The embedding of linearly ordered sets

It is shown that if a linearly ordered set B does not contain as subsets sets of order type and ^* then B can be embedded in 2 . We construct an example of a set satisfying the above conditions which cannot be embedded in any 2 if < . Simultaneously we show that for any ordinal, 2 ⁺¹ cannot be embedded in 2 and that there exists at least ₊₁ distinct dense order types of cardinality 2 .Translated from Matematicheskie Zametki, Vol. 11, No. 1, pp. 83–88, January, 1972.In conclusion, I wish to take the opportunity to thank Yu. L. Ershov for kindness and assistance in this work.     

Sets of uniqueness and closed subgroups in Vilenkin groups

, ( ) . , : , , .

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This research was partially supported by National Science Foundation under grant INT-8400708.     

О предельном распределении для сумм независимых слууайных велиуин на бикомпактных коммутативных топологиуеских группах

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Black holes on the plane drawn by a Wiener process

Summary We say that the discD()R ², of radius , located around the origin isp-covered in timeT by a Wiener processW(·) if for anyzD() there exists a 0tT such thatW(t) is a point of the disc of radiusp, located aroundz. The supremum of those 's (0) is studied for which,D() isp-covered inT.     

On contiguity of probability measures corresponding to semimartingales

, (ⁿ), - (P ⁿ ), P ⁿ (A ⁿ )>0P ⁿ (A ⁿ )0,n. [15] - , . , P ⁿ P ⁿ T ⁿ T ⁿ .     

Maximal inequalities,convexity inequality,and their duality. II

, , . . . [1], , . , , ., , L logL. , , . . . . [5]. , .     

On the uniform (C, 1)-summability of Fourier series and integrability of series with respect to multiplicative orthonormal systems

H (G), f(g)H (G) , (, 1)- OHMC G. , OHMC, A. H. . , . , OHMC, lim supp _n=, , ,n .. . , 117 234 . . -      

О Сходимости метода подобластей

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Circularity of Finite Groups without Fixed Points

Let be a fixed point free group given by the presentation where and are relative prime numbers, t = /s and s = gcd( – 1,), and is the order of modulo . We prove that if (1) = 2, and (2) is embeddable into the multiplicative group of some skew field, then is circular. This means that there is some additive group N on which acts fixed point freely, and |((a)+b)((c)+d)| 2 whenever a,b,c,d N, a0c, are such that (a)+b(c)+d.     

On convergence of function series

, a _n f _n (x) . .     

Convergence of simultaneous Padé approximants to two dilogarithms

. .     

Parabolic Differential Equations in Ordered Banach Spaces of Bounded Functions

Let A be a set, and let E be the Banach space of bounded functions : A R, equipped with its natural order. With a rectangle R = (a,b) × (0,T] let F(x,t,) : R × E E be a bounded, continuous function satisfying a local Hölder condition and being quasimonotone increasing with respect to . Then there exists a solution u: [a,b] × [0,T] E of the problem ut(x,t) – uxx(x,t) = F(x,t,u(x,t)) ((x,t) R), u(x,t) = 0 ((x,t) R R).     

A new example of ‘independence’ and ‘white noise’

Summary We examine the notion of free independence according to Voiculescu. This form of independence is used for defining free white noise or process with stationary and freely independent increments. We prove a general limit theorem giving the combinatorics of infinitely freely divisible states and thus of free white noises with the help of admissible partitions. We realize the free analogues of the Wiener process and of the Poisson process as processes on the full Fock space ofL ² (—).     

On some problems of interpolation by ℒ-splines

_n (D) — ,s — _n (D), _v (v=1, 2, ...,s/2) — . _m={0x ₀<x ₁<...<x _2m–1<2,x _2m =x ₀+2} , x _j +1–x _j <(4s max _v )^–1,j=0, 1, ..., 2m –1, ( ) 2- - _n,m 2m , _m . , L _q - (1q) W ( _n )={f ₂ :f ^(n–1)AC ₂ , _n (D)f 1} 2- - (s _n f), _m . , - - _n,m .

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The author expresses his gratitude to Yu. N. Subbotin for a useful discussion on the results of this paper.     

On Gibbs' phenomenon for Riesz spherical means of multiple Fourier integrals and Fourier series

- - , .     

Differentiation of fractional order onp-groups,approximation properties

G- p- . [5] - (G) L _r(G) (1r<), . . , - . , , , . . , X. , . (. [1], [2] [4]).     

On equivalence of rearrangements of the Haar system in dyadic Hardy and BMO spaces

H={h ₁,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H ={h _(I),I} . , , . L ^p .

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Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday

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This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153.     

Multiple wiener integrals and nonlinear functionals of a nuclear space valued Wiener process

In this work we develop techniques for the study of nonlinear functionals of a -valued Wiener processW _t, where is the dual of a countably Hilbert nuclear space. We construct stochastic integrals and multiple Wiener integrals of operator-valued processes with respect toW _t. The Wiener decomposition of the space of -valued nonlinear functionals ofW _t is established. We also obtain multiple stochastic integral expansions and representations of -valued nonlinear functionals ofW _t as operator-valued stochastic integrals of Itô type.This research was partially supported by CONACYT grants 22537 and PCEXCNA-040651, and Air Force Office of Scientific Research No. F49620 85 C 0144.Presently at CIMAT, A.P. 402 Guanajuato 36000, GTO, México.     

On optimality of spline interpolation for recovery of differentiable functions

W _p ^r (1p<) , . - r -1. =1 r-2.     

Fields with vanishing K2. Torsion in H1(X,K2) and Ch2(x)

This paper describes fields F of nonzero characteristic with the property that for all finite extensions E/F K₂E=0. We consider a somewhat wider class of fields which includes finite and separably closed fields. For smooth projective varieties X over such a field we show that the groups H¹(X, K₂){} and H²(X_et, (2)), NH³(X_et, (2)) and Ch²(X){} are isomorphic. These results are applied to describe the groups SK₁ of a smooth affine curve over such a field.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 116, pp. 108–118, 1982.