Authors:Ta Van Tu Pages: 1 - 25 Abstract: Most of the known methods for finding the efficient set of a multiple objective linear programming (MOLP) problem are bottom-up search methods. Main difficulties of the known bottom-up search methods are to find all efficient extreme points adjacent to and to enumerate all efficient faces incident to an efficient degenerate extreme point. Main drawbacks of these methods are that the computational cost is still large and an implementation of them is still difficult. In this paper we propose a new local bottom-up search method for finding all maximal efficient faces for an MOLP problem. Our method is based on the maximal descriptor index sets for efficient edges and extreme rays for the MOLP problem in which the maximal descriptor index sets for edges and extreme rays incident to an efficient degenerate extreme point are easily found on the basis of solving some special linear programming problems. In addition, all efficient extreme points adjacent to and all efficient faces incident to an efficient extreme point can be easily found without using the simplex tables corresponding to bases of this point. Our method can overcome difficulties caused by the degeneracy of faces and is easy to implement. Some comparisons of our method with the known bottom-up search methods are presented. A numerical example is given to illustrate the method. PubDate: 2017-03-01 DOI: 10.1007/s40306-015-0164-6 Issue No:Vol. 42, No. 1 (2017)

Authors:Razieh Moradi; Mahdieh Ebrahimpour Pages: 27 - 35 Abstract: Let R be a commutative ring with identity and M be a unitary R-module. Let \(\phi :S(M)\rightarrow S(M)\cup \{\emptyset \}\) be a function, where S(M) is the set of submodules of M. We say that a proper submodule N of M is a ϕ-2-absorbing primary submodule if r s x∈N∖ϕ(N) implies r x∈N, or s x∈N, or \(rs\in \sqrt {(N:M)}\) , where r,s∈R and x∈M. In this paper, we study ϕ-2-absorbing primary submodules and we prove some basic properties of these submodules. Also, we give a characterization of ϕ-2-absorbing primary submodules and we investigate ϕ-2-absorbing primary submodules of some well-known modules. PubDate: 2017-03-01 DOI: 10.1007/s40306-016-0181-0 Issue No:Vol. 42, No. 1 (2017)

Authors:Nguyen Tu Cuong; Doan Trung Cuong Pages: 37 - 60 Abstract: The aim of this paper is to study a deep connection between local cohomology annihilators and Macaulayfication and arithmetic Macaulayfication over a local ring. Local cohomology annihilators appear through the notion of p-standard system of parameters. For a local ring, we prove an equivalence of the existence of Macaulayfications, the existence of a p-standard system of parameters, being a quotient of a Cohen-Macaulay local ring, and the verification of Faltings’ Annihilator theorem. For a finitely generated module which is unmixed and faithful, we prove an equivalence of the existence of an arithmetic Macaulayfication and the existence of a p-standard system of parameters; and both are proved to be equivalent to the existence of an arithmetic Macaulayfication on the ground ring. A connection between Macaulayfication and universal catenaricity is also discussed. PubDate: 2017-03-01 DOI: 10.1007/s40306-016-0185-9 Issue No:Vol. 42, No. 1 (2017)

Authors:Pham Ngoc Anh; Le Thi Hoai An Pages: 61 - 79 Abstract: In this paper, we present new projection methods for solving multivalued variational inequalities on a given nonlinear convex feasible domain. The first one is an extension of the extragradient method to multivalued variational inequalities under the asymptotic optimality condition, but it must satisfy certain Lipschitz continuity conditions. To avoid this requirement, we propose linesearch procedures commonly used in variational inequalities to obtain an approximation linesearch method for solving multivalued variational inequalities. Next, basing on a family of nonempty closed convex subsets of \(\mathcal R^{n}\) and linesearch techniques, we give inner approximation projection algorithms for solving multivalued variational inequalities and the convergence of the algorithms is established under few assumptions. PubDate: 2017-03-01 DOI: 10.1007/s40306-015-0165-5 Issue No:Vol. 42, No. 1 (2017)

Authors:Nguyen Van Duc; Nguyen Van Thang Pages: 99 - 111 Abstract: Let H be a Hilbert space with the norm ∥⋅∥, and let A:D(A) ⊂ H → H be a positive self-adjoint unbounded linear operator on H such that −A generates a C 0 semi-group on H. Let φ be in H, E > ε a given positive number and let f : [0, T]×H → H satisfy the Lipschitz condition ∥f(t, w 1)−f(t, w 2)∥ ≤ k∥w 1−w 2∥,w 1,w 2∈H, for some non-negative constant k independent of t, w 1 and w 2. It is proved that if u 1 and u 2 are two solutions of the ill-posed semi-linear parabolic equation backward in time u t + A u = f(t, u), 0 < t ≤ T,∥u(T)−φ∥ ≤ ε and ∥u i (0)∥ ≤ E, i = 1,2, then $$\ u_{1}(t)-u_{2}(t)\ \leq 2\varepsilon^{t/T} E^{1-t/T}\exp\Big[\Big(2k+\frac{1}{4}k^{2}(T+t)\Big)\frac{t(T-t)}{T}\Big] \quad \forall t \in [0,T]. $$ The ill-posed problem is stabilized by a modification of Tikhonov regularization which yields an error estimate of Hölder type. PubDate: 2017-03-01 DOI: 10.1007/s40306-015-0163-7 Issue No:Vol. 42, No. 1 (2017)

