Issue 3, Volume 36, December 2011

2011 · Open access

1. THE WRONSKIAN SOLUTIONS OF THE MODIFIED KORTEWEG-DE VRIES EQUATION HA TIEN NGOAN, NGUYEN HUY HOANG PDF

   ▸ Abstract

   The generalized sufficient condition equations for the Wronskian determinants are proposed, which guarantee that they solve the modified Korteweg-de Vries equation (mKdV) in the bilinear form. Some new explicit Wronskian solutions to mKdV are constructed by applying variation of parameters.

   555-583
2. MAPPINGS IN $ls$-$\sigma$-FINITE PONOMAREV-SYSTEMS NGUYEN VAN DUNG PDF

   ▸ Abstract

   We introduce the notion of an $ls$-$\sigma$-finite Ponomarev-system $(f, M, X, \{\mathcal P_{\lambda,n}\})$ to give a consistent method to construct an $s$-mapping (msss-mapping, mssc-mapping, cs-mapping) f with covering-properties from a locally separable metric space $M$ onto a space $X$. As applications, we systematically get characterizations of $s$-images (msss-images, mssc-images, cs-images) with covering-properties of locally separable metric spaces.

   585-599
3. UPPER AND LOWER ESTIMATES FOR A FRÉCHET NORMAL CONE NGUYEN THANH QUI PDF

   ▸ Abstract

   This paper investigates upper and lower estimates for the Fréchet normal cone to the graph of a normal cone mapping related to a linear inequality system in a reflexive Banach space under right-hand side perturbations. Our results develop some material in the recent papers of Yao and Yen [8], and Nam [6]. In particular, by constructing suitable counterexamples, we solve the two open questions of [8] in the negative.

   601-610
4. A LINEARLY CONVERGENT CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS SUN MIN, LIU JING PDF

   ▸ Abstract

   In this paper, a new conjugate gradient method with a simple formula $\beta_k$ is given for unconstrained optimization problems. It possesses sufficient descent property for any line search. Global convergence results of the new method with the Goldstein line search and the Armijo line search are discussed. For uniformly convex functions, the method has linear convergence rate. Preliminary computational experiments are included to illustrate the efficiency of the proposed method in minimizing large-scale non-convex optimization problems.

   611-622
5. WELL-POSEDNESS OF A COMMON FIXED POINT PROBLEM FOR WEAKLY TANGENTIAL MAPPINGS MOHAMED AKKOUCHI PDF

   ▸ Abstract

   In this paper, we introduce the concept of weakly tangential mappings. This concept is a generalization of the property (E.A.) introduced by Aamri and El Moutawakil in a paper published in 2002. We study the well-posedness of the common fixed point problem for two weakly tangential and occasionally weakly compatible self-mappings of a metric space $(X, d)$ which satisfy a variant of a contractive condition considered by Ćirić in a paper published in 2005. The results established here provide natural extensions and continuations to some results obtained by Ćirić, Sharma and Yuel and Guay and Singh.

   623-635
6. ON LIFTING MODULES RELATIVE TO THE CLASS OF ALL SINGULAR MODULES DEXU ZHOU PDF

   ▸ Abstract

   Using the class $\delta$ of all singular $R$-modules, we introduce and characterize $\delta$-lifting modules, $\delta$-supplements and $\delta$-coclosed submodules, and give some equivalent conditions to characterize an amply $\delta$-supplemented module $M = \oplus_{i\in I}M_i$ to be $\delta$-lifting. We introduce relatively $\delta$-small projective to give some sufficient conditions that a finite sum of $\delta$-lifting modules is $\delta$-lifting. We also show that $R$ is $\delta$-perfect ($\delta$-semiperfect) if and only if every (finitely generated) projective right $R$-module is $\delta$-lifting.

