ««¥«¼»© ¤¥¨¥ The line parallel to the tangent k(S ) at the point x These values of the angle correspond to the fall of the ° ¬¥²° ¢®¤®®±®£® ¯« ±² disk Aquifer parameter ¤¥¨¥ ¢»±®²» ¯®° ° ¬¥²° ¢»±¢¥·¨¢ ¨¿ Fall of pressure head Parameter of lighting ¤¥¨¥ ¯°¿¦¥¨¿ ° ¬¥²° ¦¥±²ª®±²¨ ¶¥ª ·¨±« ³«¥© Estimate for the number of zeros ¶¥®· ¿ ´³ª¶¨¿ Merit function ·¥¢¨¤®
(1)
Decrease of stress Stress decrease Decrease of voltage Voltage decrease
§ °®²®° Slot of the rotor ª¥² ¯°®£° ¬¬ ¯® ° §°¥¦¥»¬ ¬ ²°¨¶ ¬ Sparse matrix package
ª¥² ±«®¥¢
Pack of layers Packet of layers
«¥© Paley
«¼¶¥®¡° §®¢ ¨¥ Fingering
Sti ness parameter Rigidity parameter
° ¬¥²° § ª°³²ª¨ Swirl number ° ¬¥²° «¨¥©»µ ° §¬¥°®¢ Length-scale parameter ° ¬¥²° £°³¦¥¨¿ Loading parameter ° ¬¥²° £°³§ª¨ Load parameter ° ¬¥²° ®¡¥§° §¬¥°¨¢ ¨¿ Nondimensionalizing parameter Nondimensionalization parameter
° ¬¥²° ®¡° ²®© ±¢¿§¨ Feedback parameter
96
¥«¥£ Peleg ¥«¥ ¢¨µ°¥¢ ¿ Vortex sheet ¥«¨ Paley ¥«¼²¼¥ Peltier ¥«¥¢¥ Painleve ¥¨£ Penning ¥°®³§ Penrose ¥°¢ ¿ ¢³²°¥¿¿ ª° ¥¢ ¿ § ¤ · Interior Dirichlet boundary value problem ¥°¢ ¿ ª° ¥¢ ¿ § ¤ · Elastic parameter The Dirichlet boundary value problem Parameter of elasticity ¥°¢ ¿ ° §®±²¼ ( ¯°¨¬¥°, ¢ § ¤ · µ ¢¨£ ° ¬¥²° · ±²®²» ¶¨¨) Single di erence Frequency parameter ° ¬¥²°¨·¥±ª®¥ ¯°®±²° ±²¢® (¯°®±²° ±²¢® ¥°¢¨· ¿ ¢®« ¯ ° ¬¥²°®¢) Original wave : : : are given in the above parameter space ¥°¢¨·»¥ ¤ »¥ ° ¬¥²°¨·¥±ª®¥ ±¥¬¥©±²¢® Primary data Raw data n -parameter family ¥°¢¨·»© °¥£³«¿²®° ° ¬¨ In pairs Primary regulator °¥²® ¥°¢®®¡° § ¿ ´³ª¶¨¿ (¤«¿ ´³ª¶¨¨) Primitive Pareto Primitive function °«¥² Parlett Antiderivative Inde nite integral °®¥ ¤¥«¥¨¥ ¥°¢»¥ ¤¢ Binary division The rst two (® ¥ two rst) equations are simpler than °»¥ °¿¤»-³° ¢¥¨¿ the third Dual series-equations °®£ §®¢ ¿ ±°¥¤ ¥°¢»©, ª²® The rst to record such e ects was Faraday Vapor-gas medium He was the rst to propose a complete theory of : : : °®¦¨¤ª®±²»© He appears to be the rst to have suggested this now Steam-and- uid accepted theory of : : : °±¥¢ «¼ ¥°¥¢ «¨¢ ¨¥ ± ®£¨ ®£³ Parseval Waddling °¶¨ «¼»© ¥°¥¢¥°³²»© ¬ ¿²¨ª Partial Inverted pendulum ±ª «¼ Pascal ¥°¥¢¥°³²¼ ±²° ¨¶³ ±¯®°² ¯°®·®±²¨ (¢ ¬¥µ ¨ª¥ £®°»µ ¯®°®¤) Next monday he plans to turn over the page of his life ¥°¥¢®¤¨²¼ ¢ Certi cate of rock strength The identity map takes each x to x ³«¨ The map taking x to x is said to be identical Pauli The operator of di erentiation takes the function f to f 0 ¸ ¥°¥£¨¡®¢ ª°¨¢ ¿ Pash Curve through the points of in ection ¸¥ ¥°¥£®°®¤ª Paschen Membrane, dividing wall, partition ¥ ® Peano ¥°¥£°³¦¥ ¿ ¤®°®£ Crowded road ¥©¤¦ ¥°¥¤ ²¥¬ ª ª Paige Before the detonation reaches the Chapman{Jouget limit, ¥ª¥°¨± the state in the unburned gas suddenly changes Pekeris ¥°¥¤ ´°®²®¬ ¥ª«¥
° ¬¥²° ¯®¢°¥¦¤¥®±²¨ Damage parameter ° ¬¥²° ¯®¤®¡¨¿ Similarity number ° ¬¥²° ¯®°¿¤ª Rank parameter ° ¬¥²° ¯°®§° ·®±²¨ Transparency parameter ° ¬¥²° °¥« ª± ¶¨¨ Relaxation parameter ° ¬¥²° ³¤ ° Impact parameter ° ¬¥²° ³¯° ¢«¥¨¿ Control parameter ° ¬¥²° ³¯°®·¥¨¿ Hardening parameter ° ¬¥²° ³¯°³£®±²¨
Ahead of the front
Peclet
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The routine abc:c passes its rst argument by value and Virtual displacement the second argument by reference ¥°¥¬¥¹¥¨¥ £°³§ Load point de ection ¥°¥¤ ¢ ²¼ ½¥°£¨¾ The particles impart (transfer) their energies to the frag- ¥°¥¬»·ª (¬¥¦¤³ ²°¥¹¨ ¬¨) ments resulting from (the) collision Bridge Energy is transmitted from the Sun to the Earth in the ¥°¥¥±¥¨¥ · « ª®®°¤¨ ² form of electromagnetic waves Change of the origin of coordinates A nite amount of energy is passed (transfered) directly ¥°¥¥±²¨ ¡®«¼¸³¾ · ±²¼ ¯®²®ª ²¥¯« to the boundary layer To carry most of the heat ux To transmit a signal
¥°¥¤ · ¨§®¡° ¦¥¨© Transmission of images
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The transfer of liquid hydrogen from the Earth's surface to orbit would be more dicult than : : :
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Transfer of momentum Before making some other estimates, we need to prove ¥°¥®± ª ±ª ¤»© that : : : Cascade transfer
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Front (anterior) surface of a (the) body Tip of a (the) wing
We now proceed to estimate the above parameters This patient can only transit to death
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Change of the origin of coordinates Transportation of solid particles Gas is transferred by underground tubes The method of proof is carried over to domains : : :
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The solution is transferred to the next coarser grid, where more iterations are performed
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Cross coupling
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Cross-multiplication
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Convective change
Transport eld Transfer eld
¥°¥®±®¥ ¯®«¥ ±ª®°®±²¥© Transport velocity eld Transfer velocity eld
Activation variable
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Inactivation variable
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Multiresolution
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Variables \velocity{height" Velocity{height variables
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: : : is needed to move the crack over a distance
Transfer acceleration
The inertial forces of moving space Retargeting
Nondimensional impressed temperature di erence The pressure di erence through the cupula Over ow
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Please nd enclosed two copies of the revised version of my paper
¥°¥±² ®¢®ª £°³¯¯ Permutation group
98
¥°¥±²°®©ª Modi cation, reconstruction, metamorphosis ¥°¥±·¥² °¥¸¥¨¿ Updating a solution ¥°¥²¿¦ª ¦¨¤ª ¿ Liquid bridge ¥°¥³¯®°¿¤®·¨¢ ¨¥ ¶¨ª« Loop reordering ¥°¥µ«¥±² Kinking ( ¯°¨¬¥°, ¯¥°¥µ«¥±² ¨²¨) ¥°¥µ«¥±² µ ° ª²¥°¨±²¨·¥±ª¨µ ª°¨¢»µ Overlapping of (the) characteristic curves ¥°¥µ®¤ Transition from laminar to turbulent ow ¥°¥µ®¤ ¢ ±®±²®¿¨¥ ±¢¥°µ¯« ±²¨·®±²¨ Transition in(to) superplasticity state ¥°¥µ®¤ ¨§ ±®±²®¿¨¿ A ¢ ±®±²®¿¨¥ B § ®¤¨ ¸ £ One-step transition from the state A to the state B ¥°¥µ®¤ ª ¯ ° ¡®«¨·¥±ª¨¬ ª®®°¤¨ ² ¬ Transition to parabolic coordinates ¥°¥µ®¤ ª ¯°¥¤¥«³ A passage to the limit similar to the above implies that
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¥°¥µ®¤ ®² ¢®«®¢®£® ¯°¨³¦¤¥¨¿ ª ª®¢¥ª²¨¢®¬³ Transition from wave forcing to convective forcing ¥°¥µ®¤ ¯¥°ª®«¿¶¨®»© ´ §®¢»© Percolating phase transition ¥°¥µ®¤ ³¤ °®© ¢®«» This is the ratio between densities at shock transition ¥°¥µ®¤ ¬ ²°¨¶ Transition matrix ¥°¥µ®¤ ¯«®²®±²¼ ¢¥°®¿²®±²¨ Transition probability density ¥°¥µ®¤ ²¥®°¨¿ Transition theory ¥°¥µ®¤¨²¼ ¢ Under the above transformations, the set X goes into a set Y
¥°¥µ®¤¨²¼ ª
We now turn to the problem of solving the linear system Ax = b
¥°¥µ®¤¨²¼ ®² ¢¥°µ¥© ²®·ª¨ ª ¨¦¥©
To go from the upper to the lower point in a minimum of time
¥°¥µ®¤ ®² ®¤®£® ¨²¥°¢ « (®²°¥§ª ) ª ¤°³£®¬³ Change of interval (segment) ¥°¥µ®¤¨²¼ ®² ¯¥°¥¬¥®© µ ª ¯¥°¥¬¥®© ³ To go (over) from the variable x to the variable y ¥°¥µ®¤ ¿ ´³ª¶¨¿ (´³ª¶¨¿ ¯¥°¥µ®¤ ) Transition function ¥°¥µ®¤»© °¥¦¨¬ Transition regime Transient regime
¥°¥·¥°ª¨¢ ²¼ To draw a short line across the equality sign ¥°¥·¨±«¨²¥«¼»© «£®°¨²¬ Enumeration algorithm ¥°¥¸¥¥ª ¬¥¦¤³ ¦¨¤ª®±²¿¬¨ Bridge between liquids
¥°¨®¤ ¨§¬¥¥¨¿ Period of change (variation) ¥°¨®¤ ¯°®±²®¿ Idle period ¥°¨®¤¨·¥±ª ¿ ¤°®¡¼ Repeating fraction ¥°¨®¤¨·¥±ª¨© ¢ ¯« ¥ This object has an in-plane periodic structure ¥°¨®¤¨·¥±ª¨© ¯® ¢°¥¬¥¨ Time-periodic ¥°ª¨± Perkins ¥°ª®«¿¶¨®»© ª« ±²¥° Percolating cluster ¥°ª®«¿¶¨®»© ¬¥µ ¨§¬ Percolation mechanism ¥°ª®«¿¶¨®»© ¯¥°¥µ®¤ Percolation transition ¥°® Perot ¥°¯¥¤¨ª³«¿° ª ±¥°¥¤¨¥
Midperpendicular is a perpendicular drawn from the middle point (midpoint) of a segment
¥°¯¥¤¨ª³«¿°® ª These waves propagate normal to the contact surface ¥°°® Perron ¥°±¨¬¬¥²°¨·¥±ª ¿ ¬ ²°¨¶ Persymmetric matrix ¥°±¯¥ª²¨¢»¥ ¨±±«¥¤®¢ ¨¿
Promising studies (® ¥ perspective | ½²® ±³¹¥±²¢¨²¥«¼®¥ ¨ ¥ ¬®¦¥² ¡»²¼ ¯¥°¥¢®¤®¬ ¯°¨« £ ²¥«¼®£®)
¥²«¿ ¥±²¥°®¢ Loop-the-loop ¥²°®¢±ª¨© Petrovskii ¥²¶¢ «¼ Petzval ¥¸«¼ Poschl ¨§¼¥ Pisier ¨ª ° Picard ¨®« Piola ¨° ¨ Pirani ¨°¥ª± Pyrex ¨°± Peirce (°¥¦¥ Pierce) ¨°±® Pearson ¨² ²¥«¼ ¿ ±°¥¤ Nutrient medium ¨²® Pitot ¨´ £®° Pythagor « ¢ ¾¹ ¿ °¨´¬¥²¨ª Floating-point arithmetic
99
« ¢® To move smoothly « §¬ ¯®¨¦¥®© ¯«®²®±²¨ Underdense plasma « §¬¥»© ±²®«¡ Plasma column « ª Planck « ¸¥°¥«¼ Plancherel « ±²¨ ¯°¿¬®³£®«¼ ¿ Rectangular plate « ±²¨ª ª®±²¨ Bone plate « ±²¨· ² ¿ °¥±±®° Leaf spring « ±²¨·¥±ª®¥ ¤¥´®°¬¨°®¢ ¨¥ Plastic deformation Plastic straining
« ±²¨·®±²¼ ¯® ±¤¢¨£³ Shear plasticity « ² ¡®«¼¸ ¿ ¯¥· ² ¿ Large printed circuit board « ²® Plateau « ²® Plato «¥ª ¯ ¤ ¾¹ ¿ Falling lm Falling-down lm
«¥ª ¯®ª°»²¨¿ Coating lm «¥ª ±²¥ª ¾¹ ¿ Flowing-down lm «¥·¨ª¨ Arms «¨² ¡¥²® ¿ Concrete slab «®±ª ¿ £° ¨¶ ° §¤¥« Plane interface «®±ª ¿ § ¤ · Plane (two-dimensional, 2D-) problem «®±ª ¿ ±²¥ª Plane wall «®±ª¨© ´®² Plane fountain «®±ª®¥ ¢° ¹¥¨¥ ¨¢¥± Givens plane rotation «®±ª®¥ ²¥«® Flat (plane) body «®±ª¨© ¬ ¿²¨ª Plane pendulum «®±ª¨© ±«®© Plane layer «®±ª®¥ ¤¢¨¦¥¨¥ ¦¨¤ª®±²¨ Two-dimensional (plane) uid motion ( ow) «®±ª®±²¼ °¬¨°®¢ ¨¿ Reinforcement plane «®±ª®±²¼ £®°¨§®² Horizon plane «®±ª®±²¼ ¨§¬¥¥¨¿ Plane of variation
«®±ª®±²¼ ª®¬¯«¥ª±®£® ¢°¥¬¥¨ The complex t(time)-plane «®±ª®±²¼ ¯ ° ¬¥²°®¢ Parameter plane «®±ª®-¯ ° ««¥«¼®±²¼ Plane-parallelism «®²®±²¼ ²¬®±´¥°» Atmospheric density «®²®±²¼ ²¬®±´¥°» ³°®¢¥ ¬®°¿ Sea-level atmospheric density «®²®±²¼ ¨§¬¥¿¾¹ ¿±¿ Variable density «®²®±²¼ ¬®¦¥±²¢ Density of the (a) set «®²®±²¼ ®£° ¨·¨¢ ¾¹¥£® ®¡º¥¬ The tightness of a bounding volume «®²®±²¼ ®¡º¥¬ ¿ Volume density «®²®±²¼ ° ±¯°¥¤¥«¥¨¿ Distribution density «®²®±²¼ ´ § Phase density «®µ ¿ (µ®°®¸ ¿) ®¡³±«®¢«¥®±²¼
This condition number re ects the ill-conditioning (wellconditioning) of matrices
«®µ®© (¯® ª ·¥±²¢³) Steel of inferior characteristics «®¹ ¤ª Area element, elementary area «®¹ ¤ª ª®² ª² Contact patch Contact area
«®¹ ¤ª ¬ ª±¨¬ «¼®£® ±¤¢¨£ Area (element) of maximal shear «®¹ ¤ª ±ª®«¼¦¥¨¿ Area element of sliding surface «®¹ ¤ª ²¥ª³·¥±²¨ ¤¨ £° ¬¬» The yield segment of the diagram «®¹ ¤¼ ¢ ¯« ¥ Projected area «®¹ ¤¼¾ : : : A rectangle 10 cm by 15 cm in area «¾ªª¥° Plucker ® A maximum of with respect to Nonlinear in
® ¡®«¼¸¥© · ±²¨ For the most part ® ¡»±²°®¤¥©±²¢¨¾
Until quite recently, computers were comparatively slow in operation
® ¢¥«¨·¨¥
Friction produces stresses similar in magnitude to the expected strain-rate e ect
® ¢¥«¨·¨¥ ¨«¨ ¯° ¢«¥¨¾
Velocity may change in magnitude or in direction with respect to time
® ¢±¥© ¯®¢¥°µ®±²¨ ª®² ª² Over the entire contact surface ® ¢±¥¬³ ¬¨°³ All over the world
100
Throughout the world World-wide
® ¯° ¢«¥¨¾ ª
The axis 0z is directed along the upward vertical
® ¯° ¢«¥¨¾ ®²
® ¢®±µ®¤¿¹¥© ¢¥°²¨ª «¨ ® ¢°¥¬¥¨
A body leaving the Earth in the direction of the Moon would experience the gravitational eld of both planets
Solar wind is continuously streaming outward from the Sun In time Acceleration is the rate of change of velocity with respect ® ¥¤®±² ²ª³ (¯® ¨§¡»²ª³) By lack (by excess) to time
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The temperature is uniform throughout the body
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With respect to the 1-norm, in the norm, in a norm Approximation in di erent norms Convergence in norm
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The leako rate over the whole fracture
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It can be imagine that day and night would not change in Along (in) a circular orbit ® ®²®¸¥¨¾ ª length With respect to the arc ® §¥¬®¬³ ¢°¥¬¥¨ Modulo E Such a trip might last millions of years in Earth time Inviscid perturbations to a trailing line vortex ® § ·¥¨¾ ¨ ±±»«ª¥ The stability of a free vortex to nonaxisymmetric perturThe routine abc:c passes its rst argument by value and bations the second argument by reference ® ¯®¢®¤³ ® ¨¬¥¨ The rst measurement of the speed of light was made by In connection with ® ¯®¤£°³¯¯¥ a Danish astronomer named Roemer in 1676 Let H be a coset of the group A with respect to its sub® ¨¬¯³«¼± ¬ group B In the momenta We prove this theorem by induction on n
