Authors:Tran Viet Anh Pages: 587 - 604 Abstract: 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. PubDate: 2017-12-01 DOI: 10.1007/s40306-016-0186-8 Issue No:Vol. 42, No. 4 (2017)

Authors:Gholamreza Pirmohammadi; Khadijeh Ahmadi Amoli; Kamal Bahmanpour Pages: 605 - 613 Abstract: 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 α(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. PubDate: 2017-12-01 DOI: 10.1007/s40306-017-0203-6 Issue No:Vol. 42, No. 4 (2017)

Authors:Ha Binh Minh; Chu Binh Minh; Victor Sreeram Pages: 615 - 635 Abstract: 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. PubDate: 2017-12-01 DOI: 10.1007/s40306-017-0215-2 Issue No:Vol. 42, No. 4 (2017)

Authors:Pham Viet Hung Pages: 637 - 651 Abstract: 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. PubDate: 2017-12-01 DOI: 10.1007/s40306-017-0212-5 Issue No:Vol. 42, No. 4 (2017)

Authors:Majid Kowkabi; Behrooz Mashayekhy; Hamid Torabi Pages: 653 - 663 Abstract: 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. PubDate: 2017-12-01 DOI: 10.1007/s40306-017-0205-4 Issue No:Vol. 42, No. 4 (2017)

Authors:Ramu Geddavalasa; P. Sam Johnson Pages: 665 - 673 Abstract: 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. PubDate: 2017-12-01 DOI: 10.1007/s40306-017-0210-7 Issue No:Vol. 42, No. 4 (2017)

Authors:Hoang Viet Long; Nguyen Thi Kim Son; Ha Thi Thanh Tam; Jen-Chih Yao Pages: 675 - 700 Abstract: 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 ∞ = [0,∞) × [0,∞). 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. PubDate: 2017-12-01 DOI: 10.1007/s40306-017-0207-2 Issue No:Vol. 42, No. 4 (2017)

Authors:Nguyen Minh Tri; Tran Tuan Nam Pages: 701 - 715 Abstract: 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 Ass R (R i D I (N)) and Ass R (R i D I, J (M,N)). PubDate: 2017-12-01 DOI: 10.1007/s40306-017-0213-4 Issue No:Vol. 42, No. 4 (2017)

Authors:Pham Viet Duc; Mai Anh Duc; Pham Nguyen Thu Trang Pages: 717 - 726 Abstract: Abstract The main goal of this article is to give necessary and sufficient conditions on the tautness modulo an analytic subset of complex spaces. PubDate: 2017-12-01 DOI: 10.1007/s40306-017-0214-3 Issue No:Vol. 42, No. 4 (2017)

Authors:Mohammad H. M. Rashid Pages: 747 - 759 Abstract: 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 ⊕ S obeys property (a B w). PubDate: 2017-12-01 DOI: 10.1007/s40306-017-0222-3 Issue No:Vol. 42, No. 4 (2017)

Authors:Cameron Gordon; Tye Lidman Pages: 775 - 776 Abstract: 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. PubDate: 2017-12-01 DOI: 10.1007/s40306-017-0216-1 Issue No:Vol. 42, No. 4 (2017)

Authors:Yan Gu Pages: 445 - 454 Abstract: Abstract Let \(\tilde {C_{n}}\) be the graph by adding an ear to C n and \(I=I(\tilde {C_{n}})\) be its edge ideal. In this paper, we prove that \(\operatorname {reg}(I^{s})=2s+\lfloor \frac {n+1}{3}\rfloor -1\) for all s ≥ 1. Let G be the bicyclic graph C m ⊔ C n with edge ideal I = I(G); we compute the regularity of I s for all s ≥ 1. In particular, in some cases, we get \(\operatorname {reg}(I^{s})=2s+\lfloor \frac {m}{3}\rfloor +\lfloor \frac {n}{3}\rfloor -1\) for all s ≥ 2. PubDate: 2017-09-01 DOI: 10.1007/s40306-017-0204-5 Issue No:Vol. 42, No. 3 (2017)

