Issue 4, Volume 42, December 2017

2017

1. An Extragradient Method for Finding Minimum-Norm Solution of the Split Equilibrium Problem Tran Viet Anh PDF

   ▸ Abstract

   The purpose of this paper is to find minimum-norm solutions of the split equilibrium problem. This problem is motivated by the least-squares solution to the constrained linear inverse problem. By using the extragradient method, we derive the strong convergence of an iterative algorithm to the minimum-norm solution of the split equilibrium problem. As special cases, minimum-norm solutions of the split variational inequality problem and the split feasibility problem can be found.

   587-604
2. Artinian Cofinite Modules and Going-up for $R\subseteq \widehat {R}$ Gholamreza Pirmohammadi , Khadijeh Ahmadi Amoli , Kamal Bahmanpour PDF

   ▸ Abstract

   Let $(R,\operatorname{\frak m})$ be a commutative Noetherian local ring. In this paper, it is shown that the going-up theorem holds for $R\subseteq \widehat{R}$ if and only if $\operatorname{Rad}(I+\operatorname{Ann}_{R} A)=\operatorname{\frak m}$ for any proper ideal $I$ of R and any non-zero Artinian $I$-cofinite module $A$. Furthermore, using the main result of Zöschinger, Arch. Math. 95, 225–231 (2010), it is shown that these equivalent conditions are equivalent to $R$ being formal catenary with $\alpha(R) = 0$ and to $\operatorname{Att}_{R} H^{\dim M}_{I}(M)=\{\operatorname{\frak p} \in \operatorname{Assh}_{R}(M)\,:\,\operatorname{Rad}(\operatorname{\frak p}+I)=\operatorname{\frak m}\}$ for any ideal I of R and any non-zero finitely generated $R$-module $ M$.

   605-613
3. Balanced Generalized Singular Perturbation Method for Unstable Linear Time Invariant Continuous Systems Ha Binh Minh , Chu Binh Minh , Victor Sreeram PDF

   ▸ Abstract

   In this paper, a balanced truncation type of reduction is proposed for unstable continuous-time systems which is based on unstable system reduction originally proposed for discrete systems. This is achieved by first deriving a link between continuous-time and discrete-time systems which is called the extended bilinear mapping. Using this mapping, an unstable continuous-time system reduction method along with its error bounds is then derived. A numerical example is provided to illustrate the effectiveness of the method and a comparison with other relevant methods in the literature is also included.

   615-635
4. Quantitative Central Limit Theorems of Spherical Sojourn Times of Isotropic Gaussian Fields Pham Viet Hung PDF

   ▸ Abstract

   We investigate the rate of convergence for the central limit theorems of sojourn times on the growing sphere of isotropic Gaussian fields defined on the whole Euclidean space. In the case of the sojourn times defined on a cube, the similar problem has been studied by using the Malliavin-Stein method. Following this idea, in this paper, we establish the explicit rate for various probability distances with a careful examination of the variance.

   637-651
5. When is a Local Homeomorphism a Semicovering Map? Majid Kowkabi , Behrooz Mashayekhy , Hamid Torabi PDF

   ▸ Abstract

   In this paper, by reviewing the concept of semicovering maps, we present some conditions under which a local homeomorphism becomes a semicovering map. We also obtain some conditions under which a local homeomorphism is a covering map.

   653-663
6. Frames for Operators in Banach Spaces Ramu Geddavalasa , P. Sam Johnson PDF

   ▸ Abstract

   A family of local atoms in a Banach space has been introduced and it has been generalized to an atomic system for operators in Banach spaces, which has been further led to introduce new frames for operators by Dastourian and Janfada, by making use of semi-inner products. Unlike the traditional way of considering sequences in the dual space, sequences in the original space are considered to study them. Appropriate changes have been made in the definitions of atomic systems and frames for operators to fit them for sequences in the dual space without using semi-inner products so that the new notion for Banach spaces can be thought of as a generalization of Banach frames. With some crucial assumptions, we show that frames for operators in Banach spaces share nice properties of frames for operators in Hilbert spaces.

