Issue 1, Volume 25, April 2000

2000 · Open access

1. AVERAGING OF NEUTRAL DIFFERENTIAL INCLUSIONS WHEN THE AVERAGE VALUE OF THE RIGHT-HAND SIDE DOES NOT EXIST TERESA JANIAK, EL\dot{Z}BIETA LUCZAK-KUMOREK PDF

   ▸ Abstract

   We consider the problem of applying the averaging method to the asymptotic approximation of solutions of functional-differential equations of neutral type $\dot{x}(t)\in\varepsilon F(t,x(t),\dot{x}(t))$ in the case where the average of the right-hand side does not exist. Our paper generalizes results of W. A. Plotnikow, W. M. Sawczenko from [8] where the generalized system $\dot{x}(t)\in\varepsilon F(t,x)$ was investigated.

   1-11
2. H-PROPERTY, NORMAL STRUCTURE AND FIXED POINTS OF NONEXPANSIVE MAPPINGS IN METRIC LINEAR SPACES WU JUNDE, T. D. NARANG PDF

   ▸ Abstract

   Abstract

   13-18
3. THE PROPERTIES $(\underline{DN})$ and $(DN_{\varphi})$ OF SPACES OF GERMS OF HOLOMORPHIC FUNCTIONS NGUYEN VAN HAO, BUI DAC TAC PDF

   ▸ Abstract

   In this note we prove that the space $[\mathcal{H}(O_E)]^\prime$ is asymptotically normable (resp. has property $(\underline{DN})$) if E is an asymptotically normable Frechet space (resp. $E$ is a Frechet $(\underline{DN})$-space) having absolute basis. We also investigate these properties of the space $[\mathcal{H}(K)]^\prime$ when $K$ is a balanced compact subset of an asymptotically normable Frechet-Hilbertisable space and $K$ is a polynomially convex conpact set in $\mathbf{C}^n$.

   19-32
4. ON THE PROPERTY $LB^{\infty}$ OF SPACES OF GERMS OF HOLOMORPHIC FUNCTIONS AND THE PROPERTIES $(\tilde{\Omega},\overline{\Omega})$ OF THE HARTOGS DOMAINS IN INFINITE DIMENSION LE MAU HAI, PHAM HIEN BANG PDF

   ▸ Abstract

   The aim of this paper is to establish the property $LB^{\infty}$ on $[H(K_{\varepsilon})]^\prime$ under the assumption that $E$ is a Frechet space with an absolute basis and $K_{\epsilon}$ is a balanced convex compact subset of $E$. At the same time, the properties $(\tilde{\Omega},\overline{\Omega})$ for the Hartogs domains associated to an open polydisc in a nuclear Frechet space with a basis will be also proved.

   33-47
5. ON LOCAL REDUCTION NUMBERS AND a-INVARIANTS OF REES ALGEBRAS OF GOOD FILTRATIONS DUONG QUOC VIET PDF

   ▸ Abstract

   Abstracr

   49-66
6. A CONVEX-CONCAVE PROGRAMMING METHOD FOR OPTIMIZING OVER THE EFFICIENT SET LE DUNG MUU PDF

   ▸ Abstract

   The problem of optimizing a real valued function over the efficient set of a multiple objective linear program has some applications in multiple objective decision making. The main difficulty of this problem arises from the fact that its feasible domain, in general, is nonconvex and not given explicitly. In this paper we formulate this problem as a linearly constrained convex-concave program where the number of “nonconvex variables” is just equal to the number of independent criteria. We propose inner and outer procedures to constructing an initial set allowing convex-concave programming decomposition methods to be applied.

   67-85
7. CHARACTERISTIC FUNCTION FOR RANDOM SETS AND CONVERGENCE OF SUMS OF INDEPENDENT RANDOM SETS MARC LAVIE PDF

   ▸ Abstract

   The purpose of this paper is to present a notion of characte- ristic function for a random set. Some basic properties of this characteristic function are given. Then, we extend classical results on the convergence of independent random variables to the case of independent random sets taking closed and bounded convex values.

   87-99
8. NORMAL CONES TO A POLYHEDRAL CONVEX SET AND GENERATING EFFICIENT FACES IN LINEAR MULTIOBJECTIVE PROGRAMMING NGUYEN THI BACH KIM, DINH THE LUC PDF

   ▸ Abstract

   In this paper we describe the normal cones to a polyhedral convex set and their polarity with the faces of the set. Then we express optimaltity conditions in terms of negative normal cones and propose a method for generating efficient solution faces of a linear multiobjective programming problem together with some computational examples.

   101-124