Issue 3, Volume 25, December 2000

2000 · Open access

1. PERMANENCE AND POSITIVE BOUNDED SOLUTIONS OF KOLMOGOROV COMPETING SPECIES SYSTEM TRINH TUAN ANH, TRAN VAN NHUNG, LE HONG LAN PDF

   ▸ Abstract

   We study the Kolmogorov equation for $n$-species. Under certain conditions, it is shown that the equation is permanent and there exists a solution defined on whole $R$ whose components are bounded above and below by positive constants.

   251-261
2. ON SOME CLASSES OF HYPERBOLIC COMPLEX SPACES DO DUC THAI, PHAM VIET DUC PDF

   ▸ Abstract

   We characterize the hyperbolicity of the following complex spaces in the sense of Kobayashi: complex spaces satisfying the Landau property, compact complex spaces and Zariski open subsets of Moishezon spaces.

   263-272
3. ON THE LOCALLY UNIFORM OPENNESS OF POLYHEDRAL SETS HUYNH THE PHUNG PDF

   ▸ Abstract

   The paper is concerned with a geometrical property of polyhedral sets. Specifically, we shall prove that every polyhedral set (denoted by $M$) is locally uniformly opening. As a consequence, we show that for any set-valued map $F$ defined on a polyhedral set $M$, $F$ is locally Lipschitz on $M$ iff it is locally Lipschitz on each component of $M$.

   273-284
4. REMARKS ON HIMMELBERG-IDZIK'S FIXED POINT THEOREM SEHIE PARK, DO HONG TAN PDF

   ▸ Abstract

   In this note we give simple proofs of generalizations of Himmelberg fixed point theorem by applying the well-known KKM principle.

   285-289
5. GROWTH OF MEROMORPHIC FUNCTIONS JIANWU SUN PDF

   ▸ Abstract

   In this paper, we prove a general result concerning the growth of meromorphic functions. Our condition is much weaker than that used by Sing-Patil. Our result contains and improves the results of Nevanlinna, Clunie and Goldberg-Ostrovoskii. As an application, we solve a problem proposed by C. C. Yang.

   291-299
6. THE STRUCTURE OF TYPE $(\Omega­)$ OF SPACES OF BANACH-VALUED HOLOMORPHIC GERMS NGUYEN VAN KHUE, NGUYEN DINH LAN PDF

   ▸ Abstract

   This paper gives a sufficient condition which implies the property of type $(\Omega­)$ of $[\mathcal H(K,X)]^\prime$, where $\mathcal H(K,X)$ is the space of germs of $X$-valued holomorphic functions on $K$.

   301-313
7. ON CONJUGATE MAPS AND DIRECTIONAL DERIVATIVES OF CONVEX VECTOR FUNCTIONS NGUYEN XUAN TAN, PHAN NHAT TINH PDF

   ▸ Abstract

   In this paper, the concepts and the properties of conjugate maps and directional derivatives of convex vector functions from a subset of $R^n$ to $R^m$ with respect to a convex, closed and pointed cone are presented on the base of the notions of Pareto-supremum and Pareto-infimum. Some well-known results in the scalar case are generalized to the vector case. An application of conjugate maps to the dual problem is shown.

   315-344
8. ON GROWTH FUNCTION OF PETRI NET PHAM TRA AN PDF

   ▸ Abstract

   In this paper we introduce the growth function of a Petri net. We show that the growth function of any Petri net is bounded by a certain polynomial. There are relations between the growth function and the representative complexity of the language which is accepted by a Petri net.
    

   347-357
9. SOME CHARACTERIZATION OF BEST APPROXIMANTS IN NORMED LINEAR SPACES S. S. DRAGOMIR PDF

   ▸ Abstract

   Some new characterization of best approximants in normed linear spaces are given.

   359-366
10. NOETHER PROPERTIES OF LINEAR OPERATORS INDUCED BY ALGEBRAIC ELEMENTS NGUYEN VAN MAU, NGUYEN TAN HOA PDF

    ▸ Abstract

    In this paper we give some algebraic characterizations of an algebraic element with the characteristic polynomial having single roots and then inverstigate the Noether properties of bounded linear operators of the form
    \begin{equation} K=\sum\limits_{(i)\in\Gamma}A_{(i)}T^{(i)},\tag{1}\end{equation}
    where
    $$\Gamma=\left\{(i)=(i_1,i_2,\dots,i_m)\, | \, 0\leq i_k\leq n_k-1, \ k=1,\dots,m\right\}$$ $$A_{(i)}=A_{i_1i_2\dots i_m},\ T^{(i)}=T_1^{i_1}T_2^{i_2}\dots T_m^{i_m},$$
    $T_k$ are the commutative algebraic elements of order $n_k$, respectively.

    367-382