   665-673
7. Ulam Stability for Fractional Partial Integro-Differential Equation with Uncertainty Hoang Viet Long , Nguyen Thi Kim Son , Ha Thi Thanh Tam , Jen-Chih Yao PDF

   ▸ Abstract

   In this paper, the solvability of Darboux problems for nonlinear fractional partial integro-differential equations with uncertainty under Caputo gH-fractional differentiability is studied in the infinity domain $J_{\infty} = [0,\infty) \times [0,\infty)$. New concepts of Hyers-Ulam stability and Hyers-Ulam-Rassias stability for these problems are also investigated through the equivalent integral forms. A computational example is presented to demonstrate our main results.

   675-700
8. Ideal Transforms with Respect to a Pair of Ideals Nguyen Minh Tri , Tran Tuan Nam PDF

   ▸ Abstract

   We introduce the ideal transform functor $D_{I,J}$ with respect to a pair of ideals $(I,J)$ which is an extension of the ideal transform functor $D_I$ of Brodmann. Some equivalent conditions on the exactness of the ideal transform functor will be shown in the paper. We also study the finiteness of the sets $\mathrm{Ass}_R (R^i D_I (N))$ and $\mathrm{Ass}_R (R^i D_{I, J} (M,N))$.

   701-715
9. On Tautness Modulo an Analytic Subset of Complex Spaces Pham Viet Duc , Mai Anh Duc , Pham Nguyen Thu Trang PDF

   ▸ Abstract

   The main goal of this article is to give necessary and sufficient conditions on the tautness modulo an analytic subset of complex spaces.

   717-726
10. New Classes of Generalized PN Spaces and Their Normability P. K. Harikrishnan , Bernardo Lafuerza Guillén , Yeol Je Cho , K. T. Ravindran PDF

    ▸ Abstract

    In this paper, we obtain some properties of invertible operators; convex, balanced, absorbing sets; and $\mathcal D$-boundedness in Šerstnev spaces. We prove that some PN spaces $(V,\nu,\tau,\tau^*)$, which are not Šerstnev spaces, in which the triangle function $\tau^*$ is not Archimedean can be endowed with a structure of a topological vector space, and we give suitable example to illustrate this result. Also, we show that the topological spaces obtained in such a manner are normable under certain given conditions: some examples are given.

    727-746
11. Property $(a B w)$ and Weyl Type Theorems Mohammad H. M. Rashid PDF

    ▸ Abstract

    In this paper, we introduces the property $(a B w)$, a variant of generalized a-Weyl’s theorem for a bounded linear operator $T$ on an infinite-dimensional Banach space $\mathbb X$. We establish several sufficient and necessary conditions for which property $(a B w)$ holds. Also, we prove that if $T\in \mathbf {L(\mathbb {X})}$ satisfies property $(a B w)$ then $T$ satisfies property $(B w)$. Certain conditions are explored on Hilbert space operators $T$ and S so that $T \oplus S$ obeys property $(a B w)$.

    747-759
12. Convergence Theorems for Variational Inequalities on the Solution Set of Ky Fan Inequalities Pham Ngoc Anh , Tran T. H. Anh , Takahito Kuno PDF

    ▸ Abstract

    Based on the subgradient methods and fixed point techniques, we develop a new iteration method for solving variational inequalities on the solution set of Ky Fan inequalities. The convergence for the proposed algorithms to the solution is guaranteed under certain assumptions in the Euclidean space $\mathcal R^{n}$.

    761-773
13. Corrigendum to “Taut Foliations, Left-Orderability, and Cyclic Branched Covers” Cameron Gordon , Tye Lidman PDF

    ▸ Abstract

    We correct an error in the statement and proof of Theorem 1.4 of our paper in Acta Mathematica Vietnamica (2014) 39(4), 599-635.

    775-776