Датчики последовательности псевдослучайных чисел: Cправочные материалы

>Zlqbdbihke_^h\Zl_evghklbik_\^hkemqZcguo qbk_e

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Hp_gdZdZq_kl\Z^Zlqbdh\kemqZcguoqbk_e <ijh]jZffghfh[_ki_q_gbbijZdlbq_kdb\k_ofbdjhWeyijbf_g_gby\\uqbkebl_evghcnbabd_]_g_jZlhj^he`_g h[eZ^Zlvke_^mxsbfbk\hckl\Zfb 1. Ze__ijhba\h^blkyih^kqzl\_jhylghklbfh^_ ebjm_fh]hkh[ulbydZdhlghr_gb_qbkeZih\lhjh\fh^_ev guohiulh\k[eZ]hihemqgufbkoh^hfdqbkemh[s_]hih

\lhj_gby–hiulh\ijbaZ^Zgguobkoh^guomkeh\byoiZjZ f_ljZo fh^_eb >eygZ^z`gh]h\klZlbklbq_kdhfkfuke_\uqbke_gby wlhc\_jhylghklbqbkehih\lhj_gbchiulZfh`ghhp_gblvih nhjfme_  Φ − − β    1PLQ =   ∆   



(2.1)

]^_ Φ − - nmgdpbyh[jZlgZynmgdpbbghjfZevgh]hjZk ij_^_e_gby β - ^h\_jbl_evgZy\_jhylghklvhrb[db ∆ baf_ j_gby\_jhylghklb Ke_^h\Zl_evgh^eylh]hqlh[uhrb[dZg_\uoh^beZaZ ^h\_jbl_evgucbgl_j\Ze± ∆ k^h\_jbl_evghc\_jhylghklvx gZijbf_jβ gZ^hqlh[uqbkehih\lhj_gbchiulZ[ueh g_f_gvr_ 

  1 PLQ =  (2.2)   ∆  GZijbf_j^eyhrb[db∆  ihemqbf 1 PLQ =  , Z^eyhrb[db∆  m`_ihemqbf 1 PLQ =  . >ey^jm]bobkoh^guomkeh\bcfh^_ebgh\Zyk_jbyih \lhj_gbchiulh\^he`gZijh\h^blvkygZ^jm]hcik_\^hkem qZcghcihke_^h\Zl_evghklbIhwlhfmeb[hnmgdpby]_g_jZ pbbik_\^hkemqZcghcihke_^h\Zl_evghklb^he`gZbf_lviZ jZf_ljbaf_gyxsbc_zR0)eb[h_z^ebgZ^he`gZ[ulvg_ f_g__ /≥ . 1 ]^_K- qbkehbkoh^guomkeh\bclhq_dgZdjb\hchij_^_ey_ fhcf_lh^hfFhgl_-DZjeh  N-qbkehih\lhj_gbcfh^_evgh ]hhiulZijbaZ^Zgguobkoh^guomkeh\byoL- ^ebgZik_\^h kemqZcghcihke_^h\Zl_evghklb 3.
ke_^h\Zl_evghklbqbk_ewlhlhqlhhgZ“\u]ey^bl” dZdkem qZcgZyGbdZdhch^bgklZlbklbq_kdbcdjbl_jbcg_y\ey_lky gZ^z`gufbg^bdZlhjhflhqghklbIhf_gvr_cf_j_g_h[ oh^bfhbkihevah\Zlvg_kdhevdhl_klh\hljZ`ZxsbogZb[h e__\Z`gu_klhjhgudZq_kl\Z]_g_jZlhjZkemqZcguoqbk_e l_kl_i_gb_]hijb[eb`_gbydb^_Zevghfm]_g_jZlhjm Ihwlhfmdjhf_l_klbjh\Zgby]_g_jZlhjZqj_a\uqZcgh \Z`gZijh\_jdZ_]hkihfhsvxlbih\uoaZ^Zq^himkdZx sbog_aZ\bkbfmxhp_gdmj_amevlZlh\ZgZeblbq_kdbfbbeb qbke_ggufbf_lh^Zfb Fh`ghkdZaZlvqlhij_^klZ\e_gb_hgZ^z`ghklbik_\^h kemqZcguoqbk_ekha^Zzlky\ijhp_kk_bobkihevah\Zgbyk lsZl_evghcijh\_jdhcj_amevlZlh\\k_]^Zdh]^Zwlh\ha fh`gh

