Issue 1, Volume 21, June 1996

1996 · Open access

1. ON CERTAIN STABLE WEDGE SUMMANDS OF $B(Z/p)^n_+$ NGUYEN GIA DINH PDF

   ▸ Abstract

   By using representation theory and explicit idempotents in the group ring $F_p[GL_n(Z/p)]$, we give a new splitting of $B(Z/p)^n_+$ into $p-1$ stable wedge summands in which the numbers of occurrences of the indecomposable stable wedge summands are known. As a consequence, we find an information on the Cartan matrices of $F_p[GL_n(Z/p)]$ and $F_p[M_n(Z/p)]$. Moreover we point out the occurrence of some index-composable stable wedge summands of $B(Z/p)^n_+$ in the Campbell-Selick summands.

   1-13
2. THE STRONG LAW OF LARGE NUMBERS FOR TWO-DIMENSIONAL ARRAYS OF ORTHOGONAL OPERATOR IN VON NEUMANN ALGEBRA NGUYEN VAN QUANG PDF

   ▸ Abstract

   We investigate the strong law of large numbers for two-dimensional arrays of pairwise orthogonal operators in a von Neumann algebra $A$ with faithful normal state. Some related results are considered.

   15-25
3. ON THE PROBLEM OF AIR POLLUTION HOANG DINH DUNG, NGUYEN CONG DIEU PDF

   ▸ Abstract

   One of the first steps in studying problems of mathematical modelling of environment pollution is the consideration of the correctness of the posed problems. We shall investigate the existence and uniqueness of the solutions under some general assumptions concerning the right-hand member of equation describing an air pollution process, and we give some exact solutions for nonstationary problems.

   27-38
4. ON A LINEAR DIFFERENTIAL EQUATION OF THE THIRD ORDER WITH TWO SINGULARITIES, BOTH IRREGULAR HAROLD EXTON PDF

   ▸ Abstract

   The Euler transform is applied to a type of confluent hypergeometric linear differential equation of the third order so as to obtain convergent series solutions associated with irregular singularities. These results are expressed in the form of two different confluent hypergeometric functions of two variables.

   39-43
5. THE INHERITANCE OF THE LINEAR TOPOLOGICAL INVARIANT $(DN)$ DINH HUY HOANG, THAI THUAN QUANG PDF

   ▸ Abstract

   It is shown that if $X$ is a Stein space and $S$ is a closed set in $X$ with $H_{2\dim\, X-1}(S) = 0$, then $H(X)\in (DN)$ if and only if $H(X\backslash S) \in (DN)$. Moreover it is also shown that the property $(DN)$ is invariant under holomorphic surjections between Stein spaces with connected fibres having the property $(DN)$.

   45-58
6. A PARAMETRIC SIMPLEX METHOD FOR OPTIMIZING A LINEAR FUNCTION OVER THE EFFICIENT SET OF A BICRITERIA LINEAR PROBLEM NGUYEN DINH DAN, LE DUNG MUU PDF

   ▸ Abstract

   The problem of optimizing a linear function over the efficient set of a multiple objective problem has many applications in multiple criteria decision making. The main difficulty of this problem is that its feasible region, in general, is a nonconvex set. In this paper we develop a fast algorithm for optimizing a linear function over the efficient set of a bicriteria linear programming problem. The method is a parametric simplex procedure using one parameter in the objective function.

   59-67
7. LINEALLY CONVEX HARTOGS DOMAINS CHRISTER O. KISELMAN PDF

   ▸ Abstract

   We study lineally convex domains of a special type, viz. Hartogs domains, and prove that such sets can be characterized by local conditions if they are smoothly bounded.

   69-94
8. PSEUDOCONVEXITÉ DES DOMAINES D'EXISTENCE DES FONCTIONS MÉROMORPHES À VALEURS VECTORIELLES TRAN HUU NAM, BUI DAC TAC PDF

   ▸ Abstract

   Dans cet article il est démontré que tout domaine d'existence d'une fonction méromorphe définie sur un domaine étalé au-dessus d'un espace de Banach à valeurs dans un dual de l'espace de Fréchet ou dans un espace de Fréchet possédant une norme continue est pseudoconvexe.

   95-108
9. ON REPRESENTATIONS OF ENTIRE FUNCTIONS BY DIRICHLET SERIES IN INFINITE DIMENSION PHAN THIEN DANH PDF

   111-123
10. VOLTERRA RIGHT INVERSES FOR WEIGHTED DIFFERENCE OPERATORS IN LINEAR SPACES NGUYEN VAN MAU, NGUYEN VU LUONG PDF

    ▸ Abstract

    Let $X$ be a linear space over a field $\mathcal F$ of scalars and let $X_{\omega}$ be the set of all infinite sequences $x = (x_0, x_1, \dots )$, where $x_j\in X$. Let  $A = (A_0,A_1, \dots)$ be a sequence in $L_0(X)$. Consider the weighted difference operator in $X_{\omega}: D_Ax = (x_{n+1}- A_nx_n)$. The scalar cases of weighted difference operators have been investigated, among others, by Przeworska-Rolewicz [3] and Kalfat [6]. In this paper we describe the set of all right inverses and the set of all initial operators for $D_A$. Properties of fundamental right inverses and fundamental initial operators are studied. In particular, we give conditions for a fundamental right inverse to be Volterra and apply this result to solve the corresponding initial value problem.

    125-134
11. REGULARIZATION BY LINEAR OPERATORS NGUYEN BUONG PDF

    ▸ Abstract

    The purpose of this paper is to investigate convergence rates for an operator version of Tikhonov regularization for ill-posed problems involving monotone operators. The obtained results are presented in combination with finite-dimensional approximations for the space. An iterative process for regularized solution is studied for illustration.

    135-145
12. ON THE POINTWISE BEHAVIOR OF SOME LACUNARY WAVELET SERIES NOLI N. REYES PDF

    ▸ Abstract

    We show that the pointwise behavior of certain lacunary wavelet series at a neighborhood of a singularity, under certain conditions on the coefficients, cannot be worse than that of the logarithm's at zero.

    147-153
13. SPLINE COLLOCATION METHODS FOR A SYSTEM OF NONLINEAR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS NGUYEN MINH CHUONG, NGUYEN VAN TUAN PDF

    ▸ Abstract

    In this paper we shall apply spline collocation methods to solve approximately a system of nonlinear Fredholm-Volterra integral equations. We shall study existence and uniqueness conditions for collocation solution, and estimate the convergence rate. Some applications are shown.

    155-169