Authors:Jochen Heinloth Pages: 45 - 66 Abstract: These are a slightly expanded notes of an expository talk on V. Lafforgue’s construction of one direction (called automorphic to Galois) of the Langlands correspondence for function fields. PubDate: 2018-03-01 DOI: 10.1007/s40306-017-0244-x Issue No:Vol. 43, No. 1 (2018)

Authors:Le Tuan Hoa; Tran Nam Trung Pages: 67 - 81 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: 2018-03-01 DOI: 10.1007/s40306-017-0225-0 Issue No:Vol. 43, No. 1 (2018)

Authors:Dinh Dũng Pages: 83 - 110 Abstract: We proved direct and inverse theorems on B-spline quasi-interpolation sampling representation with a Littlewood-Paley-type norm equivalence in Sobolev spaces \({W^{r}_{p}}\) of mixed smoothness r. Based on this representation, we established estimates of the approximation error of recovery in L q -norm of functions from the unit ball \({U^{r}_{p}}\) in the spaces \({W^{r}_{p}}\) by linear sampling algorithms and the asymptotic optimality of these sampling algorithms in terms of Smolyak sampling width \({r^{s}_{n}}({U^{r}_{p}}, L_{q})\) and sampling width \(r_{n}({U^{r}_{p}}, L_{q})\) . PubDate: 2018-03-01 DOI: 10.1007/s40306-017-0230-3 Issue No:Vol. 43, No. 1 (2018)

Authors:Le Anh Tuan; Nguyen Thanh Dieu; Nguyen Huu Du Pages: 111 - 124 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: 2018-03-01 DOI: 10.1007/s40306-017-0220-5 Issue No:Vol. 43, No. 1 (2018)

Authors:Fred Rohrer Pages: 125 - 136 Abstract: Let R be a ring, let \(\mathfrak {a}\subseteq R\) be an ideal, and let M be an R-module. Let \({\Gamma }_{\mathfrak {a}}\) denote the \(\mathfrak {a}\) -torsion functor. Conditions are given for the (weakly) associated primes of \({\Gamma }_{\mathfrak {a}}(M)\) to be the (weakly) associated primes of M containing \(\mathfrak {a}\) , and for the (weakly) associated primes of \(M/{\Gamma }_{\mathfrak {a}}(M)\) to be the (weakly) associated primes of M not containing \(\mathfrak {a}\) . PubDate: 2018-03-01 DOI: 10.1007/s40306-017-0233-0 Issue No:Vol. 43, No. 1 (2018)

Authors:Le Mau Hai; Tran Van Thuy; Nguyen Xuan Hong Pages: 137 - 146 Abstract: In this paper, we consider subextensions of plurisubharmonic functions on bounded hyperconvex domains. Under some conditions, we prove the convergence in capacity of maximal subextensions with given boundary values. PubDate: 2018-03-01 DOI: 10.1007/s40306-017-0234-z Issue No:Vol. 43, No. 1 (2018)

Authors:Vu Van Dong; Nguyen Nang Tam Pages: 155 - 174 Abstract: We propose conditions for the existence of solutions for nonconvex quadratic programming problems whose constraint set is defined by finitely many convex linear-quadratic inequalities in Hilbert spaces. In order to obtain our results, we use either properties of the Legendre form or properties of compact operators with closed range. The results are established without requesting the convexity of the objective function or the compactness of the constraint set. As a special case, we obtain some on the existence of solutions results for the quadratic programming problems under linear constraints in Hilbert spaces. PubDate: 2018-03-01 DOI: 10.1007/s40306-017-0237-9 Issue No:Vol. 43, No. 1 (2018)

Authors:Le Quang Thuy; Nguyen Thi Toan Pages: 175 - 199 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: 2018-03-01 DOI: 10.1007/s40306-017-0224-1 Issue No:Vol. 43, No. 1 (2018)

Authors:Đoàn Trung Cường; Phạm Hồng Nam; Phạm Hùng Quý Abstract: For an ideal I in a Noetherian local ring \((R, \mathfrak {m})\) , we prove that the integer-valued function \(\ell _{R}(H^{0}_{\mathfrak {m}}(R/I^{n + 1}))\) is a polynomial for n big enough if either I is a principal ideal or I is generated by part of an almost p-standard system of parameters and R is unmixed. Furthermore, we are able to compute the coefficients of this polynomial in terms of length of certain local cohomology modules and usual multiplicity if either the ideal is principal or it is generated by part of a standard system of parameters in a generalized Cohen-Macaulay ring. We also give an example of an ideal generated by part of a system of parameters such that the function \(\ell _{R}(H^{0}_{\mathfrak {m}} (R/I^{n + 1}))\) is not a polynomial for n ≫ 0. PubDate: 2018-02-02 DOI: 10.1007/s40306-018-0245-4

