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Abstract: In this paper, we obtain some Lyapunov-type inequalities for a class of higher-order linear differential equations. The results of this paper generalize and improve some earlier results on this topic. [Copyright &y& Elsevier]

Abstract: There is an abundant literature on inequalities for the (Euler’s) Gamma function Γ and its various related functions. Yet, only very recently, several authors began to study inequalities for the (Barnes’) double Gamma function . Here, in this paper, we aim at presenting several two-sided inequalities for the multiple Gamma functions . In our investigation of these two-sided inequalities for the multiple Gamma functions , we employ and extend a method based upon Taylor’s formula and express as series involving the Zeta functions. We also give a more convenient explicit form of the multiple Gamma functions being the set of positive integers. The main two-sided inequalities for the multiple Gamma functions (which we have presented in this paper) are presumably new and their derivations provide a fruitful insight into the corresponding problem for the multiple Gamma functions when . [Copyright &y& Elsevier]

Abstract: In this paper we study t-norms on the lattice of closed subintervals of the unit interval. Unlike for t-norms on a product lattice for which there exists a straightforward characterization of t-norms which are join-morphisms, respectively meet-morphisms, the situation is more complicated for t-norms in interval-valued fuzzy set theory. In previous papers several characterizations were given of t-norms in interval-valued fuzzy set theory which are join-morphisms and which satisfy additional properties, but little attention has been paid to meet-morphisms. Therefore, in this paper, we focus on t-norms which are meet-morphisms. We consider a general class of t-norms and investigate under which conditions t-norms belonging to this class are meet-morphisms. We also characterize the t-norms which are both a join- and a meet-morphism and which satisfy an additional border condition. [Copyright &y& Elsevier]

Abstract: The paper provides variety-based extensions of the concepts of (lattice-valued) interchange system and space, introduced by Denniston, Melton and Rodabaugh, and shows that variety-based interchange systems incorporate topological systems of Vickers, state property systems of Aerts, Chu spaces (over the category of sets in the sense of Pratt) of P.-H. Chu and contexts (of formal concept analysis) of Wille. The paper also provides an explicit description of (co)limits in the category of variety-based topological systems and applies the obtained results to extend the claim of Denniston et al. that the category of topological systems of Vickers is small initially topological over the category of sets. [Copyright &y& Elsevier]

Abstract: Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we correct some of the problematic cases in a previous paper by Aktaş and Çag˜man [H. Aktaş, N. Çag˜man, Soft sets and soft groups, Inf. Sci. 177 (2007) 2726–2735]. Moreover, we introduce the concepts of normalistic soft group and normalistic soft group homomorphism, study their several related properties, and investigate some structures that are preserved under normalistic soft group homomorphisms. [Copyright &y& Elsevier]

Abstract: Let . For or , has been determined by Hanani. In this paper, we investigate the case of . It is easy to see that if , then . It is known that by Hanani and that by a previous paper of the author. We shall focus on the case of . It is proved that and . [Copyright &y& Elsevier]

An L P H T S ( v ) is a collection of 4 ( v − 2 ) disjoint pure Hybrid triple systems on the same set of v elements. In Fan (2010), it is showed that there exists an L P H T S ( v ) for v ≡ 0 , 4 mod 6. In this paper, we establish the existence of an L P H T S ( v ) for v ≡ 1 , 3 mod 6, v > 3 . Finally, the spectrum for L P H T S s is completely determined. [ABSTRACT FROM AUTHOR]

In this paper we characterize the sets of all B ∈ B ( H ) such that AρB and the sets of all B ∈ B ( H ) such that BρA , where A ∈ B ( H ) is given and ρ ∈ { ≤ − , ≤ ⁎ , ≤ # , ≤ ⊕ } . [ABSTRACT FROM AUTHOR]

In this paper, we show that the primitive degree set of nonnegative primitive tensors with order m ( ≥ 3 ) and dimension n is { 1 , 2 , … , ( n − 1 ) 2 + 1 } , which implies that the results of the case m ≥ 3 (the case of tensors) is totally different from the case m = 2 (the case of matrices), and we also propose some open problems for further research. [ABSTRACT FROM AUTHOR]

In this paper we characterize the pairs 〈 A 0 , A 1 〉 of disjoint subsets of topological space X which can be separated by a cliquish function. [ABSTRACT FROM AUTHOR]

In this paper we study new class is called of generalized α b-irresolute mappings (denoted by g α b-irresolute) and study some of their properties. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of smg-closed sets in biminimal structure space and a new notion of a pair wise smg-closed set is defined and studied some of its properties. [ABSTRACT FROM AUTHOR]

