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In this note, we slightly generalize Theorem 2 in the paper by M. Tunç and point out that the assumption of Theorem 3 is not sufficient. A misuse of the term 'mean' is also discussed. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the bases of a semimodule over a commutative semiring R are investigated. Some properties and characterizations of the bases are discussed and some equivalent conditions for a basis to be a free basis in a finitely generated free semimodule over R are given. The different possible cardinalities for a basis in a finitely generated free semimodule over R are considered and some equivalent descriptions are obtained for a commutative semiring R satisfying the property that any two bases for a finitely generated free R-semimodule have the same cardinality. Partial results obtained in the paper develop and generalize the corresponding results for commutative join-semirings and for commutative zerosumfree semirings. [Copyright &y& Elsevier]

In this paper, a new class of (G, C, ρ)-type I functions and their generalizations are introduced. We consider a class of differentiable multiobjective optimization problems and establish sufficient optimality conditions. The results of the paper are more general than those existing in the literature. [ABSTRACT FROM AUTHOR]

Abstract: Let be a family of subsets of an -element set. Sperner’s theorem says that if there is no inclusion among the members of then the largest family under this condition is the one containing all -element subsets. The present paper surveys certain generalizations of this theorem. The maximum size of is to be found under the condition that a certain configuration is excluded. The configuration here is always described by inclusions. More formally, let be a poset. The maximum size of a family which does not contain as a (not-necessarily induced) subposet is denoted by . The paper is based on a lecture of the author at the Jubilee Conference on Discrete Mathematics [Banasthali University, January 11–13, 2009], but it was somewhat updated in December 2010. [Copyright &y& Elsevier]

Abstract: This paper is mainly concerned with the classical KKT reformulation and the primal KKT reformulation (also known as an optimization problem with generalized equation constraint (OPEC)) of the optimistic bilevel optimization problem. A generalization of the MFCQ to an optimization problem with operator constraint is applied to each of these reformulations, hence leading to new constraint qualifications (CQs) for the bilevel optimization problem. - and -type stationarity conditions tailored for the problem are derived as well. Considering the close link between the aforementioned reformulations, similarities and relationships between the corresponding CQs and optimality conditions are highlighted. In this paper, a concept of partial calmness known for the optimal value reformulation is also introduced for the primal KKT reformulation and used to recover the -stationarity conditions. [Copyright &y& Elsevier]

In this paper we introduce FG-coupled fixed point, which is a generalization of coupled fixed point for nonlinear mappings in partially ordered complete metric spaces. We discuss existence and uniqueness theorems of FGcoupled fixed points for different contractive mappings. Our theorems generalizes the results of Gnana Bhaskar and Lakshmikantham [1]. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the main results of Guo and Isaacs, Archiv der Mathematik 105 (2015) 215-222. We also obtain some criteria for -nilpotency of a finite group. [ABSTRACT FROM AUTHOR]

The generalized k-connectivity Kk(G) of a graph G, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized k-edge- connectivity λk(G). In this paper, graphs of order n such that Kk(G) = n -k/2- 1 and λk(G) = n -k/2- 1 for even k are characterized. [ABSTRACT FROM AUTHOR]

In this paper, we first construct a class of weight modules, called ϕ-imaginary Verma modules, for the toroidal Lie algebras. Then a criterion for the irreducibility of the ϕ-imaginary Verma modules is obtained and the irreducible quotients for the reducible ones are studied. Furthermore, we construct a more general class of Zn-graded modules for the toroidal Lie algebras and we discuss their irreducibility. This class of modules includes the ϕ-imaginary Verma modules as special examples [ABSTRACT FROM AUTHOR]

It is well known that a pseudo-Kähler structure is one of the natural generalizations of a Kähler structure. In this paper, we consider signatures of invariant pseudo-Kähler metrics on generalized flag manifolds from the viewpoint of T -root systems. [ABSTRACT FROM AUTHOR]

Abstract: An LRMTS is a large set consisting of pairwise disjoint resolvable Mendelsohn triple systems defined over the same -element set. In this paper a new product construction for LRMTS is displayed by using generalized LR-designs. As well, several new existence families of LRMTS are constructed via 3-wise balanced designs. Finally the existence result of LRMTS is expanded by combining all the known constructions. [Copyright &y& Elsevier]