Authors:Ramu Geddavalasa; P. Sam Johnson Pages: 665 - 673 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:Cameron Gordon; Tye Lidman Pages: 775 - 776 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:Mai Duc Thanh; Dao Huy Cuong Abstract: A van Leer-type numerical scheme for the model of a general fluid in a nozzle with variable cross section is presented. The model is nonconservative, making it hard for standard numerical schemes. Exact solutions of local Riemann problems are incorporated in the construction of this scheme. The scheme can work well in regions of resonance, where multiple waves are colliding. Numerical tests are conducted, where we compare the errors and orders of accuracy for approximating exact solutions between this scheme and a Godunov-type scheme. Results from numerical tests show that this van Leer-type scheme has a much better accuracy than the Godunov-type scheme. PubDate: 2017-12-29 DOI: 10.1007/s40306-017-0242-z

Authors:Pham Huu Anh Ngoc; Tran The Anh Abstract: Using a novel approach, we present some new explicit criteria for the uniform asymptotic stability and the exponential stability of nonlinear Volterra integro-differential equations. Some examples are given to illustrate the obtained results. PubDate: 2017-12-21 DOI: 10.1007/s40306-017-0243-y

Authors:Le Minh Triet; Luu Hong Phong; Pham Hoang Quan Abstract: In this work, we investigate an abstract parabolic problem associated with the final data, with one specific case of the abstract parabolic problem being considered in polar coordinates. Specially, the present paper gives the first treatment which is not only more general but also more applicable in the case the backward heat problem (BHP) is not symmetric and not axisymmetric in polar coordinates. In general, the above problem is severely ill-posed in the sense of Hadamard. Here, we propose the modified quasi-boundary value (MQBV) method in order to obtain the stability of the regularized solution for the problem. To our knowledge, our results are new and they improve the results of two previous papers (see Cheng and Fu (Inverse Probl. Sci. Eng. 17(8), 1085–1093 2009), (Acta Math. Sinica, English Series 26(11), 2157–2164 2010)) while the authors only considered axisymmetric or radially symmetric data. Finally, a numerical example is given to demonstrate the feasibility and efficiency of our method. PubDate: 2017-12-15 DOI: 10.1007/s40306-017-0238-8

Authors:Johannes Nicaise Abstract: We explain the proof, obtained in collaboration with Chenyang Xu, of a 1999 conjecture of Veys about poles of maximal order of Igusa zeta functions. The proof technique is based on the Minimal Model Program in birational geometry, but the proof was heavily inspired by ideas coming from non-archimedean geometry and mirror symmetry; we will outline these relations at the end of the paper. This text is intended to be a low-tech introduction to these topics; we only assume that the reader has a basic knowledge of algebraic geometry. PubDate: 2017-12-14 DOI: 10.1007/s40306-017-0241-0

Authors:Nguyen Ngoc Luan Abstract: Piecewise linear vector optimization problems in the locally convex Hausdorff topological vector space setting are considered in this paper. The efficient solution set of these problems are shown to be the unions of finitely many semi-closed generalized polyhedral convex sets. If, in addition, the problem is convex, then the efficient solution set and the weakly efficient solution set are the unions of finitely many generalized polyhedral convex sets and they are connected by line segments. Our results develop the preceding ones of Zheng and Yang (Sci. China Ser. A. 51, 1243–1256 2008), and Yang and Yen (J. Optim. Theory Appl. 147, 113–124 2010), which were established in the normed space setting. PubDate: 2017-12-07 DOI: 10.1007/s40306-017-0239-7

Authors:Kathlén Kohn; Bernd Sturmfels; Matthew Trager Abstract: Visual events in computer vision are studied from the perspective of algebraic geometry. Given a sufficiently general curve or surface in 3-space, we consider the image or contour curve that arises by projecting from a viewpoint. Qualitative changes in that curve occur when the viewpoint crosses the visual event surface. We examine the components of this ruled surface and observe that these coincide with the iterated singular loci of the coisotropic hypersurfaces associated with the original curve or surface. We derive formulas, due to Salmon and Petitjean, for the degrees of these surfaces, and show how to compute exact representations for all visual event surfaces using algebraic methods. PubDate: 2017-12-06 DOI: 10.1007/s40306-017-0240-1

Authors:Rasoul Aghalary; Mahdi Jahani Rad Abstract: In this paper, we introduce a new subclass of harmonic functions defined by shear construction. Among other properties of this subclass, we study the convolution of its elements of it with some special subclasses of harmonic functions. Also, we provide coefficient conditions leading to harmonic mappings which are starlike of order \(\alpha \) . Some interesting applications of the general results are also presented. PubDate: 2017-12-05 DOI: 10.1007/s40306-017-0235-y

Authors:Bertram Arthur Frederick Wehrfritz Abstract: An element a of a group G is said to be anticentral in G if G ′ = {[g, a] : g ∈ G} and antisemicentral in G if {[g,a] : g ∈ G} contains a normal subgroup of G of finite index in G ′. We study such elements in various types of infinite soluble group. PubDate: 2017-12-02 DOI: 10.1007/s40306-017-0236-x

Authors:Pham Ngoc Anh; Tran T. H. Anh; Takahito Kuno 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