Issue 2, Volume 30, August 2005

2005 · Open access

1. THE GROWTH OF COMPOSITE MEROMORPHIC FUNCTIONS WITH DEFICIENT FUNCTIONS JIANWU SUN PDF

   ▸ Abstract

   Let $f$ be a transcendental meromorphic function of order $\rho_f ,$ $g$ a transcendental entire function of lower order $\lambda_g$ $(\lambda_g < +\infty)$, and $a_i(z)$ $(i = 1, 2, \dots , n; n \leq \infty)$ be entire functions satisfying $T(r, a_i(z)) = \circ(T(r, g))$. If $\sum_{i=1}^n\partial(a_i(z),g)=1$ $\partial(a_i(z),g) > 0$ and $a_i(z)\not\equiv\infty$ for each $i$, then
   $$\overline{\lim\limits_{r\to\infty}}\log(T(r,f(g)))/T(r,g)=\pi\rho_f.$$

   103-112
2. DIFFERENTIAL SUBORDINATION ASSOCIATED WITH LINEAR OPERATORS DEFINED FOR MULTIVALENT FUNCTIONS V. RAVICHANDRAN, M. DARUS, M. HUSSAIN KHAN, K. G. SUBRAMANIAN PDF

   ▸ Abstract

   In this paper we give certain sufficient conditions for functions defined through the Dziok-Srivastava linear operator and the multiplier transformation.

   113-121
3. ON THE ASYMPTOTIC BEHAVIOR OF GENERALIZED SOLUTION OF PARABOLIC SYSTEMS IN A NEIGHBORHOOD OF CONIC POINT NGUYEN MANH HUNG, PHAM TRIEU DUONG PDF

   ▸ Abstract

   The purpose of this paper is to develop the well-known theory on the elliptic, hyperbolic and parabolic equations in nonsmooth domains that has been presented by such Russian mathematicians as V. A. Kondratiev, V. G. Mazya, B. A. Plamenevsky and S. A. Nazarov. We will obtain an asymptotic expansion of the generalized solutions of first initial boundaryvalue problems for strongly parabolic systems near the conic point on the boundary of the infinite cylinder.

   123-136
4. ON THE ROBUSTNESS OF ASYMPTOTIC STABILITY FOR A CLASS OF SINGULARLY PERTURBED SYSTEMS WITH MULTIPLE DELAYS VU HOANG LINH PDF

   ▸ Abstract

   This paper is concerned with the stability robustness of a class of singularly perturbed systems of linear functional differential equations. First, the stability radius for the reduced systems is proposed. Then, asymptotic behavior of the structured complex stability radius for the singularly perturbed systems is established as the small parameter tends to zero.

   137-151
5. SOME STRONG COMPARISON PRINCIPLES AND CONVERGENCE THEOREMS IN THE CAPACITY AND THE DIRICHLET PROBLEM IN THE CLASS $\mathcal F_p(h)$ LE MAU HAI, TANG VAN LONG PDF

   ▸ Abstract

   The aim of this paper is to establish the strong comparison principle of Xing type ([Xi1], [Xi2]) for the classes $\mathcal E_p$ and $\mathcal F_p$. As an application of the obtained results, we investigate the convergence in the capacity of the complex Monge-Ampère operator for the class $\mathcal F_p$ as well as solve the Dirichlet problem in the class $\mathcal F_p(h)$.

   153-168
6. OPTIMALITY CONDITIONS IN DC-CONSTRAINED OPTIMIZATION M. LAGHDIR PDF

   ▸ Abstract

   This paper studies the necessary and sufficient optimality conditions associated with the problem of minimizing a DC-function (difference of two convex functions) subject to a DC-constraint.

   169-179
7. SHARP WEIGHTED INEQUALITY FOR MULTILINEAR COMMUTATOR OF THE LITTLEWOOD-PALEY OPERATOR ZHANG MINGJUN, LIU LANZHE PDF

   ▸ Abstract

   In this paper, we prove the sharp inequality for multilinear commutator related to Littlewood-Paley operator. By using the sharp inequality, we obtain the weighted $L^p$-norm inequality for the multilinear commutator.

   181-189
8. ON LOCAL PARETO OPTIMA OF REAL ANALYTIC MAPPINGS HA HUY VUI, PHAM TIEN SON PDF

   ▸ Abstract

   This paper deals with the local problem of optimizing several analytic functions at the same time. We prove that the Milnor number of an isolated complete intersection singularity at a local Pareto optimal point is odd. Furthermore, high-order necessary and almost sufficient conditions are given, allowing one to recognize from the Newton diagram of an analytic mapping at the origin whether this point is a local Pareto optimum.

   191-202