Authors:Pham Ky Anh; Tran Viet Anh; Le Dung Muu Pages: 413 - 429 Abstract: Abstract In this paper, we investigate a bilevel split variational inequality problem (BSVIP) involving a strongly monotone mapping in the upper-level problem and pseudomonotone mappings in the lower-level one. A strongly convergent algorithm for such a BSVIP is proposed and analyzed. In particular, a problem of finding the minimum-norm solution of a split pseudomonotone variational inequality problem is also studied. As a consequence, we get a strongly convergent algorithm for finding the minimum-norm solution to the split feasibility problem, which requires only two projections at each iteration step. An application to discrete optimal control problems is considered. PubDate: 2017-09-01 DOI: 10.1007/s40306-016-0178-8 Issue No:Vol. 42, No. 3 (2017)

Authors:Dao Quang Khai Pages: 431 - 443 Abstract: Abstract In this paper, we study local well-posedness for the Navier-Stokes equations with arbitrary initial data in homogeneous Sobolev spaces \(\dot {H}^{s}_{p}(\mathbb {R}^{d})\) for \(d \geq 2, p > \frac {d}{2}\) , and \(\frac {d}{p} - 1 \leq s < \frac {d}{2p}\) . The obtained result improves the known ones for p > d and s = 0 (see [4, 6]). In the case of critical indexes \(s=\frac {d}{p}-1\) , we prove global well-posedness for Navier-Stokes equations when the norm of the initial value is small enough. This result is a generalization of the one in [5] in which p = d and s = 0. PubDate: 2017-09-01 DOI: 10.1007/s40306-016-0192-x Issue No:Vol. 42, No. 3 (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:Si Duc Quang; Do Phuong An Pages: 455 - 470 Abstract: Abstract Let V be a projective subvariety of \(\mathbb P^{n}(\mathbb C)\) . A family of hypersurfaces \(\{Q_{i}\}_{i=1}^{q}\) in \(\mathbb P^{n}(\mathbb C)\) is said to be in N-subgeneral position with respect to V if for any 1≤i 1<⋯<i N+1≤q, \( V\cap (\bigcap _{j=1}^{N+1}Q_{i_{j}})=\varnothing \) . In this paper, we will prove a second main theorem for meromorphic mappings of \(\mathbb C^{m}\) into V intersecting hypersurfaces in subgeneral position with truncated counting functions. As an application of the above theorem, we give a uniqueness theorem for meromorphic mappings of \(\mathbb C^{m}\) into V sharing a few hypersurfaces without counting multiplicity. In particular, we extend the uniqueness theorem for linearly nondegenerate meromorphic mappings of \(\mathbb C^{m}\) into \(\mathbb P^{n}(\mathbb C)\) sharing 2n+3 hyperplanes in general position to the case where the mappings may be linearly degenerated. PubDate: 2017-09-01 DOI: 10.1007/s40306-016-0196-6 Issue No:Vol. 42, No. 3 (2017)

Authors:M. Aminian; S. M. B. Kashani Pages: 471 - 490 Abstract: Abstract In this paper, we introduce L k -biharmonic hypersurfaces M in simply connected space forms R n+1(c) and propose L k -conjecture for them. For c=0,−1, we prove the conjecture when hypersurface M has two principal curvatures with multiplicities 1,n−1, or M is weakly convex, or M is complete with some constraints on it and on L k . We also show that neither there is any L k -biharmonic hypersurface M n in \( \mathbb {H}^{n+1} \) with two principal curvatures of multiplicities greater than one, nor any L k -biharmonic compact hypersurface M n in \( \mathbb {R}^{n+1} \) or in \( \mathbb {H}^{n+1} \) . As a by-product, we get two useful, important variational formulas. The paper is a sequel to our previous paper, (Taiwan. J. Math., 19, 861–874, 5) in this context. PubDate: 2017-09-01 DOI: 10.1007/s40306-016-0195-7 Issue No:Vol. 42, No. 3 (2017)

Authors:Mehmet Akif Akyol Pages: 491 - 507 Abstract: Abstract As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give examples, and investigate the geometry of foliations which arise from the definition of a conformal submersion and show that there are certain product structures on the total space of a conformal semi-invariant submersion. Moreover, we also find necessary and sufficient conditions for a conformal semi-invariant submersion to be totally geodesic. PubDate: 2017-09-01 DOI: 10.1007/s40306-016-0193-9 Issue No:Vol. 42, No. 3 (2017)

