Issue 1, Volume 27, April 2002

2002 · Open access

1. AN EXTENSION OF RENYI’S CHARACTERISTIC THEOREM TO TWO-SIDED EXPONENTIAL DISTRIBUTIONS TRAN KIM THANH PDF

   ▸ Abstract

   In studying geometric composed random variable, A. Rényi showed a characteristic property of the exponential distribution. In this paper, using the geometric compounding we extend R´enyi’s idea to the case of two-sided exponential distributions and get one characteristic property of the set of distributions.

   1-4
2. ON THE FIRST OCCURENCE OF IRREDUCIBLE REPRESENTATIONS OF THE MATRIX SEMIGROUP TON THAT TRI PDF

   ▸ Abstract

   Let $M_n = M(n, F_p)$ be the semigroup of all $n\times n$ matrices over the field $F_p$ of $p$ elements, $p$ a prime number. As well known, each irreducible $M_n$-module appears as a composition factor of the space of homogeneous polynomials in some degree $d$. The purpose of the paper is to determine the lowest degree $d$ for some irreducibles modules.

   5-11
3. ON THE CONTINUITY OF VECTOR CONVEX MULTIVALUED FUNCTIONS NGUYEN BA MINH, NGUYEN XUAN TAN PDF

   ▸ Abstract

   The well-known Banach Steinhaus Theorem is extended to the case of convex and concave functions and its applications are shown to find necessary and sufficient conditions for the $C$-continuity of vector convex functions. Relations between upper and lower $C$-continuities are also obtained.

   13-25
4. APPROXIMATING SOLUTIONS OF THE EQUATION $x = T(x, x)$ W. A. KIRK PDF

   ▸ Abstract

   Let $D$ be a bounded closed convex subset of a Banach space, and let $T : D\times D \to D$ be a continuous mapping which satisfies for all $x, y, z, t \in D$, 
   $$\|T(x,y)-T(z,t)\|\leq \max \{\|x-z\|,\|y-t\|\}$$
   with strict inequality holding when $\|x-z\|\not=\|y-t\|$. Suppose $T$ condensing in the sense that
   $$\gamma(T(U,V)) < \max \{\gamma(U),\gamma(V)\}$$
   for subsets $U, V$ of $D$ for which  $\gamma(U\backslash V ) > 0$ (where $\gamma$ denotes the usual Kuratowski set-measure of noncompactness). A projection-iteration method is shown to converge to a solution of $x = T (x, x)$. The significance of this result is that it holds in arbitrary spaces.

   27-31
5. NONSMOOTH B-PREINVEX FUNCTIONS DO VAN LUU, LE MINH TUNG PDF

   ▸ Abstract

   Necessary and sufficient conditions under which a locally Lipschitz function is B-preinvex are established in terms of Clarke’s generalized gradients.

   33-40
6. AUTOMATA WITH A TIME-VARIANT STRUCTURE AND SUPPLY-DEMAND THEOREMS PHAM TRA AN PDF

   ▸ Abstract

   We consider automata with a time-variant structure. In these automata not only the function of state transition may be time-variant, but the set of states itself may be also time-variant. We show that there are a lot of supply-demand theorems for the automata. Some applications of these theorems for different processing systems are investigated.

   41-52
7. THE NORMALIZED DUALITY MAPPING AND TWO RELATED CHARACTERISTIC PROPERTIES OF A UNIFORMLY CONVEX BANACH SPACE BUI TRONG KIEN PDF

   ▸ Abstract

   This paper is devoted to the study of some properties of the normalized duality mapping and two related characteristic properties of a uniformly convex Banach space. In particular, a theorem due to J. Prüß is extended. Based on this extention of the theorem of Prüß, some new results on the continuity of the metric projection onto a family of closed convex sets in uniformly convex Banach spaces are obtained.

   53-67
8. A NON-HOMOGENEOUS $P$-LAPLACE EQUATION IN BORDER CASE PHAM XUAN DU, DUONG MINH DUC PDF

   ▸ Abstract

   Searching minimizers of functions on the convenient level set of the constraint function we obtain generalized solutions of a non-homogeneous $p$-Laplace equation in border case without using the regularity results of linear elliptic equations.

   69-75
9. EFFICIENCY EQUIVALENT POLYHEDRA FOR THE FEASIBLE SET OF MULTIPLE OBJECTIVE LINEAR PROGRAMMING NGUYEN THI BACH KIM PDF

   ▸ Abstract

   We propose an outer approximation algorithm for constructing a simple efficiency equivalent polyhedron for the feasible set of the multiple objective linear programming problem in the case where the ordering cone induced by the criteria functions is pointed and has a nonempty interior.

   77-85
10. GENERALIZED TRANSLATION OPERATORS AND THEIR RELATED MARKOV PROCESSES CAO VAN NUOI PDF

    ▸ Abstract

    We study properties of generalized translation operators and their relations with the associated Markov processes. Some relations between a Levitan family of generalized translation operators and its associated random convolution (in the sense of Vol’kovich) are established. The generalized differential operator introduced by N. V. Thu (1994) is also investigated.

    87-95
11. GEOMETRIC SOLUTIONS OF NONLINEAR SECOND ORDER HYPERBOLIC EQUATIONS MIKIO TSUJI, NGUYEN DUY THAI SON PDF

    ▸ Abstract

    We will consider the Cauchy problem for nonlinear hyperbolic equations of second order with smooth data. It is well known that the Cauchy problem has a smooth solution in a neighbourhood of the initial curve. But it might fail to admit a smooth solution in the whole space. This means that singularities appear generally in finite time. We are interested in the global theory. Therefore our problem is how to extend the solution after the appearance of singularities. For this purpose, we will first lift the solution surface into cotangent space so that the singularities would disappear, and we will construct globally a geometric solution there. Next we will project it to the base space. In this procedure we will meet the singularities of smooth mappings.

    97-117