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 Acta Mathematica VietnamicaJournal Prestige (SJR): 0.27 Number of Followers: 0      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0251-4184 - ISSN (Online) 2315-4144 Published by Springer-Verlag  [2352 journals]
• Some Stability Properties of Parametric Quadratically Constrained
Nonconvex Quadratic Programs in Hilbert Spaces
• Authors: Vu Van Dong
Abstract: Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal value function, assuming that the problem data undergo small perturbations.
PubDate: 2018-06-01
DOI: 10.1007/s40306-017-0221-4

• On Permutations Induced by Tame Automorphisms Over Finite Fields
• Authors: Keisuke Hakuta
Abstract: The present paper deals with permutations induced by tame automorphisms over finite fields. The first main result is a formula for determining the sign of the permutation induced by a given elementary automorphism over a finite field. The second main result is a formula for determining the sign of the permutation induced by a given affine automorphism over a finite field. We also give a combining method of the above two formulae to determine the sign of the permutation induced by a given triangular automorphism over a finite field. As a result, for a given tame automorphism over a finite field, if we know a decomposition of the tame automorphism into a finite number of affine automorphisms and elementary automorphisms, then one can easily determine the sign of the permutation induced by the tame automorphism.
PubDate: 2018-06-01
DOI: 10.1007/s40306-017-0217-0

• Differential Stability of Convex Discrete Optimal Control Problems
• Authors: Duong Thi Viet An; Nguyen Thi Toan
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: 2018-06-01
DOI: 10.1007/s40306-017-0227-y

• Quasi-interpolation Representation and Sampling Recovery of Multivariate
Functions
• Authors: Nguyen Manh Cuong; Mai Xuan Thao
Abstract: In this paper, we prove a multivariate generalization of the quasi-interpolation representation of functions in Besov-type spaces by B-spline series with some equivalent discrete quasi-norms. Moreover, by using this representation, we construct linear sampling methods which give the asymptotic order of optimal linear sampling methods.
PubDate: 2018-06-01
DOI: 10.1007/s40306-017-0223-2

• Semilinear Hyperbolic Boundary Value Problem Associated to the Nonlinear
Generalized Viscoelastic Equations
• Authors: Abita Rahmoune
Abstract: Consider a semilinear hyperbolic boundary value problem associated to the nonlinear generalized viscoelastic equations with Direchlet-Neumann boundary conditions. Then, the global existence of a weak solution is established. The uniqueness of the solution has been obtained by eliminating some hypotheses that have been imposed by other authors for different particular problems.
PubDate: 2018-06-01
DOI: 10.1007/s40306-017-0229-9

• A New Simple Parallel Iteration Method for a Class of Variational
Inequalities
• Authors: Nguyen Song Song Ha; Nguyen Buong; Nguyen Thi Thu Thuy
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: 2018-06-01
DOI: 10.1007/s40306-017-0228-x

• Unique Path Lifting from Homotopy Point of View
• Authors: Mehdi Tajik; Behrooz Mashayekhy; Ali Pakdaman
Abstract: The paper introduces some notions extending the unique path lifting property from a homotopy viewpoint and studies their roles in the category of fibrations. First, we define some homotopical kinds of the unique path lifting property and find all possible relationships between them. Moreover, we supplement the full relationships of these new notions in the presence of fibrations. Second, we deduce some results in the category of fibrations with these notions instead of unique path lifting such as the existence of products and coproducts. Also, we give a brief comparison of these new categories to some categories of the other generalizations of covering maps. Finally, we present two subgroups of the fundamental group related to the fibrations with these notions and compare them to the subgroups of the fundamental group related to covering and generalized covering maps.
PubDate: 2018-06-01
DOI: 10.1007/s40306-017-0219-y