An order-of-magnitude optimal solution This estimate is an order of magnitude better At other air humidity, these values are greater by an order of magnitude
® ¨²³¨¶¨¨ By intuition
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This axis is directed along the tangent to the line drawn By (inductive) assumption through the point A ® ¯°¥¤¯®«®¦¥¨¾ ¨¤³ª¶¨¨ ® ª®®°¤¨ ² ¬ By the induction hypothesis (assumption), the matrix A In (with respect to) the coordinates is positive de nite for n = 2 This function has a zero of at least third order at x with If a medium is frictionless, a body moves in it without norm at least equal to 1 doing any work against gravity The coordinate x is at least as large (in order of magni- ® ¯°¨¶¨¯³ tude) as y On the principle ( ¯°¨¬¥°, to work on the principle) : : : in at least some neighborhood of the point x = ® ¯°¨·¨ ¬ ® ¬ «®¬³ ¯ ° ¬¥²°³ For reasons (® ¥ causes) that will become clear later : : : The rst term of the (an) expansion in small parameter " ® ¯°¨·¨ ¬, ³ª § »¬ ¢»¸¥ ® ¬¥°¥ For reasons given (above) To converge in measure ® ¯°®±²° ±²¢¥®© ª®®°¤¨ ²¥ ® ¬¥°¥ ²®£® ª ª This solution can be represented as a Fourier series in the As the wheel came in contact with the surface spatial coordinate The blood moves more and more slowly as it travels far- ® ° §¬¥°³ ther and farther along the arterial channels Both (the) graphs should be symmetric in size ® ¬¥°¥ ³¤ «¥¨¿ ®² ¶¥²° Separation of particles by size With distance from the center ® ° §¬¥°³ ¡®«¼¸¥ (¬¥¼¸¥) ® ¬¥¨¾ ¢²®° Bigger (smaller) in size In the opinion of the author ® °¿¤³ ¯°¨·¨ In the author's opinion For a number (variety) reasons
® ¬®¤³«¾
® ±¢®¥¬³ ±³¹¥±²¢³ Analogue computers are not inherently fast ® ±³²¨ In fact ® ²¥®°¥¬¥ 1 By Theorem 1, this estimate is always valid ® ¯° ¢«¥¨¾ The elastic properties of this material may vary direction- ® ²®«¹¨¥ In modulus, integer modulo m, in absolute value Less than unity in modulus The angular velocity becomes larger in magnitude This term is less than 1 in absolute value (in modulus)
This material is homogeneous over its thickness
ally
101
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This steady-state evolution rate is apparently caused by a surface reaction
An algorithm optimal with respect to accuracy An accuracy optimal algorithm
®¢®° ·¨¢ ²¼(±¿) ¢®ª°³£ ®±¨ To turn about an (the) axis through an angle of 2 This class of matrices forms a group under multiplication ®¢®°®² k-ª° ²»© ³£®« Consider (the) invariant points of the compound transfor® ³±«®¢¨¾
® ³¬®¦¥¨¾ By hypothesis By condition
® ³±«®¢¨¾ ¥¯°¥°»¢®±²¨ By continuity
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At the discretion of the author
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To this order in Mach number
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The study of behavior of solutions
®¢¥°µ®±² ¿ £°³§ª Surface load
®¢¥°µ®±² ¿ ¯«®²®±²¼ Surface density Areal density
®¢¥°µ®±²»© ½´´¥ª² Skin e ect
®¢¥°µ®±²¼ ¢²®°®£® °®¤ Surface of genus 2
®¢¥°µ®±²¼ ª®² ª² Contact surface
®¢¥°µ®±²¼ £°³¦¥¨¿ Loading surface
®¢¥°µ®±²¼ ¯®±²®¿®£® ¤ ¢«¥¨¿ Isobaric surface Constant-pressure surface
®¢¥°µ®±²¼ ¯®±²®¿®£® ±ª ² ( ª«® ) Surface of constant inclination Constant inclination surface
®¢¥°µ®±²¼ ¯®±²®¿®© ¯«®²®±²¨ Constant-density surface
®¢¥°µ®±²¼ ¯°®´¨«¿ Pro le surface
®¢¥°µ®±²¼ ° §¤¥« ¯«®±ª ¿ Plane interface
®¢¥°µ®±²¼ ° §°»¢ ¥¯°¥°»¢®±²¨ Discontinuity surface
®¢¥°µ®±²¼ ±¢¿§¨ Constraint surface
®¢¥°µ®±²¼ ±ª ² ( ª«® ) Surface of inclination
®¢¥°µ®±²¼ ±ª®«¼¦¥¨¿ Sliding surface
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Apparently, evidently This device appears to di er from the old ones Presumably, it is likely that
mation T R , where R denotes k-fold rotation through an angle of 2 n
k
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It was necessary to provide an adequate protection against thermal failure
®¢°¥¦¤¥ ¿ ±°¥¤ Damaged medium ®¢°¥¦¤¥®±²¨ ¯ ° ¬¥²° Damage parameter ®¢°¥¦¤¥®±²¼ Damage ®¢±¾¤³ The air ow in this case remains steady throughout ®¢²®° ¿ ®°²®£® «¨§ ¶¨¿ Reorthogonalization ®¢²®°®¥ ¨±¯®«¼§®¢ ¨¥ ¤ »µ Data reuse ®¢²®°®¥ £°³¦¥¨¥ Repeated loading ®¢²®°»© Repeated application of Lemma 1 enables us to write : : : ®¢»±¨²¼ ° £ (¬ ²°¨¶») To rise (® ¥ raise) the rank (of the (a) matrix) ®¢»¸¥¨¥ ³°®¢¿ Rise (® ¥ raise) of groundwater level ®¢»¸¥ ¿ ª®¶¥²° ¶¨¿ Enhanced concentration ®£«®¹ ¾¹ ¿ £° ¨¶ Absorbing boundary ®£«®¹¥¨¥ ²¥¯« Heat absorption ®£® ¿ ¯«®²®±²¼ Linear density is a measure of mass per unit of length ®£° ¨· ¿ · ±²¨¶ Boundary particle ®£°¥¸®±²¼ ®ª°³£«¥¨¿ Roundo error ®£°³¦¥®¥ ®²¢¥°±²¨¥ Submerged ori ce Submerged outlet
®¤ ¤¥©±²¢¨¥¬ ¯°¿¦¥¨© Under the action of stresses ®¤ ¤¥©±²¢¨¥¬ ±¨«» ²¿¦¥±²¨ By gravity ®¤ ¤¥©±²¢¨¥¬ ±¨«» ²¿¦¥±²¨ ¤¢¨¦¥¨¥ Gravity-forced motion
102
®¤ ¤¥©±²¢¨¥¬ ±¨«» ²¿¦¥±²¨ (®±¥¤ ²¼, ¯¥°¥¬¥- ®¤ª®°¥®© Under the radical sign ¹ ²¼±¿) Gravitate ®¤ª° ¸¥ ¿ ¢®¤ Colored water Under the action of gravity ®¤«®¦ª ®¤ § ª®¬ Substrate Under the integral sign Within the norm signs ®¤¬ ²°¨·»© «£®°¨²¬ ®¤ §¢ ¨¥¬ Submatrix algorithm This distribution function is known under the name of ®¤¨¬ ²¼ ²¥¬¯¥° ²³°³ (¤ ¢«¥¨¥) To raise temperature (pressure) Student's distribution ®¤¨¬ ²¼±¿ ®¤ ³·»¬ °³ª®¢®¤±²¢®¬ Under scienti c supervision The Sun rises in the East and sets in the West ®¤ ¥³«¥¢»¬ ³£«®¬ ² ª¨ ¯®²®ª ®¤¿²¨¥ ª ¯¨««¿°®¥ Capillary elevation Flow at incidence ®¤ ³«¥¢»¬ ³£«®¬ ² ª¨ ®¤¿²¼±¿ ± At zero incidence (angle) At zero attack angle
An airplane has not only to be able to raise itself from the ground but also be controllable
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In this case, the plasma motion is directed at an angle to the magnetic eld
Horseshoe-shaped
Similarity of curves Curve similarity
Similarity of triangles means that the three angles in one triangle are equal to the three angles of another triangle and, as a consequence, the corresponding sides are in the same ratio
®¤®¡® To operate like a rudder ®¤®¡»¥ ²°¥³£®«¼¨ª¨
If the three angles of each triangle are equal, then these triangles are said to be similar
®¤®¸¢ £®°» Foot of a hill (mountain) ®¤¯°®±²° ±²¢® °»«®¢ Krylov subspace ®¤¯°®±²° ±²¢® ³¯° ¢«¥¨¿ Controllable subspace ®¤°®¡® To study in detail See [1] for more details
®¤°®¡®¥ ° ±±¬®²°¥¨¥ Detailed consideration is given to uid compressibility ®¤±¢¥²ª £« § Eye highlight ®¤±¥²®ª ¬¥²®¤ Subgrid method ®¤±²° ¨¢ ²¼±¿ ¯®¤
This parameter is adjusted to the experimental pressure di erences
®¤±·¥² ·¨±« ®¯¥° ¶¨© Operation count ®¤²¢¥°¦¤ ²¼ ½ª±¯¥°¨¬¥² «¼® Previously, this fact was experimentally substantiated ®¤²¢¥°¦¤ ¾¹¨© «¨§ ¤ »µ Con rmatory data analysis ®¤·¥°ª¨¢ ²¼ Many authors place emphasis on the fact that : : : ®¤·¨¥ ¿ ¬ ²°¨· ¿ ®°¬ Subordinate matrix norm ®¤º¥¬ ¿ ±¨« (¢»² «ª¨¢ ¨¿) Buoyancy ®¤»²¥£° «¼®¥ ¢»° ¦¥¨¥
103
Expression under the integral sign
®¤½° Pedal curve ®§ ¤¨ ´°®² Behind the front ®§¤¥¥ At a later time ®¥§¤, ¢µ®¤¿¹¨© ¢ ¯®¢®°®² Turning train ®§¢®«¿²¼ °¥¸¨²¼
®ª°»²¨¥ ²¥¯«®§ ¹¨²®¥ Heat-shielding coating Heat protection coating
®« £ ²¼ ¯® ®¯°¥¤¥«¥¨¾ By de nition, put A = x 2 T jx is a limit point ®« £ ²¼ ° ¢»¬ The potential is set equal to zero
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To have (place) reliance on The property of positive de niteness makes it possible (al- ®« £ ¿ lows one) to solve this system Setting (putting) n = 1, we can reduce this equation to This approach enables solving a number of problems im- : : : (® ¥ this equation can be reduced to : : :) portant for plasma con nement ®«¥ ²®¬ ®§¨¶¨® ¿ ª®®°¤¨ ² Atomic eld Positional coordinate ®«¥ ¢¨µ°¥© (¢¨µ°¥¢®¥ ¯®«¥) ®§¨¶¨® ¿ ¯¥°¥¬¥ ¿ Vorticity eld Positional variable ®«¥ ¤¥©±²¢¨²¥«¼»µ ·¨±¥« ®§¨¶¨® ¿ ±¨« Field of real numbers Positional force ®«¥ ¯° ¢«¥¨© ¤«¿ ¤¨´´¥°¥¶¨ «¼®£® ³° ¢-
®§¨¶¨® ¿ ±ª®°®±²¼ Positional velocity ®¨±ª ª®°¥© Root nding ®¨±ª ¯® ¬¥²®¤³ ¨¡® ··¨ Fibonacci search ®¨±ª{³ª«®¥¨¥ Search{evasion ®© Polya ®©²¨£ Poynting ®ª ¥¨§¢¥±² ¿ ´³ª¶¨¿ f is a yet unknown function ®ª § ¨¿ £° ¤¨¥²®¬¥²° Readings of the gradiometer ®ª § ²¥«¥© ±²¥¯¥¥© § ª® Law of indices ®ª § ²¥«¼ ¦¥±²ª®±²¨ Index of rigidity Rigidity index Index of sti ness Sti ness index
®ª § ²¥«¼ ª ·¥±²¢ Quality index ®ª § ²¥«¼ ª®°¿ Index of a (the) radical ®ª § ²¥«¼ ±²¥¯¥¨ ¤°®¡»© Fractional exponent ®ª § ²¥«¼ ¿ ª°¨¢ ¿ Exponential curve ®ªª¥«¼± Pockels ®ª®®°¤¨ ²»© ¢¨¤ Coordinate form ®ª®¿¹ ¿±¿ ±¬¥±¼ Quiescent mixture ®ª®¿¹¨©±¿ £ § Quiescent gas Gas at rest Quiet gas
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Venus is hidden under a mask of dense clouds
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Field of directions for a di erential equation
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Electric eld across the body surface
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Field of current Current eld
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Destination eld
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Research on nuclear rockets may yield information useful to the construction of such a device
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®«§³·¥¥ ¤¢¨¦¥¨¥ ¦¨¤ª®±²¨ Creeping motion of a liquid ( uid)
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®«§³·¥±²¼ ¯°¨ ±¤¢¨£¥ Shear creep
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®«¨¢»¯³ª«®±²¼ Polyconvexity
®«¨¤¨±¯¥°± ¿ ±¬¥±¼ (®¡« ª®) Polydispersed mixture (cloud)
®«¨®¬¨ «¼»© ¯°¥¤®¡³±«®¢«¨¢ ²¥«¼ Polynomial preconditioner
104
®« ¿ ¯¯°®ª±¨¬ ¶¨¿ Full approximation ®« ¿ ¢ °¨ ¶¨¿ Total variation ®« ¿ ¢®¤ High water ®« ¿ ¢»±®² Overall height ®« ¿ ¤¥´®°¬ ¶¨¿ Total strain ®« ¿ ¤¨±±¨¯ ¶¨¿ Full dissipation ®« ¿ ¤«¨ Full length ®« ¿ § ¤ · ±®¡±²¢¥»µ § ·¥¨© Complete eigenproblem ®« ¿ ¯¥°¥®°²®£® «¨§ ¶¨¿ Complete reorthogonalization ®« ¿ ¯« ±²¨·®±²¼ Full plasticity ®« ¿ ° ±¯°®¤ ¦ Clearance sale ®« ¿ ±¢¥°²ª ²¥§®° Full contraction of a tensor ®« ¿ ±¨« (²¥¬¯¥° ²³° , ½¥°£¨¿) Total force (temperature, energy) ®« ¿ ½¥°£¨¿ Total energy ®«®¥ ¨§¬¥¥¨¥ Total variation ®«®¥ ®°²®£® «¼®¥ ¯°®±²° ±²¢® Complete orthogonal space ®«®¥ ®°²®£® «¼®¥ ° §«®¦¥¨¥ Complete orthogonal decomposition ®«®¥ ¯®¨¬ ¨¥ Full understanding ®«®¥ ° ±±¬®²°¥¨¥ Full consideration ®«®¥ ±®¡° ¨¥ ±®·¨¥¨© The complete works ®«®° §¬¥° ¿ § ¤ · ´¨«¼²° ¶¨¨ Full-sized ltering problem ®«®±²¼¾ Print your name and address in full ®«®±²¼¾ ¨±¯®«¼§³¥²±¿ Full advantage is taken of these properties ®«®±²¼¾ ª ² «¨²¨·¥±ª ¿ ¯®¢¥°µ®±²¼ Full catalytic surface ®«®±²¼¾ ¯®«®¦¨²¥«¼® ®¯°¥¤¥«¥ ¿ ¬ ²°¨¶ Totally positive de nite matrix ®«®±²¼¾ ±¢¿§ »¥ ±¨±²¥¬» Completely connected systems ®«®±²¼¾ ³¯° ¢«¿¥¬ ¿ ±¨±²¥¬ Completely controllable system ®«®²³°¡³«¥²»© Fully turbulent ®«»¥ ¯°¿¦¥¨¿ Total stresses ®«»© ¢»¡®° ¢¥¤³¹¥£® ½«¥¬¥² Complete pivoting ®«»© ¯®«¥²»© ¢¥± All-up weight
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A matrix is of full rank if its rows or its columns are linearly independent
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As before, the linear dimensions are related to half the layer thickness G is half the sum of negative roots On the average, about half the list is tested J contains an interval of half its length in which : : :
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The author will review the state-of-the-art in the eld of mathematics and mechanics
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If all the eigenvalues of a symmetric matrix are positive, then this matrix is said to be positive de nite
®«®¦¨²¥«¼® ®¯°¥¤¥«¥»© Positive de nite ®«®¦¨²¥«¼® ¯®«³®¯°¥¤¥«¥ ¿ ¬ ²°¨¶ Positive semide nite matrix ®«®¦¨²¥«¼»© ¯®¢®°®² Positive rotation is clockwise about the axis of rotation ®«®¦¨²¼ ° ¢»¬ b a is set to b ®«®¦¨²¼ ° ¢»¬ The value of a is set equal to b In this case, the bending rigidity is set to zero
