Issue 2, Volume 24, August 1999

1999 · Open access

1. THE REGULARITY OF SPACES OF GERMS OF FRECHET-VALUED BOUNDED HOLOMORPHIC FUNCTIONS NGUYEN HA THANH PDF

   117-128
2. SOLUTIONS D'UNE ÉQUATION DIFFÉRENTIELLE FONCTIONNELLE SEMI-LINÉAIRE À RETARD INFINI DANS UN ESPACE DE BANACH SGHIR ABDELHAQ PDF

   ▸ Abstract

   This paper is concerned with the existence of solutions to the initial value problem for a semilinear functional differential equation with infinite delay in a Banach space:
   $$\begin{cases}x^\prime(t)=Lx_t+f(t,x_t),\quad t\in[0,a]\ (a > 0)\\ x(t)=\varphi(t),\quad t\in ]-\infty,0].\end{cases}$$The result is based on the Leray-Schauder alternative and a priori bounds on solutions.

   129-145
3. A CLASSIFICATION OF A CLASS OF MARTINGALE-LIKE SEQUENCES DINH QUANG LUU PDF

   ▸ Abstract

   A sequence $(X_n)$ is said to be a game fairer with time if for every $\varepsilon > 0$ we have $\lim_n\sup_{m\geq n}P(\| E_n(X_m)-X_n\| > \varepsilon)=0$. It is known that every $L^1$-bounded Banach space-valued game fairer with time has a unique Riesz-Talagrand decomposition: $X_n=M_n+P_n$, where $(M_n)$ is a uniformly integrable martingale and $(P_n)$ converges to zero in probability. The aim of this note is to give a classification of a class of martingale-like sequences considerably more general than games fairer with time for which the above Riesz-Talagrand decomposition still holds.

   147-156
4. A COMPLEXITY CHARACTERISTIC OF PETRI NET LANGUAGES PHAM TRA AN PDF

   ▸ Abstract

   A new complexity characteristic of Petri net languages is introduced. Some necessary conditions for Petri net languages are established and a series of simple languages not acceptable by Petri nets are given.

   157-167
5. COEFFICIENT MULTIPLIERS FOR SOME CLASSES OF DIRICHLET SERIES IN SEVERAL COMPLEX VARIABLES LE HAI KHOI PDF

   ▸ Abstract

   This paper deals with coefficient multipliers for some classes of Dirichlet series with complex frequencies, including those that define
   entire functions in $\mathbf{C}^n$.

   169-182
6. ON A REPRESENTATION OF CONVEX VECTOR FUNCTIONS AND THE MAXIMAL CYCLIC MONOTONICITY OF THEIR SUBDIFFERENTIAL PHAN NHAT TINH PDF

   ▸ Abstract

   In this paper, we give a formula expressing a convex vector function as the supremum of a certain collection of affine functions and
   prove the maximal cyclic monotonicity of its subdifferential.

   183-191
7. UNIQUENESS OF GLOBAL SEMICLASSICAL SOLUTIONS FOR SOME SYSTEMS OF FIRST-ORDER NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS LE VAN HAP PDF

   ▸ Abstract

   We consider the Cauchy problem for weakly coupled systems of first-order nonlinear partial differential equations and prove some
   uniqueness results of global semiclassical solutions. Our method is based on the theory of multivalued functions and of differential inclusions.

   193-205
8. AN OPERATIONAL METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO DERIVATIVES YURII LUCHKO, RUDOLF GORENFLO PDF

   ▸ Abstract

   In the present paper, we first develop the operational calculus of Mikusi\'{n}ski's type for the Caputo fractional differential operator. This calculus is used to obtain exact solutions of an initial value problem for linear fractional differential equations with constant coefficients and fractional derivatives in Caputo's sense. The initial conditions are given in terms of the field variable and its derivatives of integer order. The obtained solutions are expressed through Mittag-Leffler type functions. Special cases and integral representations of solutions are presented.

   207-233
9. POINCARÉ SERIES OF QUANTUM SPACES ASSOCIATED TO HECKE OPERATORS PHUNG HO HAI PDF

   ▸ Abstract

   We prove that the dimension of the homogeneous components of the quadratic algebras associated to a Hecke operator is a Pólya
   frequency (P-) sequence. This result enables us to give some characterizations on the Poincaré series of these quadratic algebras.

   235-246