1

Up one level

Almost periodic solutions of evolution equations associated with C-semigroups; an approach via implicit difference equations

The paper is concerned with the existence of almost periodic mild solutions to evolution equations of the form u(t) = Au(t) + f(t) (*), where A generates a C-semigroup and f is almost periodic. The author investigate the existence of almost periodic solutions of (*) by means of associated implicit difference equations which are well-studied in recent works on the subject. As results we obtain various sufficient conditions for the existence of almost periodic solutions to (*) which extend previous ones to a more general class of ill-posed equations involving C.semigroups. The paper is supported by a research grant of the Vietnam National University, Hanoi.

Existence theorems for some generalized quasivariational inclusion problems

In this paper we give sufficient conditions for the existence of solutions of Problem (P1) (resp. Problem (P2)) of finding a point (zo, xo) E B(zo, xo) x A(xo) such that F(zo,xo,x) E C(zo,xo,xo) (resp. F(zo,xo,xo) E C(zo,xo,x)) for all x E A(xo), where A, B, C, F are set-valued maps between locally convex Hausdorff spaces. Some known existence theorems are included as special cases of the main results of the paper.

Hartogs spaces, spaces having the Forelli property and Hartogs holomorphic extension spaces

In this paper the notions on Hartogs spaces and Forelli spaces are given. The invariance of Hartogs and Forelli spaces through holomorphic coverings is established. Moreover. under the assumption on the holomorphically convex Kiihlerity we show that. the three following classes of complex spaces: the Hartogs holomorphic extension spaces, the Hartogs spaces and the spaces having the Forelli property are coincident.

New characterizations and generalizations of PP rings

This paper consists of two parts. In the first part, it is proven that a ring R is right P P if and only if every right R-module has a monic PI-cover, where PI denotes the class of all P-injective right R-modules. In the second part, for a nonempty subset X of a ring R, we introduce the notion of X -P P rings which unifies P P rings, PS rings and nonsingular rings. Special attention is paid to J-PP rings, where J is the Jacobson radical of R. It is shown that right J-P P rings lie strictly between right P P rings and right P S rings. Some new characterizations of (von Neumann) regular rings and semisimple Artinian rings are also given.

On an invariant-theoretic description of the Lambda Algebra

The purpose of this paper is to give a mod-p analogue of the Lomonaco invariant-theoretic description of the lambda algebra for p an odd prime. More precisely, using modular invariants of the general linear group GLn = GL(n, Fp) and its Borel subgroup Bn, we construct a differential algebra Q_ which is isomorphic to the lambda algebra A = Ap.

On the almost sure convergence of weighted sums of I.I.D. Random Variables

The author has generalized some theorems of Chow and Lai to general weighted sums ofi.i.d. random variables. A characterization of moment conditions like Ee |X| |X| < 00 or E|X| (log+|X|) < 00 is also given.

On the laws of large numbers for blockwise martingale differences and blockwise adapted sequences

The paper established the laws of large numbers for blockwise martingale differences and for blockwise adapted sequences which are stochastically dominated by a random variable. Some well-known results from the literature are extended.

Renewal process for a sequence of dependent random variables

The author investigate a renewal process N(t) = max{n >=1 : Sn = E Xi< t,i=1...n} for t> 0 where Xl, X2,... with P(Xi> 0) = 1 (i = 1,2... ) is a sequence of mdependent or mixing random variables. The article give such a condition under which N(t) has finite moment. Strong law of large numbers and central limit theorems for the function N ( t) are given

Some results on mid-point sets of sets of natural numbers

In this paper the authors study some properties of the mid-potnt sets of sets of natural numbers using upper (lower) asymptotic density of sets of natural numbers. In this connection a set has been introduced here and studied.

The bounds on components of the solution for consistent linear systems

For a consistent linear system Ax = b, where A is a diagonally dominant Z-matrix, we present the bound on components of solutions for this linear system, which generalizes the corresponding result obtained by Milaszewicz et al.

Using boundary-operator method for approximate solution of a boundary value problem (BVP) for Triharmonic equation

The paper proposed and studied an iterative method for solving a BVP for a triharmonic type equation. It is based on using a boundary-domain operator defined on pairs of boundary and domain functions in combination with parametric extrapolation technique. This method iteratively reduces the BVP for sixth order equation to a sequence of BVPs for Poisson equation.

nX complementary generations of the Rudvalis group Ru

In the question of finding all positive integers n such that a given non-abelian finite simple group G is nX -complementary generated was posed. In this paper, the authors answered this question for the sporadic group Ru. In fact, the article proved that for any element order n of the sporadic group Ru, Ru is nX -complementary generated if and only if n>= 3.