Authors:Nguyen Manh Cuong; Mai Xuan Thao Pages: 113 - 127 Abstract: In this paper, we extend results obtained by Dinh Dũng on optimal methods of adaptive sampling recovery of functions by sets of a finite capacity which is measured by their cardinality or pseudo-dimension, to univariate Besov-type classes of functions with bounded modulus of smoothness. PubDate: 2017-03-01 DOI: 10.1007/s40306-016-0175-y Issue No:Vol. 42, No. 1 (2017)

Authors:Fethi Soltani; Akram Nemri Pages: 129 - 147 Abstract: In this work, we establish some versions of Heisenberg-type uncertainty principles for the Dunkl-type Fock space \(F_{k}(\mathbb {C}^{d})\) . Next, we give an application of the classical theory of reproducing kernels to the Tikhonov regularization problem for operator \(L:F_{k}(\mathbb {C}^{d})\rightarrow H\) , where H is a Hilbert space. Finally, we come up with some results regarding the Tikhonov regularization problem and the Heisenberg-type uncertainty principle for the Dunkl-type Segal-Bargmann transform \(\mathcal {B}_{k}\) . Some numerical applications are given. PubDate: 2017-03-01 DOI: 10.1007/s40306-016-0188-6 Issue No:Vol. 42, No. 1 (2017)

Authors:Dang Vo Phuc; Nguyen Sum Pages: 149 - 162 Abstract: Let P k be the graded polynomial algebra \(\mathbb {F}_{2}[x_{1},x_{2},{\ldots } ,x_{k}]\) over the prime field of two elements, \(\mathbb {F}_{2}\) , with the degree of each x i being 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for P k as a module over the mod-2 Steenrod algebra, \(\mathcal {A}\) . In this paper, we explicitly determine a minimal set of \(\mathcal {A}\) -generators for P k in the case k = 5 and the degree 4(2 d −1) with d an arbitrary positive integer. PubDate: 2017-03-01 DOI: 10.1007/s40306-016-0190-z Issue No:Vol. 42, No. 1 (2017)

Authors:Calvin Tadmon Pages: 163 - 186 Abstract: In this work, we solve the evolution problem associated with the Einstein-Vlasov system, with initial data specified on two transversally intersecting null hypersurfaces. The main existence and uniqueness result of the paper is obtained by a contracting mapping principle, combined with Sobolev inequalities and Moser estimates as well as energy inequalities for first order and second order linear hyperbolic systems. The whole investigation is conducted in appropriate weighted Sobolev spaces. PubDate: 2017-03-01 DOI: 10.1007/s40306-016-0189-5 Issue No:Vol. 42, No. 1 (2017)

Authors:Thieu Huy Nguyen; Van Bang Pham Pages: 187 - 207 Abstract: We prove the existence and attraction property of an unstable manifold for solutions to the partial neutral functional differential equation of the form \(\left\{\begin{array}{ll} \frac{\partial}{\partial t}Fu_{t}= B(t)Fu_{t} +\varPhi(t,u_{t}),\quad t\ge s;~ t,s\in \mathbb{R},\ u_{s}=\phi\in \mathcal{C}:=C([-r, 0], X) \end{array}\right.\) under the conditions that the family of linear operators \((B(t))_{t\in \mathbb {R}}\) defined on a Banach space X generates the evolution family (U(t, s)) t≥s having an exponential dichotomy on the whole line \(\mathbb {R}\) , the difference operator \(F:\mathcal {C}\to X\) is bounded and linear, and the nonlinear delay operator Φ satisfies the ϕ-Lipschitz condition, i.e., \(\ \Phi (t,\phi ) -\Phi (t,\psi )\ \le \phi (t)\ \phi -\psi \ _{\mathcal {C}}\) for \(\phi ,~ \psi \in \mathcal {C}\) , where ϕ(⋅) belongs to an admissible function space defined on \(\mathbb {R}\) . Our main method is based on Lyapunov-Perron’s equations combined with the admissibility of function spaces and the technique of choosing F-induced trajectories. PubDate: 2017-03-01 DOI: 10.1007/s40306-016-0183-y Issue No:Vol. 42, No. 1 (2017)

