Issue 3, Volume 29, December 2004

2004 · Open access

1. MINIMAX THEOREMS REVISITED HOANG TUY PDF

   ▸ Abstract

   Very general conditions are established that ensure the existence of a saddle-value for a function $F(x, y) : C \times D \to \mathbb R$, where $C, D$ are subsets of two topological spaces $X, Y$ , respectively. These conditions are much weaker than those generally required in the literature. As consequences, several minimax theorems are obtained that include as special cases refinements of various minimax theorems developed recently in nonlinear analysis and optimization for quasiconvex quasiconcave functions. Despite the generality of the results, the proof is very simple and is independent of separation or fixed point arguments on which most best known minimax theorems are based.

   217-229
2. ON THE WEAK LAW OF LARGE NUMBERS FOR ADAPTED SEQUENCES IN VON NEUMANN ALGEBRA NGUYEN VAN QUANG PDF

   ▸ Abstract

   We investigate the weak law of large numbers for adapted sequences of measurable operators. As corollaries of the main theorem we obtain non-commutative versions of some related results presented in the monograph ''Martingale limit theory and its application" of P. Hall and C. C. Heyde.

   231-236
3. DUALITIES AND DIMENSIONS OF IRREDUCIBLE REPRESENTATIONS OF PARABOLIC SUBGROUPS OF LOW DEGREES NGUYEN DANG HO HAI, TON THAT TRI PDF

   ▸ Abstract

   Let $GL_{n_1,\dots,n_r}$ be a parabolic subgroup of the general linear group $GL_n$ over the prime field $\mathbb F_p$ of $p$ elements. A complete set of distinct irreducible modules for $\mathbb F_p[GL_{n_1,\dots,n_r} ]$ was explicitly constructed in [7]. In this paper, we use this construction to determine the contragredient dual module of each $\mathbb F_p[GL_{n_1,\dots,n_r} ]$-irreducible module and prove that its dimension can be computed via the dimensions of some $\mathbb F_p[GL_{n_i} ]$-irreducible modules.

   237-249
4. NORMALITY OF A FAMILY OF BANACH-VALUED HOLOMORPHIC MAPS LE MAU HAI, NGUYEN VAN KHUE, PHAM NGUYEN THU TRANG PDF

   ▸ Abstract

   The aim of this paper is to give conditions under which a family of holomorphic maps from the unit disc $\Delta$ in $\mathbb C$ with values in a Banach analytic manifold $X$ is non-normal.

   251-257
5. COMMUTATIVE GROUP ALGEBRAS OF $p^{\omega+n}$ - PROJECTIVE ABELIAN GROUPS PETER DANCHEV PDF

   ▸ Abstract

   Suppose $G$ is an abelian group and $R$ is a unitary commutative ring of prime characteristic $p$. The first main result is that the $p^{\omega+1}$-projective $p$-group $G$ is a direct factor of the group of normed units $V(RG)$ and $V(RG)/G$ is totally projective provided $R$ is perfect. The second main result is that the complete set of invariants for the $R$-algebra $RG$ consists of $G$, in the cases when $G$ is splitting or $G$ is with torsion-free rank one and in both situations the torsion part of $G$ is a $p^{\omega+1}$-projective $p$-group. These claims strengthen a theorem due to Beers-Richman-Walker.

   259-270
6. SOME STABILITY RESULTS FOR THE SEMI-AFFINE VARIATIONAL INEQUALITY PROBLEM NGUYEN NANG TAM PDF

   ▸ Abstract

   This paper establishes two theorems on the stability of a semi-affine variational inequality problem and gives a characterization of the stability of the generalized linear complementarity problem when the defining matrix is copositive plus on the constraint cone. One of our results gives an affirmative answer to the second open problem stated by M. S. Gowda and T. S. Seidman in their paper ''Generalized linear complementarity problems" (Math. Programming Vol. 46, 1990, 329–340).

   271-280
7. ON THE CAUCHY PROBLEM FOR MULTIDIMENSIONAL MONGE-AMPÈRE EQUATIONS HA TIEN NGOAN, NGUYEN THI NGA PDF

   ▸ Abstract

   The Cauchy problem for Monge-Ampère equations with several variables is formulated and reduced to that for a normal system of first-order nonlinear partial differential equations. The noncharacteristic condition for the Cauchy problem of multidimensional Monge-Ampère is given. The local solvability of the noncharacteristic Cauchy problem for these equations in the class of analytic functions is proved.

   281-298
8. SOME FIXED POINT THEOREMS FOR MAPPINGS OF TWO VARIABLES TRAN QUOC BINH PDF

   ▸ Abstract

   The existence of fixed points $x = T(x, x)$ and the convergence of implicit iteration $x_n = T(x_n, x_{n-1})$ to the fixed points for generalized nonexpansive type mappings of two variables are investigated.

   299-308
9. EXISTENCE OF SOLUTIONS OF GENERALIZED QUASIVARIATIONAL INEQUALITIES WITH SET-VALUED MAPS LE ANH TUAN, PHAM HUU SACH PDF

   ▸ Abstract

   This paper gives existence theorems for solutions of the problem of finding a point $(z_0, x_0, y_0)\in B(z_0, x_0)\times A(x_0)\times F(z_0, x_0, x_0)$ such that, for all $x \in A(x_0), F(z_0, x_0, x)- y_0 \not\subset C(z_0, x_0, x_0)$, where $A, B,C$ and $F$ are set-valued maps between topological vector spaces. Our results generalize some known existence theorems for quasivariational inequalities.

   309-316