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105
Double-lid-driven cavity
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Lid-driven cavity
Polya
One-and-a-half degrees of freedom Half the length of a (the) segment
Field of symmetries of third degree Atmospheric disturbances
Semi-iterative method Semilinear equation
Outside interference (disturbances)
Half-moon Semilunar
Interference (im)pulse
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Seminorm
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The columns of the matrix A are stored in the columns of the doubly subscripted array B
Seminormalized
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Half-inverse problem
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Aside (apart) from safety consideration, we must take into account emergency situations
Half-lowered eyelids
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The designer must always keep in mind the purpose for which : : :
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A (the) half century
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Pressure reduction
Capillary depression
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The term containing n2 comes from the errors : : :
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A person under test was given an instruction
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To gain approval To meet with approval
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Semivertex angle
Pressure fall
The recipient's computer
The Routh reduction
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Reduction of order of a (the) di erential equation
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Measurement of fall of pressure
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Better understanding of the meaning of these operations can sometimes be gained by studying them from a di erent viewpoint
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Hooke's law of elasticity named after its discoverer states that : : : To gain acceptance
The region in the gure is thought of as being divided up into : : : Poncelet
We have arrived at this results on (under) the assumption Pontry(j)agin that : : : ®¿²¨¥ ®«³¸¨°¨ «¥²» Concept of the force Semi-bandwidth The concept of the limit of a sequence The notions of residual, error, and relative error are de®«³½««¨¯± ned for n-vectors regarded as n 1 matrices Semi-ellipse Semi-ellipsoid Pohlhausen
Understandable behavior Comprehensible argument
106
®®¤¨®·ª¥ One at a time ®¯ °® ¥¯¥°¥±¥ª ¾¹¨¥±¿ ¯®¤¬®¦¥±²¢ Pairwise disjoint subsets ®¯ °® ¥¯¥°¥±¥ª ¾¹¨¥±¿ ¶¨ª«» Pairwise disjoint cycles ®¯ °® ¯°®±²®© Prime in pairs ®¯ °® ²®¦¤¥±²¢¥»© (° ¢»©) Pairwise identical ®¯¥°¥· ¿ ¤¨±¯¥°±¨¿ Transverse dispersion ®¯¥°¥· ¿ ª®¬¯®¥² ±ª®°®±²¨ Transverse velocity component ®¯¥°¥· ¿ ª®®°¤¨ ² Transverse coordinate ®¯¥°¥· ¿ ¯®¢¥°µ®±² ¿ £°³§ª Transverse surface load ®¯¥°¥·®¥ ¯°¿¦¥¨¥ Lateral stress Transverse stress
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Percolation threshold
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The subgraph B is induced by the graph A Condition (1) requires the residual to be orthogonal to space spanned by the test functions
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If the matrix A is of order unity and positive de nite, then L is uniquely de ned
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This quadrature formula is exact for all polynomials of degree less than or equal to n The convergence rate of this iterative method is of order less than or equal to n
®°¿¤ª ¥ ¡®«¼¸¥ n Of order at most n
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When the error goes to zero as fast as h2 , we say that the di erence formulas are second order accurate
¡¥±ª®¥·® ¬ «»µ A curvilinear rod of parallelogram cross section is consid- ®°¿¤®ª Order of in nitesimals ered ®°¿¤®ª ¢¥«¨·¨» ®¯¥°¥·®¥ ³±¨«¨¥ The temperature is at least by several orders of magnitude Transverse force lower than : : : ®¯¥°¥·»© ª ®°¿¤®ª ±¢¿§®±²¨ The magnetic eld vibrates in a direction transverse to Order of connectivity the direction the electromagnetic wave is traveling ®± ¤ª ¢»³¦¤¥ ¿ ®¯¥°¥·»© ª®½´´¨¶¨¥² Emergency landing Transverse coecient Forced landing ®¯¥°¥·»© ° §«¥² ®± ¤ª ¢®¤³ Transverse separation Water landing ®¯¥°¥·»© ° §¬¥° Landing on water Transverse size ®¯®« ¬ We divide this segment in half ®¯®«¥¨¥ ¬ ±±» Mass augmentation ®¯° ¢ª ( !) Correction ( !) ®¯° ¢ª ¨²¥°¯®«¿¶¨® ¿ Interpolation correction ®¯° ¢ª ®²±°®·¥ ¿ (®²«®¦¥ ¿) Deferred correction ®¯° ¢ª ²¢¥¸ Eotvos correction ®¯° ¢®·»© ª®½´´¨¶¨¥² Correction factor ®¯³²® Along the way ®°®¢®¥ ¤ ¢«¥¨¥ Pore pressure ®°®£ (ª®°® ) ¢®¤®±«¨¢ Crown of a weir Overfall crest
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Dedicated to the blessed memory of : : :
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Dedicated to the memory of : : :
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Upon evaluation of the integral After applying a linear transformation, we may assume that : : : On substituting (1) into (2) we get : : : Upon returning to the Earth : : : On connecting the wires : : :
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After being heated in the reactor, the gas would be exhausted through a rocket nozzle to obtain thrust
Threshold of instability
107
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After I selected . . . , I discovered . . . With the above theorem proved and the new matrix constructed, we come to the conclusion that : : : After the complete program has been read stored, the computer starts to obey it
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To set into one-to-one correspondence with : : : To put into correspondence with this set of matrices Let us assign the point y = f (x) to each point x Let us assume that the point y = f (x) corresponds to the point x We assign positive numbers to the right (left, upper, lower) half-line of X We may associate one such basis function with each grid point
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To pose a question on the motion of liquid suspensions and on the formation and disappearance of bubbles
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To pose (formulate) a dicult design problem
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Formulation of the problem, problem statement
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Universal gravitation constant (or gravity constant)
Sequential trajectory Sequential path
®±²®¿ ¿ ¬¥ Lame constant
®±«¥¤®¢ ²¥«¼® ¤°¥±³¥¬»© ½«¥¬¥² Sequentially addressable element ®±«¥¤®¢ ²¥«¼®¥ ®¶¥¨¢ ¨¥ Sequential estimation ®±«¥¤®¢ ²¥«¼®±²¼ ²³°¬ Sturm sequence ®±«¥¤®¢ ²¥«¼»¥ ±®¯°¿¦¥»¥ ¨§®¡° ¦¥¨¿ Successive conjugate images ®±«¥¤®¢ ²¥«¼»© «£®°¨²¬
®±²®¿ ¿ ¯® ¢¥«¨·¨¥ ±ª®°®±²¼ Constant speed (velocity)
®±²®¿ ¿ ¯°³¦¨» Spring constant
®±²®¿ ¿ ±®«¥· ¿ The solar constant
®±²®¿® ¤¥©±²¢³¾¹¨¥ ¢®§¬³¹¥¨¿ Time-varying perturbations (disturbances)
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Serial algorithm Sequential algorithm
The ever-present force of gravity : : :
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®±«¥¤³¾¹¥¥ ¢®§¢° ¹¥¨¥ ¥¬«¾ Subsequent return to the Earth ®±«¥¤³¾¹¥¥ ®¡° §®¢ ¨¥ Subsequent formation ®±«¥¤³¾¹¥¥ ±³¬¬¨°®¢ ¨¥
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Research (work) and experimental investigations (studies) are constantly in progression to nd : : :
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Ever-expanding Universe with ever-increasing entropy
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Step-by-step (trial-end-error) method Method of successive approximations
Ever-increasing ( ¯°¨¬¥°, entropy) Constant rotation
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Multiplying the rst relation by 2 followed by summation, we come to the concise form of the above equation After-image Post image
®±«¥³¤ ° ¿ ¤¥´®°¬ ¶¨¿ Post-image deformation Post-image strain
®±«®©»© °®±² Faceting growth
®±²®¿»© ¯® ¢°¥¬¥¨ Constant over time Constant in (with) time Constant ow ( ux)
®±²³¯ ²¥«¼®¥ ¤¢¨¦¥¨¥ Translation
®±²³¯«¥¨¥ ®¢»µ ª«¥²®ª Entering new cells
®±²³¯«¥¨¥ ±®«¥·®© ° ¤¨ ¶¨¨ Incoming of solar radiation
108
®²®ª ± ¡®«¼¸¨¬ ·¨±«®¬ ¥©®«¼¤± High Reynolds number ow ®²®ª ±ª «¿°®£® ¯®«¿ Flux of a (the) scalar eld ®²®ª ¯ ° Vapor ow ®²®ª ¯¥°¥¬¥®© ¯«®²®±²¨ Variable density ow at low Reynolds numbers ®²®ª ±¬¥¸¥¨¿ Mixing ux ( ow) ®²®ª ²¥¯« ¿¢»© Sensible heat ux ®²®ª®¢»© ¨²¥°´¥©± Streaming interface ®²° ¥ª²®°»© Trajectory-wise ®²°¥¡®±²¼ ¢ The increasing demand for oil ®²°¥¡®¢ ²¼±¿ It takes an hour to carry out this experiment ®µ®¦¨ These two models are alike ®µ®¦¨ ( «®£¨·») ¯® ¢¨¤³ Similar in appearance ®µ®¦¨¬ ®¡° §®¬ In much the same way ®·²¨ This light beam is nearly vertical ®·²¨ ¢® ¢±¥µ
®±»« ²¼ ±¨£ « To send out a (the) signal ®²¥¶¨ « ¤¢®©®£® ±«®¿ Double-layer potential ®²¥¶¨ « ¤¥´®°¬ ¶¨© Strain potential ®²¥¶¨ « ³° £ Murnaghan potential ®²¥¶¨ « ³«¥¢®£® ° ¤¨³± Zero-range potential ®²¥¶¨ « ³«¥¢®£® ³°®¢¿ Zero-level potential ®²¥¶¨ « ¼¾²® Newtonian potential ®²¥¶¨ « ¯®¯¥°¥·»µ ¢®« Transverse wave potential ®²¥¶¨ « ¯°®±²®£® ±«®¿ Simple-layer potential ®²¥¶¨ « ¯°®´¨«¼»µ ¢®« Longitudinal wave potential ®²¥¶¨ «¼ ¿ ±¨« Potential force Potential eld force
®²¥¶¨ «¼®¥ ¯®«¥ ±¨« Potential eld of force ®²¥¶¨ «¼»© ¯®²®ª Potential ow ( ux) ®²¥¶¨°®¢ ¨¥ Exponentiation Taking antilogarithms
®²¥°¨ ¦¨¤ª®±²¨ ¯°®¯¨²ª³ ¡®ª®¢»µ ±²¥®ª ª « Fluid loss ®²¥°¨ ¯®° ¨§¬¥°¥¨¥ Measurement of loss of pressure ®²¥°¿ A similar loss in signi cant digits : : : ®²¥°¿ ¢¥°»µ (§ · ¹¨µ) ¶¨´° Cancellation ®²¥°¿ ¨¬¯³«¼± Loss of momentum ®²¥°¿ ¥±³¹¥© ±¯®±®¡®±²¨ ¯« ±²¨» Ultimate strength of a (the) plate ®²¥°¿ ®°²®£® «¼®±²¨ Loss of orthogonality ®²¥°¿ ±ª®°®±²¨ Velocity (speed) loss ®²¥°¿ ³±²®©·¨¢®±²¨ Loss in stability Stability loss Loss of stability
®²¥°¿ ½¥°£¨¨ Energy loss Loss of energy
®²®ª ¢¥ª²®°®£® ¯®«¿ Flux of a (the) vector eld ®²®ª (¤ »µ) Thread ®²®ª ¬ £¨²®© ¨¤³ª¶¨¨ Magnetic induction ux ®²®ª ¬¥² «« Metal ow
The derivative of the function f is continuous at almost all points of the plane
®·²¨ ¢±¾¤³ X is almost everywhere dense in Y ®·²¨ ¤«¿ ¢±¥µ
The report contains detailed perfomace ratings for nearly all of the signi cant products o ered for sale in the marketplace
®·²¨ ¥¤¨¨¶ (¯®·²¨ ° ¢»© ¥¤¨¨¶¥) When x is near unity, : : : ®·²¨ «¨¥©® ¯® To increase almost linearly with ®·²¨ ¬¨¨¬ ª±¨¬ «¼®¥ ¯®«¨®¬¨ «¼®¥ ¯°¨¡«¨¦¥¨¥ Near-minimax polynomial approximation ®·²¨ ° ¢®¬¥°»© Tests of loading the material under nearly uniform stress and strain rates
®·²¨ ¯®«®±²¼¾ Almost wholly ®·²¨ ±¨¬¬¥²°¨· ¿ ±¨±²¥¬ A nearly symmetric system ®·²¨ ² ª®© ¦¥ Much the same ®·²¨ ²°¥³£®«¼ ¿ ¬ ²°¨¶ Hessenberg matrix Almost triangular matrix
®¸ £®¢ ¿ ¯°®¶¥¤³° Stepwise procedure ®½²®¬³ This (that) is why we need such a normalization constant ®¿¢«¥¨¥ ª®¢¥ª¶¨¨ The onset of convection
109
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Right-handed system Right-hand system
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Right-handed coordinate system Right-handed system of coordinates
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° ¢ ¿ ²°¥³£®«¼ ¿ ¬ ²°¨¶ Right triangular matrix ° ¢ ¿ · ±²¼ ³° ¢¥¨¿ Right-hand side of an (the) equation ° ¢¤®¯®¤®¡»© ´¨§¨·¥±ª¨ (¤¨ ¯ §®) Physically plausible (range) ° ¢¨«® ®°¥° Horner's rule ° ¢¨«® ¥ª °²
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The synchronous energy release of a pretorqued elastic bar (rod) is used to initiate the processes of loading
°¥¤¢ °¨²¥«¼® ° ±²¿³² ¿ °¬ ²³° Prior extended reinforcement
°¥¤¢¥±²¨ª (¯«¥ª -¯°¥¤¢¥±²¨ª) Precursor lm
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Rule of Descartes Cartesian rule
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Endurance limit