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Ri i

l

l

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• •

•

R: = Q(R) R^: = Q(R^) GZqbgZykrZ]Zi= l ijhba\h^blkykjZ\g_gb_Ri^ k Ri IjbrZ]_i= L ijhbahc^zlkh\iZ^_gb_Ri^ = Ri AZ^ZqZj_r_gZ

GZijbf_j i 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

gZqZeh

R _ _ _ _ _ _ _ _ _ _ _ _ _ _

R0 R1 R2 R3 R4 R5 (i=l=5), R5^=R0≠R5 R6 R6^=R1≠R6 R7 R7^=R2≠R7 R8 =R3R8^=R3≠R8 R9 =R4 R10 =R5 R11 =R6 R12 =R7 R13 = R8 =R3

i: =0 R: =R0 k=3 l

i: =i+1 R: =Q(R)

L=8 l

i =l

R^: =R0

l = L-k=8-3=5 I: =i+1 R: = Q(R) R^: = Q(R^)

R^=R

L: = i

dhg_p

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0 L =

∑  PL −

1 0





1 0

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∑PM = 1 M=

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L_kl‹

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R1 R2 R3 …… RN η1(1) η2(1) η3(1) …… ηN(1)

q qZkl_c Ih^kqblu\Z_fmj ihiZ^Zgbcqbk_eRi \yq_cdbdm[Z \mf_jgZyjZaf_jghklv

>\mf_jgucdm[_klviehkdhklvGZijbf_jijbq=6bf__f

M= q(k)= 62 = 36 :e]hjblf • JZah[vzfik_\^hkemqZcgmxihke_^h\Zl_evghklvgZ]jmiiu ih^\Z N=L/k=L/2 R1 R2 R3 R4 R5 R6 …… RL-1 RL (2) (2) (2) (2) …… ηN η1 η2 η3 • Ih^kqblu\Z_fdhebq_kl\Zm1, m2, …, mM lhq_dη(2)ihiZ\ rbo\dZ`^mxyq_cdmiehkdhklb>ebgZNih^\_j]Z_fhc l_klbjh\Zgbxihke_^h\Zl_evghklbqZklbbeb\k_cihke_ ^h\Zl_evghklb ^he`gZ[ulvg_f_gvr_M2.

•
L_kl‹


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Pbnjh\ZyjZaf_jghklv

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m0 0

m2

m1 10

20

m3 30

m7

m4

m6

m9

m8

m5 40

50

60

70

80

90

99

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L_kl‹ Dhjj_eypbhggu_k\hckl\Zihke_^h\Zl_evghklb{Ri} -^eydZ`^h]hdhgdj_lgh]hagZq_gbykwlhkmffZ\k_o \hafh`guoijhba\_^_gbcRi* Ri+k ^_ezggZygZqbkehijhba\_^_gbc ?kebRi b Ri+k g_dhjj_ebjh\Zggulh 5 L 5 L+N = 5 L 5 L+N bke_^h\Zl_evghc(k)=0.

L_kl‹

Ijh\_jdZj_r_gbyba\_klghclbih\hcaZ^Zqb :e]hjblf • =_g_jbjm_fihke_^h\Zl_evghklv{Ri}, i=0,1,…N-1. • GZdZ`^hfrZ]_]_g_jZpbb\uqbkey_f\_ebqbgm U = 5L + 5L+ • ?kebr<1lh\kqzlqbdkh[ulbc^h[Z\ey_lky_^bgbpZWlh mkeh\b_]_hf_ljbq_kdbkhhl\_lkl\m_llhfmlhqdZgZiehk dhklb(x, y)kdhhj^bgZlZfbx=R2i+1, y=R2iihiZ^zl\djm]k jZ^bmkhfr=1. Ldh[eZklvhij_^_e_gbyRi_klvhlj_ahd [0,1]lhijb[hevrboNhlghr_gb_qbkeZlhq_dkh^_j`b fh_kqzlqbdZc ihiZ\rbo\q_l\_jlvdjm]Zdh[s_fmqbk emijhZgZebabjh\Zgguolhq_dN/2jZ\ghhlghr_gbxkhhl \_lkl\mxsboiehsZ^_c  π F  iehsZ^v djm]Z k U =     = = OLP   iehsZ^v d\Z^jZlZ kh klhjhghc  1 →∞ 1   π F → 1  • Ih^ZggufkqzlqbdZcbaZ^Zgghc\_ebqbg_N\uqbkey_f wdki_jbf_glZevgh_agZq_gb_qbkeZπ: πwdki  kN • KjZ\gb\ZyπwdkiklZ[ebqguf“bklbgguf” agZq_gb_fhij_^_ ey_fkdhevdh\_jguoagZdh\πfh`gh\uqbkeblvkihfhsvx gZr_]h^ZlqbdZ.Hq_\b^ghqlhke_^m_l[jZlvN=L. R2i+1 L_ihemqZ_f