A hyperoval of a point–line geometry is a nonempty set of points meeting each line in either 0 or 2 points. In this paper, we study hyperovals in line Grassmannians of finite polar spaces of rank 3, hereby often imposing some extra regularity conditions. We determine an upper bound and two lower bounds for the size of such a hyperoval. If equality occurs in one of these bounds, then there is an associated interesting point set of the polar space, like a tight set, an m -ovoid or a set of points having two possible intersection sizes with generators. With the aid of a computer, we have determined all hyperovals of the line Grassmannians of Q + ( 5 , 2 ) , Q ( 6 , 2 ) and Q − ( 7 , 2 ) . Several of the bounds we have found are actually tight for these geometries. [ABSTRACT FROM AUTHOR]

Let S = R ∪ B be a point set in the plane in general position such that each of its elements is colored either red or blue, where R and B denote the points colored red and the points colored blue, respectively. A quadrilateral with vertices in S is called a 4-hole if its interior is empty of elements of S . We say that a 4-hole of S is balanced if it has 2 red and 2 blue points of S as vertices. In this paper, we prove that if R and B contain n points each then S has at least n 2 − 4 n 12 balanced 4-holes, and this bound is tight up to a constant factor. Since there are two-colored point sets with no balanced convex 4-holes, we further provide a characterization of the two-colored point sets having this type of 4-holes. [ABSTRACT FROM AUTHOR]

Vincular or dashed patterns resemble classical patterns except that some of the letters within an occurrence must satisfy an adjacency requirement. In this paper, we show some general equivalences concerning the avoidance of vincular patterns by multiset permutations. We prove our results by defining bijections between various avoidance classes that preserve the number of occurrences of each letter. As a consequence, we obtain for multiset permutations the complete Wilf-classification of patterns of type (2, 1, 1), which also yields the complete classification for compositions and k-ary words when taken with numerical evidence. [ABSTRACT FROM AUTHOR]

In this paper, we present the clique arrangement A(G) for a chordal graph G to describe the intersections between the maximal cliques of G more precisely than in clique trees or related concepts. In particular, the node set of A(G) contains a node X = C1 ∩ C2 ∩ ... for every set C1, C2, ... of maximal cliques of G. In A(G), there is an arc from a node X to a node Z, if X is a subset of Z and there is no node Y, that is a superset of X and a subset of Z. As clique arrangements may have exponential size, we analyze this notion for strongly chordal graphs G. We provide a new characterization of strongly chordal graphs in terms of forbidden cyclic structures in the corresponding clique arrangements and we show how to compute the clique arrangement of a strongly chordal graph efficiently. [ABSTRACT FROM AUTHOR]

In this paper we study the relation between the local spectrum of a vertex set C and the local spectra of its subconstituents. In particular, it is shown that, when C is a completely regular code, such spectra are uniquely determined by the local spectra of C. Moreover, we obtain a new characterization for completely pseudo-regular codes, and consequently for completely regular codes, in terms of the relation between the local spectrum of an extremal set of vertices and the local spectrum of its antipodal set. We also present a new proof of the version of the spectral excess theorem for extremal sets of vertices. [ABSTRACT FROM AUTHOR]

A k-walk of a graph is a spanning closed walk meeting each vertex at most k times. In this paper, we consider sets of forbidden subgraphs that imply the existence of a k-walk in a connected graph of sufficiently large order, and give a characterization of such sets for k=2. [ABSTRACT FROM AUTHOR]

The vertex arboricity a(G) of a graph G is the minimum k such that V(G) can be partitioned into k sets where each set induces a forest. For a planar graph G, it is known that a(G)≤3. In two recent papers, it was proved that planar graphs without k-cycles for some k∈{3,4,5,6,7} have vertex arboricity at most 2. For a toroidal graph G, it is known that a(G)≤4. Let us consider the following question: do toroidal graphs without k-cycles have vertex arboricity at most 2? It was known that the question is true for k=3, and recently, Zhang proved the question is true for k=5. Since a complete graph on 5 vertices is a toroidal graph without any k-cycles for k≥6 and has vertex arboricity at least three, the only unknown case was k=4. We solve this case in the affirmative; namely, we show that toroidal graphs without 4-cycles have vertex arboricity at most 2. [ABSTRACT FROM AUTHOR]

Abstract: Given integers and with , the rose window graph is the graph with vertex set and edges and for every where addition in subscripts is modulo . In this paper we give necessary and sufficient conditions for two rose window graphs to be isomorphic. [Copyright &y& Elsevier]

