Issue 2, Volume 35, August 2010

2010 · Open access

1. AN $N$-ORDER ITERATIVE SCHEME FOR A NONLINEAR KIRCHHOFF-CARRIER WAVE EQUATION ASSOCIATED WITH MIXED HOMOGENEOUS CONDITIONS LE THI PHUONG NGOC, LE XUAN TRUONG, NGUYEN THANH LONG PDF

   ▸ Abstract

   In this paper, a high-order iterative scheme is established in order to get a convergent sequence at a rate of order $N$ $(N \geqslant 1)$ to a local unique weak solution of a nonlinear Kirchhoff – Carrier wave equation associated with mixed homogeneous conditions. This extends recent corresponding results where recurrent sequences converge at a rate of order 1 or 2.

   207-227
2. ON LOCAL COHOMOLOGY OF A TETRAHEDRAL CURVE DÔ HOÀNG GIANG, LÊ TUÂN HOA PDF

   ▸ Abstract

   It is shown that the diameter $\mathrm{diam}(H_{\mathfrak{m}}^1(R/I))$ of the first local cohomology module of a tetrahedral curve $C = C(a_1, \dots, a_6)$ can be explicitly expressed in terms of the ai and is the smallest non-negative integer k such that $\mathfrak{m}^kH_{\mathfrak{m}}^1(R/I) = 0$. From that one can describe all arithmetically CohenMacaulay or Buchsbaum tetrahedral curves.

   229-241
3. ON SOME GENERALIZED NEW TYPE DIFFERENCE SEQUENCE SPACES DEFINED BY A MODULUS FUNCTION AYHAN ESI PDF

   ▸ Abstract

   The idea of difference sequence spaces were defined by Kizmaz [6] and generalized by Et and Ҫolak [3]. Later Tripathy et al. [16] introduced the notion of the new difference operator $\Delta_m^nx_k$ for fixed $n, m \in \mathbb N$. In this paper we introduce some new type difference sequence spaces defined by a modulus function and the new concept of statistical convergence. We give various properties and inclusion relations on these new type difference sequence spaces.

   243-252
4. ON THE STABILITY OF SOLUTIONS OF ITO DIFFERENTIAL EQUATIONS NGUYEN THI THUY QUYNH PDF

   ▸ Abstract

   In this paper, we discuss the relationship between different types of stability of stochastic differential equations. We prove that for linear Ito stochastic differential equations, stability in probability is equivalent to almost sure stability. Almost sure stability does not depend on initial time. In the case of 1-dimensional Ito stochastic differential equation with constant coefficients satisfying nondegeneracy condition, we show that stability in probability is equivalent to weak stability in probability.

   253-261
5. FOURIER AND HERZ ALGEBRAS OF A COMPACT TENSOR HYPERGROUP MASSOUD AMINI, ALI REZA MEDGHALCHI PDF

   ▸ Abstract

   We study the basic properties of the Fourier and Herz spaces $A(K)$ and $A_p(K)$ of a compact hypergroup $K$ and associate them with subspaces of the Cartesian product of matrix algebras on the dual hypergroup. When $K$ is a tensor hypergroup we show that $A(K)$ is a regular Banach algebra whose spectrum is $K$. We also compute some of the corresponding multiplier algebras.

   263-274
6. MAPPINGS IN $\sigma$-PONOMAREV-SYSTEMS NGUYEN VAN DUNG PDF

   ▸ Abstract

   We use the $\sigma$-Ponomarev-system $(f, M, X, \{\mathcal P_n\})$ to give a consistent method to construct an $s$-mapping (msss-mapping, mssc-mapping) $f$ with covering-properties onto a space $X$ from a metric space $M$. As applications, we systematically get characterizations of $s$-images (msss-images, mssc-images) of metric spaces.

   275-287
7. ORDER STRUCTURE AND ENERGY OF CONFLICTING CHIP FIRING GAME LE MANH HA, PHAN THI HA DUONG PDF

   ▸ Abstract

   In this paper, we introduce a variation of the chip-firing game on a directed acyclic graph $G = (V, E)$. Starting from a given chip configuration, we can fire a vertex $v$ by sending one chip along one of its outgoing edges to the corresponding neighbors if $v$ has at least one chip. Our main result is to give the collection of energies to show the partial order structure of the configuration space of the game. After that, we consider the case when support graph has only one source, we give the characterization of its reachable configurations and of its fixed points.

   289-301
8. ON THE GENERALIZED CONVOLUTION FOR THE FOURIER SINE AND THE KONTOROVICH-LEBEDEV TRANSFORMS TRINH TUAN, NGUYEN XUAN THAO, NGUYEN VAN MAU PDF

   ▸ Abstract

   A generalized convolution for the Fourier sine transform and the Kontorovich - Lebedev integral transform is introduced. Several properties of this generalized convolution and its application to solve certain systems of integral equations are considered.

   303-317
9. STABILITÉ ET INSTABILITÉ D’UNE ÉQUATION DIFFÉRENTIELLE FONCTIONNELLE SEMI-LINÉAIRE À RETARD FINI DANS DES ESPACES DE BANACH SGHIR ABDELHAQ PDF

   ▸ Abstract

   In this paper, we discuss methods for determining stability and instability of the solution $x = 0$ of the functional differential equation $u^\prime(t) = Lu_t + F(t, u_t)$ without use of Lyapunov functionals.

   319-328
10. CYCLIC MODULES OVER SIMPLE GOLDIE RINGS DINH VAN HUYNH, DINH DUC TAI PDF

    ▸ Abstract

    In [10, Theorem A] it was shown that if every cyclic singular right module over a simple ring $R$ is CS, then $R$ is right noetherian. In this note we extend this result to cyclic modules over a simple right Goldie ring, and apply it to characterize simple noetherian rings and simple SI rings by using a single nonzero principal one-sided ideal of the ring.

    329-334