Issue 1, Volume 32, April 2007

2007 · Open access

1. PSEUDO-DIFFERENTIAL OPERATORS RELATED TO ORTHONORMAL EXPANSIONS OF GENERALIZED FUNCTIONS AND APPLICATION TO DUAL SERIES EQUATIONS NGUYEN VAN NGOC PDF

   ▸ Abstract

   The aim of the present work is to introduce some functional spaces for investigating pseudo-differential operators involving orthogonal expansions of generalized functions and their application to dual series equations.

   1-14
2. ON SOME GENERALIZED VECTOR EQUILIBRIUM PROBLEMS WITH SET-VALUED MAPS LE ANH TUAN, PHAM HUU SACH PDF

   ▸ Abstract

   In this paper we consider the generalized vector equilibrium problem $(P_{\alpha})$ of 0nding a point $z_0, x_0)\in E \times K$ such that $x_0 \in A(z_0, x_0)$ and $$\forall \eta\in A(z_0,x_0), \exists z\in B(z_0,x_0,\eta), \quad (F(z,x_0,\eta), C(z,x_0,\eta))\in \alpha,$$ where $\alpha$ is an arbitrary relation on $2^Y$, and $A,B,C$ and $F$ are set-valued maps between finite-dimensional spaces. Existence results are obtained under assumptions di3erent from those of [17]. Some special cases of Problem $(P_{\alpha})$ are discussed in detail.

   15-32
3. ON A SUFFICIENT CONDITION FOR THE CENTRAL LIMIT THEOREM PHAM XUAN BINH PDF

   33-40
4. CONDITIONAL MARTINGALES DARIUSZ MAJEREK, WIESŁAW ZIȨBA PDF

   ▸ Abstract

   In this paper we would like to present a concept of conditional martingales given $\sigma$-field $\mathcal F$, which is a natural generalization of martingales. Based on $\mathcal F$-independence, we are able to show that there exist conditional martingales, which are not martingales in pure sense. In the first part of the paper we will show different types of conditional convergence and relations between them. This article is intended to give a generalization of the theorem about almost sure convergence of martingales and some properties of conditional martingales.

   41-50
5. GENERALIZED $\ell$-ISOMORPHISMS OF $\ell$-GROUPS XINMIN LU PDF

   ▸ Abstract

   By using large and small convex $\ell$-subgroups of an $\ell$-group introduced in [3] and [4], we extend $\ell$-isomorphisms of $\ell$-groups to quasi-$\ell$-isomorphisms and co-quasi-$\ell$-isomorphisms. Then we will establish some sufficient and necessary conditions under which two $\ell$-groups are quasi-$\ell$-isomorphic or co-quasi-$\ell$-isomorphic.

   51-60
6. SOLUTIONS FAIBLES D’UNE INCLUSION DIFFÉRENTIELLE FONCTIONNELLE SEMI-LINÉAIRE À RETARD INFINI SUR UN ESPACE DE BANACH SGHIR ABDELHAQ PDF

   ▸ Abstract

   The aim of this note is to prove the existence of mild solutions for functional differential inclusion with infinite delay in a Banach space: $$\left\{\begin{array}{l}  x^\prime (t)\in Lx_t+F(t,x_t), & t\in [0,a]~(a > 0)\\ x(t)=\varphi(t), & t\in ]-\infty,0]. \end{array}\right.$$ The results are proved by using a variation of suitable constants formula with infinite delay and a direct application of topological transversality methods based on the degree theory for $\chi$- Lipschitz multimappings.

   61-70
7. MINIMIZING POLYNOMIAL FUNCTIONS HA HUY VUI, PHAM TIEN SON PDF

   ▸ Abstract

   We effectively compute a finite set containing all critical values and the infimum value of a real multivariate polynomial function. Besides, some relations between Newton polytopes and bounded below polynomials are also established.

   71-82
8. ON ZALCMAN COMPLEX SPACES AND NOGUCHI-TYPE CONVERGENCE-EXTENSION THEOREMS FOR HOLOMORPHIC MAPPINGS INTO WEAKLY ZALCMAN COMPLEX SPACES NGUYEN VAN TRAO, PHAM NGUYEN THU TRANG PDF

   ▸ Abstract

   In this article, some Noguchi-type convergence-extension theorems for holomorphic mappings into weakly Zalcman complex subspaces for a complex space are given. Moreover, the tautness of unbounded domains of a complex space with non-compact automorphism groups is investigated from the viewpoint of the theory of Zalcman complex spaces.

   83-97
9. DYNAMICS OF PREDATOR-PREY POPULATION WITH MODIFIED LESLIE-GOWER AND HOLLING-TYPE II SCHEMES NGUYEN HUU DU, NGUYEN MINH MAN, TONG THANH TRUNG PDF

   ▸ Abstract

   In this paper, we investigate a predator-prey population modeled by a system of differential equations modified Leslie-Gower and Holling-Type II schemes with time-dependent parameters. We establish a sufficient criterion posed on the behavior at infinity of coefficients for the permanence of systems, globally asymptotic stability of solutions. In the case where the coefficients of equations are periodic functions with a same period, it is proved that there exists a unique periodic orbit which attracts every solution starting in $\mathrm{int}\,\mathbb R^2_+$.

   99-111