Issue 1, Volume 17, June 1992

1992 · Open access

1. ON THE STRUCTURE OF COCOMMUTATIVE COALGEBRAS NGUYEN VIET DUNG PDF

   3-8
2. THE CONVECTIVE MOTION OF AN INCOMPRESSIBLE VISCOUS FLUID CONTAINED IN AN ELASTIC CYLINDRICAL SHELL NGO HUY CAN, TRAN THU HA PDF

   9-29
3. SEMI-CONTINUOUS ARBITRARILY VARYING CHANNELS WITH GENERAL STATE CONSTRAINTS BUI VAN THANH PDF

   31-50
4. NONCONVEX PERTURBATION OF DIFFERENTIAL INCLUSIONS WITH MEMORY TRUONG XUAN DUC HA PDF

   51-65
5. ON THE CONTROLLABILITY OF SINGULAR SYSTEMS IN BANACH SPACES VU NGOC PHAT, K. BALACHANDRAN PDF

   ▸ Abstract

   The paper presents necessary and sufficient conditions for global controllability to a subset of singular linear discrete-time systems with constrained controls in Banach spaces. The main tool of the proof is based on extension of the surjectivity theorem to set-valued functions.

   67-76
6. ON A FREE BOUNDARY PROBLEM ARISING FROM MATHEMATICAL MODELS FOR SORPTION OF SWELLING SOLVENTS IN GLASSY POLYMER PHAN HUU SAN, NGUYEN DINH TRI PDF

   77-89
7. PROBLEMS OF VECTOR OPTIMIZATION PHAN QUOC KHANH, DINH THE LUC PDF

   ▸ Abstract

   The paper discusses results in main problems of vector optimization. Optimality notions and general existence theorems presented with an emphasis on proper efficiency. Norm scalarization in normed spaces ordered by general convex cone and other scalar representations are considered. For duality, we propose a scheme of constructing dual problems in an axiomatic approach, which includes Lagrangean duality as a special case. Furthermore, both necessary optimality conditions and sufficient conditions are obtained under relaxed assumptions and for general problems so that the Pontryagin maximum principle for cooperative differential gemes can be derived as consequences. Finally, we extend Ekeland's variational principle to vector optimization problems in a general setting.

   91-112
8. ON ASSOCIATED PRIMES OF MODULES OVER A NON-COMMUTATIVE GOREINSTEIN RING HO DINH DUAN PDF

   113-126
9. ON THE ALMOST SURE CONVERGENCE OF TWO-PARAMETER MARTINGLES AND THE STRONG LAW OF LARGE NUMBERS IN BANACH SPACES NGUYEN VAN HUNG, NGUYEN DUY TIEN PDF

   ▸ Abstract

   Let $(\Omega, F, P)$ be a probability space, $N^2 = N \times N$ denote the set of parameters with the partial order defined by $(m_1, n_1)\leq (m_2, n_2)$ if and only if $m_1\leq m_2$ and $n_1\leq n_2$ $(m_1, n_1, m_2, n_2\in N)$. Let $F_{mn}$ be an increasing family of sub-$\delta$-fields of $F$ satisfying the usual condition $(F_4)$ and $(M_{mn}, F_{mn})$ a two-parameter martingale taking values in a Banach space $(B, \| \cdot \|)$. In this paper we investigate the interrelation between geometric properties of Banach spaces and Martingale convergence theorems. Moreover we also study Marcinkiewicz-Zygmund's type strong law of large numbers for two-parameter Banach-valued martingales and the integrability of two-parameter Banach-valued martingale maximal functions.

   127-143
10. HOLOMORPHIC EXTENSION SPACES AND FINITE PROPER HOLOMORPHIC SURJECTIONS LE MAU HAI PDF

    145-155
11. LEFT $SF$-RINGS WHOSE COMPLEMENT LEFT IDEALS ARE IDEALS XHANG JULE, DU XIANNENG PDF

    ▸ Abstract

    A ring $R$ is called a left (right) $SF$-ring if every simple left (right) $R$-module is flat. It is known that von Neumann regular rings are left and right $SF$-rings. In this note, we prove that if $R$ is a left $SF$-ring whose complement left ideals are ideals, then $R$ is strongly regular.

    157-159
12. ON THE UNIQUENESS OF GLOBAL CLASSICAL SOLUTIONS OF THE CAUCHY PROBLEM FOR HAMILTON-JACOBI EQUATIONS TRAN DUC VAN, NGUYEN DUY THAI SON PDF

    ▸ Abstract

    We consider the Cauchy problem for Hamilton-Jacobi equations in $n$-dimensional space $(n\geq 1)$ and prove some uniqueness results for classical global solutions. Our method is based on the theory of multivalued mappings and of differential inclusions.

    161-167