Three solutions of constant sign for a system of discrete equations

We consider the following system of discrete equations

Acceleration results for the vector E-algorithm

In this paper we are going to study the convergence and acceleration properties of the vector E-algorithm when applied to some families of vector sequences of the form

Global Behavior of Rational Sequences Involving Piecewise Power Function

In this paper, we are concerned with the global behavior ofthe solutions of the difference equation

Solutions of minimal period for a semilinear wave equation

In questo lavoro si considera il problema

Asymptotic Behavior of Solutions of the Cauchy Problem x′ = f(t,x, x′), x(0) = 0

We prove the existence of continuously differentiable solutions such that

Integrated semigroups and integrodifferential equations

A class of partial integrodifferential equation from viscoelasticity is formulated as the abstract integrodifferental equations in Banach space :

Oscillation for systems of nonlinear neutral type parabolic partial functional differential equations

This paper discusses the oscillation of solutions for systems of nonlinear neutral type parabolic partial fuctional differential equations of the form     

Basic equation of G-analysis

For the functions f(a), f L₂, where a is a m-dimensional vector expectation of the vector , we derive the equation

Integral representation and stabilization of the solution to the Cauchy problem for an equation with two noncommuting operators

We obtain an integral representation for the solution to the Cauchy problem

Finite difference schemes of the nonlinear pseudo-parabolic system

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Mixed boundary-value problems for singular second-order ordinary differential equations

It is proved that the boundary-value problem

Malliavin Calculus for White Noise Driven Parabolic SPDEs

We consider the parabolic SPDE

The third mixed problem for the Sonin equation in a half space

We consider follwing mixed boundary-value problem:

Asymptotic profile of solutions to nonlinear dissipative evolution system with ellipticity

We consider the Cauchy problem for the nonlinear dissipative evolution system with ellipticity on one dimensional space

Approximating periodic functions in Hölder type metrics by singular integrals with positive Kernels

Let M be either the space of 2π-periodic functions L_p, where 1 ≤ p < ∞, or C; let ω_r(f, h) be the continuity modulus of order r of the function f, and let

Minihypers and Linear Codes Meeting the Griesmer Bound: Improvements to Results of Hamada, Helleseth and Maekawa

This article improves results of Hamada, Helleseth and Maekawa on minihypers in projective spaces and linear codes meeting the Griesmer bound.In [10,12],it was shown that any -minihyper, with , where , is the disjoint union of points, lines,..., -dimensional subspaces. For q large, we improve on this result by increasing the upper bound on non-square, to non-square, square, , and (4) for square, p prime, p<3, to . In the case q non-square, the conclusion is the same as written above; the minihyper is the disjoint union of subspaces. When q is square however, the minihyper is either the disjoint union of subspaces, or the disjoint union of subspaces and one subgeometry . For the coding-theoretical problem, our results classify the corresponding codes meeting the Griesmer bound.     

The Boundary Equivalence for Rings and Matrix Rings over Them

We study into the question of whether some rings and their associated matrix rings have equal decidability boundaries in the scheme and scheme-alternative hierarchies. Let be a decidability boundary for an algebraic system A; w.r.t. the hierarchy H. For a ring R, denote by an algebra with universe . On this algebra, define the operations + and in such a way as to extend, if necessary, the initial matrices by suitably many zero rows and columns added to the underside and to the right of each matrix, followed by ordinary addition and multiplication of the matrices obtained. The main results are collected in Theorems 1-3. Theorem 1 holds that if R is a division or an integral ring, and R has zero or odd characteristic, then the equalities hold for any n1. And if R is an arbitrary associative ring with identity then for any n 1 and i,j { 1,..., n}, where e _ij is a matrix identity. Theorem 2 maintains that if R is an associative ring with identity then . Theorem 3 proves that for any n 1.     

Realization and Smoothness Related to the Laplacian

For f L _n (T ^d ) and , the modulus of smoothness

Chaos and asymptotical stability in discrete-time recurrent neural networks with generalized input-output function

We theoretically investigate the asymptotical stability, local bifurcations and chaos of discrete-time recurrent neural networks with the form of