ACTA Mathematica Vietnamica

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A non-homogeneous p-Laplace equation in border case: Searching minimizers of functions on the convenient level set of the constraint function, the author obtain generalized solutions of a non-homogeneous p-Laplace equation in border case without using the regularity results of linear elliptic equations.
An extension of Renyi's characteristic theorem to two-sided exponential distributions: In studying geometric composed random variable, A. Renyi showed a characteristic property of the exponential distribution. In this paper, using the geometric compounding, the author extend Renyi's idea to the case of two-sided exponential distributions and get one characteristic property of the set of distributions.
Approximating solutions of the equation x=T(x, x): Let D be a bounded closed convex subset of a Banach space, and let T:DxD-D be a continuous mapping which satisfies for all x, y, z, t D, // T(x, y)-T(z, t)//< max {//x-z//, //y-t//} with strict inequality holding when //x-z// //y-t//. Suppose T condensing in the sense that (T(u, v))< max { (u), (v)} for subsets U, V of D for which (UW)>0 (where denotes the usual kuratowski set-measere of noncompactness). A projection-iteration method is shown to converge a solution of x=T(x, x). The significance of this result is that it holds in arbitrary spaces.
Automata with a time-variant structure and supply-demand theorems: The author 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 it self may be also time-variant. The paper show that there are a lot of supply-demand theorems for automata. Some applications of these theorems for diffirent processing systems are investigated.
Efficiency equivalent polyhedra for the feasible set of multiple objective linear programming: The paper propese 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 interion.
Generalized translation operators and their related Markov processes: The author conducted study on the 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 are established. The generalized differential operator introduced by N. V. Thu (1994) is also investigated.
Geometric solutions of nonlinear second order hyperbolic equations: The Cauchy problem has been considered for nonlinear hyperbolic equations of second order with smooth data. It is well known that the Cauchy problem has a smooth solution in a neigh bourhood of the initial curve. But it might fail to admit a smooth solution in the whole space. This means that singularities apear generally in finite time. The author was interested in the global theory. Therefore, the problem is how to extend the solution after the appearance of singularities. for this purpose, the author has lift the solution surface into contangent space to that the singularities would disappear, and construct globally a geometric solution there. After that the author projected it to the base space. The final results are showing the singularities of smooth mappings.
Non smooth B-preinvex functions: Necessary and sufficient conditions under which a locally Lipschitz functions is B-preinvex are established in terms of Clarke's generalized gradients.
On the continuity of vector convex multivalued functions: The well known Banach Steinhaustheoremis extended to the case of convex and concave functions and its applications are showed to find necessary and sufficient conditions for the C-continuity of vector functions. Relations between upper and lower C-continuities are also obtained.
On the first occurence of irreducible representations of the matrix semigroup: Let Mn=M(n, Fp) bethe semigroup of all nxn matrices over the fiald Fp of p elements, p is a prime number. As well known, each irreducible Mn-module appears as a composition factor of the space of homogeneous polynomials in some degree d. The punpose of the paper is to determine the lowest degree d for some irreducible modules.
The normalized duality mapping and two related characteristic properties of a uniformly convex Banach space: The paper is devoted to study on some properties of the normalized duality mapping and two related characteristic properties of anuniformly convex Banach space. In particular, a theorem due to J. Prub is extended. Based on this extention of the Prub theorem, some new results on the continuity of the metric projection onto a family of closed convex sets in uniformly convex Banach spaces are obtained.