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°¥¤¥« ²¥ª³·¥±²¨ Yield limit Yield point
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Shear yield stress of the material Shear yield point Shear yield stress for a perfect plastic ow
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The referee indicated various corrections on the Limit probability manuscript submitted for (the) publication in the Jour- °¥¤¥«¼ ¿ ¢»±®² nal \Numerical Methods and Programming" Limiting height (altitude) ° ª²¨·¥±ª ¿ § ¤ · °¥¤¥«¼ ¿ ¤¨±±¨¯ ¶¨¿ Problem encountered in practice Limiting dissipation Practical problem °¥¤¥«¼ ¿ ¯°®·®±²¼ ° §°»¢ ° ¤²«¥¢±ª®¥ ±ª®«¼¦¥¨¥ Ultimate tensile strength Prandtl's sliding
° ¤²«¼ Prandtl ° °®¤¨²¥«¼ Progenitor (ancestor) °¥¢®±µ®¤¨²¼
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°¥¤¥«¼ ¿ ³¯°³£ ¿ ¤¥´®°¬ ¶¨¿ Ultimate elastic strain
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A device capable of converting electrical energy into mechanical energy
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Limit relation Asymptotic relation
°¥¤¸¥±²¢³¾¹ ¿ ®¡° ¡®²ª Prior processing °¥¤¸¥±²¢³¾¹¨© «¨§ The preceding analysis °¥¤»¤³¹¨© (¨§ ¤¢³µ) The former °¥¦¤¥ ¢±¥£®
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Limit process Limiting regime
°¥¤¥«¼»© ±¤¢¨£ (±«³· ©) Limiting shear (case) °¥¤¥«¼»© ±«³· © Limiting case °¥¤« £ ²¼ To suggest a plan °¥¤ § ·¥ ¤«¿ ¨±¯®«¼§®¢ ¨¿ This book is intended for use by researchers who need : : : °¥¤®¡³±«®¢«¥»© ¬¥²®¤ ±®¯°¿¦¥»µ £° ¤¨¥²®¢ Preconditioned conjugate gradient method °¥¤®¡³±«®¢«¨¢ ¨¥ Preconditioning °¥¤®¡³±«®¢«¨¢ ²¥«¼ Preconditioner °¥¤®±²®°®¦®±²¨ ¬¥°» ¢ ¬¥²®¤¥ ¼¾²® Safeguards for Newton's methods °¥¤®²¢° ²¨²¼ Prevent any strati cation from forcing : : : °¥¤¯®« £ ²¼
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°¥¦¤¥ ·¥¬ ¤®ª §»¢ ²¼ Before we prove : : : °¥¨¬³¹¥±²¢® ¢ : : : ¤ : : :
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°¥¥¡°¥£ ²¼ We ignore the work of external forces °¥®¡« ¤ ¾¹ ¿ ±²° ²¥£¨¿ Dominant strategy °¥®¡° §®¢ ¨¥ ³±± Gauss transformation °¥®¡° §®¢ ¨¥ ¨¢¥± Givens reduction Givens transformation
°¥®¡° §®¢ ¨¥ ½«¨ Cayley transform The scientists suggested that ssion of the nucleous would °¥®¡° §®¢ ¨¥ ¬ ²°¨¶ Transformation of matrices result in a tremendous outburst of energy Matrix transformation °¥¤¯®« £ ²¼±¿ ¯®±²®¿»¬ °¥®¡° §®¢ ¨¥ ¨®«» The speci c heats are considered constant Piola transform °¥¤¯®« £ ¾²±¿ ¨§¢¥±²»¬¨ °¥®¡° §®¢ ¨¥ ¯®¤®¡¨¿ These parameters are assumed to be known Similarity transformation °¥¤¯®«®¦¥¨¿ ²¥®°¥¬» Similarity transform Assumptions of Theorem 1 °¥®¡° §®¢ ¨¥ ±®±² ¢®¥ °¥¤° §°³¸¥¨¥ ¬ ²¥°¨ « Compound transformation Prefracture of a (the) material °¥®¡° §®¢ ¨¥ ³±µ®«¤¥° °¥¤±² ¢¨²¥«¼®¥ ¯°®±²° ±²¢® Householder transformation Representative space °¥®¡° §®¢ ²¼ ¢±¾ ½¥°£¨¾ ¢ ²¥¯«® °¥¤±² ¢¨²¼ ±¥¡¥ The energy is all transformed into heat Let us think of a point as an exact location in space °¥®¡° §®¢ ²¼ ²¥¯«® ¢ ° ¡®²³ °¥¤±² ¢¨²¼ ±² ²¼¾ ¤«¿ ¯³¡«¨ª ¶¨¨ I would like to submit the enclosed manuscript for (the) To transform heat into work publication in the Journal \Numerical Methods and Pro- °¥®¡° §®¢»¢ ²¼±¿ The elastic energy is transformed to the kinetic energy gramming" spent for the separation of fragments °¥¤±² ¢«¥¨¥ ¢ ¢¨¤¥ °¿¤ °¥¯°¨² Series representation °¥¤±² ¢«¥¨¥ ¬ ²°¨·®¥ Preprint of the Keldysh Institute of Applied Mathematics Representation by matrices °¥²¥°¯¥¢ ²¼ ° §°»¢ Undergo a discontinuity Matrix representation °¥¤±² ¢«¥¨¥ ²®·¥ª ¨ ¢¥ª²®°®¢ ¬ ±±¨¢ ¬¨ ª®- °¥²¥°¯¥¢ ²¼ ±ª ·®ª Undergo a jump ®°¤¨ ² Array representation °¥¶¨§¨®®±²¨ «¨§ °¥¤±² ¢«¿²¼ § ª«¾·¥¨¥ (° ±±¬®²°¥¨¥) Precision analysis To submit for conclusion (consideration) °¨ : : :, where Bx = dx and y B = y with y x = 1 °¥¤±² ¢«¿²¼ ¶¥®±²¼ For n = 2, inequality (2.2) holds with = 0 To be of value In solving the problem : : : °¥¤³¯°¥¦¤ ²¼ ®¡ ®¯ ±®±²¨ T
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111
°¨ ¡®«¼¸¥© £«³¡¨¥ At greater depth °¨ ¡®«¼¸¨µ § ·¥¨¿µ P At larger P °¨ ¡®«¼¸¨µ (¬ «»µ) t For (at, with) large (small) t °¨ ¡®«¼¸¨µ (¬ «»µ) ·¨±« µ ¥©®«¼¤± At high (low) Reynolds numbers °¨ ¡»±²°®¬ ¤¢¨¦¥¨¨ When in rapid motion, electrons can produce energy °¨ ¢¥°¸¨¥ r
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The sign of the normal force at a bilateral constraint can (may) change
°¨ ±²³¯«¥¨¨ ¯« ±²¨·®±²¨ At the onset of plasticity To measure the required angle at the vertex A, we must °¨ ±»¹¥¨¨ At saturation nd the angular distance between Venus and the Sun °¨ ²¿¦¥¨¨ °¨ ¢µ®¤¥ ¢ ²¬®±´¥°³ Under tension On entering the atmosphere °¨ ¨§ª¨µ · ±²®² µ °¨ ¢»¢®¤¥ At low frequencies In deriving equation (1) we have used the fact that : : : °¨ ³«¥¢®¬ ¢¥ª²®°¥ °¨ ¢»±®ª¨µ · ±²®² µ This function is positive except at the zero vector At high frequencies °¨ ®¡¦ ²¨¨ °¨ ¢»·¨±«¥¨¨ In the calculation of the number of holes : : :
°¨ ¢»·¨±«¥¨¨ ¨²¥£° «®¢ When evaluating (the) integrals °¨ ¤ «¼¥©¸¥¬ ¤¢¨¦¥¨¨ On further motion °¨ ¤ «¼¥©¸¥¬ ³¢¥«¨·¥¨¨ " With further increase in " °¨ ¤¢¨¦¥¨¨
Under compression At compression
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°¨ ®²®¡° ¦¥¨¨ The image of the set X under the mapping M °¨ ®²° ¦¥¨¨ Flow structure in motion of a spherical drop in a uid Under re ection °¨ ¯ ¤¥¨¨ (®°¬ «¼®¬) medium At normal incidence The dynamics of bubbles in motion in liquids In any inertial frame, the velocity of light depends on °¨ ¯¥°¥µ®¤¥
whether the light is emitted by a body at rest or by a When passing from the plane problem of perfect plasticity to a \similar" spatial one, we obtain : : : body in motion The ability to change direction quickly while the body is In passing from (1) to (2) we have ignored the fact that : : : The free energy change from the liquid to the gaseous state in motion The optokinetic re ex stabilizes the eye when the body is °¨ ¯¥°¥µ®¤¥ ª In passing to Lagrangian form, we should scale this eld in motion This is a device that provides reactive force when in mo- °¨ ¯®¢®°®²¥ When rotated about its sensitivity axis, the sensor protion relative to the surrounding air vides a linear vibration in capacitance °¨ ¤¥´®°¬ ¶¨¿µ °¨ ¯®¤¤¥°¦ª¥ At strain(s) (deformation(s)) The work was (partially) supported by the Russian FounUnder strain(s) (deformation(s)) dation for Basic Research °¨ ¤®ª § ²¥«¼±²¢¥ The estimate we obtained in the course of proof seems to °¨ ¯®«³·¥¨¨ In obtaining the resolving equation, we should avoid some be of independent interest additional diculties In proving Theorem 1, we showed rst that : : : Theorem 1 was used when deriving the above equation °¨ ¨§£¨¡¥ Under bending °¨ ¯®¬®¹¨ By igniting the mixture : : : °¨ ¨±¯®«¼§®¢ ¨¨ In (when) using this formula, we should keep in mind By applying this method : : : °¨ ¯®¯¥°¥·®¬ ¨§£¨¡¥ that : : : Under lateral bending °¨ ª®¥·®© ¬¯«¨²³¤¥ Secondary ows appearing at a nite amplitude of an ini- Under transverse bending °¨ ¯®±²®¿®¬ ¤ ¢«¥¨¨ tial perturbation : : : At constant pressure °¨ ª®¥·»µ ¤¥´®°¬ ¶¨¿µ °¨ ¯°¥¤¯®«®¦¥¨¿µ At (under) nite strains Under the same hypotheses (assumptions), : : : At (under) nite strain At (under) nite deformations °¨ ¯°¥®¡° §®¢ ¨¿µ ¯®¤®¡¨¿ Under similarity transformations At (under) nite deformation
°¨ «¨¥©®© ¯¯°®ª±¨¬ ¶¨¨ ¯® µ In the linear approximation in x
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112
Let us consider the behavior of the ow at xed a when accelerate your car This function retains its properties at the approach to the the initial values are varied above critical point °¨ ´¨ª±¨°®¢ ®¬ ®¡º¥¬¥ The body of this shape has a minimal surface at a xed °¨ ¯°¨¬¥¥¨¨ volume (or a minimal volume at a xed surface area) Being applied in chemistry, this method : : : °¨¡ ¢«¿²¼ ª °¨ ¯°®¨§¢®«¼®¬ 6= 0 In order to obtain the above expansion, we added x to For (at, with) arbitrary 6= 0 both sides of expression (1) °¨ ¯°®²¨¢®±²®¿¨¨ (¯« ¥²) °¨¡«¨¦¥¨¥ At opposition Iterations of this form converge to the solution for an ar°¨ ¯°®µ®¦¤¥¨¨ ·¥°¥§ ²®·ª³ bitrary initial guess To change sign on passing through this point
°¨¡«¨¦¥¨¥ ¤¨ ¡ ²¨·¥±ª®¥ Adiabatic approximation °¨¡«¨¦¥¨¥ ¢ ¥¯°¥°»¢®¬ ¢°¥¬¥¨ °¨ ° §°³¸¥¨¨ Continuous time approximation At fracture °¨¡«¨¦¥¨¥ ¤® °¨ ° ±±¬®²°¥¨¨ In (when) considering the capabilities of computers, it is To compute an approximation (up) to (1 ") °¨¡«¨¦¥¨¥ ± ¢¥±®¬ necessary to emphasize : : : Weighted approximation °¨ ° ±²¿¦¥¨¨ ¨ ±¦ ²¨¨ °¨¡«¨¦¥¨¥ ±¬ §ª¨ Under tension and compression Lubrication approximation °¨ ±¤¢¨£ µ °¨¡«¨¦¥¨¥ ²®«±²®£® ²¥« This transformation is invariant under shifts Thick-body approximation °¨ ±«³· ¥ °¨¡«¨¦¥¨¥ ²®ª®£® ²¥« On occasion Slender-body approximation °¨ ±¬¥¥ ¡«¾¤ ²¥«¿ °¨¡«¨¦¥¨¥ ²®ª®£® ²¥¯«®¢®£® ¯®£° ¨·®£® Under a change of a observer ±«®¿ °¨ ±²¥¯¥¿µ The thin thermal boundary-layer approximation Equating the coecients at the powers of x enables us to °¨¡«¨§¨²¥«¼® obtain the above-written solution There were about ve hundred people there °¨ ±²®«ª®¢¥¨¨ °¨¡«¨§¨²¥«¼® ° ¢¥ The probability of adsorption at collision of the particle N is about kn with the completely free surface is equal to 1=2 °¨¢¥¤¥¨¥ °¨ ²¥¬¯¥° ²³° µ ±¢»¸¥ : : : °¨ ¯°®·¨µ ° ¢»µ ³±«®¢¨¿µ Other conditions being equal
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The process of bringing a fractional number to lower terms This process may have originated at temperatures is called reducing a fraction above 85 C °¨¢¥¤¥¨¥ (¤°®¡¨) ª ¯°®±²¥©¸¥¬³ ¢¨¤³ °¨ ²¥¬¯¥° ²³°¥ Reduction to lowest terms At room temperature, at high temperatures °¨¢¥¤¥¨¥ ª ¡±³°¤³ °¨ ²¥¬¯¥° ²³°¥ ¢ 100 Reductio ad absurdum At 100 centigrade °¨¢¥¤¥¨¥ ª ®°¬ «¼®© ´®°¬¥ °¨ ³¢¥«¨·¥¨¨ Reduction to normal form The work involved in pivoting is proportional to p2 and, °¨¢¥¤¥¨¥ ª ®¡¹¥¬³ § ¬¥ ²¥«¾ consequently, becomes insigni cant as p increases Reduction to (a) common denominator
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°¨¢¥¤¥¨¥ ¬ ²°¨¶» ª ¨¦¥²°¥³£®«¼®¬³ ¢¨¤³ Lower triangularization °¨¢¥¤¥¨¥ ¬ ²°¨¶» ª ²°¥³£®«¼®¬³ ¢¨¤³ Matrix triangularization Triangularization Triangular reduction
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°¨¢¥¤¥¨¥ ¬ ²°¨¶» ª ²°¥µ¤¨ £® «¼®¬³ ¢¨¤³ °¨¤ ¢ ²¼ ° ª¥²¥ · «¼³¾ ±ª®°®±²¼ To impart initial speed to a (the) rocket Matrix tridiagonalization Tridiagonalization °¨¤¥°¦¨¢ ²¼±¿ ¬¥¨¿ To be of the opinion Tridiagonal reduction °¨¥¬ °¨¢¥¤¥¨¥ ¯® ¬®¤³«¾ p Trick Reduction mod p °¨¥¬«¥¬»© °¨¢¥¤¥¨¥ ¯®¤®¡»µ ·«¥®¢ Reduction of similar terms Acceptable, reasonable °¨§ ª ±¡°®± °¨¢¥¤¥ ¿ ¤¨ ¬¨·¥±ª ¿ ®¸¨¡ª Escape bit Reduced dynamic error °¨§ ª ±µ®¤¨¬®±²¨ ®¸¨ °¨¢¥¤¥ ¿ ¬ ²°¨¶ Cauchy's test for convergence Reduced matrix °¨§ ¨¥ °¨¢¥¤¥ ¿ ¯«®²®±²¼ Acceptance of a new theory Reduced density °¨¢¥¤¥ ¿ ±¨« ²¿¦¥±²¨ °¨ª¨¤ª Rough estimate Speci c gravity force °¨ª«¥¨²¼ °¨¢¥¤¥®¥ ¯¥°¥¬¥¹¥¨¥ Attach Reduced displacement °¨ª°¥¯«¥ ª °¨¢¥¤¥»© ¨¦¥ The above phenomena is illustrated by this and all exam- : : : are rigidly attached to the frame °¨« £ ¥¬®¥ ³±¨«¨¥ ples to follow Imposed stress °¨¢¥¤¥»© ³°®¢¥¼ Datum level °¨« £ ²¼ ¢±¥ ³±¨«¨¿ To exert every e ort °¨¢«¥ª ²¥«¼»© ¢¨§³ «¼® °¨«¨¢ ¿ ±¨« Visually pleasing Tidal force °¨¢«¥ª ²¼ ¢¨¬ ¨¥ The author wishes to express his gratitude to : : : for draw- °¨«®¦¥®¥ ¯¥°¥¬¥¹¥¨¥ Applied displacement ing the author's attention to : : : °¨«®¦¥»© ¨§¢¥, ¢¥¸¨© °¨¢®¤ Impressed Actuator °¨¬¥¥»© °¨¢®¤ ®² ®±¥¢®£® ª®¬¯°¥±±®° This new form of equations as applied to (for) natural Axial-compressor drive systems can be considered as : : : °¨¢®¤ ®² ¶¥²°®¡¥¦»µ ª®¬¯°¥±±®°®¢ °¨¬¥¨¢ Centrifugal compressor drive Having applied this method, we : : : °¨¢®¤¨²¼ ¢ ¤¢¨¦¥¨¥ °¨¬¥¨¬»© ª To set in motion This theory is directly applicable to engineering problems °¨¢®¤¨²¼ ¢ ¤¥©±²¢¨¥ °¨¬¥¨²¼ ª To bring into action (operation) To use the minimax theorem on the matrix B to obtain °¨¢®¤¨²¼ ¢ ¨±¯®«¥¨¥ an expression for : : : To bring (call, carry, put) into e ect °¨¬¥¿¥¬»© ¤«¿ °¨¢®¤¨²¼ ¢ ¯®°¿¤®ª The method being applied for : : : To put (set) in order °¨¬¥°® °¨¢®¤¨²¼ ¢ ±®¢°¥¬¥®¥ ±®±²®¿¨¥ p ² ª ¦¥ ¯°¨¡«¨¦ ¥²±¿ ª : : : ª ª Since 20 is about as near to 4 as to 5 , : : : To bring up to date °¨¬¥±¨ ¯ ±±¨¢»¥ °¨¢®¤¨²¼ ¢ ±®±²®¿¨¥ ¢®§¡³¦¤¥¨¿ Passive impurities The system is brought into the exited state °¨¬¥±»© ½«¥ª²°®«¨² °¨¢®¤¨²¼ ª Fission of the nucleous would result in a tremendous out- Foreign electrolyte °¨¬»ª ¾¹¨© burst of energy : : : is close to °¨¢®¤¨²¼ ª ¯°®²¨¢®°¥·¨¾ °¨£±µ ©¬ To lead to a contradiction Pringsheim °¨¢®¤¨²¼ ¬ ²°¨¶³ ª ¢¨¤³ This subroutine reduces a general rectangular matrix to °¨£±µ¥©¬ (¡¥§ °²¨ª«¿) real bidiagonal form (to upper Hessenberg Pringsheim °¨¨¬ ²¼ form) by an orthogonal transformation This subroutine computes the Cholesky factorization of a We adopt the convention that 0 1 = 0 °¨¨¬ ²¼ ¢® ¢¨¬ ¨¥ symmetric positive de nite band (banded) matrix To take account of this special characteristic °¨£° ¨·»¥ ³§«» ±¥²ª¨ °¨¨¬ ²¼ ¢¥°³ Near-boundary mesh nodes To take for granted °¨¤ ¢ ²¼ ®±®¡®¥ § ·¥¨¥ Great emphasis is placed on the development of high en- °¨³¦¤¥¨¥ ¢®«®¢®¥ (²¥¯«®¢®¥) 2