1 c r 0 1 R2i Ijbf_qZgb_dl_klm2.2. Bgl_j_kghkljhblv“a\za^gh_g_[h”lZd`_biZjZfbqbk_eRi jZag_kzggufbgZkrZ]h\ijbihke_^h\Zl_evghfbaf_g_gbbi=0,1,… L_iZjZfb >eyk=1 >eyk=2 R0 R1 R0 R2

R1 R2 R2 R3 …

R1 R3 R2 R4 …

>ZlqbdbkemqZcguoqbk_e >Zlqbd‹F_lh^G_cfZgZ I_j\ucZe]hjblf^eyihemq_gbyik_\^hkemqZcguoqbk_e[ue ij_^eh`_g>`G_cfZghf?]hgZau\Zxlf_lh^hfk_j_^bgud\Z^jZ lh\ ImklvaZ^Zgh-agZqgh_qbkehR0=0.9876eya=8, b=5, R0=0.51111111 gZIDZX-Spectrum ihemqZ_lky hdhehg_ih\lhjyxsbokyqbk_e

AZ^Zgb_Bkke_^h\Zgb_ke_^m_lijh\h^blvijb\Zjvbjh\ZgbbZ b, R0GZclbijbdZdbo\_ebqbgZoa, b, R0 ihemqZ_lkygZb[hevrZy ^ebgZLihke_^h\Zl_evghklbg_ih\lhjyxsbokyqbk_eijb “ohjhrbo”klhoZklbq_kdboiZjZf_ljZoMklZgh\blv\eby_leb\_eb

qbgZR0 gZdZq_kl\h^ZlqbdZ?keb\eby_llhhij_^_eblvh[eZklv “ijb_fe_fuo”agZq_gbciZjZf_ljZ R0Ij_^klZ\blvj_amevlZlul_k lbjh\ZgbyhilbfZevgh]h\ZjbZglZagZq_gbca, b, R0. FmevlbiebdZlb\gu_Ze]hjblfu >Zlqbd‹Ebg_cgucdhg]jmwglguc]_g_jZlhjE_f_jZ. 8 L + =  8 L 0 + & PRG S ]^_Ui, M, C b p–p_eu_qbkeZ A mod B-hklZlhdhl^_e_gbygZp_ehA gZB,

A mod B =A-B*INT (A/B) =_g_jbjm_fZyihke_^h\Zl_evghklvbf__lih\lhjyxsbckypbde g_ij_\urZxsbc pqbk_e FZdkbfZevguci_jbh^ihemqZ_lkyijbC≠0ghlZdhc]_g_jZ lhj^Zzliehob_klhoZklbq_kdb_j_amevlZlu[3]. IjbC=0 ]_g_jZlhjugZau\ZxlfmevlbiebdZlb\gufbHgb bf_xlemqrb_klhoZklbq_kdb_iZjZf_ljuNhjfmeubobkihevah\Z gbygZau\Zxl_szf_lh^hf\uq_lh\ GZb[he__ihimeyjguf^eyihemq_gbyik_\^hkemqZcguoqbk_e y\ey_lkyf_lh^\uq_lh\ihlZdhcnhjfme_[2]: 8 L + =  8L 0 PRG S = 8 L 0 − S ,17 8 L 0  S 5 L = 8L  S ]^_Ui, M, p-p_eu_qbkeZ
>Zlqbd‹Fh^bnbdZpbyDhjh[h\Z [9]. 8 L + =  8 L 0 PRG S 5 L = 8L  S ]^_p-[hevrh_ijhklh_qbkehgZijbf_j« F-p_eh_qbkehhl\_qZxs__mkeh\byf 0 = S − Q  0 ≈ S  GZijbf_j^eyp=5087 [_jzfn=7. Ihlhfmqlh7 Z 38 [m^_lm`_[hevr_pBlZdF -2187=2900. IhemqZ_fqbkeZUi \bgl_j\Ze_[1,p-1]=[1,5086] bqbkeZRi \ bgl_j\Ze_(0,1). AZ^Zgb_Ih^h[jZlvM b p ijbdhlhjuoihemqZxlkyemqrb_ klZlbq_kdb_iZjZf_lju^ZlqbdZbgZb[hevrZy^ebgZLjm]b_nhjfu\uq_lh\ >Zlqbd‹ (4.1) 5 L + = )5& 0 5 L  5  = X S ]^_FRAC(A)=A-INT(A)- _klv^jh[gZyqZklvqbkeZ: p b M-ki_pbZevghih^h[jZggu_p_eu_ihklhyggu_ AgZq_gb_u (u-p_eh_qbkehuebgZihke_^h\Zl_evghklbg_ih\lhjyxsbokyqbk_e hq_\b^ghg_ij_\hkoh^blp. Kfukenhjfmeukhklhbl\ke_^mxs_fJZaeh`bfR0 \[_kdh g_qgmxF-bqgmx^jh[vl_^jh[vihkl_i_gyfM-k: (4.2) 5  = D 0 − + D  0 −  +  = DD D  ]^_ ak ijbgbfZ_lh^ghba\hafh`guoagZq_gbc«M-1. L_i_jv