Authors:Nguyen Song Song Ha; Nguyen Buong; Nguyen Thi Thu Thuy Abstract: Abstract In this paper, we propose a new simple parallel iterative method to find a solution for variational inequalities over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm. Our parallel iterative method is simpler than the one proposed by Buong et al. (Numer. Algorithms 72, 467–481 2016). An iterative method of Halpern type for common zeros of an infinite family of m-accretive mappings is shown as a special case of our result. Two numerical examples are also given to illustrate the effectiveness and superiority of the proposed algorithm. PubDate: 2017-10-16 DOI: 10.1007/s40306-017-0228-x

Authors:Le Quang Thuy; Nguyen Thi Toan Abstract: In this paper, we study the Mordukhovich coderivative and the local metric regularity in Robinson’s sense of the solution map to a parametric dynamic programming problem with linear constraints and convex cost functions. By establishing abstract results on the coderivative and the local metric regularity of the solution map to a parametric variational inequality, we obtain the Mordukhovich coderivative and the local metric regularity in Robinson’s sense of the solution map to a parametric discrete optimal control problem. PubDate: 2017-09-20 DOI: 10.1007/s40306-017-0224-1

Authors:Pham Ngoc Anh; Tran T. H. Anh; Takahito Kuno Abstract: 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 \(\mathcal R^{n}\) . PubDate: 2017-09-19 DOI: 10.1007/s40306-017-0226-z

Authors:Le Anh Tuan; Nguyen Thanh Dieu; Nguyen Huu Du Abstract: Abstract This paper is concerned with some sufficient conditions ensuring the stochastic stability and the almost sure exponential stability of stochastic differential equations on time scales via Lyapunov functional methods. This work can be considered as a unification and generalization of works dealing with these areas of stochastic difference and differential equations. PubDate: 2017-09-18 DOI: 10.1007/s40306-017-0220-5

Authors:Le Tuan Hoa; Tran Nam Trung Abstract: Abstract Let I be a monomial ideal in a polynomial ring \(R = k[x_{1},\dots ,x_{r}]\) . In this paper, we give an upper bound on \(\overline {\text {dstab}} (I)\) in terms of r and the maximal generating degree d(I) of I such that \(\text {depth} R/\overline {I^{n}}\) is constant for all \(n\geqslant \overline {\text {dstab}}(I)\) . As an application, we classify the class of monomial ideals I such that \(\overline {I^{n}}\) is Cohen-Macaulay for some integer n ≫ 0. PubDate: 2017-09-15 DOI: 10.1007/s40306-017-0225-0

Authors:Duong Thi Viet An; Nguyen Thi Toan Abstract: Abstract Differential stability of convex discrete optimal control problems in Banach spaces is studied in this paper. By using some recent results of An and Yen (Appl. Anal. 94, 108–128, 2015) on differential stability of parametric convex optimization problems under inclusion constraints, we obtain an upper estimate for the subdifferential of the optimal value function of a parametric convex discrete optimal control problem, where the objective function may be nondifferentiable. If the objective function is differentiable, the obtained upper estimate becomes an equality. It is shown that the singular subdifferential of the just mentioned optimal value function always consists of the origin of the dual space. PubDate: 2017-09-13 DOI: 10.1007/s40306-017-0227-y

Authors:P. K. Harikrishnan; Bernardo Lafuerza Guillén; Yeol Je Cho; K. T. Ravindran Abstract: 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,ν,τ,τ ∗), which are not Šerstnev spaces, in which the triangle function τ ∗ 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. PubDate: 2017-08-24 DOI: 10.1007/s40306-017-0218-z

Authors:Nipen Saikia; Chayanika Boruah Abstract: Abstract For any positive integer ℓ, let B ℓ (n) denotes the number of ℓ-regular partition triples of a positive integer n. By employing q −series identities, we prove infinite family of arithmetic identities and congruences modulo 4 for B 2(n), modulo 2 and 9 for B 3(n), modulo 2 for B 4(n) and modulo 2 and 5 for B 5(n). PubDate: 2017-04-25 DOI: 10.1007/s40306-017-0206-3