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Transition from wave forcing to thermal forcing
114
°¨±®¥¤¨¥»© ¢¥ª²®° Associated vector °¨±®¥¤¨¨²¼, ¯°¨ª°¥¯¨²¼ Attach to °¨¶¨¯ ¢¨°²³ «¼»µ ¯¥°¥¬¥¹¥¨© The principle of virtual work, or in terms of the nite °¨±²³¯¨²¼ ª We are now in a position to prove : : : element method, the principle of virtual displacements °¨±³²±²¢³¾¹¨© °¨¶¨¯ ¢®§¬®¦®© ° ¡®²» The atomic number tells the number of proton present Virtual work principle °¨±³¹¨© Principle of virtual work The uncertainty inherent to the local methods is elimi°¨¶¨¯ ¢®§¬®¦»µ ¯¥°¥¬¥¹¥¨© nated Virtual work principle °¨²®ª ²¥¯« Principle of virtual work °¨¶¨¯ ¢¨°²³ «¼®© ° ¡®²» Virtual work principle Principle of virtual work
Heat in ow Heat ux from the ocean to the atmosphere
Principle of virtual displacements Virtual displacement principle
°¨²¿£¨¢ ¾¹¨© ¶¥²° Attracting center °¨²¿¦ ²¥«¼»© ¯ ¤¥¦ (the genitive or possessive case). °¨¬¥°» ¯°¥¤«®¦¥¨©
°¨¶¨¯ ¨¬¥¼¸¥© ° ¡®²» Principle of least work
°¨¶¨¯ ¥¢¿§ª¨ Residual principle
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The coordinates of the molecules' position are bounded by the nite size of the container Each element of A is compared with the corresponding element of the other process's matrices This program allows the experienced user to take advantage of his system's actual layout The problem of life's beginning has been considered for at least several millennia This rm's leadership is well known : : : The essentials of the system's operation in response to stress are as follows The canyon forms 5 percent of the satellite's surface When the company's daily production of 200 units is considered, : : : The satellite's atmosphere is 90 percent methane The early atmosphere's complete dissimilarity from that of today : : : The importance of research to the country's economy : : : Most of the substance's actions in animal cells remain to be explored The train's arrival The plan's importance The ship's funnel The paragraph's meaning The volcano's eruption The report's conclusion The university's president The book's author That car's door
Constraint release mechanism
°¨¶¨¯ ¯¥°¬ ¥²®±²¨ Principle of permanence Principle of permanency
°¨¶¨¯ \° §¤¥«¿© ¨ ¢« ±²¢³©" Divide-and-conquer principle
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It is customary to represent vectors graphically
°¨¿²»© ¢ ±²®¿¹¥¥ ¢°¥¬¿ Currently accepted
°¨¿²¼ ¡¥§ ¤®ª § ²¥«¼±²¢ (§ ª±¨®¬³) To take for granted
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The addition is taken as a basic operation
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Thank you very mach for accepting my paper for (the) publication in the Journal \Numerical Methods and Programming"
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To acquire (gain) knowledge Atoms become ions when they gain or lose electrons
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Both mediums acquire the same velocity
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Near-axial recirculation zones
°¨° ¢¨¢ ¨¥ ª®½´´¨¶¨¥²®¢ ¯°¨ ®¤¨ ª®¢»µ ±²¥¯¥¿µ To equate the coecients of like powers
°¨°®¤»¥ ¯« ±²» Natural rocks
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This variable is assigned a value that is never used
°¨±®¥¤¨¥¨¥ ¯®²®ª Flow attachment
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: : :, then we come to the Fredholm integral equation of the second kind : : :
Adjunction of elements
°¨±®¥¤¨¥ ¿ ¬ ±± Added mass
°¨±®¥¤¨¥ ¿ ³¤ ° ¿ ¢®« Attached shock wave
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The folowing conclusions are reached
°¨µ®¤¨²¼ ª § ª«¾·¥¨¾ To arrive at (to come to) a (the) conclusion °¨µ®¤¨²¼ ª ¡®«¥¥ ²®·®¬³ ®¯°¥¤¥«¥¨¾
To arrive at this more precise de nition, it is necessary to introduce the concept of limits
Adsorbed atom
115
°¨µ®¤¨²¼ ª ¯°®²¨¢®°¥·¨¾ To arrive at a contradiction
°¨·¨ ¨ ±«¥¤±²¢¨¥ Cause and consequence
°®¤®«¦ ²¼ § The function f is continued beyond the domain D °®¤®«¦¥¨¥
Bisectors of vertical angles are continuations one of the other
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°®¤®«¦¥¨¥ ¨§®¬®°´¨§¬ Extension of isomorphism °¨·¨ ¨§¬¥¥¨¿ Cause (® ¥ reason for) of a change in the distribution °®¤®«¦¥¨¥ ¥«¨¥©®£® °¥¸¥¨¿ Continuation of the nonlinear solution of precipitation °®¤®«¦¥¨¥ ®²®¡° ¦¥¨¿ (¤®) °¨·¨¨²¼ ¢°¥¤ To reach (arrive at) an agreement
Extension of the map(ping) M on : : : Extension of the map(ping) M by the identity to : : :
The explosion gases may harm the personnel
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°®¤®«¦¥¨¥ ¯® ·¨±«³ ¥©®«¼¤± Continuation in the Reynolds number °®¤®«¦¨²¥«¼®¥ ¢°¥¬¿ °®¡¨¢ ¨¥ This satellite will not circulate for long The probability of vehicle skin penetration by meteorites °®¤®«¦¨²¥«¼®±²¼ ª®«¥¡ ¨¿ Perforation Duration (period) of oscillation °®¡®© ¯°¿¦¥¨¿ °®¤®«¦¨²¥«¼®±²¼ ®¡¹ ¿ Voltage breakdown : : : to measure the total time of the above process °®¡±²¨ °®¤®«¦¨²¥«¼®±²¼ ¯°®²¥ª ¨¿ ¯¥°¥µ®¤®£® Probstien ª®«¥¡ ²¥«¼®£® ¯°®¶¥±± °®¡» ¢®§¤³µ Time response to oscillation (vibration) Samples of air °®¤®«¦¨²¼ «¨¨¾ (®²°¥§®ª) °®¢¥°¿²¼ To extend the (a) line (segment) It is easily veri ed that : : : °®¤®«¦¨²¼ °®¢®¤¨¬®±²¼ ª « : : :, where x runs over a nite set of closed intervals The variable x ranges over [a; b]
To extend the function f (the map M ) to the set X (to the map M1 )
Channel conductance
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°®¤®«¦¨²¼ ¯°®¶¥±± Continuing the process inde nitely is rather dicult °®¢®¤¨¬®±²¼ ²®ª ³²¥·ª¨ °®¤®«¦¨²¼ ± ®²°¥§ª Leakage current conductance To continue the solution from the segment [a; b] to : : : Leakage current conduction °®¤®«¦¨²¼ ·¥°¥§ °®¢®¤¨²¼ ®¯»² To continue the function f across the arc A To carry out (conduct, make, perform, run) an experiment °®¤®«¼ ¿ ¤¨±¯¥°±¨¿ °®¢®¤¨²¼ ° §«¨·¨¥ Longitudinal dispersion To draw a distinction °®¤®«¼ ¿ ¦¥±²ª®±²¼ °®¢®¤¨²¼ ° ±·¥² Longitudinal sti ness Single-channel conductance
To perform computation at billions of oating-point op- Longitudinal rigidity erations per second (giga ops) Extension sti ness To perform computation on data that has been encoded Extension rigidity and shared among several processes °®¤®«¼ ¿ ±ª®°®±²¼ ¢®«» °®¢®¤¨²¼ ½ª±¯¥°¨¬¥²» Longitudinal wave velocity To perform experiments on an (the) algorithm °®¤®«¼®¥ ¯¥°¥¬¥¹¥¨¥ To conduct experiments on laboratory models Longitudinal displacement To carry out experiments on a wide range of algorithms In-plane displacement °®£¨¡ ®°¬ «¼»© Longitudinal movement Normal de ection In-plane movement
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°®£° ¬¬ ª³°±®¢ «¥ª¶¨© Curriculum of lecture courses
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°®¤®«¼®¥ ° ±²¿¦¥¨¥ Longitudinal extension In-plane extension
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Longitudinal displacement In-plane displacement
Program threads
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°®¤®«¼»© ª®½´´¨¶¨¥² Longitudinal coecient °®¤®«£®¢ ²»© ½««¨¯±®¨¤ °®¤®«¼»© ° §¬¥° Prolate ellipsoid Longitudinal size Oblong ellipsoid °®¤³ª²» ¤¥²® ¶¨¨ °®¤®«¦ ²¼ ¤ «¼¸¥ (¯®±²³¯ ²¼, ±®¢¥°¸ ²¼, Products of detonation °®¥ª²¨°®¢ ¨¥ ª®±²°³ª¶¨© ¤¥©±²¢®¢ ²¼) The advance of science
Structural design
To proceed further
116
°®¥ª²¨°®¢ ¨¥ ²¥µ¨·¥±ª®¥ Project engineering °®¥ª²¨°®¢ ¨¥ ½±ª¨§®¥ Preliminary design °®¥ª²¨°®¢ ²¼ ¯®¤¯°®±²° ±²¢¥ To project on(to) this subspace °®¨§¢¥¤¥¨¥
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°®¨§¢¥¤¥¨¥ ±ª «¿° ¢¥ª²®° Product of a scalar and a vector °®¨§¢®¤ ¿ ¢»±¸¥£® ¯®°¿¤ª Derivative of higher order °®¨§¢®¤ ¿ ¥¿¢®© ´³ª¶¨¨ Derivative of an (the) implicit function °®¨§¢®¤ ¿ ®¡° ²®© ´³ª¶¨¨ Derivative of an (the) inverse function °®¨§¢®¤ ¿ ¯® µ
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Arrival of meteorites in the atmosphere
°®¨ª³²¼ ¢ ±³¹®±²¼ ·¥£®-«¨¡® To gain an insight into
°®¨¶ ¥¬®±²¼ ¢ ª³³¬ Permeability of vacuum
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Kinetic energy is the product of mass by velocity squared, Dielectric constant whereas momentum (known as quantity of movement °®¨¶ ¥¬®±²¼ ¬ £¨² ¿ (motion)) is the product of mass by speed (velocity) Permittivity Saturation rate
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The minimally possible mass decreases in proportion to the third power of x with increase in the kinetic energy The energy of the particle is proportional to the square of the velocity at collision
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Segments of lengths a, b, c, and d are said to be proporThe x-derivative («³·¸¥, ·¥¬ the derivative with respect tional if a is to b as c is to d to x) °®¯®°¶¨® «¼»¥ · ±²¨ °®¨§¢®¤ ¿ ¯® ¢¥¸¥© (¢³²°¥¥©) ®°¬ «¨ Proportional parts These boundary conditions specify the outward(inward)- °®¯®°¶¨¿ ¢¥¸¿¿ pointing derivative along the entire boundary External ratio °®¨§¢®¤ ¿ ¯® ¤«¨¥ ¤³£¨ °®¯³±ª ¿ ±¯®±®¡®±²¼ (²° ±¯®°² ) Derivative with respect to arc length Trac capacity Derivative along : : : Derivative in the direction : : : Directional derivative
Time decimation
°®°¥¦¨¢ ¨¥ ¯® · ±²®²¥ Frequency decimation
°®¨§¢®¤ ¿ ¯® ¯°®±²° ±²¢¥®© ª®®°¤¨ ²¥
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Spatial derivative Space derivative
Sliding
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°®¨§¢®¤ ¿ ¯® ¯°®±²° ±²¢³ Spatial derivative Space derivative
Slip coecient
°®¨§¢®¤ ¿ ¯®°¿¤ª n The nth derivative °®¨§¢®¤±²¢® ½²°®¯¨¨ Production of the entropy °®¨§¢®¤¿¹ ¿ ´³ª¶¨¿ ( ¯°¨¬¥°, ¤«¿ ¬®£®·«¥®¢ ¥¦ ¤° ) Generating function °®¨±µ®¤¨²¼ Wide temperature changes occur in the atmosphere °®¨±µ®¤¨²¼ ± : : : is happening to the individual components °®«¥² ª°»« Span of a wing °®¬ µ ° ±±²®¿¨¥ Miss-distance °®¬ µ³²¼±¿ ¬¨¬® ¶¥«¨ ¥ª®²®°®¥ ° ±±²®¿¨¥ To miss the target by a certain distance °®¬¥¦³²®·®¥ ¯°®£° ¬¬®¥ ®¡¥±¯¥·¥¨¥ Middleware °®¬»¢ª ±»¯³·¨µ ¬ ²¥°¨ «®¢ Washing of loose materials °®¨ª ¾¹ ¿ ±¯®±®¡®±²¼ Penetrating power °®¨ª ¾¹¨© ± °¿¤
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If energy changes are followed backward in the past, it becomes apparent that : : :
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A nonderogatory matrix has the following property: each eigenvalue has unit geometric multiplicity
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While this operation is merely a notational change, : : :
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Idle waiting
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Penetrating shell
117
This solution can be represented as a Fourier series in the spatial coordinate
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Spatial derivative Space derivative
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Three-dimensional coordinate system Spatial (space) coordinate system
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Antiparallel lines