Using a generalized Dunkl translation, we obtain an analog of Theorem 5.2 in Younis' paper for the Dunkl transform for functions satisfying the (δ, γ)-Dunkl Lipschitz condition in the space L² (ℝ, |x|2α+1dx). [ABSTRACT FROM AUTHOR]

Abstract: The structure of Terwilliger algebras of wreath products by thin schemes or one-class schemes was studied in [A. Hanaki, K. Kim, Y. Maekawa, Terwilliger algebras of direct and wreath products of association schemes, J. Algebra 343 (2011) 195–200]. In this paper, we will consider the structure of Terwilliger algebras of wreath products by quasi-thin schemes. This gives a generalization of their result. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to give a description of Lie derivations of generalized matrix algebras. As a consequence Lie derivations of full matrix algebras are determined. [Copyright &y& Elsevier]

In this paper we establish interior regularity for weak solutions and partial regularity for suitable weak solutions of the perturbed Navier-Stokes system, which can be regarded as generalizations of the results in L. Caffarelli, R. Kohn, L. Nirenberg: Partial regularity of suitable weak solutions of the Navier-Stokes equations, Commun. Pure. Appl. Math. 35 (1982), 771-831, and S. Takahashi, On interior regularity criteria for weak solutions of the Navier-Stokes equations, Manuscr. Math. 69 (1990), 237-254. [ABSTRACT FROM AUTHOR]

In this paper, the concept of dual normal relations on sets is introduced and generalized. Intrinsic characterizations of them are obtained. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to show that every GTS can be realized as a μ-closed subspace of a generalized hyperconnected space. Also, we give more characterizations of generalized hyperconnected spaces. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we deal with the convergence of the sequence for a given sequence . Then we consider the summability that generalizes the (C,1) summability and characterize the equivalence between the convergence of and the convergence of the sequence ; and the equivalence between the convergence of and the convergence of . [Copyright &y& Elsevier]

The aim of this paper is to apply the notion of semiclosed sets, to obtain a new class of generalized semi closed sets using Grills. Also we investigate the properties of the above mentioned sets. Further the concept is extended to derive some applications of generalized semi closed sets via Grills. [ABSTRACT FROM AUTHOR]

Abstract: A nonbinary Ford sequence is a de Bruijn sequence generated by simple rules that determine the priorities of what symbols are to be tried first, given an initial word of size which is the order of the sequence being generated. This set of rules is generalized by the concept of a preference function of span , which gives the priorities of what symbols to appear after a substring of size is encountered. In this paper, we characterize preference functions that generate full de Bruijn sequences. More significantly, we establish that any preference function that generates a de Bruijn sequence of order also generates de Bruijn sequences of all orders higher than , thus making the Ford sequence no special case. Consequently, we define the preference function complexity of a de Bruijn sequence to be the least possible span of a preference function that generates this de Bruijn sequence. [Copyright &y& Elsevier]

In this paper, we study the class of Jordan dialgebras (also called quasi-Jordan algebras). We develop an approach for reducing problems on dialgebras to the case of ordinary algebras. It is shown that straightforward generalizations of the classical Cohn's, Shirshov's, and Macdonald's Theorems do not hold for dialgebras. However, we prove dialgebraic analogues of these statements. Also, we study multilinear special identities which hold in all special Jordan algebras and do not hold in all Jordan algebras. We find a natural correspondence between special identities for ordinary algebras and dialgebras. [ABSTRACT FROM AUTHOR]

In this paper we analyse the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimes. We consider first the case of compact spacelike hypersurfaces, completing some previous results given in [2]. We next extend these results to the complete noncompact case. In that case, our approach is based on the use of a generalized version of the Omori–Yau maximum principle for trace type differential operators, recently given by the authors in [3]. [ABSTRACT FROM PUBLISHER]

Abstract: In the paper we generalize the main results presented in Bentkus and Paulauskas (2004) by giving rates of approximation of some semigroups of operators of the order , . Also two classes of operators, generalizing sectorial and quasi-sectorial operators, are introduced and their properties are studied. [Copyright &y& Elsevier]

In the present paper we generalize the concept of groups with triality and apply it to the theory of the Moufang, Bol and Bruck loops. Such generalizations allow us to reduce certain problems from the loop theory to problems in the theory of groups. [ABSTRACT FROM AUTHOR]

Abstract: The main results of this paper include a detailed analysis of the notion of generalized order optimality and some sufficient conditions for a point satisfying the necessary optimality condition of Mordukhovich (2006) for being a generalized order solution of the optimization problem under consideration. [Copyright &y& Elsevier]

