Issue 3, Volume 35, December 2010

2010 · Open access

1. RANDOM MATRICES I: COMBINATORIAL PROBLEMS TRAN VINH LINH, VAN VU PDF

   ▸ Abstract

   This is the first part of a series of surveys on random matrices. In this part, we focus on problems and results of combinatorial nature.

   335-354
2. ON THE RATIONAL RECURSIVE TWO SEQUENCES $x_{n+1}=ax_{n-k}+bx_{n-k}/(cx_n+\delta dx_{n-k})$ E. M. E. ZAYED, M. A. EL-MONEAM PDF

   ▸ Abstract

   The main objective of this paper is to study some qualitative behavior of the solutions of the two difference equations $$x_{n+1}=ax_{n-k}+bx_{n-k}/(cx_n+\delta dx_{n-k}),\ \ n=0,1,2,\dots,$$ where the initial conditions $x_{−k}, \dots , x_{−1}, x_0$ are arbitrary positive real numbers and the coefficients $a, b, c$ and $d$ are positive constants, while $k$ is a positive integer number and $\sigma = \pm 1$. Some numerical examples are given to illustrate our results.

   355-369
3. CONVERGENCE OF A MODIFIED CONJUGATE DESCENT METHOD IN THE PRESENCE OF ERRORS MIN SUN PDF

   ▸ Abstract

   The conjugate gradient method is a useful method for solving large-scale minimization problems. Errors may arise because of inexact computation. In this paper we study the global convergence of a modified conjugate descent method with strong Wolfe line search in the presence of errors. Preliminary numerical experiments are given to show the efficiency and robustness of the method.

   371-378
4. MINIMUM $L_1$-NORM ESTIMATION FOR MIXED FRACTIONAL ORNSTEIN-UHLENBECK TYPE PROCESS YU MIAO PDF

   ▸ Abstract

   In the present paper, the asymptotic properties of the minimum $L_1$-norm estimator of the drift parameter for mixed fractional Ornstein-Uhlenbeck type process satisfying a linear stochastic differential equation driven by a mixed fractional Brownian motion are obtained.

   379-386
5. WEAK LAWS OF LARGE NUMBERS FOR DOUBLE ARRAYS OF RANDOM ELEMENTS IN BANACH SPACES LE VAN DUNG PDF

   ▸ Abstract

   In this paper, we establish the weak laws of large numbers with or without random indices for double arrays of random elements in Banach spaces. Our results are more general and stronger than some well-known ones.

   387-398
6. CONVERGENCE THEOREMS OF MULTI-STEP ITERATION WITH ERRORS FOR FINITE FAMILIES OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS GURUCHARAN SINGH SALUJA, HEMANT KUMAR NASHINE PDF

   ▸ Abstract

   The aim of this paper is to study weak and strong convergence of common fixed points for multi-step iterative scheme with errors for finite families of asymptotically nonexpansive mappings in real uniformly convex Banach spaces. Our results extend and improve the corresponding results of Khan and Takahashi [13], Schu [22], Takahashi and Tamura [26], Rhoades [21], Xu and Noor [28], Khan and Fukhar-ud-din [12], Plubtieng et al. [20] and many others.

   399-410
7. PARAMETRIZED SADDLE POINTS DOREL I. DUCA, EUGENIA DUCA PDF

   ▸ Abstract

   In this paper, one considers the vector saddle point problem with respect to a cone which depends on two parameters. Necessary and sufficient conditions for a point to be a solution of the parameterized cone saddle point problem are given. Then the parameterized cone saddle point problem is related to the parameterized cone vector variational inequality problem. One shows that, under some hypotheses, the problems of parameterized cone vector saddle point and of parameterized cone vector variational inequality have the same solution set. Also, an existence result for a parameterized cone vector saddle point problem to have a solution is given.

   411-425
8. ROBUST STABILIZATION OF LINEAR POLYTOPIC CONTROL SYSTEMS WITH MIXED DELAYS LE VAN HIEN, VU NGOC PHAT PDF

   ▸ Abstract

   In this paper, a class of uncertain linear polytopic systems with mixed delays in state and control is studied. Using an improved parameter dependent Lyapunov-Krasovskii functional approach and linear matrix inequality technique, delay-dependent sufficient conditions for the robust stabilization of the system are first established in terms of the Mondié-Kharitonov type’s linear matrix inequality (LMI) conditions. A numerical example is presented to demonstrate that the feedback control designed based on the obtained condition is effective, even though neither nominal control systems are controllable.

   427-437
9. A UNICITY THEOREM WITH TRUNCATED COUNTING FUNCTION FOR MEROMORPHIC MAPPINGS PHAM HOANG HA PDF

   ▸ Abstract

   In this article, a unicity theorem with truncated multiplicities of meromorphic mappings in several complex variables sharing few targets are given. It gives some remarkable improvements for the results in [15].

   439-456