• A New Type of Operator Convexity
• Authors: Trung-Hoa Dinh; Thanh-Duc Dinh; Bich-Khue T. Vo
Abstract: Let $$r, s$$ be positive numbers. We define a new class of operator $$(r, s)$$ -convex functions by the following inequality $$f \left( \left[\lambda A^{r} + (1-\lambda)B^{r}\right]^{1/r}\right) \leq \left[\lambda f(A)^{s} +(1-\lambda)f(B)^{s}\right]^{1/s},$$ where $$A, B$$ are positive definite matrices and for any $$\lambda \in [0,1]$$ . We prove the Jensen, Hansen-Pedersen, and Rado type inequalities for such functions. Some equivalent conditions for a function f to become operator $$(r, s)$$ -convex are established.
PubDate: 2018-04-17
DOI: 10.1007/s40306-018-0259-y

• Negative Index Materials: Some Mathematical Perspectives
• Authors: Hoai-Minh Nguyen
Abstract: Negative index materials are artificial structures whose refractive index has a negative value over some frequency range. These materials were postulated and investigated theoretically by Veselago in 1964 and were confirmed experimentally by Shelby, Smith, and Schultz in 2001. New fabrication techniques now allow for the construction of negative index materials at scales that are interesting for applications, which has made them a very active topic of investigation. In this paper, we report various mathematical results on the properties of negative index materials and their applications. The topics discussed herein include superlensing using complementary media, cloaking using complementary media, cloaking an object via anomalous localized resonance, and the well-posedness and the finite speed propagation in media consisting of dispersive metamaterials. Some of the results have been refined and have simpler proofs than the original ones.
PubDate: 2018-04-17
DOI: 10.1007/s40306-018-0258-z

• Norm Ratios Under a Weak Order Relation in M m ⊗ M n ${\mathbb {M}}_{m}\otimes {\mathbb {M}}_{n}$
• Authors: Tsuyoshi Ando
Abstract: In the real Hilbert space of self-adjoint elements of the tensor product $${\mathbb {M}}_{m}\otimes {\mathbb {M}}_{n}$$ , there are two natural cones besides the cone $${\mathfrak {P}}_{0}$$ of positive semi-definite elements. The one is and the other is the cone $${\mathfrak {P}}_{-}$$ , dual to $${\mathfrak {P}}_{+}$$ with respect to the inner product. Then, $${\mathfrak {P}}_{+} \subset {\mathfrak {P}}_{0} \subset {\mathfrak {P}}_{-}.$$ A weak order relation ≽ is introduced by Our interest is in finding bounds for the ratio T / S for S ≽T ≽ 0, where ⋅ is one of the operator norm, the trace norm, and the Hilbert-Schmidt norm.
PubDate: 2018-04-11
DOI: 10.1007/s40306-018-0260-5

• The Backward Problem for a Nonlinear Riesz-Feller Diffusion Equation
• Authors: Dinh Nguyen Duy Hai; Dang Duc Trong
Abstract: In this paper, we reconstruct the solution u(x,t) of the backward space-fractional diffusion problem with a locally Lipschitzian nonlinear source This problem is severely ill-posed in the Hadamard sense, hence, a regularization is in order. In the paper, we introduce one spectral regularization method and establish stability error estimates with optimal order under an a priori choice of regularization parameter. Finally, numerical implementations are given to show the effectiveness of the proposed regularization methods.
PubDate: 2018-03-27
DOI: 10.1007/s40306-018-0255-2

• Discrete Embeddings for Lagrangian and Hamiltonian Systems
• Authors: Jacky Cresson; Isabelle Greff; Charles Pierre
Abstract: The topic of this paper is to study the conservation of variational properties for a given problem when discretising it. Precisely, we are interested in Lagrangian or Hamiltonian structures and thus with variational problems attached to a least action principle. Consider a partial differential equation (PDE) deriving from a variational principle. A natural question is to know whether this structure is preserved at the discrete level when discretising the PDE. To address this question, a concept of coherence is introduced. Both the differential equation (the PDE translating the least action principle) and the variational structure can be embedded at the discrete level. This provides two discrete embeddings for the original problem. If these procedures finally provide the same discrete problem, we will say that the discretisation is coherent. Our purpose is illustrated with the Poisson problem. Coherence for discrete embeddings of Lagrangian structures is studied for various classical discretisations. For Hamiltonian structures, we show the coherence between a discrete Hamiltonian and the discretisation of the mixed formulation of the Poisson problem.
PubDate: 2018-03-26
DOI: 10.1007/s40306-018-0257-0

