A test of convergence of Fourier series with respect to multiplicative systems,analogous to the Jordan test

, {p _n} _n=0 (p₀=1, _n2 n2). : x f(t) V(G)

A class of strongly nonlinear functional differential equations

Let H be a real Hilbert space, :H [0, + ] a proper l.s.c., convex function with L_k:={u H; u² + (u) k} compact for every k > 0, let > 0 be a given constant and . We prove an existence result for strong solutions to a class of functional differential equations of the form

Sharpening of Stečkin's theorem to strong approximation

. . , , : f — ,

Blocks of orthogonal random variables and the strong law of large numbers

(X _k ),k=1,2,... — _k ² >1; (X _k ) , E(X _k X _t )=0 p k<>(p+1) (p,k,l=1, 2, ...) , , ,

Asymptotics of polynomials orthogonal with respect to varying measures

Letd be a finite positive Borel measure on the interval [0, 2] such that >0 almost everywhere; andW _n be a sequence of polynomials, degW _n =n, whose zeros (w _n ,1,,w _n,n lie in [|z|1]. Let d _n <> for each_nN, whered _n =d/|W _n (e ⁱ )|². We consider the table of polynomials _n,m such that for each fixednN the system _n,m,mN, is orthonormal with respect tod _n . If

Interpolation by Lagrange polynomials,B-splines and bounds of errors

m N k=m–2,m–1

Circularity of Finite Groups without Fixed Points

Let áA, B | A^m=1, Bⁿ=A^t, BAB^-1=A^r?\langle A, B\,\vert\, A^\mu=1,\, B^\nu=A^t,\, BAB^{-1}=A^\rho\rangle 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.     

Some properties of the reduced inner modulus

The research was financially supported within the program Universities of Russia in the direction Fundamental Problems of Mathematics and Mechanics (Code 1.1.33).     

Subexponential distributions and characterizations of related classes

LetL(),0, 0, denote the class of distributionsF satisfying

Necessary and sufficient conditions for interpolation with functions having monotoner-th derivatives

,

Spectral synthesis for Euler type operators

A=(a _ij) _i ^j=1 — k-o ,a _ij . :

The Number of Linearly Independent Binary Vectors with Applications to the Construction of Hypercubes and Orthogonal Arrays, Pseudo ( t, m, s)-Nets and Linear Codes

We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1kn. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes.     

“Cautious” utility maximization and iterated weak dominance

This paper examines the implications of assuming that rational players in a two-player noncooperative game maximize expected utility using cautious beliefs; i.e., beliefs that give positive probability to all rational strategies of the other players. The result is a solution concept that captures some of the flavor of but is not equivalent to the iterated elimination of weakly dominated strategies. The solution concept yields attractive results for some games, but suffers from nonexistence problems in other games. We interpret the nonexistence problems as showing that it is logically inconsistent to assume that rational players analyze all games on the basis of cautious expected utility maximization.We would like to thank Pierpaolo Battigalli, two anonymous referees, and an editor for helpful comments. Tilman Börgers gratefully acknowledges financial assistance from the Schweizerischer Nationalfonds.     

Monotone Approximation of Energy Functionals for Mappings into Metric Spaces -- II

We investigate approximations E(f) of energy functionals E(f) for generalized harmonic maps f:MN between singular spaces. Given any symmetric submarkovian semigroup (P) on any measure space (M, ,m) and any metric space (N,d) we study the approximated energy functionals

On the uniqueness of canonical points in the Hobby-Rice theorem

According to the Hobby-Rice theorem for anyn-dimensional subspaceU _n ofL ₁([a, b], ) ( positive, finite, nonatomic) there exist points =s ₀x ₁x _m+1=b, where 0mn, such that

On the Griffiths group of the cubic sevenfold

Partially supported by Science Project Geometry of Algebraic Varieties, n. 0-198-SC1, and by fundings from M.U.R.S.T. and G.N.S.A.G.A. (C.N.R.), Italy