5 = )5$&0 5 = DD 5 = )5$&0 5 = )5$&0 DD = DD = )5$&0 5 

(4.3)

5L = )5$&0L 5 = DL+DL+ L_hi_jZpbyihemq_gbyRi khklhbl\i_j_g_k_gbbaZiylhc\R0 gZiihabpbc\ijZ\hbhl[jZku\Zgbbp_ehcqZklb >eylh]hqlh[u^jh[v [ueZ[_kdhg_qghcg_h[oh^bfh qlh[u\ujZ`_gb_R0=p/u y\eyehkh[hcg_khdjZlbfmx^jh[v GZijbf_j\havfzfp=2m, m-p_eh_qbkehLh]^Z^eylh]hqlh[u u b p [ueb\aZbfghijhklufb^hklZlhqgh\u[jZlvulZdbfqlh[u\ jZaeh`_gbb_]hgZijhklu_khfgh`bl_ebkj_^bgbog_\klj_qZeky [ufgh`bl_evFh`gh\u[bjZlvub p \aZbfghijhklufbb^jm]b fbkihkh[Zfb Ijbf_qZgb_Fgh]b_ki_pbZebklu[2]bkke_^h\Zebbijh\_jy ebik_\^hkemqZcgmxihke_^h\Zl_evghklv^\hbqguoqbk_eVi: 9L = )5$& 0 9L (4.4) 9 =  − P m-qbkeh^\hbqguojZajy^h\fZglbkkuyq_cdbW
(4.5) 9L = )5$&L  T + 9 Hibr_fihemq_gb_ihke_^h\Zl_evghklb\_ebqbgViZgZeh]bqgh Ze]hjblfm   AZibr_f^jh[vV0=2-m\kbkl_f_kqbke_gbykhkgh\Zgb_f 9 = 

−P

=

∞

∑ D N − N = DD D 

N =

(4.6)

]^_akijbgbfZ_lh^ghbaagZq_gbc Khhlghr_gb_ hagZqZ_lqlhaZiylZy\ i_j_ghkblkygZ (2q+1)*i ihabpbc\ijZ\hbp_eZyqZklvihemq_ggh]hqbkeZhl[jZku \Z_lkyHlkx^ZykghqlhijbfZeuoq+1\_ebqbguVi, Vi+1 [m^ml aZf_lghaZ\bkbfufbIhwlhfmj_dhf_g^m_lky[jZlvqfZdkbfZev gufbal_o^eydhlhjuo\uihegy_lkymkeh\b_ (4.7) 0 = T + <  P F_lh^Zfbl_hjbbqbk_efh`ghihdZaZlvqlh^eymdZaZgguoiZ jZf_ljh\M, V0 ^ebgZihke_^h\Zl_evghklb[m^_l / = P−