Authors:Kyoji Saito Abstract: We are interested in the zero locus of a Chapoton’s F-triangle as a polynomial in two real variables x and y. An expectation is that (1) the F-triangle of rank l as a polynomial in x for each fixed y∈[0,1]has exactly l distinct real roots in [0,1], and (2) ith root x i (y) (1≤i≤l) as a function on y∈[0,1]is monotone decreasing. In order to understand these phenomena, we slightly generalized the concept of F-triangles and study the problem on the space of such generalized triangles. We analyze the case of low rank in details and show that the above expectation is true. We formulate inductive conjectures and questions for further rank cases. This study gives a new insight on the zero loci of f +- and f-polynomials. PubDate: 2017-03-14 DOI: 10.1007/s40306-017-0202-7

Authors:Kazumasa Inaba; Masaharu Ishikawa; Masayuki Kawashima; Nguyen Tat Thang Abstract: We will show that for each k≠1, there exists an isolated singularity of a real analytic map from \(\mathbb {R}^{4}\) to \(\mathbb {R}^{2}\) which admits a real analytic deformation such that the set of singular values of the deformed map has a simple, innermost component with k outward cusps and no inward cusps. Conversely, such a singularity does not exist if k=1. PubDate: 2017-01-20 DOI: 10.1007/s40306-016-0200-1

Authors:Tadashi Ishibe Abstract: Let Φ be an irreducible (possibly noncrystallographic) root system of rank l of type P. For the corresponding cluster complex Δ(P), which is known as pure (l − 1)-dimensional simplicial complex, we define the generating function of the number of faces of Δ(P) with dimension i − 1, which is called f-polynomial. We show that the f-polynomial has exactly l simple real zeros on the interval (0, 1) and the smallest root for the infinite series of type A l , B l , and D l monotone decreasingly converges to zero as the rank l tends to infinity. We also consider the generating function (called the f +-polynomial) of the number of faces of the positive part Δ+(P) of the complex Δ(P) with dimension i − 1, whose zeros are real and simple and are located in the interval (0, 1), including a simple root at t = 1. We show that the roots in decreasing order of f-polynomial alternate with the roots in decreasing order of f +-polynomial. PubDate: 2017-01-19 DOI: 10.1007/s40306-016-0201-0

Authors:Nguyen Viet Dung; Nguyen Van Ninh Abstract: Let ð“ be a fiber type arrangement of hyperplanes in ℂ n with complement M(ð“) (see Orlik, O., Terao, H. 1992). In this paper, we will give an explicit formula for the higher topological complexity T C n for the complement M(ð“) in terms of exponents of the arrangement ð“. PubDate: 2017-01-12 DOI: 10.1007/s40306-016-0199-3

Authors:Na Tang; Xianhua Li Pages: 539 - 548 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. PubDate: 2016-12-01 DOI: 10.1007/s40306-015-0153-9 Issue No:Vol. 41, No. 4 (2016)

Authors:Sang Og Kim; Abasalt Bodaghi Pages: 583 - 594 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. PubDate: 2016-12-01 DOI: 10.1007/s40306-015-0156-6 Issue No:Vol. 41, No. 4 (2016)

Authors:Tran Duc-Anh Pages: 711 - 714 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. PubDate: 2016-12-01 DOI: 10.1007/s40306-016-0169-9 Issue No:Vol. 41, No. 4 (2016)

Authors:Katsusuke Nabeshima; Shinichi Tajima Abstract: Complex analytic invariants of hypersurface isolated singularities are considered in the context of symbolic computation. The motivations for this paper are computer calculations of μ ∗-sequences that introduced by B. Teissier to study the Whitney equisingularity of deformations of complex hypersurfaces. A new algorithm that utilizes parametric local cohomology systems is proposed to compute μ ∗-sequences. Lists of μ ∗-sequences of some typical cases are also given. PubDate: 2016-12-19 DOI: 10.1007/s40306-016-0198-4

Authors:Lê Quy Thuong Abstract: In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these invariants. A purpose of this note is to show how the conjecture arises. Because of the integral identity’s nature, we shall give a quick tour on theories of motivic integration, which lead to a proof of the conjecture for algebraically closed ground fields of characteristic zero. PubDate: 2016-12-19 DOI: 10.1007/s40306-016-0197-5

Abstract: We study the capitulation of 2-ideal classes of an infinite family of imaginary biquadratic number fields consisting of fields \(\mathbb {k} =\mathbb {Q}(\sqrt {pq_{1}q_{2}}, i)\) , where \(i=\sqrt {-1}\) and q 1≡q 2≡−p≡−1 (mod 4) are different primes. For each of the three quadratic extensions \(\mathbb {K}/\mathbb {k}\) inside the absolute genus field ð•œ (∗) of ð•œ, we compute the capitulation kernel of \(\mathbb {K}/\mathbb {k}\) . Then we deduce that each strongly ambiguous class of \(\mathbb {k}/\mathbb {Q}(i)\) capitulates already in ð•œ (∗). PubDate: 2016-11-04 DOI: 10.1007/s40306-016-0194-8