Spatial point
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Space-distributed
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Three-dimensional (spatial) uid motion ( ow)
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Upwind di erence scheme Upwind scheme
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Spatial (three-dimensional, 3D{) problem
Spatial instability Spatial frequency Space-invariant Space-periodic
Spatial stress state Spatial state
Three-dimensional (spatial, 3) ow
Spatial variable (coordinate) Space interval
°®±²° ±²¢¥»© ¨§£¨¡ Spatial bending
Flow reactor
An extended reverse ow zone is formed The extent of the atmosphere Interface pro le Edge pro le
Wing pro le
Shell pro le
Distribution pro le
Flow velocity pro le
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: : : the only known planets that travel closer to the Sun than the Earth does
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Spatial operator
Spatial tensor
Intrapore space (area)
°®±²° ±²¢® ¢®§¬³¹¥¨© Disturbance space Perturbation space
Sink working
Line (plane) passing through the origin Procedure for solving
About 40 percent (® ¥ percents) of the energy is dissipated
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Strain space
Representative space
Design space
Free parameter space
Process proceeds
The process of crack evolution Age-dependent process
Memory-to-memory processor
°®±²° ±²¢® ´³ª¶¨© ®£° ¨·¥®© ¢ °¨ ¶¨¨ °®¶¥±±®° ²¨¯ \°¥£¨±²°-°¥£¨±²°" The space of bounded variation functions
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Register-to-register processor
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118
±¥¢¤®±ª®°®±²¼ Pseudovelocity ³ §¥©«¼ °®·®±² ¿ ±®±² ¢«¿¾¹ ¿ Poiseuille Solid-state component ³ ª °¥ °®·®±²¼ £®°»µ ¯®°®¤ Poincare Rock strength ³ ±® °®·®±²¼ £°³² ±°¥§ Poinsot Shear strength of (a) soil ³ ±±® Soil shear strength Poisson °®·®±²¼ ¬ ²¥°¨ « ³¡«¨ª ¶¨¿ £«¨©±ª®¬ ¿§»ª¥ Strength of a material English-language publication °®·®±²¼ ¨§«®¬ ³«¼± ¶¨¿ ¯³§»°¿ Fracture strength Bubble pulsation °®·®±²¼ ° §°»¢ (²¥« ) ³«¼±¨°³¾¹¥¥ ¤¢¨¦¥¨¥ ¦¨¤ª®±²¨ Tensile strength Pulsating
ow of a liquid ( uid) °®·®±²¼ ±¦ ²¨¥ ³±²¼ ¤ (±«¥¤³¾¹ ¿) ¬ ²°¨¶ : : : Compressive strength Suppose we are given the following matrix : : : °®·®±²¼ ¯« ±²¨ª ³²¥¢ ¿ ±ª®°®±²¼ Durability (strength) of a plastics Ground speed °®·»© ¬ ²¥°¨ « ³²¥¸¥±²¢®¢ ²¼ ¯® ±²° ¥ Durable material To travel about the country °®¹¥«ª¨¢ ¨¥ ³²¨ ¯° ¢¨«¼®¬ (¥¯° ¢¨«¼®¬) µ®¤¨²¼±¿ Snap-through To be on the right (wrong) line °®¿¢«¿²¼ (¯®ª §»¢ ²¼) ³²¼ ¤¥´®°¬¨°®¢ ¨¿ To exhibit an increase of (in) resistance Strain path °³² °¬ ²³°» ¦¥«¥§®¡¥²® ³·®ª ¢®«®±ª®¢ Rebar Hair bundle Reinforcement bar ³·®ª ¢®«®±ª®¢»µ ª«¥²®ª °¿¬ ¿ Hair-cell bundle Straight line ³·®ª «³·¥© °¿¬® ¯°®²¨¢®¯®«®¦» Pencil of rays The actions of two bodies on each other are equal and ³·®ª ±²¥°¥®¶¨«¨© directly opposite Stereocilia bundle °¿¬®¥ ¡«¾¤¥¨¥ ³·®ª · ±²¨¶ Direct observation Beam of particles °¿¬®¥ ²¥·¥¨¥ ´ ´´ Forward ow Pfa °¿¬®© «¨§ ®¸¨¡®ª ´³¤ Forward error analysis Pfund °¿¬®© ª°³£®¢®© ª®³± ¼¥§®¤ ²·¨ª Right circular cone Piezotransducer °¿¬®© ±²¥°¦¥¼ ¼¥§®¬¥²°¨·¥±ª®¥ ¤ ¢«¥¨¥ Rectilinear rod Piezometric pressure °¿¬®© (®¡° ²»©) ¨¦¨¨°¨£ ½¦¨ Forward (reverse) engineering Perzyna °¿¬®«¨¥© ¿ ®±¼ ½«¨ Rectilinear axis Paley °¿¬®«¨¥©®¥ £ °¬®¨·¥±ª®¥ ¤¢¨¦¥¨¥ ¾¨§¥ Simple harmonic motion Puiseux °¿¬®«¨¥©®¥ ¤¢¨¦¥¨¥ ¿²¨±«®©»© Straight-line motion Five-layer °¿¬®³£®«¼»© ° ¢®¡¥¤°¥»© ²°¥³£®«¼¨ª ¿²¨²®·¥·»© ¸ ¡«® °®·®±² ¿ ¥®¤®°®¤®±²¼ Strength inhomogeneity
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119
¢®¬¥°®¥ ¢° ¹¥¨¥ Steady (uniform, permanent) rotation ¢®¬¥°®¥ ¤ ¢«¥¨¥ (° ±¯°®±²° ¥¨¥) Uniform pressure (propagation) ¢®¬¥°®¥ ª°³£®¢®¥ ¤¢¨¦¥¨¥ Uniform circular motion Pressure work ¢®¬¥°®¥ ¯°¿¬®«¨¥©®¥ ¤¢¨¦¥¨¥ Work done by pressure (forces) Uniform rectilinear motion ¡®² ²°¥¨¿ Friction work ¢®¬¥°®¥ ° §¬¥¹¥¨¥ Uniform allocation Work lost in friction ¢®®²±²®¿¹¨¥ ²®·ª¨ ¡®² ²¼ The receiver is performing (performs) according to its Equally spaced (grid) points speci cations ¢®±²®°®¿¿ ª®´¨£³° ¶¨¿ Equilateral con guration ¡®² ²¼ ¤¢ · ± To work for two hours ¢®¶¥»© Of equal value ¡®² ²¼ To work at a laboratory ¢®½« ±²¨·®±²¼ ¡®² ²¼ ¤ ª¨£®© Isoelasticity To work on the book ¢»¥ ³«¾ The (a) vector with all entries zero except (for) the kth ¡®²» ¯® (° ¡®²», ¯®±¢¿¹¥»¥ : : :) Computers are being used a great deal in works on guided which is one (with the last k entries zero) missiles ¢»¥ ±²®°®» ²°¥³£®«¼¨ª ¡®· ¿ ¯ ¬¿²¼ Congruent sides of a (the) triangle Scratch storage ¤ ° ¤ «¼¥£® ®¡ °³¦¥¨¿ Early warning radar ¡®· ¿ · ±²¼ ®¡° §¶ ¤¨ «¼ ¿ ¤¥´®°¬ ¶¨¿ Gauge length of the (a) specimen ¡®·¥¥ ¤ ¢«¥¨¥ Radial strain Actuating pressure Radial deformation ¤¨ «¼ ¿ ¨¥°¶¨¿ ¡®·¨¥ µ ° ª²¥°¨±²¨ª¨ ¯°®£° ¬¬ Radial inertia To evaluate the performance of programs ¤¨ «¼ ¿ · ±²®² ¡®·¨© ¬ ±±¨¢ Work (working, scratch) array Radial frequency ¡®·¨© ¯°¨¥¬¨ª (¢ § ¤ · µ ¢¨£ ¶¨¨) ¤¨ «¼®¥ ¯°¿¦¥¨¥ (¯¥°¥¬¥¹¥¨¥) Radial stress (displacement) Rover receiver ¤¨ «¼»© ®²°¥§®ª ¡®·¨© ¶¨«¨¤° Radial segment Actuating cylinder ¤¨ ¶¨®®¥ ®µ« ¦¤¥¨¥ ¢¥ ³«¾ Degree of stability equal (to) zero Radioactive cooling ¢¥±²¢® ¢¥ª²®°®¢ ¤¨³± ª°¨¢¨§» Curvature radius Equality of vectors ¤¨³± ¯®¢¥°µ®±²¨ ²¥ª³·¥±²¨ ¢®¢¥«¨ª¨© Of equal size Yield surface radius ¢®¢¥°®¿²®¥ ° §¬¥¹¥¨¥ ¤¨³± ° ¤¨ ¶¨®»© Equiprobable allocation Radiation radius ¤® ¢®¢¥°®¿²»© Radon Of the same probability § ¢®¢¥±¨¥ ¯®§» Postural equilibrium We may now integrate this function k times to conclude that ¢®¢¥±¨¿ (¬®¦¥±²¢¥®¥ ·¨±«® ¨¬¥¥²±¿) § ¨ ¢±¥£¤ Equilibria ¢®¢¥± ¿ ®°¨¥² ¶¨¿ Once and for all Equilibrium orientation ° § ¨§ ¤¥±¿²¨ ¢®¬¥° ¿ ¯¯°®ª±¨¬ ¶¨¿ : : : nine times out of ten Uniform approximation §¡¨¥¨¥ A piecewise polynomial de ned on this partition is a poly ¢®¬¥° ¿ ±¥²ª Equally (uniformly) spaced grid nomial of low degree on each element For a uniform quid, the error in making these approxima- §¡¨¥¨¥ ¬ ²°¨¶» tions is : : : There are two conventional ways to construct partitioned matrices: a row partition and a column partition ¢®¬¥°® ¥®¤®°®¤ ¿ ¯®¢¥°µ®±²¼ Partitioning a matrix in rows and columns Evenly nonuniform surface We partition the product C = AB into blocks (into sub ¢®¬¥°® ¯® ¸¨°¨¥ ¡®² ¯® ¯°¥®¤®«¥¨¾ The work against ( ¯°¨¬¥°, external pressure) ¡®² ¯® ®²°»¢³ The work for separation ¡®² ±¨« ¤ ¢«¥¨¿
matrices)
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The (a) Taylor (Laurent) series expansion in powers of x A box 1 cm1 cm1 cm in size The (a) power series expansion of a function in x §¬¥±²¨²¼ An (the) expansion in series of this function in powers of x An important task is to place radio transmitters in di erExpansion of f in a series in x ent areas of the Moon §«®¦¥¨¥ ¢ °¿¤ ¥©«®° ¯® x ¢ ²®·ª¥ µ = a §¬¥²ª ²¥ª±² A (the) Taylor series expansion of f (x) in x about x = a Text markup Velocity expansion up to zeroth order Temperature expansion to order Re
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The expansion in a power series of perturbations that are Upwind di erence scheme multiples to n 1 §®±²¼ °¨´¬¥²¨·¥±ª®© ¯°®£°¥±±¨¨ §«®¦¥¨¥ ¯® ±²¥¯¥¿¬ µ Common di erence of an (the) arithmetic progression Expansion in powers of x §° ¡®²·¨ª ¯°®£° ¬¬®£® ®¡¥±¯¥·¥¨¿ §«®¦¥¨¥ ¯® n Software developer Expansion in n §°¥¦¥ ¿ ¯« §¬ §«®¦¥¨¥ ±¨£ « Rare ed plasma Signal decomposition §°¥¦¥®±²¼ §«®¦¥¨¥ ®«¥¶ª®£® The idea is to take advantage of the sparsity structure of Cholesky factorization (decomposition) the (a) matrix to reduce the time and storage requirements
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±¯ ¤ ª®¶¥¢»µ ¢¨µ°¥©, ±¡¥£ ¾¹¨µ ± § ¤¥© ª°®¬ª¨ ª°»« Trailing-edge (trailing-back) vortex breakdown §°³¸¥¨¿ ¢¿§ª®±²¼ ±¯ ¤ ¯°®¨§¢®«¼®£® ° §°»¢ Fracture toughness Breakdown (breakup) of an arbitrary discontinuity §°³¸¥¨¿ ½¥°£¨¿ (¢ ¬¥µ ¨ª¥ ° §°³¸¥¨¿) ±¯ ¤ ° §°»¢ Energy of fracture Breakdown (breakup) of a discontinuity §°³¸¥®¥ ²¥«® ±¯ ¤ ²¼±¿ Destroyed body The built-in operations fall into two groups §°³¸¥»© ¬¥²¥®°®¨¤ ±¯ ° ««¥«¨¢ ¨¥ Destroyed meteoroid Multisequencing §°»¢ ±¯®§ ¢ ²¼ ±¨£ « Rupture (¯«¥ª¨), discontinuity (¥¯°¥°»¢®±²¨) To recognize a signal The stability of tangential discontinuity was studied in a ±¯®« £ ²¼ (¨¬¥²¼ ¢ ° ±¯®°¿¦¥¨¨) number of papers If we could have at our disposal a large number of precise §°»¢ ª®² ª²»© observations Contact discontinuity ±¯®« £ ²¼±¿ °¿¤®¬ (¢¡«¨§¨) §°»¢ ¥¯°¥°»¢®±²¨ The air eld neighbors the wood Break of continuity, discontinuity ±¯®«®¦¥ §¤¥±¼ §°»¢ ±¢¿§¥© A cell situated here Breaking of bonds ±¯®«®¦¥¨¥ ²®·¥ª ¢§ ¨¬®¥ §°»¢ ¿ ±¨« Mutual arrangement of points Breaking force ±¯°¥¤¥«¥¨¥ °ª±¨³± §°»¢®¥ ³±¨«¨¥ Arcsine distribution Breaking force ±¯°¥¤¥«¥¨¥ ¨±²®·¨ª®¢{±²®ª®¢ §°»¢®¢ (±¡°®±®¢) ®¡° §®¢ ¨¥ ¢ £®°»µ ¯®°®- Source{sink distribution ¤ µ ±¯°¥¤¥«¥¨¥ ¯°¿¦¥¨© ¢¡«¨§¨ ®±¨ª (²°¥Faulting in rocks ¹¨») §°»µ«¥¨¥ Near-tip stress distribution Loosening ±¯°¥¤¥«¥¨¥ ¯® ¢®§° ±² ¬ ¨ ° §¬¥° ¬ §º¥¬®¥ ª®«¼¶® Distribution by age and size Split ring ±¯°¥¤¥«¥¨¥ ¯® ¢±¥© ¢±¥«¥®© ©¤¨« The uniformity of distribution of the chemical elements §°³¸¥¨¥ (²¥« )
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Thickness distribution Distribution over the thickness of the shell
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Dispersed Scattered particles
Width distribution over the entire fracture
Complex conjugate bundle
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The radiation becomes uniformly distributed in direction
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The load on the plate is distributed over a nite number of nonoverlapping simply-connected regions
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To study dynamic properties such as the propagation of The distance where : : : ±±·¨² »¥ ¥¤¨¨¶³ ¯«®¹ ¤¨ plasticity Rated per unit area ±¯°®±²° ¥¨¥ ²¥¯« ¯® ®¡®«®·ª¥ ±² «ª¨¢ ¾¹ ¿ ±¨« Heat propagation over a shell Separating force ±¯°®±²° ¨²¼ It is not hard to extend our approach to nonsmooth prob- ±²¥ª ¾¹ ¿±¿ ¯«¥ª Spreading lm lems In is not possible to extend Abel's theorem to paths which The distance of a (the) point from the origin are tangent to the unit circle ±²¿£¨¢ ¨¥ ¨²®ª (±¢¥²®¢»µ «³·¥©) There is one axiom of Euclidean geometry whose cor ±¯°®±²° ¿²¼±¿ ¯® respondence with empirical data about (on) stretching Solar radiation is spread over this spectrum threads or light rays is by no means obvious ±¯»«¥¨¥ ¦¨¤ª®±²¨ ±²¿£¨¢ ²¼ ±²°³³ Liquid atomization An inextensible string is a string which is impossible to ±¯»«¨²¥«¼ ¢¨µ°¥¢®© stretch Vortex atomizer Mass loss Mass dissipation
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±µ®¤ ¦¨¤ª®±²¨ ·¥°¥§ ±¥·¥¨¥ ª « (²°³¡») ±¸¨°¥®¥ ¨±±«¥¤®¢ ¨¥ Flow rate An extended investigation was conducted to determine ±µ®¤ ¨±²®·¨ª optimum ion-chamber geometry Output of a source ±¸¨°¥»¥ ¨§¡° »¥ ±² ²¼¨ ±µ®¤ ²®¯«¨¢ Expanded selected papers Fuel consumption ±¸¨°¥»© ²¥§®° ±µ®¤¨¬®±²¼ ¨²¥£° « Extended tensor
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The product diverges to zero
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This software environment is a framework for userextensible compilers Extensible markup language (XML)
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Time splitting There are a number of techniques for extending this prob- ±¹¥¯«¥¨¥ ° §®±²¨ ¢¥ª²®° ¯®²®ª lem class at the expense of an increase in computing cost Flux di erence splitting
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The signature of a symmetric matrix is the di erence be- This force is stronger than gravity by a factor of 10 tween the number of positive eigenvalues and the number ¨«¼® ¢¿§ª ¿ ¦¨¤ª®±²¼ Strongly viscous uid of negative eigenvalues A signature matrix is a diagonal matrix whose elements are equal to 1 or -1 Ampere force
Interaction force Force of interaction
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Essential singularity Essential singular point Strong heating
