Issue 4, Volume 41, December 2016

2016

1. New Criteria of Supersolvability of Finite Groups Na Tang , Xianhua Li PDF

   ▸ Abstract

   In this paper, we investigate the influence of weakly s-semipermutable subgroups of prime power order on the structure of finite groups. We obtain a new criteria for supersolvability of finite group and improve some known results.

   539-548
2. On a Polyconvolution with a Weight Function for Fourier Cosine and Laplace Transforms N. M. Khoa PDF

   ▸ Abstract

   In this paper, we introduce the generalized convolution with a weight function for the Hartley and Fourier cosine transforms. Several algebraic properties and applications of this generalized convolution to solving a class of integral equations of Toeplitz plus Hankel type and a class of systems of integral equations are presented.

   549-562
3. Picard Values and Uniqueness for p-adic Meromorphic Functions Phan Duc Tuan , Nguyen Thanh Quang PDF

   ▸ Abstract

   In this paper, we discuss Picard values and the uniqueness problems for a differential polynomial of the form $f^n + a f^{(k)}$.

   563-582
4. Hyperstability of Jordan Triple Derivations on Banach Algebras Sang Og Kim , Abasalt Bodaghi PDF

   ▸ Abstract

   In this article, it is proved that a functional equation of (linear) Jordan triple derivations on unital Banach algebras under quite natural and simple assumptions is hyperstable. It is also shown that under some mild conditions approximate Jordan triple derivations on unital semiprime Banach algebras are (linear) derivations.

   583-594
5. Strong $\Gamma$-Statistical Convergence in Probabilistic Normed Spaces Celaleddin Şençimen , Serpil Pehlivan PDF

   ▸ Abstract

   The concept of statistical cluster point of a sequence which presents random deviations is very important in the study of optimal paths and turnpike theory. In this study, we investigate some properties of the set of all strong statistical cluster points of a sequence in a probabilistic normed (PN) space in which the norms of the vectors are represented by probability distribution functions due to randomness. In this context, we also introduce the concept of strong $\Gamma$-statistical convergence in a PN space, and examine some of its basic properties.

   595-606
6. A Stochastic Conservation Law with Nonhomogeneous Dirichlet Boundary Conditions Kazuo Kobayasi , Dai Noboriguchi PDF

   ▸ Abstract

   This paper discusses the initial-boundary value problem (with a nonhomogeneous boundary condition) for a multi-dimensional scalar first-order conservation law with a multiplicative noise. One introduces a notion of kinetic formulations in which the kinetic defect measures on the boundary of a domain are truncated. In such a kinetic formulation, one obtains a result of uniqueness and existence. The unique solution is the limit of the solution of the stochastic parabolic approximation.

   607-632
7. Color Partition Identities Arising from Ramanujan’s Theta-Functions M. S. Mahadeva Naika , B. Hemanthkumar , H. S. Sumanth Bharadwaj PDF

   ▸ Abstract

   We establish several partition identities with distinct colors that arise from Ramanujan’s theta-function identities and formulas for multipliers in the theory of modular equations. Also, we deduce few partition congruences as a corollary of some partition identities.

   633-660
8. Compactness for the Commutator of the Multilinear Fourier Multiplier on the Morrey Space Peng Li , Jiang Zhou PDF

   ▸ Abstract

   Given $s_1,\dots, s_m \in (n/2, n]$, let $T_{\sigma}$ be a multilinear Fourier multiplier operator associated with a multilinear multiplier $\sigma$ satisfying a Sobolev regularity condition $\sup_{\ell \in \mathbb{Z}}\|\sigma_{\ell }\|_{W^{s_{1},\ldots ,s_{m}}(\mathbb{R}^{mn})}<\infty .$ By the strongly precompactness of Banach space, the authors prove that if $b_{1},\ldots ,b_{m}\in CMO(\mathbb{R}^{n})$, then the commutator $T_{\sigma,\Sigma b}$ is a compact operator from the product Morrey space $L^{p_{1},\lambda }(\mathbb{R}^{n})\times \cdots \times L^{p_{m},\lambda }(\mathbb{R}^{n})$ to the Morrey space $L^{p,\lambda }(\mathbb{R}^{n})$. As an application, the compactness of the commutator $T_{\sigma,\Sigma b}$ from the product Morrey space $L^{p_{1},\lambda }(\mathbb{R}^{n})\times \cdots \times L^{p_{m},\lambda }(\mathbb{R}^{n})$ to the Morrey space $L^{p,\lambda }(\mathbb{R}^{n})$ is also obtained under the Sobolev regularity condition $\sup _{\ell \in \mathbb{Z}}\|\sigma _{\ell }\|_{W^{s}(\mathbb{R}^{mn})}<\infty$ for $s\in (m n/2, m n]$.

   661-676
9. Some Characterizations of Solution Sets of Vector Optimization Problems with Generalized Order Nguyen Van Tuyen PDF

   ▸ Abstract

   We establish some necessary and sufficient conditions for optimal solutions to vector optimization problems, where the optimality notion is understood in the sense of generalized order from Mordukhovich (2006, Definition 5.53). Moreover, some criteria for the closedness and the connectedness of the set of generalized order solutions are also given. Many examples are provided to illustrate the obtained results.

   677-694
10. The Cylindrical Symmetry Einstein-Vlasov System with Charged Particles in Expansion Pierre Noundjeu , David Tegankong PDF

    ▸ Abstract

    We prove the property of being global in time for the solution of the Cauchy problem that corresponds to the cylindrically symmetric Einstein-Vlasov-Maxwell Scalar field (EVMS) system with general (in size) data. It is shown that if there is no singularity at the axis of symmetry, then the local solutions given by Choquet-Bruhat (Ann. Inst. Fourier 21(3):181–201, 2) can be extended to the global one. We notice that these results generalize those already known for the uncharged case.

    695-709
11. On the Non-Existence of Limit E-Brody Curves Tran Duc-Anh PDF

    ▸ Abstract

    We give a simple proof of the non-existence of limit E-Brody curves, in the sense of Do Duc Thai, Mai Anh Duc, and Ninh Van Thu, for a class of manifolds including $\mathbb {C}^{n}$ and $(\mathbb {C}^{\ast })^{2}$ which were studied by these authors in Do et al. (Kyushu J. Math 69(1) 2015), by constructing a suitable holomorphic interpolation function.

    711-714
12. On BDF-Based Multistep Schemes for Some Classes of Linear Differential-Algebraic Equations of Index at Most 2 Mikhail Valeryanovich Bulatov , Vu Hoang Linh , Liubov Stepanovna Solovarova PDF

    ▸ Abstract

    A family of efficient multistep difference schemes for solving some classes of linear non-autonomous differential-algebraic equations of index at most 2 is proposed. It is shown that if the popular backward differentiation formulas (BDFs) are applied to a reformulated form of the original problem, then the methods preserve the stability property and the convergence order that the corresponding BDF methods possess in the ODE case. Further issues such as numerical differentiation that may be involved in the implementation and computational errors are also discussed. Finally, several numerical experiments are given which confirm the theoretical results.

    715-730
13. $L_p$-Regularity for the Cauchy-Dirichlet Problem for Parabolic Equations in Convex Polyhedral Domains Vu Trong Luong , Nguyen Thanh Anh , Do Van Loi PDF

    ▸ Abstract

    In this paper, we study the regularity of the solution of the initial-boundary value problem with Dirichlet boundary conditions for second-order divergence parabolic equations in a domain of polyhedral type. We establish several results on the regularity of the solution in weighted $L_p$-Sobolev spaces.

    731-742