Abstract: A graph is -Hamilton-connected ( -hamiltonian) if is Hamilton-connected (hamiltonian) for every set with . In the paper, we prove that [(i)] every 5-connected claw-free graph with minimum degree at least 6 is 1-Hamilton-connected, [(ii)] every 4-connected claw-free hourglass-free graph is 1-Hamilton-connected. As a byproduct, we also show that every 5-connected line graph with minimum degree at least 6 is 3-hamiltonian. [Copyright &y& Elsevier]

Abstract: In this paper, our main purpose is to establish the existence of entire large positive solutions to the quasilinear equation . We give also necessary conditions for the existence and nonexistence of such solutions. We distinguish the cases when is radial and when it is nonradial. [Copyright &y& Elsevier]

Abstract: In Suzuki (1998) [7] Suzuki gave a classification of association schemes with multiple Q-polynomial structures, allowing for one exceptional case which has five classes. In this paper, we rule out the existence of this case. Hence Suzukiʼs theorem mirrors exactly the well-known counterpart for association schemes with multiple P-polynomial structures, a result due to Eiichi Bannai and Etsuko Bannai in 1980. [Copyright &y& Elsevier]

In this paper we develop an algebraic framework that allows us to extend families of two-valued states on orthomodular lattices to Baer *-semigroups. We apply this general approach to study the full class of two-valued states and the subclass of Jauch–Piron two-valued states on Baer *-semigroups. [Copyright &y& Elsevier]

Abstract: In this paper, we are interested in computability aspects of subshifts and in particular Turing degrees of two-dimensional subshifts of finite type (SFTs) (i.e., tilings). To be more precise, we prove that, given any class of , there is an SFT such that is recursively homeomorphic to , where is a computable set of points. As a consequence, if contains a computable member, and have the exact same set of Turing degrees. On the other hand, we prove that, if contains only non-computable members, some of its members always have different but comparable degrees. This gives a fairly complete study of Turing degrees of SFTs. [Copyright &y& Elsevier]

Abstract: In the paper we introduce general classes of multivalent analytic functions defined by the subordination. In particular, we define the class of multivalent prestarlike functions. By using the Ruscheweyh’s duality theory we investigate convolution properties related to multivalent prestarlike functions and various inclusion relationships between defined classes of functions. Some applications involving well-known classes of functions defined by linear operators are also considered. [Copyright &y& Elsevier]

Abstract: In this paper the core partial order introduced by Baksalary and Trenkler has been studied further. New characterizations of the core partial order have been derived. Relationship between the core partial order and some known partial orders has been also investigated. [Copyright &y& Elsevier]

Abstract: A signed graph is a pair , where is a graph (in which parallel edges are permitted, but loops are not) with and . The edges in are called odd edges and the other edges of E even. By we denote the set of all symmetric matrices with if i and j are adjacent and all edges between i and j are even, if i and j are adjacent and all edges between i and j are odd, if i and j are connected by even and odd edges, if and i and j are non-adjacent, and for all vertices i. The stable inertia set of a signed graph is the set of all pairs for which there exists a matrix with p positive and q negative eigenvalues which has the Strong Arnold Property. In this paper, we study the stable inertia set of (signed) graphs. [Copyright &y& Elsevier]

Abstract: Let be a graph with vertex set . A moplex of is both a clique and a module whose neighborhood is a minimal separator in or empty. A moplex ordering of is an ordered partition of for some integer into moplexes which are defined in the successive transitory elimination graphs, i.e., for , is a moplex of the graph induced by and induces a clique. In this paper we prove the terminal vertex by an execution of the lexicographical depth-first search (LexDFS for short) algorithm on belongs to a moplex whose vertices are numbered consecutively and further that the LexDFS algorithm on defines a moplex ordering of , which is similar to the result about the maximum cardinality search (MCS for short) algorithm on chordal graphs [J.R.S. Blair, B.W. Peyton, An introduction to chordal graphs and clique trees, IMA Volumes in Mathematics and its Applications, 56 (1993) pp. 1–30] and the result about the lexicographical breadth-first search (LexBFS for short) algorithm on general graphs [A. Berry, J.-P. Bordat, Separability generalizes Dirac’s theorem, Discrete Appl. Math., 84 (1998) 43–53]. As a corollary, we can obtain a simple algorithm on a chordal graph to generate all minimal separators and all maximal cliques. [Copyright &y& Elsevier]

Abstract: In this paper we deal with cover–incomparability graphs of posets, or briefly C–I graphs. These are graphs derived from posets as the edge-union of their cover graph and their incomparability graph. We answer two recently posed open questions. Which distance-hereditary graphs are C–I graphs? Which Ptolemaic (i.e. chordal distance-hereditary) graphs are C–I graphs? It follows that C–I graphs can be recognized efficiently in the class of all distance-hereditary graph whereas recognizing C–I graphs in general is known to be NP-complete. [Copyright &y& Elsevier]

