Issue 1, Volume 26, April 2001

2001 · Open access

1. BOUNDARY VALUE CONJUGATION PROBLEMS FOR ELLIPTIC EQUATIONS IN VARIABLE DOMAINS HOANG QUOC TOAN PDF

   ▸ Abstract

   We study the behaviour of the solutions of boundary value conjugation problems for high order elliptic equations in variable domains $(\Omega_t,G^\prime_t)$ $(0 < t\leq 1)$ which depend smoothly on a parameter t in Krein’s sense. Considering the domain $$ as the limit of domains $(\Omega_0,G_0^\prime)$ when$t$ tends 0, we prove the existence and the uniqueness of the solution of the boundary value conjugation problem in $(\Omega_0,G_0^\prime).$

   1-15
2. A CLASS OF MINIMAX PROBLEMS SOLVABLE IN POLYNOMIAL TIME TRAN VU THIEU, TRAN THI HUE PDF

   ▸ Abstract

   We develop a polynomial-time algorithm for solving a class of 0-1 production-transportation problems. The objective function is the maximum of $n$ monotonic functions of the production volume. The transportation cost is assumed to be small as compared to the production cost and is omitted. The proposed algorithm is based on a labeling technique for improving feasible solutions.

   17-26
3. LIE SUPERALGEBRAS OF STRING THEORIES PAVEL GROZMAN, DIMITRY LEITES, IRINA SHCHEPOCHKINA PDF

   ▸ Abstract

   We describe simple complex Lie superalgebras of vector fields on “supercircles” - stringy superalgebras - in intrinsic terms. This is an announcement of a classification: there are four series of such algebras and four exceptional stringy superalgebras.

   We also describe Lie superalgebras close to the simple stringy ones, namely, 12 of the simple stringy Lie superalgebras are distinguished: only they have nontrivial central extensions and since one of the distinguished superalgebras has three nontrivial central extensions each, there exist exactly 14 superizations of the Liouville action, Schrödinger equation, KdV hierarchy, etc. We also present the three nontrivial cocycles on the $N = 4$ extended Neveu–Schwarz superalgebra in terms of primary fields.

   One of these stringy superalgebras is a Kac–Moody superalgebra $\mathfrak{g}(A)$ with a nonsymmetrizable Cartan matrix $A$. It can not be interpreted as a central extension of a twisted loop algebra.

   In the literature the stringy superalgebras are often referred to with an unfortunate term superconformal. We show that only three of simple stringy superalgebras are indeed conformal.

   27-63
4. REVERSE POLYBLOCK APPROXIMATION FOR OPTIMIZATION OVER THE WEAKLY EFFICIENT SET AND EFFICIENT SET LE TU LUC PDF

   ▸ Abstract

   A new method is developed for maximizing a concave function over the weakly efficient set, or the efficient set. The method consists of converting the problem into a monotonic optimization problem and solving the latter by a reverse polyblock approximation algorithm.

   65-80
5. ENTIRE EIGENFUNCTIONS OF THE LAPLACIAN OF EXPONENTIAL TYPE WITH RESPECT TO THE LIE NORM AND THE DUAL LIE NORM KEIKO FUJITA PDF

   ▸ Abstract

   We consider entire functions of exponential type with respect to the Lie norm and the dual Lie norm. We characterize them by the growth condition of harmonic components in their double series expansion. Special attention will be paid to the eigenfunctions of the Laplacian.

   81-94
6. FONCTION DE LITTLEWOOD-PALEY ET ESPACES DE LIPSCHITZ ALAIN SALLAZ PDF

   ▸ Abstract

   In this paper we study the action of the Littlewood-Paley operator on the Lipschitz functions. The used method is very elementary and allows us to complete some earlier results. 

   95-113
7. OPTIMALITY CONDITIONS FOR CONTROLS ACTING AS COEFFICIENTS OF A NONLINEAR ORDINARY DIFFERENTIAL EQUATION OF SECOND ORDER MOHAMED AKKOUCHI, ABDELLAH BOUNABAT, MANFRED GOEBEL PDF

   ▸ Abstract

   We study in this paper a control problem associated to a semilinear second order ordinary differential equation with pointwise state constraints. The control acts as a coefficient of the state equation. For this problem, we prove the existence of optimal controls and obtain a necessary optimality condition. This condition looks somehow like Pontryagin’s maximum principle. We end this work by giving illustrative examples where we apply our results.

   115-124