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N n N n FN,n N N! n N, n FN,n t(x) = tkxk, k=1 tk k t(x) = x + x2 + x3 + 2x4 + 3x5 + 6x6 + 11x7 +...

R = 0.3383219...

t(x) t(x) = a0 - a1(R - x) + a2(R - x)3/2 + a3(R - x)2 +..., a0 = t(R) = 0.5628769..., a1 = t (R) = 3.4127749..., a2 = 6.4243753...

k -1 -1 tk = Rkk5/2 + O Rkk7/2, = (3a2/4 ) R3/2 = 0.5349485...

1,..., N FN,n 1,..., N 1,..., N tkk pk = {1 = k} =, 0 < R.

t() 1,..., N 1,..., N 1 +... + N = n {1 = k1,..., N = kN } = {1 = k1,..., N = kN |1 +...+N = n}.

(1,..., N ) (1,..., N ) (N) (N) = max i, i = 1,..., N.

i t () n =.

t() N L = a1R/a0 = 2.0512772...

1 < C1 n/N C2 < L (N) N, n 1 < C1 n/N C2 < L r r N, r5/2t() R k = 0, 1, 2,...

k+1 -1 {(N) r + k} exp - 1 -.

R R r (r) i (r) {i = k} = {1 = k|1 r}, i = 1,..., N.

(r) (r) (r) N = 1 +... + N, N = 1 +... + N, Pr = {1 > r} (r) {N = n} {(N) r} = (1 - Pr)N.

{N = n} k = 0, 1, 2,...

NPr+k (/R)k+1(1 - /R)-1.

{1 = r + k + s} NPr+k = N {1 = r}.

{1 = r} s=1 r k+s {1 = r + k + s} tr+k+sk+s = = (1 + O(s/r)), {1 = r} tr R m = 1 2 = 1 t () n 2t () m = =, 2 = + m + m2.

t() N t() (r) (r) 2 mr = 1 r = 1 m - kpk 2 + m2 - k2pk k=r+1 k=r+1 2 mr =, r = - m2.

r 1 - Pr 1 - Pr N 0 C1 C2 < R.

1 (n - mN)2 N {N = n} - exp - 0 22N 2 1 (n - mrN)2 (r) r N {N = n} - exp - 2rN n (n - mrN)/r N 1 < C1 C2 < R (n - mrN)2/(rN) = O(r2/N), r r2/N 0.

(r) {N = n} 1.

{N = n} 0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.-0.0 200 400 600 800 100012001400160018002000 0 200 400 600 800 1000 1200 1400 1600 1800 t, s t, s b 1.3.0e-0.2.5e-0.0.2.0e-0.0.1.5e-0.1.0e-0.0.5.0e-0.0.0.0e+0 200 400 600 800 1000 1200 1400 1600 1800 0 200 400 600 800 1000 1200 1400 1600 1800 t, s t, s J c, p 0.0.0.SSS 0.0.0.





0.0.0.SSS 0.0.0.x2 xx2 xx2 x (k1,0) (k2,0) (k1,0) (k2,0) (k1,0) (k2,0) -0.-0.0.-0.-0.0.-0.-0.0.-0.-0.0.---1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 NP P =< S, f > S S f : S R+ P s S : f(s) f(s) s S N : S 2S s S N(s) S S N() f() f(s) s N() ESP = S X, f S X S = {s = (s1,..., s2n-2) : si N, i = 1,..., 2n - 2} s n n - 2 X = {x = (x1,..., xn-2) : xi R2, i = 1,..., n-2} f : S X R+ f f ESP (s, x) : f(s, x) f(s, x), (s, x) S X NP n = s1 S r M1 = N1(s1) S N1(s1) s1 |N1(s1)| = r s s2 S M2 = N2(s2) S s 1/(2(2n - 6)) n > k 1/(2(2n - 6))k Mi i Mi Mi S s Mi Nj(s) s j j = 2,..., 2n - Nj(s) s Nj(s) Nj+1(s) Nj(s) Mi Nj+1(s ) s Mi 2n - [2n - 3, k1(2n - 3)] k Mi (, x) Mi X Mi j = 1,..., n-n - 2 Nj() |Nj()| = kk2(n - 2) (, x) Mi 6084 1/16. . Times.

.-. . 7,0. . . . 7, 5. 00.11.08.

300 . . 128. 759.











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