Issue 3, Volume 34, December 2009

2009 · Open access

1. PERSISTENCE AND GLOBAL ATTRACTIVITY IN THE MODEL $A_{n+1} = A_nF_n(A_n, A_{n−1},\dots, A_{n−m})$ DANG VU GIANG PDF

   ▸ Abstract

   First, we prove the uniform persistence for discrete model $A_{n+1} = A_nF_n(A_n, A_{n−1},\dots, A_{n−m})$ of population growth, where $F_n : (0, \infty)^{m+1}\to (0,\infty)$ are continuous all. Second, we investigation the effect of delay $m$ on the global attractivity of the unique positive equilibrium.

   299-304
2. DUAL INTEGRAL EQUATIONS INVOLVING FOURIER TRANSFORMS WITH INCREASING SYMBOLS NGUYEN VAN NGOC PDF

   ▸ Abstract

   The aim of the present work is to propose a method for investigating and solving dual integral equations involving Fourier transfom with increasing symbols.

   305-318
3. WEIGHTED ENDPOINT ESTIMATES FOR MULTILINEAR COMMUTATOR OF MARCINKIEWICZ OPERATOR ZHOU XIAOSHA PDF

   ▸ Abstract

   In this paper, we prove the weighted endpoint estimates for multilinear commutator of Marcinkiewicz operator.

   319-334
4. AN ALTERNATING PROJECTIONS ALGORITHM FOR SOLVING LINEAR PROGRAMS PHAM CANH DUONG, LE THANH HUE PDF

   ▸ Abstract

   The method of alternating projections was first introduced by Von Neumann in 1933 for finding the projection of a given point onto the intersection of closed subspaces of a Hilbert space. Since its introduction this method has received considerable attention and has found application in many areas of mathematics and physics as well as in other fields of science and engineering. In this paper we show that recent results of the method of alternating projections for general convex feasibility problems may be used to construct a simple algorithm for solving linear programs. This new algorithm is simple to implement, computationally stable and is inherently parallel.

   335-343
5. KALLIN’S LEMMA FOR RATIONAL CONVEXITY KIEU PHUONG CHI PDF

   ▸ Abstract

   In this paper, we give a version of Kallin’s lemma for rationally convex sets. As an application, we give sufficient conditions so that the union of a totally real graphs in $\mathbf{C}^2$ is locally rationally convex.

   345-350
6. ON UNIQUE RANGE SETS FOR HOLOMORPHIC MAPS SHARING HYPERSURFACES WITHOUT COUNTING MULTIPLICITY HA TRAN PHUONG PDF

   ▸ Abstract

   In 1975, Fujimoto showed a result on the unique range set counting multiplicity for meromorphic maps from $\mathbb C^m$ to $\mathbb P^n(\mathbb C)$ with hyperplanes. Here we will prove some sufficient conditions of unique range sets ignoring multiplicity for algebraically non-degenerate holomorphic maps with hypersurfaces.

   351-360
7. INNER PRODUCT INEQUALITIES FOR TWO EQUIVALENT NORMS AND APPLICATIONS S. S. DRAGOMIR PDF

   ▸ Abstract

   Some inequalities for two inner products $\langle\cdot,\cdot\rangle_1$ and $\langle\cdot,\cdot\rangle_2$ which generate the equivalent norms $\|\cdot\|_1$ and $\|\cdot\|_2$ with applications for invertible bounded linear operators, positive definite self-adjoint operators, integral and discrete inequalities are given.

   361-369
8. A NOTE ON THE FINITENESS PROPERTY RELATED TO DERIVED FUNCTORS AMIR MAFI, HERO SAREMI PDF

   ▸ Abstract

   Let $R$ be a commutative Noetherian ring, $\mathfrak{a}$ an ideal of $R$, and $M, N$ two finitely generated $R$-modules. Let $t$ be a non-negative integer. It is shown that for any finitely generated $R$-module $L$ with $\mathrm{Supp}(L) \subseteq \mathrm{Supp}(M)$, the following statements hold:

   (i) $\mathrm{Supp}(\mathrm{Ext}^t_R(L; N)) \subseteq \cup^t_{i=0} \mathrm{Supp}(\mathrm{Ext}^i_R(M; N))$;

   (ii) $\mathrm{Ass}(\mathrm{Ext}^t_R(L; N)) \subseteq\mathrm{Ass}(\mathrm{Ext}^t_R(M; N)) \cup (\cup_{i=0}^{t-1}\mathrm{Supp}(\mathrm{Ext}^i_R(M; N)))$.

   As an immediate consequence, we deduce that if $\mathrm{Supp}(H_{\mathfrak{a}}^i(N))$ or $\mathrm{Supp}(H_{\mathfrak{a}}^i (M; N))$ is finite for all $i < t$, then the set $\cup_{n\in\mathbb N} \mathrm{Ass}(\mathrm{Ext}^t_R(M/\mathfrak{a}^nM, N))$ is finite. In particular, if $\mathrm{grade}(\mathfrak{a}, N) \geqslant t$ then the set  $\mathrm{Ass}(\mathrm{Ext}^t_R(M/\mathfrak{a}^nM, N))$ is finite.

   371-374
9. REMARKS ON THE KOBAYASHI HYPERBOLICITY OF COMPLEX SPACES NGUYEN VAN TRAO, TRAN HUE MINH PDF

   ▸ Abstract

   The purpose of this article is threefold. The first is to show the hyperbolicity and the tautness of certain Hartogs type domains. The second is to investigate the hyperbolic imbeddedness of an unbounded domain in a complex space. The third is to consider the uniform convergence of Green functions with multiple poles (Lempert functions with multiple poles, Caratheodory functions with multiple poles, respectively) on decreasing domains.

   375-387
10. SOME REMARKS ON THE AR-PROBLEM LE HOANG TRI, NGUYEN HOANG THANH PDF

    ▸ Abstract

    The aim of this paper is to introduce a possible scheme for constructing counterexamples (if there are any) of the AR-problem for compact sets. In fact, this is an extension of Kalton-Peck-Roberts’ result. We also have similar results on the AR-problem for the case of non-compact sets.

    389-400
11. A NOTE ON LE-PHẠM’S PAPER - CONVERGENCE IN $\delta\mathcal E_p$ SPACES RAFAŁ CZYŻ PDF

    ▸ Abstract

    Let $\delta\mathcal E_p$, $p > 0$, be the real vector space containing functions of the form $u_1−u_2$, where $u_1$ and $u_2$ are non-positive plurisubharmonic functions with finite pluricomplex $p$-energy. We prove a convergence theorem and give an example of interesting continuous mappings on this quasi-Banach space.

    401410