Abstract: In this paper, the uniform cubic B-spline collocation method is implemented to find the numerical solution of the generalized Black–Scholes partial differential equation. We use the horizontal method of lines to discretize the temporal variable and the spatial variable by means of a -method, ( corresponds to the back-ward Euler method and corresponds to the Crank–Nicolson method), and a cubic B-spline collocation method on uniform meshes, respectively. The method corresponding to is shown to be unconditionally stable and first order accurate with respect to the time variable and second order accurate with respect to the space variable while the method corresponding to is shown to be unconditionally stable and second order accurate with respect to both the variables. Finally, the numerical examples demonstrate the stability and accuracy of the method. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to generalize the functions with bounded Mocanu variation and define the class of functions with bounded Mocanu variation which map the open unit disk onto conic domain. Many interesting properties of these functions are investigated. [Copyright &y& Elsevier]

Abstract: In this paper, we define generalized -Horadam sequence . After that, we study the properties of the generalized -Horadam sequence and prove some of these properties by means of determinant. Also, we obtain a generating function for the generalized -Horadam sequence. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze the relation between some classes of matrices with variants of the diagonal dominance property. We establish a sufficient condition for a generalized doubly diagonally dominant matrix to be invertible. Sufficient conditions for a matrix to be strictly generalized diagonally dominant are also presented. We provide a sufficient condition for the invertibility of a cyclically diagonally dominant matrix. These sufficient conditions do not assume the irreducibility of the matrix. [Copyright &y& Elsevier]

In this paper, we study the generalized anisotropic potential integral K α, γ⊗ f and anisotropic fractional integral I Ω,α, γ f with rough kernels, associated with the Laplace–Bessel differential operator Δ B . We prove that the operator f→K α, γ⊗ f is bounded from the Lorentz spaces to for 1≤p

Abstract: In this paper, we establish a functional generalization of the diamond- integral reverse Hölder inequality on time scales. Some related inequalities are also considered. [Copyright &y& Elsevier]

In this paper, a generalization of the class of semicommutative rings is investigated. A ring R is called central semicommutative if for any a; b ∈ R, ab = 0 implies arb is a central element of R for each r ∈ R. We prove that some results on semicommutative rings can be extended to central semicommutative rings for this general settings. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we give necessary and sufficient conditions for generalized solution and periodicity of the difference equation with -periodic coefficients, where , . Also, we obtain that the generalized solution is periodic with -period. [Copyright &y& Elsevier]

In this paper, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by using the equivalences on S/ℒ, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup. [ABSTRACT FROM AUTHOR]

Abstract: The competition graph of a doubly partial order is an interval graph. The competition-common enemy graph, a variant of the competition graph, of a doubly partial order is also an interval graph if it does not contain a 4-cycle as an induced subgraph. It is natural to ask whether or not the same phenomenon occurs for other interesting variants of the competition graph. In this paper, we study the -step competition graph, a generalization of the competition graph, of a doubly partial order. We show that the -step competition graph of a doubly partial order is an interval graph for every positive integer . We also show that given a positive integer , an interval graph with sufficiently many isolated vertices is the -step competition graph of a doubly partial order. [Copyright &y& Elsevier]

In this paper we discuss various refinements and generalizations of a theorem of Sankar Dutta and Paul Roberts. Their theorem gives a criterion for $ d$-dimensional Noetherian Cohen-Macaulay local ring to be a system of parameters, i.e., to have height $ d$ [ABSTRACT FROM AUTHOR]

We study the almost Daugavet property, a generalization of the Daugavet property. We analyze what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well. The main result of the paper is that if $ Z$ such that the quotient space $ X/Z$, then $ Z$ [ABSTRACT FROM AUTHOR]

Abstract: In this paper we establish some new generalizations and refinements of Hölder’s inequality and some related inequalities. We also show that many existing inequalities related to the Hölder inequality are special cases of the inequalities presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we establish some new generalizations of Aczél’s inequality and of Bellman’s inequality; we will conclude by presenting some refinements of these inequalities. [Copyright &y& Elsevier]

The idea of difference sequence spaces was introduced by Kizmaz [6], and this concept was generalized by Bektas and Colak [1]. In this paper, we define the sequence spaces c0(F, Δmu x) and l∞(F, Δmu x), where F = (fk) is a sequence of modulus functions, and examine some inclusion relations and properties of these spaces. [ABSTRACT FROM AUTHOR]