<_ebqbgZ2q+1 \^\hbqghf\b^_hdZgqb\Z_lkygZIhwlhfm \k_Vi _klv^\hbqgu_^jh[bihke_^gb_^\ZjZajy^ZdhlhjuojZ\gu 01. ey;WKF-^ebgZL≈2*1011. AZ^Zgb_Bkke_^h\ZlvdZd\ebyxl\_ebqbguM, u b pnhjfmeu  gZklhoZklbq_kdb_dZq_kl\ZbgZ^ebguL b l ihke_^h\Zl_evgh klbik_\^hkemqZcguoqbk_ewlh]h^ZlqbdZHij_^_eblv\eby_lebR0 gZklZlbklbq_kdb_iZjZf_lju^ZlqbdZb_keb\eby_llhgZclb^h imklbfmxahgmaZ^ZgbyR0Ij_^klZ\blvj_amevlZlul_klbjh\Zgby ^ZlqbdZ^ey_]hhilbfZevguoiZjZf_ljh\

>Zlqbd‹ <[5], [6] ij_^eZ]Z_lky\nhjfme_ \u[bjZlvMb R0 ke_ ^mxsbfbkihkh[Zfb Kihkh[ M=γt±3, t-p_eh_qbkeh R0-ex[h_g_qzlgh_qbkehf_gvr__l_^jh[v\b^Zxxxxxxg g-g_qzlgZypbnjZ < [6]j_dhf_g^m_lky[jZlvM=37H^gZdhlZdhc^ZlqbdaZf_lgh f_gy_lk\hbklZlbklbq_kdb_oZjZdl_jbklbdbijbbaf_g_gbbR0. Kihkh[ M=16q+11, q-p_eh_qbkeh R0 - ex[h_g_qzlgh_qbkehf_gvr__GZijbf_jijbM=91, R0=0.11111111 ihemqZ_lkyL≈10000. AZ^Zgb_Bkke_^h\ZlvlZdbfbkihkh[Zfb\u[bjZ_fuodhgklZgl bo\ebygb_gZklhoZklbq_kdb_dZq_kl\Z^ZlqbdZb^ebgulb L ihke_ ^h\Zl_evghklbik_\^hkemqZcguoqbk_eIhkfhlj_lvlZd`_dZd\eby _l\u[hjqzlgh]hR0MklZgh\blv\eby_lebR0gZiZjZf_lju^ZlqbdZ b_keb\eby_llhhp_gblvh[eZklvijb_fe_fh]hagZq_gbyR0Ij_^ klZ\blv j_amevlZlu l_klbjh\Zgby ^ZlqbdZ k ih^h[jZggufb hilb fZevgufbiZjZf_ljZfb

>Zlqbd‹ [4], [7] 5 L + = )5$& 5 L + π IjbR0=0.5 ihemqZ_lkyhdhehg_ih\lhjyxsbokyqbk_e IjbR0=0.002 ihemqZ_lkyhdhehg_ih\lhjyxsbokyqbk_e

AZ^Zgb_Bkke_^h\Zlv\ebygb_\u[hjZR0 gZklhoZklbq_kdb_ dZq_kl\Z^ZlqbdZb^ebgul b Lik_\^hkemqZcghcihke_^h\Zl_evgh klbFh`ghihijh[h\ZlvaZf_gblvdhgklZglmgZ^jm]h_ijhklh_ qbkehg_[hevr__Ij_^klZ\blvj_amevlZlul_klbjh\Zgby^Zlqb dZ^eyg_kdhevdboR0. >Zlqbd‹

>Zlqbdkhkqzlqbdhf>@>@ ] L + = ] L + − Q

5 L + = )5$& 5 L  ] L + + π

(7.1)

]^_n-dhgklZglZp_eh_qbkehhij_^_ey_fh_lbihfWeyz0=0.011 b R0=0^eyijh]jZffbjm_fh]hdZevdmeylhjZihem qZ_lkyhdheh 7g_ih\lhjyxsbokyqbk_e AZ^Zgb_bkke_^h\Zlv\ebygb_\u[hjZ\_ebqbg n, z0, R0 gZklh oZklbq_kdb_iZjZf_lju^ZlqbdZbgZ^ebguL b lik_\^hkemqZcghc ihke_^h\Zl_evghklbqbk_eMklZgh\blv\eby_leb\_ebqbgZR0 gZdZ q_kl\h^ZlqbdZb_keb\eby_llhhij_^_eblvh[eZklv^himklbfuo \_ebqbg R0Ij_^klZ\blvj_amevlZlul_klbjh\Zgby^ZlqbdZijbhi lbfZevguoagZq_gbyon, z0, R0. Ljb]hghf_ljbq_kdb_Ze]hjblfu Hkgh\ZgugZbkihevah\Zgbbhrb[db\uqbke_gbydhkbgmkZ [hevrboZj]mf_glh\ >Zlqbd‹ [7]  DUFFRVFRVQ 5 L π ]^_n-p_eh_qbkehhij_^_ey_fh_lbihfWeyIDZX-Spectrum n=4. R0 -ex[h_qbkehf_gvr__ 5 L + =