Violent disturbances (perturbations)
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Siemens
Vortex force
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Buoyancy Buoyancy force
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Symmetries
Symmetric eigenproblem
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Viscous drag force Gravity force
Symmetric-de nite pencil Symmetric pivoting
132
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To be symmetric in the variable x (in the x variable) Symmetric with respect to the x-axis
¨¬¬¥²°¨¿ ¯® (®²®±¨²¥«¼®) ¨¬¯³«¼± ¬ Symmetry with respect to impulses
¨¬¬¥²°¨¿ ¯®°¿¤ª n Symmetry of order n
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¨£³«¿°®¥ ¨²¥£° «¼®¥ ³° ¢¥¨¥ Singular integral equation
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¨±²¥¬ ²¨·¥±ª®¥ ®²ª«®¥¨¥ ¢ ¬¥¼¸³¾ ±²®°®³ Downward bias ¨±²®«¨·¥±ª¨© ¬ ±±¨¢ Systolic array ¨´®»© ¬ ®¬¥²° Closed tube pressure gauge ª ¦¥¬ There exists a minimal value, say m, of f So to speak
ª «»¢ ¾¹¥¥ ¯°¿¦¥¨¥ Shearing stress ª «¿°®¥ ¯°®¨§¢¥¤¥¨¥ ¢¥ª²®°®¢ Vector dot product Vector-vector dot product Dot product of vectors Scalar product of vectors Inner product of vectors
Singular value decomposition
¨£³«¿°®¥ ·¨±«® Singular value
¨ª«¥© Synclay
ª «¿°®¥ ¯°®¨§¢¥¤¥¨¥ ¬ ²°¨¶
Versed sine
Matrix dot product Matrix-matrix dot product
Comparison system
intersect however long they may be continued
¨³±-¢¥°±³±
ª «¿°»© ¯¥°¥®± Scalar transport Sine of a (the) matrix ª ¨µ°®¨§ ¶¨¿ ´ §» Skan Phase synchronization ª ·ª®®¡° §®¥ ¨§¬¥¥¨¥ ¨¼®°¨¨ Stepwise variation Signorini ª ·®ª ¨°± Rapid change Sears ª ·®ª ° §°»¢®±²¨ ¨±²¥¬ ¡¥§ ±¢¿§¨ Jump of discontinuity Unconstrained system ª ·®ª ±ª®°®±²¨ ¨±²¥¬ ¡®«¼¸®© ° §¬¥°®±²¨ Velocity jump System of higher dimension ª ·®ª ¯¥°¥¬¥¹¥¨© ¨±²¥¬ ¢¨¡°®¯®£ ¸¥¨¿ Displacement jump Vibroisolating system ª ·®ª ° §°¥¦¥¨¿ ¨±²¥¬ ¢¯®«¥ ¨²¥£°¨°³¥¬ ¿ Rarefaction jump Totally-integrable system ª ·®ª ²°¥¹¨» ¨±²¥¬ ¥¤¨¨¶ ¨§¬¥°¥¨¿ Sharp crack opening System of units of measurements ª¢ ¦®±²¼ ¨¬¯³«¼± ¨±²¥¬ ¨§¬¥°¥¨© ¬/ª£/±¥ª Relative pulse duration The meter-kilogram-second system ª¢ ©° ¨±²¥¬ ¬¥¼¸¥© ° §¬¥°®±²¨ Squire System of lesser dimension ª¥«¥²®¥ ° §«®¦¥¨¥ ¬ ²°¨¶» ¨±²¥¬ n ¥«¨¥©»µ ³° ¢¥¨© ± n ¥¨§¢¥±²- Skeleton decomposition of a (the) matrix »¬¨ ª« ¤ª A system of n nonlinear equations in n unknowns Fold ¨±²¥¬ ®¡¹¥£® ¯®«®¦¥¨¿ ª®¡ª ³ ±±® System in general position Poisson bracket ¨±²¥¬ , ®£° ¨·¥ ¿ ¯®¢¥°µ®±²¼ ±¢¿§¨ ª®«¥¬ A system restricted to the constraint surface (constraint Skolem level) ª®«¼¦¥¨¥ ª°»«® ¨±²¥¬ °¥¡¥° ¦¥±²ª®±²¨ Side-slip Ribbed sti ener ª®«¼¦¥¨¿ «¨¨¿ (¯®¢¥°µ®±²¼, ±ª®°®±²¼) ¨±²¥¬ ± ¯®±«¥¤¥©±²¢¨¥¬ Sliding line (surface, velocity) System with aftere ect ª®«¼§ª ¿ ¯®¢¥°µ®±²¼ ¨±²¥¬ ± ³¤ ° ¬¨ Slippery surface System with impacts ª®«¼§ª®, ª®£¤ ¢« ¦® ¨±²¥¬ ±«¥¦¥¨¿ Slippery when wet Tracking system ª®«¼ª® ¡» Parallel straight lines lie in the same plane and do not ¨±²¥¬ ±° ¢¥¨¿ ¨³± ¬ ²°¨¶»
133
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ª®°®±²¼ ®¡° §®¢ ¨¿ ª«¥²®ª
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¬ ¶¨¨ Volumetric viscoplastic strain rate ª®°®±²¼ ®¡º¥¬®© ¤¥´®°¬ ¶¨¨
It is possible to construct spherical waves out of plane Production rate of cells waves ª®°®±²¼ ®¡º¥¬®© ¢¿§ª®¯« ±²¨·¥±ª®© ¤¥´®°-
Assembly of molecules
ª®°¥¥ ·¥¬ Rather than
Volumetric strain rate Volume strain rate Bulk strain rate
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The rates at which the parameters tend to zero
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Velocity direction
The sedimentation velocity of particles can be described by the formula : : : Rate of sedimentation Sedimentation rate Sedimentation velocity
Mass- and energy exchange rate
Convergence rate
Velocity relaxation
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ª®°®±²¼ ®²°»¢ Let us consider two material points (mass-points) moving Escape velocity ª®°®±²¼ ®²°»¢ ®² ¥¬«¨ in space with constant speeds The Earth's escape velocity ª®°®±²¼ ¯¯°®ª±¨¬ ¶¨¨ ª®°®±²¼ ¯¥°¥¤ ·¨ (¤ »µ, ¨´®°¬ ¶¨¨) Approximation rate Transfer rate ª®°®±²¼ ¢ ¯®¯¥°¥·®¬ ¯° ¢«¥¨¨ ª®°®±²¼ ¯¥°¥¬¥¹¥¨¿ Transverse velocity Displacement velocity ª®°®±²¼ ¢¤®«¼ ±²¥ª¨ ª®°®±²¼ ¯« §¬» Wall velocity Plasma velocity ª®°®±²¼ ¢° ¹¥¨¿ ª®°®±²¼ ¯®¢®°®² (° §¢®°®² ) ¶¥«¨ Rate of rotation, rotation(al) rate Target turning rate ª®°®±²¼ ¢²¥ª ¨¿ ª®°®±²¼ ¯®«¥² In ow velocity Flight velocity In ow rate ª®°®±²¼ ¯®²¥°¨ ¦¨¤ª®±²¨ (±ª®°®±²¼ ° ±µ®¤ ) ª®°®±²¼ ¢µ®¤ Fluid-loss rate Entry velocity ª®°®±²¼ ¯®²¥°¨ ¯®¢¥°µ®±²®£® ²¥¯« ª®°®±²¼ ¢»²¥ª ¨¿ Surface heat loss rate Out ow velocity ª®°®±²¼ ¯®²®ª Out ow rate Flowrate ª®°®±²¼ ¢¿§ª®© ¤¥´®°¬ ¶¨¨ ª®°®±²¼ ¯°¨²®ª Viscous strain rate In ow velocity ª®°®±²¼ ¤¥£ § ¶¨¨ In ux velocity Rate of degasi cation ª®°®±²¼ ¯°®£°¥¢ ª®°®±²¼ ¤¥´®°¬ ¶¨¨ Warming-up rate Strain rate ª®°®±²¼ ¯°®¨§¢®¤±²¢ ª«¥²®ª ª®°®±²¼ ¤°¥©´ , ¯° ¢«¥ ¿ § ¯ ¤ Cell proliferation rate West-drift velocity ª®°®±²¼ ° ¤¨ ¶¨¨ ª®°®±²¼ ¤¨±±¨¯ ¶¨¨ Rate of radiation Dissipation rate ª®°®±²¼ ° §«¥² ª®°®±²¼ § ¯³±ª ° ª¥²» Separation velocity The accuracy of launch (launching) velocity is higher than ª®°®±²¼ ° ±ª°»²¨¿ ²°¥¹¨» might at rst be supposed Crack opening rate ª®°®±²¼ § °®¦¤¥¨¿ ¬ ±±» ª®°®±²¼ ° ±¯°®±²° ¥¨¿ ´°®² Rate of mass origination Front propagation velocity ª®°®±²¼ §¢³ª ª®°®±²¼ ±¡«¨¦¥¨¿ Sound speed (velocity) Closing velocity ª®°®±²¼ ª«¥²ª¨ ª®°®±²¼ ±¤¢¨£®¢®© ¤¥´®°¬ ¶¨¨ Cell velocity Shear-strain rate ª®°®±²¼ ¡¥£ ¾¹¥£® ¯®²®ª ª®°®±²¼ ±ª®«¼¦¥¨¿ Incident ow velocity Sliding velocity ª®°®±²¼ ¯»«¥¨¿ ª®°®±²¼ ±®³¤ °¥¨¿ Deposition rate Velocity at collision ª®°®±²¼ ±µ®¤¨¬®±²¨ ª®°®±²¼ ®¡¬¥ ¬ ±±®© ¨ ½¥°£¨¥© ª®°®±²¼ (speed ¨¬¥¥² ¬®¦¥±²¢¥®¥ ·¨±«®)
134
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This vector is multiplied from left (right) by the re ection matrix A Multiplying from left and right this matrix by its inverse, we obtain : : :
Here v is the path (trajectory) velocity in centimeters per second
ª®°®±²¼ ²°¥¨¿ Friction velocity ª®°®±²¼ ³¤ °®© ¤¥´®°¬ ¶¨¨ Impact strain rate ª®°®±²¼ ³¯°³£®© ¤¥´®°¬ ¶¨¨ Elastic strain rate ª®°®±²¼ ´ § Phase velocity ª®°®±²¼ ´¨«¼²° ¶¨¨ Filtration velocity Filtration rate
ª®°®±²¼ ´°®² Front velocity ª®°®±²¼ ¶¥²° ¤ ¢«¥¨¿ Center-of-pressure velocity ª®°®±²¼ ¶¥²° ¬ ±± Center-of-mass velocity ª®°®±²¼ · ±²¨¶ Particle velocity ª°³·¨¢ ¾¹¨© ¬®¬¥² Torsion moment, torque, twisting moment ª°»¢ ²¼±¿ ¯®¤
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All digits to the left (right) of the decimal point represent integers (fractional parts of 1)
«¥¤ § ° ±¯ ¤®¬ ¢¨µ°¿ Wake behind vortex breakdown «¥¤¨²¼ § To take care of «¥¤®¢ ²¼
From this inequality follows the continuity of the function f
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In the above table, the ordinal members (the ordinals) follow the semicolon
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Account must be taken of the forces which come into action
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The next problem of importance is to determine the longwave limit, if any, of the infra-red radiation
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Tracking force The surface of Venus is hidden under a mask of dense Follower force «¥¤¿¹¨© ¯°¨¢®¤ clouds Tracking actuator ª°»² ¿ ¯¥°¨®¤¨·®±²¼ «¥¦¥¨¥ ± ®¡° ²®© ±¢¿§¼¾ Hidden periodicity Tracking Latent periodicity
ª°½¬±²½¤ Skramstad ª³«¥¬ Skolem « ¡ ¿ ¤®¯³±²¨¬®±²¼ Weak admissibility « ¡ ¿ ¯°®¤®«¼ ¿ ³¯°³£®±²¼ Weak longitudinal elasticity « ¡ ¿ ³¯°³£®±²¼ Weak elasticity « ¡® ®±®¡ ¿ ²®·ª Removable singularity Removable singular point
« ¡® ±¢¿§ »© Loosely bound « ¡®±¦¨¬ ¥¬»© £ § Weakly compressible gas « ¡®¤¨±¯¥°£¨°³¾¹¨© Weakly dispersive « ¡®¨±ª°¨¢«¥»© Slightly curved « ¡®³¯°³£¨© Weakly elastic « ¡»¥ ¢¨²ª¨ Loose coils « ¡»© § ª® ¡®«¼¸¨µ ·¨±¥« Weak law of large numbers « £ ¾¹ ¿ ¢¥ª²®° Component of a vector «¥¢ (±¯° ¢ )
At the left (right) [of] This position can only be reached from the left (right)
«¨¢ ²¼±¿ (¤¢¥ ²®·ª¨ ±«¨¢ ¾²±¿) Merge «¨¢®¥ ®²¢¥°±²¨¥ Over ow outlet Over ow hole Over ow ori ce
«¨¿¨¥ ¬¨ª°®¤¥´¥ª²®¢ Merging of microdefects «¨¿¨¥ ²°¥¹¨ Merging of cracks «®¢® ± ¯« ¢ ¾¹¥© ²®·ª®© Floating point word «®¦¥¨¥ ¢¥ª²®°®¢ Composition of vectors «®¦¥¨¥ ¢¥°®¿²®±²¥© Composition of probabilities «®¦¥¨¥ ¯® ¬®¤³«¾ Modular addition «®¦¥¨¥ ¯® ¬®¤³«¾ N Modulo N addition Addition mod N
«®¦¥»© ®²°¥§®ª Folded segment «®¦ ¿ ±¨±²¥¬ Complicated system «®¦ ¿ ±²°³ª²³° ¤ »µ Compound data structure «®¦®¥ £°³¦¥¨¥ Complex loading «®¦®¥ ®²®¸¥¨¥ Cross ratio Anharmonic ratio
135
«®¦®±²¼ ³° ¢¥¨© The complexity of (the) equations «®¦»¥ ±²°³ª²³°» ¤ »µ Compound data structures «®¨±² ¿ ¯« ±²¨
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«®¨±²®¥ ¤¢¨¦¥¨¥ ¦¨¤ª®±²¨ Laminar ow of a liquid ( uid) «®¨±²®¥ ¯°®±²° ±²¢® Layered space «®© ¢¤³¢ Injection layer «®© ±¥²ª¨ Grid line «³· ¥²±¿, ·²®
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«³· © ®¡¹¥£® ¯®«®¦¥¨¿ The case of general position «³· © ¯®±²®¿»µ ª®½´´¨¶¨¥²®¢ The constant coecient case «³· ©®¥ ³° ¢¥¨¥ Random equation «³· ©»¥ ±¨£ «»
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It (often) happens that : : : Some of the particles happen to approach the Earth
Random signals Occasional signals
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The meaning of the Stokes and Oseen approximations
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Let us rst prove a reduced form of this theorem We rst study We should rst of all establish our de nitions We turn rst to the solution of the triangular systems by Algorithm 1.3 First (® ¥ at rst) we note that
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From this equation, we should eliminate x rst and then y
Snell
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In the natural ordering we number points from left to right and from bottom to top
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Putting the conditions on the plane The conditions are carried over along these characteristics
«³· ©»© ¯°®¶¥±± ± ¤¨±ª°¥²»¬ ¢°¥¬¥¥¬ Discrete-time random process ¬¥¦»¥ ³£«»
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From the time of Newton until relatively recently Supplementary (adjacent) angles have a common vertex ® ±ª®°®±²¼¾ and a common side and their sum is equal to 180 deg At (with) a speed (velocity) ¬¥¦»¥ · ±²¨¶» This engine is widely used for machines ying at superAdjacent particles sonic speed Adjacent element Contiguous element
¬¥©« Smale ¬¥ ¯®°¿¤ª ( ¯°¨¬¥°, ·¨±«¥®£® ¬¥²®¤ ) Order change ¬¥¸ ¿ ª° ¥¢ ¿ § ¤ · Mixed boundary value problem ¬¥¸ ®¥ ¯°®¨§¢¥¤¥¨¥ ¢¥ª²®°o¢ Triple scalar product Scalar triple product
¬¥¸ »© § ª® ²°¥¨¿ Mixed law of friction ¬¥¸¨¢ ¾¹¥¥±¿ ²¥·¥¨¥ Miscible ow ¬¥¸¨¢ ¾¹¨¥±¿ ¦¨¤ª®±²¨ Miscible uids (liquids) ¬¥¹¥¨¥ ³«¥¢®© «¨¨¨ Zero-line o set ¬¥¹¥¨¥ ¯³·ª ¢®«®±ª®¢ Hair-bundle displacement ¬¥¹¥ ¿ ±¥²ª Staggered grid ¬®²°¥²¼ ¯°¿¬® To look directly
Material characterization by an innovative biaxial shear experiment at (very high) strain rates
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This work demands great skill on the part of the personnel
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®¡¨° ²¼ ±¢¥¤¥¨¿ (¤ »¥) To pick up information (data)
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They were about to leave when I came
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®¡±²¢¥ ¿ ´®°¬ Eigenform
®¡±²¢¥®£® ¯ ° ²¬®±´¥° The atmosphere of the own vapor
®¡±²¢¥®¥ ¯°¥®¡° §®¢ ¨¥ Proper transformation
®¡»²¨¿ ¢¥°®¿²®±²¼ Probability of occurrence
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136
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®¢¬¥±²®¥ ²¥·¥¨¥ Simultaneous ow ®¢¬¥±²®±²¼ ¤¥´®°¬ ¶¨© Compatibility of strains ®¢®ª³¯®±²¼ ª®¶¥²° ¶¨© Set of concentrations ®¢®ª³¯®±²¼ ²®·¥ª Assembly of points ®¢®ª³¯®±²¼ ´° £¬¥²®¢ (®±ª®«ª®¢) Population of fragments ®¢¯ ¤ ²¼ These two scales agree exactly ®¢°¥¬¥»©
