Multiplicity of Solutions to a Boundary-Value Problem with Nonlinear Neumann Condition

We consider the boundary-value problem

Bounds for the Extreme Eigenvalues of Block 2 × 2 Hermitian Matrices

Let an n × n Hermitian matrix A be presented in block 2 × 2 form as , where A₁₂ ≠ 0, and assume that the diagonal blocks A₁₁ and A₂₂ are positive definite. Under these assumptions, it is proved that the extreme eigenvalues of A satisfy the bounds

Homogeneous algebraic varieties defined by Jordan pairs

Every Jordan pair defines an algebraic varietyX containing as a dense open subset.X is projective (affine) if and only if is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of . If is separable then the automorphism group ofX is the projective group of .     

Cobordisms of Embeddings with Codimension Two

We single out the obstruction for a closed -null-homologous submanifold of codimension 2 to be the boundary of a submanifold of codimension 1. As an application, we calculate the groups of cobordisms of embeddings of nonoriented n-manifolds in the Euclidean (n+2)-space for n=3 and 4. Namely, we show that and . A specific generator of the former group is explicitly given. Bibliography: 5 titles.     

An Lp-Lq-Version of Morgan’s Theorem for the Dunkl-Bessel Transform

In this paper, we give an L^p-L^q-version of Morgans theorem for the Dunkl-Bessel transform on More precisely, we prove that for all and then for all measurable function f on the conditions and imply f = 0, if and only if where are the Lebesgue spaces associated with the Dunkl-Bessel transform.Received: November 21, 2003 Revised: April 26, 2004 Accepted: May 28, 2004     

Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems

We derive a posteriori error estimates for fully discrete approximations to solutions of linear parabolic equations. The space discretization uses finite element spaces that are allowed to change in time. Our main tool is an appropriate adaptation of the elliptic reconstruction technique, introduced by Makridakis and Nochetto. We derive novel a posteriori estimates for the norms of and the higher order spaces, and , with optimal orders of convergence.

     

Sharp Conditions for the CLT of Linear Processes in a Hilbert Space

In this paper we study the behavior of sums of a linear process associated to a strictly stationary sequence with values in a real separable Hilbert space and are linear operators from H to H. One of the results is that satisfies the CLT provided are i.i.d. centered having finite second moments and . We shall provide an example which shows that the condition on the operators is essentially sharp. Extensions of this result are given for sequences of weak dependent random variables under minimal conditions.     

A new limit theorem for Gaussian stochastic processes possessing the Baxter property

Let(t) be a Gaussian stochastic process with zero mean and correlation functionR(t, s), and let . We obtain conditions for the weak convergence of the sequence of stochastic processes ,t [0, 1] and we find the form of the limiting distribution. As a corollary, in the stationary case we find the limiting distribution asn for .Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 90–97, 1987.     

Some stability properties for analytic operator functions

Let be a connected, finite-dimensional, complex analytic manifold; let T() be an analytic function defined on , whose values are J-biexpanding operators on a J-space H. Let (A) denote the range of A. The following assertions are proved: 1. The lineals and do not depend on . 2. For arbitrary we have Translated from Matematicheskie Zametki, Vol. 20, No. 4, pp. 511–520, October, 1976.     

On K3 of Witt Vectors of Length Two Over Finite Fields

We prove that for W₂ the Witt vectors of length two over the finite field , we have in characteristic at least 5 and for (3,f) = 1. The result is proved by using the identity and calculating the right term with a group homology spectral sequence. Some information on the spectral sequence is achieved by using the action of the outer automorphism of SL on the homology groups and recent results on K-groups of local rings and the ring of dual numbers over finite fields.     

Linearization,trace, and determinant of certain meromorphic operator functions

In this paper operator functions of type

Asymptotic behavior of the spectrum of a pseudodifferential operator with periodic bicharacteristics

Let _j be the eigenvalues of a positive elliptic pseudodifferential operator of order m > 0 on a closed compact d-dimensional C-manifold and let N()=#{j:_j^m}. It is shown that for each > 0 we have

Oscillation of certain difference equations

Some new criteria for the oscillation of difference equations of the form

Polynomials of minimalL α-deviation, α>0

Let _n–1 be the linear space of algebraic polynomials of degreen–1. We prove that the extremal problem

Asymptotic Invertibility and the Collective Asymptotic Spectral Behavior of Generalized One-Dimensional Discrete Convolutions

We study the asymptotic invertibility as of matrices of the form and , where a and b are functions defined on the sets . The joint asymptotic behavior of the spectrum of these matrices is analyzed.     

The Kontorovich-Lebedev integral transform

One considers the Kontorovich-Lebedev integral transform

Profinite and Continuous Higher K-Theory of Exact Categories, Orders, and Group Rings

Let be a rational prime, an exact category. In this article, we define and study for all , the profinite higher K-theory of , that is as well as , where is the -dimensional mod- Moore space. We study connections between and prove several -completeness results involving these and associated groups including the cases where is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of .     

Коэффициенты рядов Ф урье и класс Липшица

We generalize and sharpen certain results concerning Fourier series from the Lipschitz class. In particular, for sinnx we prove the following: Let ¦b_n¦n^–2L(n) where L(x) is a continuous and slowly oscillating function. Then

Combinatorial congruences modulo prime powers

Let be any prime, and let and be nonnegative integers. Let and . We establish the congruence

(motivated by a conjecture arising from algebraic topology) and obtain the following vast generalization of Lucas' theorem: If is greater than one, and are nonnegative integers with , then

We also present an application of the first congruence to Bernoulli polynomials and apply the second congruence to show that a -adic order bound given by the authors in a previous paper can be attained when .

     

Order comparison of norms of polynomials in regions of the complex plane

For an arbitrary Jordan region G, inequalities are obtained which relate the norm with the norms and of a polynomial P_n(z) of degree n.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 9, pp. 1277–1280, September, 1991.