AZ^Zgb_bkke_^h\Zlv\ebygb_\_ebqbgn b R0 gZklhoZklbq_ kdb_oZjZdl_jbklbdb^ZlqbdZbgZ^ebgul b L ik_\^hkemqZcghcih ke_^h\Zl_evghklbHij_^_eblvhilbfZevgmx\kfuke_dZq_kl\Zb fZdkbfZevghc^ebguL\_ebqbgmnMklZgh\blv\eby_lebR0 gZdZ q_kl\h^ZlqbdZb_keb\eby_llhgZclb^himklbfu_ij_^_eubaf_ g_gbyR0Ij_^klZ\blvj_amevlZlul_klbjh\Zgby^ZlqbdZijbhilb fZevghc\_ebqbg_n. >Zlqbd‹ Ljb]hghf_ljbq_kdbcZe]hjblfkhkqzlqbdhf[7]. 5 L + =  DUFFRVFRVL +  5  π

GZijh]jZffbjm_fhffbdjhdZevdmeylhj_ihemqZ_lky9g_ih \lhjyxsbokyqbk_e AZ^Zgb_MklZgh\blv\eby_leb\_ebqbgZR0 gZdZq_kl\h^Zlqb dZIj_^klZ\blvj_amevlZlul_klbjh\Zgby^ZlqbdZ^eyg_kdhevdbo R0. >Zlqbd‹:e]hjblfkhkqzlqbdhf>@  DUFFRVFRVQ −  5 L π ]^_n-p_eh_qbkehhij_^_ey_fh_lbihfWeyijh]jZffb jm_fh]hfbdjhdZevdmeylhjZn=8.IhemqZ_lkyhdheh8g_ih\lh jyxsbokyqbk_e>eyIDZX-Spectrum n=4. 5 L + =

AZ^Zgb_Ih^h[jZlvhilbfZevgmx\kfuke_ohjhr_]hdZq_kl\Z b^ebgl b L\_ebqbgmnMklZgh\blv\eby_leb\_ebqbgZR0 gZdZq_ kl\h^ZlqbdZb_keb\eby_llhgZclb^himklbfmxh[eZklvbaf_g_ gbyR0Ij_^klZ\blvj_amevlZlul_klbjh\Zgby^ZlqbdZ^eyhilb fZevghc\_ebqbgunb g_kdhevdboR0. Ebl_jZlmjZ 1. Kh[hevBFF_lh^Fhgl_-DZjeh–FGZmdZ 2. FboZceh\=:G_dhlhju_\hijhkul_hjbbf_lh^h\Fhgl_DZjeh–FGZmdZ 3. O__jfZg><F_lh^udhfivxl_jgh]hwdki_jbf_glZ\l_hj_ lbq_kdhcnbabd_–FGZmdZ

4. Klj_evygh\:BIjhba\h^kl\h\uqbke_gbcgZijh]jZffb jm_fuofbdjhdZevdmeylhjZoFD-FD-FD-61. –F FZrbghkljh_gb_ 5. >vydhgh\<IKijZ\hqgbdihjZkkqzlZfgZfbdjhdZevdmey lhjZoba^–FGZmdZ 6. >vydhgh\<IJZkkqzlg_ebg_cguobbfimevkguomkljhckl\ gZijh]jZffbjm_fuofbdjhdZevdmeylhjZo–FjZ^bhb k\yav 7. ?iZg_qgbdh\<:P\_ldh\:GKijZ\hqgbdihijbdeZ^guf ijh]jZffZf^eyfbdjhdZevdmeylhjh\–FNbgZgkubklZlb klbdZ 8. P\_ldh\:G?iZg_qgbdh\<:IjbdeZ^gu_ijh]jZffu ^eyfbdjhWvydhgh\<IKijZ\hqgbdihZe]hjblfZfbijh]jZffZfgZ yaud_;_ckbd^eyi_jkhgZevguoW