• The Einstein-Vlasov-Scalar Field System with Gowdy or T 2 Symmetry in
Contracting Direction
• Authors: Alex Lassiye Tchuani; David Tegankong; Norbert Noutchegueme
Abstract: We prove in the case of cosmological models for the Einstein-Vlasov-scalar field system with Gowdy symmetry, that the solutions exist globally in the past. The sources of the equations are generated by a distribution function and a scalar field, subject to the Vlasov and the wave equations respectively. The result is generalized for the case of T2 symmetry. Using previous results, we deduce geodesic completeness.
PubDate: 2018-03-17
DOI: 10.1007/s40306-018-0256-1

• Completely Positive Matrices: Real, Rational, and Integral
• Authors: Abraham Berman; Naomi Shaked-Monderer
Abstract: This paper was presented as an invited talk in the 6th International Conference on Matrix Analysis and Applications, Duy Tan University, Da Nang City, Vietnam, June 15–18, 2017. All the matrices in the paper are real. We survey known results and present some new problems. The paper has six parts. What is complete positivity' Why are completely positive matrices important' How can we tell if a given matrix is completely positive' Does every rational completely positive matrix have a rational cp-factorization' cp-rank. Which integral completely positive matrices have an integral cp-factorization'
PubDate: 2018-03-16
DOI: 10.1007/s40306-018-0254-3

• On Chromatic Numbers of Two Extensions of Planar Graphs
• Authors: Khosro Tajbakhsh
Abstract: In this paper, the acyclic chromatic and the circular list chromatic numbers of a simple H-minor free graph G is considered, where H ∈{K5, K3,3}. It is proved that the acyclic chromatic number (resp. the circular list chromatic number) of a simple H-minor free graph G where H ∈{K5, K3,3} is at most 5 (resp. at most 8) and we conclude that G is star 20-colorable. These results generalize the same known results on planar graphs. Moreover, some upper bounds for the coloring numbers of H-minor free graphs for H ∈{K5, K3,3, Kr, s} and r ≤ 2 are obtained. These results generalize some known results and give some new results on group choice number, group chromatic number, and the choice number of the mentioned graphs with much shorter proofs.
PubDate: 2018-03-15
DOI: 10.1007/s40306-018-0252-5

• Indecomposable Exposed Positive Bi-linear Maps Between Two by Two Matrices
• Authors: Seung-Hyeok Kye
Abstract: Positive bi-linear maps between matrix algebras play important roles to detect tri-partite entanglement by the duality between bi-linear maps and tri-tensor products. We exhibit indecomposable positive bi-linear maps between 2 × 2 matrices which generate extreme rays in the cone of all positive bi-linear maps. In fact, they are exposed, and so detect entanglement of positive partial transpose (PPT) whose volume is nonzero.
PubDate: 2018-03-14
DOI: 10.1007/s40306-018-0249-0

• Codes Induced by Alternative Codes
• Authors: Ngo Thi Hien; Do Long Van
Abstract: Alternative codes, an extension of the notion of ordinary codes, have been first introduced and considered by Huy and Nam (2004). As seen below, every alternative code, in its turn, defines an ordinary code. Such codes are called codes induced by alternative codes or alt-induced codes, for short. In this paper, we consider these alt-induced codes and subclasses of them. In particular, characteristic properties of such codes are established, and an algorithm to check whether a finite code is alt-induced or not is proposed.
PubDate: 2018-02-13
DOI: 10.1007/s40306-018-0247-2

• On the Length Function of Saturations of Ideal Powers
• 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

• On a Backward Heat Conduction Problem Associated with Asymmetric Final
Data
• 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

• Piecewise Linear Vector Optimization Problems on Locally Convex Hausdorff
Topological Vector Spaces
• 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

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