   637-649
7. IDEAL AMENABILITY OF VARIOUS CLASSES OF BANACH ALGEBRAS A. JABBARI PDF

   ▸ Abstract

   Let $\mathcal A$ be a Banach algebra. If $n \in \mathbb N$ and $\mathcal I$ is a closed two sided ideal in $\mathcal A$, then $\mathcal A$ is $n−\mathcal I−$weakly amenable if the first cohomology group of $\mathcal A$ with coefficients in the $n−$th dual space $\mathcal I^{(n)}$ is zero, i.e., $H^1(\mathcal A, \mathcal I^{(n)} ) = \{0\}$. Further, $\mathcal A$ is $n−$ideally amenable (ideally amenable) if $\mathcal A$ is $n − \mathcal I−$weakly amenable $(1 − \mathcal I−$weakly amenable) for every closed two sided ideal $\mathcal I$ in $\mathcal A$. In this paper we investigate $(2m + 1) − \mathcal I−$weakly amenability of Banach algebras for $m \geq 1$, and ideal amenability of Segal algebras and triangular Banach algebras $T = \begin{bmatrix} \mathcal A & \mathcal M\\  &\mathcal B\end{bmatrix}$ (where $\mathcal A$ and $\mathcal B$ are Banach algebras and $\mathcal M$ is a $\mathcal A$, $\mathcal B−$module).

   651-658
8. NEW RESULTS FOR BOUNDARY VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED BOUNDARY CONDITIONS BASHIR AHMAD PDF

   ▸ Abstract

   In this paper, a boundary value problem of nonlinear fractional differential equations of order $q \in (1, 2]$ with non-separated boundary conditions is studied. Some new existence and uniqueness results are obtained by using Leray-Schauder degree theory and fixed point theorems. Some interesting observations are presented.

   659-668
9. SUR LES POINTS FIXES ET LES CYCLES RÉPULSIFS AU VOISINAGE D’UNE SINGULARITE ESSENTIELLE ISOLÉE À L’INSTAR DE LA MÉTHODE DE RENORMALISATION DE ZALCMAN CLAUDI MENEGHIN PDF

   ▸ Abstract

   Soit $g$ une fonction holomorphe au voisinage d’une singularité essentielle isolée $v$: nous prouvons que, si $g$ y omet une valeur complexe, alors $v$ peut être approché par une suite de points fixes répulsifs de $g$, dont les multiplicateurs divergent à $\infty$. Nous montrons aussi que, si $v$ n’est pas une valeur exceptionnelle au sens de Picard pour $g$, alors $v$ peut être approchée par une suite de points périodiques d’ordre deux de $g$, ces cycles étant répulsifs (avec multiplicateurs divergeant à $\infty$) si $v$ n’est pas une valeur complètement ramifiée.

   669-676
10. STRONG REGULARITY OF $SF$−RINGS JUNCHAO WEI, NANJIE LI PDF

    ▸ Abstract

    In this paper, we study the strong regularity of left $SF$−rings and obtain the following results: Let $R$ be a left $SF$−ring. If $R$ satisfies one of the following conditions, then $R$ is a strongly regular ring: 1) $R$ is a left WZI ring; 2) $R$ is a right WZI ring; 3) $R$ is a left PZI ring; 4) $R$ is a right PZI ring; 5) $R$ is a semicommutative ring; 6) $R$ is a reversible ring.

    677-683
11. ON THE GINI MEAN DIFFERENCE PHAM XUAN BINH PDF

    ▸ Abstract

    Gini mean difference (GMD) was proposed by Gini in 1912 for measuring income inequalities or economic wealth. The aim of this paper is to prove an estimation of this GMD in the general case of distribution.

    685-694
12. AN ASYMPTOTIC EXPANSION OF A WEAK SOLUTION FOR A NONLINEAR WAVE EQUATION LE THI PHUONG NGOC, LE KHANH LUAN, NGUYEN THANH LONG PDF

    ▸ Abstract

    In this paper, we consider a nonlinear wave equation associated with the Dirichlet boundary condition. First, the existence and uniqueness of a weak solution are proved by using the Faedo-Galerkin method. Next, we present an asymptotic expansion of high order in many small parameters of a weak solution. This extends recent corresponding results where an asymptotic expansion of a weak solution in two or three small parameters is established.

    695-722