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:Nguyen Manh Cuong; Mai Xuan Thao Abstract: 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: 2017-08-25 DOI: 10.1007/s40306-017-0223-2

Authors:Vu Van Dong Abstract: 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: 2017-08-24 DOI: 10.1007/s40306-017-0221-4

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:Mehdi Tajik; Behrooz Mashayekhy; Ali Pakdaman Abstract: 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: 2017-08-24 DOI: 10.1007/s40306-017-0219-y

Authors:Keisuke Hakuta Abstract: 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: 2017-08-23 DOI: 10.1007/s40306-017-0217-0

Authors:Mohammad H. M. Rashid 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: 2017-08-19 DOI: 10.1007/s40306-017-0222-3

Authors:Cameron Gordon; Tye Lidman 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: 2017-06-28 DOI: 10.1007/s40306-017-0216-1

Authors:Ha Binh Minh; Chu Binh Minh; Victor Sreeram 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: 2017-06-23 DOI: 10.1007/s40306-017-0215-2

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

Authors:Edoardo Ballico Abstract: Abstract We give the stratification by the symmetric tensor rank of all degree d ≥ 9 homogeneous polynomials with border rank 5 and which depend essentially on at least five variables, extending previous works (A. Bernardi, A. Gimigliano, M. Idà, E. Ballico) on lower border ranks. For the polynomials which depend on at least five variables, only five ranks are possible: 5, d + 3, 2d + 1, 3d − 1, 4d − 3, but each of the ranks 3d − 1 and 2d + 1 is achieved in two geometrically different situations. These ranks are uniquely determined by a certain degree 5 zero-dimensional scheme A associated with the polynomial. The polynomial f depends essentially on at least five variables if and only if A is linearly independent (in all cases, f essentially depends on exactly five variables). The polynomial has rank 4d − 3 (resp. 3d − 1, resp. 2d + 1, resp. d + 3, resp. 5) if A has 1 (resp. 2, resp. 3, resp. 4, resp. 5) connected component. The assumption d ≥ 9 guarantees that each polynomial has a uniquely determined associated scheme A. In each case, we describe the dimension of the families of the polynomials with prescribed rank, each irreducible family being determined by the degrees of the connected components of the associated scheme A. PubDate: 2017-04-22 DOI: 10.1007/s40306-017-0211-6

Authors:Si Tiep Dinh; Huy Vui Ha; Tien Son Pham Abstract: Abstract Let F := (f 1, …, f p ): ℝ n → ℝ p be a polynomial map, and suppose that S := {x ∈ ℝ n : f i (x) ≤ 0,i = 1, …, p}≠∅. Let d := maxi =1, …, p deg f i and \(\mathcal {H}(d, n, p) := d(6d - 3)^{n + p - 1}.\) Under the assumptions that the map F : ℝ n → ℝ p is convenient and non-degenerate at infinity, we show that there exists a constant c > 0 such that the following so-called Hölder-type global error bound result holds \(c d(x,S) \le [f(x)]_{+}^{\frac {2}{\mathcal {H}(2d, n, p)}} + [f(x)]_{+} \quad \textrm { for all } \quad x \in \mathbb {R}^{n},\) where d(x,S) denotes the Euclidean distance between x and S, f(x) := maxi=1, …, p f i (x), and [f(x)]+ := max{f(x),0}. The class of polynomial maps (with fixed Newton polyhedra), which are non-degenerate at infinity, is generic in the sense that it is an open and dense semi-algebraic set. Therefore, Hölder-type global error bounds hold for a large class of polynomial maps, which can be recognized relatively easily from their combinatoric data. This follows up the result on a Frank-Wolfe type theorem for non-degenerate polynomial programs in Dinh et al. (Mathematical Programming Series A, 147(16), 519–538, 2014). PubDate: 2017-04-21 DOI: 10.1007/s40306-017-0209-0

Authors:Mohamed Zitane Abstract: Abstract In this work, we study the existence of periodic solutions for some non-autonomous nonlinear partial functional differential equation of neutral type. We assume that the linear part is non-densely defined and generates an evolution family under the conditions introduced by N. Tanaka. The delayed part is assumed to be ω-periodic with respect to the first argument. Using a fixed-point theorem for multivalued mapping, some sufficient conditions are given to prove the existence of periodic solutions. An example is shown to illustrate our results. PubDate: 2017-04-17 DOI: 10.1007/s40306-017-0208-1