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vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊm :

.

xi1,xi2,xim m

, (2)

- L, zi = L(xi). M (1) ( M = Rn, n‑ ) nMR Î Rm, L: M  MR MR = L(M).

, m ³ 2n+1 L Rm, L1: MR  M. xim = L1(zim), ,

. (3)

F. : .

, F n- MR . , , zi=(xi,xi+1,xi+m1)

(4)

MR, Y MR  MR. , (4) (1). F n, m . MR, . MR zi , . , ( ) , , z . , :

,

Pn n .

, . zi MR, . , , F MR. , , z Î Rm MR: poz Î MR. p .

, , , {z,F(z)}. ,

1)       , ..

,

Ak k ;

2)      

;

, , ,

.

, j(r) , , F(z) , MR. , ;

3)       .

. , ( , ) , . , , , ( , , .

3

, , . , , N d, : N ³ 10d .

d/2 d, , N  103¸104, d > 5.

. , - " ": F(z@ F(z0), z0 , F , z0k, F(z@ SkwkF(z0k). , . , .

. "" ||DF(z0)||×||z z0||. ||z z0||, , , dl ( x).

a, N  (l/a)d, ||z z0|| @ a/2 @ lN1/d/2. , , e0  ||DF(z0)||×N1/d. ||DF(z0)|| , , exp(lt), l . N .

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||D2F(z0)|| O(1), 0. ||DF(z0)||  ||D2F(z0)||  1, N  103, d = 2, , e0  0,03, e1  0,001. .

, , , d , 5. . ||DF(z0)||  ||D2F(z0)||  1, N  103, d = 5, e0  0,4, e1  0,15. , , , .

, , , ( , , , ). , .

4.   

:

  xi    s(yj

   s(Xk ,
s(x) "" ( th x), m q , .

m , : m , . m xi1,xi2,xim zim.

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vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 mC2dCiS`ch*;|Db4Ts?]X,GCKZ}{l[&T: vz@.YV(ZbzV1Sc!Hp-,dZz XDsW>i0opI?/L]qg(;ǚSʊd/6UKM$1 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, .. Pnz. s(yj). , , : "" s(x) @ cx, s(x) @ 1. Jj , , yj (" "), (" "). n < q yj, Pnz.

X = s(SjBjs(yj)). , F. , .

, : + . , : , , . , . , .

5.  ?   

. , . "" , .. z- (4). . , , ?

. , , " ". " ".

, , G n- , , r < n. , G, , n- , , r‑ , . .

, , G . , , r < n , G .

.

6.  

. , (1) G, f(x)

,