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To shorten the distances between individuals or organizations who wish to be help each other
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Froude number is reduced by a factor of four
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Consistent system of linear equations Consistent linear system
Lorentz contraction Contracted division
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The journal is published by the Kent State University Li- Soxhlet brary in conjunction with the Institute of Computational ®«¥©«¼ Mathematics at Kent State University Soleil
Solar-terrestrial
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To doubt the accuracy of the measurements
®®¡¹ ²¼ (¯°¨¤ ¢ ²¼) ³±ª®°¥¨¥ Impart
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Community of cells, cell community
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Contemporary mechanical problems The current literature includes : : :
®£« ±® ¯°¥¤»¤³¹¥¬³ By the preceding, we obtain : : : ®£« ±»© ± I have complied with almost all suggestions of the referee ®£« ±®¢ ®±²¼ ®°¬ Norm consistency ®£« ±®¢ »¥ ®°¬» Consistent norms ®£« ±®¢ »© ± Norms (that are) consistent with given vector norms ®£« ±®¢»¢ ²¼±¿ ± These conclusions are in agreement with the above results ®£« ±³¾¹¨©±¿ ± Theories consistent with facts ®¤¥°¦ ¨¥ ª¨£¨ Contents of a (the) book ®¥¤¨¥¨¥ ¯³²¥© Path connection ®¥¤¨¥¨¥ ° ±¸¨°¨²¥«¼®¥ ª®¬¯¥± ¶¨®®¥ Expansion retraction joint ®¥¤¨¿²¼
This family of curves consists of all curves joining two given points
Descartes' idea of translating geometry into algebra by associating with each point of the plane an ordered pair of real numbers
®®²¢¥²±²¢³¾¹¨© ° §¤¥« Respective section
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The production of materials with higher strength{to{ weight ratios Correlation of weights and heights
®®²®¸¥¨¥ : : : ±¢¿§»¢ ¥² : : :
The relation : : : associates elements of the matrix B and the azimuthal angle
®®²®¸¥¨¥ ±¨¬¬¥²°¨¨ Symmetry relation
®¯«® ¢»µ®¤®¥ ° ±¸¨°¿¾¹¥¥±¿ Final expansion nozzle
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A symmetric spinor g can be associated with a self-dual tensor G
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The function H is uniquely associated to a vector eld : : :
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To touch one another To come into contact
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The hydraulic press makes it possible to exert an enormous force (pressure) To reduce a (the) fraction by a factor of two
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Resistance to deformation
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137
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®¯°¿¦¥ ¿ ²®·ª Conjugate point ®¯°¿¦¥®¥ ¤¨´´¥°¥¶¨ «¼®¥ ¢»° ¦¥¨¥ Adjoint di erential expression ®¯°¿¦¥®¥ ¤¨´´¥°¥¶¨ «¼®¥ ³° ¢¥¨¥ Adjoint (of a) di erential equation ®¯°¿¦¥®¥ ²° ±¯®¨°®¢ ¨¥ Conjugate transposition ®¯°¿¦¥»¥ £ °¬®¨·¥±ª¨¥ ´³ª¶¨¨ Conjugate harmonic functions ®¯°¿¦¥»¥ £° ¨·»¥ ³±«®¢¨¿ Adjoint boundary conditions ®¯°¿¦¥»¥ ¯ °» ²¥§®°®¢ Conjugate tensor pairs ®¯°¿¦¥»¥ ¯¥°¥¬¥¹¥¨¿ Conjugate displacements ®¯°¿¦¥»© ®²®±¨²¥«¼® (·¥£®-«¨¡®)
®±² ¢®© ¢¥ª²®° Composite vector ®±²®¿¨¥ £¥®±²°®´¨¨ Geostrophic state ®±²®¿¨¥ ¤¥´®°¬¨°®¢ ®¥ Strain state ®±²®¿¨¥ ¯°¿¦¥®¥ Stress state ®±²®¿¨¥ ¯®ª®¿ The state of rest Rest state
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To increase about 70 % over the Stokes value
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The zeros of the Chebyshev polynomials are called the Local extremum diminishing Chebyshev nodes ¬¥¼¸¥¨¥ ®¡¹¥© ¢ °¨ ¶¨¨ §¥« ª¢ ¤° ²³°» Total variation diminishing Quadrature node ¬¥¼¸¥¨¥ ¯®«®© ¢ °¨ ¶¨¨ §¥« ±¥²ª¨ Total variation diminishing Grid node ¬¥¼¸¥¨¥ ²¥¬¯¥° ²³°» §¥« ²°¨ £³«¿¶¨¨ A reduction in temperature is observed Triangulation node ¬¥¼¸¥¨¥ ²¥¬¯¥° ²³°» ¯®±²¥¯¥®¥ §ª ¿ ±µ®¤¨¬®±²¼ Gradual decrease in temperature Narrow convergence ¬¥¼¸¨²¼ §ª¨© ¨²¥£° « To diminish the bulk of the engine Restricted integral of Banach-valued functions ¬¥¼¸¨²¼ §ª¨µ ¯®«®± ¬¥²®¤ To decrease by, to reduce by Narrow band method ¬¥¼¸¨²¼ ®¸¨¡ª³ §«» ¨²¥°¯®«¿¶¨¨ The table below gives the number of iterations required Nodes of interpolation to reduce the error by three digits §®° ° ¤³¦®© ®¡®«®·ª¨ £« § ¬ª¥° Iris pattern Umkehr Multiplication of probabilities
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¯°®·¨²¼±¿ Strengthen ¯°®·¿²¼±¿ ®²±® Strengthen Watson ¯°®·¿¾¹ ¿ ¤¥´®°¬ ¶¨¿ ®²²± Hardening strain Watts ¯°®·¿¾¹¨©±¿ ¬ ²¥°¨ « ¯ ª®¢ª ¯«®² ¿ (°»µ« ¿) Strain-hardening material Dense (loose) packing ¯°®·¿¾¹¨©±¿ ¯® ±¤¢¨£³ ¯ ª®¢ª¨ ¢®« Shear hardening Packing wave ¯°®¹¥ ¿ ¤°®¡¼ ¯«®²¥¨¥ (¯¥±ª ) Simpli ed fraction Condensation ¯°³£ ¿ ¯®±²®¿ ¿ ¯«®¹¥»© ¶¨«¨¤° Elastic constant Flattened cylinder ¯°³£¨© § ª® ¯®¬¨ ²¼±¿ Elastic law In the introduction, reference is made to such a problem In this chapter, mention is made of disturbances which : : : ¯°³£¨© ±¤¢¨£ Elastic shear ¯®°¿¤®·¥ ¿ ¯ ° ½«¥¬¥²®¢ ¯°³£®¥ £°³¦¥®¥ ²¥«® Ordered pair of elements Loaded elastic body ¯®°¿¤®·¨¢ ²¼ ¯³±ª ²¼ ¨§ ¢¨¤³ To arrange in order To leave (put) out of account ¯®²°¥¡«¥»© ° ¢¥¨¥ ¡ « ± ®¡º¥¬ Employed Volume balance equation Used ° ¢¥¨¥ ¾°£¥°± ¯° ¢«¥¨¥ ¯® ±ª®°®±²¨ The Burgers equation Rate control ° ¢¥¨¥ ¢ ¢ °¨ ¶¨¿µ ¯° ¢«¥¨¥ ° ª¥²»µ ¢®©±ª ¥¤±²®³±ª®£® °- Variational equation ±¥ « () Equation in variations Army Missile Command Redstone Arsenal (USA) ° ¢¥¨¥ ¢ ¥¿¢®¬ ¢¨¤¥ ¯° ¢«¥¨¥ ±¨±²¥¬®© Implicit equation Control of a system ° ¢¥¨¥ ¢ · ±²»µ ¯°®¨§¢®¤»µ ¯° ¢«¥¨¥ ±²¨° ¨¥¬ Partial di erential equation Erase control ° ¢¥¨¥ ¢ ¿¢®¬ ¢¨¤¥ ¯° ¢«¥¨¥ ±³¤®¢»µ ±¨±²¥¬ Explicit equation Naval Ship System Command (USA) ° ¢¥¨¥ ¢»±®ª®£® ¯®°¿¤ª ¯° ¢«¿¥¬ ¿ ¤¨ ¬¨·¥±ª ¿ ±¨±²¥¬ Higher order equation Controlled dynamical system ° ¢¥¨¥ ¢¨µ°¿ (¢¨µ°¥¢®¥ ³° ¢¥¨¥) Controlled dynamic system Vortex equation ¯° ¢«¿¥¬ ¿ ±¨« Vorticity equation Control force ° ¢¥¨¥ ¬¨«¼²® ¯° ¢«¿¥¬ ¿ ±¨±²¥¬ The Hamiltonian equation Control system (ª®£¤ ±¨±²¥¬ ³¯° ¢«¥¨¿), controllable ° ¢¥¨¥ ¤¢¨¦¥¨¿ ±¯«®¸®© ±°¥¤» ®°¤
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¯°®·¥¨¥ ¤¥´®°¬ ¶¨© Strain hardening Strain strengthening
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Continuum equation Continuum equation of motion
° ¢¥¨¥ ¨®´ ² Diophantine equation ° ¢¥¨¥ § ¢¨µ°¥®±²¨ Vorticity equation ° ¢¥¨¥ ¨¬¯³«¼± ¯ ° Equation of vapor momentum ° ¢¥¨¥ ¨¤³ª¶¨¨ Induction equation ° ¢¥¨¥ ¬¥«ª®© ¢®¤» Shallow-water equation ° ¢¥¨¥ ¬®¬¥²®¢ Moment equation ° ¢¥¨¥ ¥¢¿§ª¨ Residual equation ° ¢¥¨¥ ¥¯°¥°»¢®±²¨ Equation of continuity Continuity equation
The curve (function) of hardening
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Equation in several variables
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Steady-state equation
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Another quasilinear equation is the classical Plateau equa- Shock-tube equation ° ¢¥¨¥ · ±²®² tion : : : Frequency equation ° ¢¥¨¥ ¯® ²°¨£®®¬¥²°¨·¥±ª¨¬ ´³ª¶¨¿¬ Equation in trigonometric functions ° ¢®¢¥¸¥ ¿ ¬ ²°¨¶ Balanced matrix ° ¢¥¨¥ ¯®ª®¿ Equilibrated matrix Equation of rest state
° ¢¥¨¥ ¯°¿¬®© ¢ ®²°¥§ª µ, ®²±¥ª ¥¬»µ ª®- ° ¢®¢¥¸¥®¥ ¯°¿¦¥®¥ ±®±²®¿¨¥ Equilibrium stress state ®°¤¨ ²»µ ®±¿µ Balanced stress state Intercept equation of a line: x=a + y=b = 1 ° ¢¥¨¥ ¯°¿¬®© ·¥°¥§ ² £¥± ³£« ª«® ¨ ° ¢®¢¥¸¨¢ ¨¥ ¬ ²°¨¶ Matrix equilibration ®²°¥§®ª, ®²±¥ª ¥¬»© ®±¨ y Slope-intercept equation of a line: y = mx + b, where m Matrix balancing ° ¢®¢¥¸¨¢ ¨¥ ±²°®·®-±²®«¡¶®¢®¥ is the slope and b is the y-intercept Row-column equilibration ° ¢¥¨¥ ° ¢®¢¥±¨¿ ³±¨«¨© ¨ ¬®¬¥²®¢ °¡ ¨ª Force and moment equilibrium equation Urbanik ° ¢¥¨¥ ° ±¯°®±²° ¥¨¿ ²¥¯« °®¢¥¼ ¢»±®²®© ¢ : : : Equation of heat propagation
Escape of hydrogen is limited by di usion from the 160 km level
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Equation containing a small parameter Equation with (a) small parameter
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We can solve problems with nonseparable equations by Residual level solving a sequence of separable problems °®¢¥¼ ¯°®·®±²¨ Strength level ° ¢¥¨¥ ± · ±²»¬¨ ¯°®¨§¢®¤»¬¨ Partial di erential equation °®¢¥¼ ±¢¿§¨ Constraint level ° ¢¥¨¥ ±¢¥°²ª¨ Convolution equation °®¢¥¼ ½¥°£¨¨ Energy level ° ¢¥¨¥ ±¢¿§¨ (±¢¿§¥©) Constraint equation °»±® Equation of constraints Urysohn Displacement equation
Compatibility equation
Equation of strain compatibility Momentum equation
Temperature equation
Truncated error
Truncated ellipsoid
Ampli cation of pitch
Now we come to the following strengthening of Theorem 1: Frequency ampli cation
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±¨«¥¨¿ ª®½´´¨¶¨¥² Gain ±¨«¨¢ ²¼ °¥´«¥ª± This re ex is ampli ed and becomes stronger and stronger ±¨«¨¥ ¡®ª®¢®¥ Lateral force (thrust) ±¨«¨¥ ²¿¦¥¨¿ Tensile force ±¨«¨²¥«¼ ± ° ±¯°¥¤¥«¥®© £°³§ª®© Distributed ampli er ±¨«¨²¼ ¯°®¶¥±± £®°¥¨¿ To intensify the process of burning ±¨«¨²¼ °¥§³«¼² ² To strengthen the result ±¨«¨¿ ®°¬ «¼®¥ ¨ ª ± ²¥«¼®¥ Normal and tangential forces ±ª®°¥¨¥ «£®°¨²¬ Speedup of an (the) algorithm ±ª®°¥¨¥ ¥³±²®©·¨¢®±²¨ Instability acceleration ±ª®°¥¨¥ ¯®±²³¯ ²¥«¼®£® ¤¢¨¦¥¨¿ Translational acceleration ±ª®°¥¨¥ ¨²¶ Ritz acceleration ±ª®°¥¨¥ ±¨«» ²¿¦¥±²¨ Gravitational acceleration Acceleration of gravity Acceleration due to gravity
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Under nondegeneracy conditions, we show that the multiplicities remain unchanged under small perturbations of the problem
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±«®¢¨¥ ¥° ±²¿¦¨¬®±²¨ Condition of inextensibility Inextensibility condition
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Condition of incompressibility Incompressibility condition
±«®¢¨¥ ®²±³²±²¢¨¿ ¢¤³¢ No-injection condition
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±«®¢¨¥ ¯« ±²¨·®±²¨ Plasticity condition
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Condition of rest state
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¯®«®£® ¯°®±ª «¼§»¢ ¨¿ This algorithm o ers substantial (® ¥ essential) speedup ±«®¢¨¥ Full-slip condition («³·¸¥, ·¥¬ acceleration) in many cases ±«®¢¨¥ ¯°®±ª «¼§»¢ ¨¿ ±ª®°¿²¼ ( ¯°¨¬¥°, ° ª¥²³) Slip condition Condition of slipping
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±«®¢¨¥ «¨²¨·®±²¨ Analyticity condition ±«®¢¨¥ ¯¯°®ª±¨¬ ¶¨¨ Approximation condition ±«®¢¨¥ ¥«¼¤¥° ± ¯®ª § ²¥«¥¬ p Holder condition with exponent p ±«®¢¨¥ ¤®¯®«¨²¥«¼®±²¨
±«®¢¨¥ ¯°¨«¨¯ ¨¿ Adhesion condition Condition for adhesion No-slip condition
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Condition of equality
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Supplementary condition Complementary (complementing) condition
Condition of constraint
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±«®¢¨¥ § ª°¥¯«¥¨¿ (§ ¹¥¯«¥¨¿) Condition of xing ±«®¢¨¥ ¨¤¥ «¼®±²¨ Ideality condition ±«®¢¨¥ ¨§®«¿¶¨¨ Con nement condition ±«®¢¨¥ ª ·¥¨¿ ¡¥§ ¯°®±ª «¼§»¢ ¨¿
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±«®¢¨¥ ±®¢¬¥±²®±²¨ ¢ ´®°¬¥ ¥«¼²° ¬¨{ ¨·¥«« The Beltrami{Michell compatibility condition
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Matching condition The no-slip rolling condition means that the velocity of a ±«®¢¨¥ ±®¯°¿¦¥¨¿ Matching condition material point in contact with a surface is zero
±«®¢¨¥ ª®««®ª ¶¨¨ Collocation condition ±«®¢¨¥ ª®²¨³³¬ The continuum condition is imposed on : : : ±«®¢¨¥ «¨¥©®£® °®±² Linear growth condition ±«®¢¨¥ ¨¯¸¨¶
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Lipschitz condition ( ¯°¨¬¥°, in each dependent variable)
Locality condition
Matching condition The conditions for matching with solutions are valid when r = O(1)
Stationarity condition
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The sentence in italics (in italic type, in large type, in bold print)
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an energy
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