Abstract: By counting 1’s in the “right half” of consecutive rows, we locate the main diagonal of any doubly infinite permutation matrix with bandwidth w. Then the matrix can be correctly centered and factored into block-diagonal permutation matrices. Part II of the paper discusses the same questions for the much larger class of band-dominated matrices. The main diagonal is determined by the Fredholm index of a singly infinite submatrix. Thus the main diagonal is determined “at infinity” in general, but from only rows for banded permutations. [Copyright &y& Elsevier]

Abstract: To any metric on a finite set , one can associate a metric space known as its tight span. Properties of often reveal salient properties of . For example, cut sets of , i.e., subsets of whose removal disconnect , can help to identify clusters suggested by and indicate how (and hence ) may be decomposed into simpler components. Given a bipartition or split of , we introduce in this paper a real-valued index that comes about by considering cut sets of . We also show that this index is intimately related to another, more easily computable index whose definition does not directly depend on . In addition, we provide an illustration for how these two new indices could help to extend and complement current distance-based methods for phylogenetic network construction such as split decomposition and NeighborNet. [Copyright &y& Elsevier]

Abstract: Cluster algebras of finite type is a fundamental class of algebras whose classification is identical to the famous Cartan–Killing classification. More recently, Fomin and Zelevinsky introduced another central notion of cluster algebras with principal coefficients. These algebras are determined combinatorially by mutation classes of certain rectangular matrices. It was conjectured, by Fomin and Zelevinsky, that finite type cluster algebras with principal coefficients are characterized by the mutation classes which are finite. In this paper, we prove this conjecture. [Copyright &y& Elsevier]

Abstract: In this paper we study the periodic orbits of the third-order differential equation , where is a small parameter and the function is of class . [Copyright &y& Elsevier]

Abstract: For two n-by-n matrices, A,B, the product field of values is the set . In this paper, we establish basic properties of the product field of values. The main results are a proof that the product field is a simply connected subset of the complex plane and a characterization of matrix pairs for which the product field has nonempty interior. [Copyright &y& Elsevier]

Abstract: In this paper we present the classification of a subclass of naturally graded Leibniz algebras. This subclass has the nilindex and the characteristic sequence where n is the dimension of the algebra. In fact, this result completes the classification of naturally graded Leibniz algebras of nilindex . [Copyright &y& Elsevier]

Abstract: For a connected graph , an edge-cut is called a restricted edge-cut if contains no isolated vertices. And is said to be super restricted edge-connected, for short super-, if each minimum restricted edge-cut of isolates an edge. Let denote the set of the minimum degree vertices of . In this paper, for a super- graph with diameter and minimum degree , we show that the induced subgraph contains no complete graph . Applying this property we characterize the super restricted edge connected graphs with diameter which satisfy a type of neighborhood condition. This result improves the previous related one which was given by Wang et al. [S. Wang, J. Li, L. Wu, S. Lin, Neighborhood conditions for graphs to be super restricted edge connected, Networks 56 (2010) 11–19]. [Copyright &y& Elsevier]

Abstract: The paper investigates formal properties of reaction systems introduced by Ehrenfeucht and Rozenberg. A reaction system defines a function from the set of subsets of a finite set into itself. We investigate properties of such functions, and characterize situations when the function is total. We also introduce and characterize the property of functional completeness. Function classes defined by different types of reaction systems are compared. Comparisons are carried out also between different methods of generating long sequences and cycles. [Copyright &y& Elsevier]

Abstract: In this paper a mathematical problem with linear flexible constraints is considered. In order to solve the problem an approach is proposed based on multiobjective linear programming. Indeed, allowing violations for the constraints, and using multiobjective linear programming to minimize these violations, a subset of solution set which has less violations, namely efficiently feasible set, is obtained. Then, the corresponding objective function is optimized over efficiently feasible set in order to obtain an optimal solution. An application of the proposed approach in pattern classification is introduced. [Copyright &y& Elsevier]

Abstract: The main purpose of this paper is to introduce a numerical method for the computation of cubature rules on the square that are almost minimal, i.e. with few points w.r.t. the degree of precision . In particular for all the sets and the weights are new. New rules are also achieved for degrees 15, , 19 and respectively with 43, 54, 67 and 96 points. [Copyright &y& Elsevier]

Abstract: In this paper, the concept of an -fuzzy sublattice (ideal, filter) and -fuzzy sublattice (ideal, filter) in a lattice is introduced, which is a generalization of the concept as given by Davvaz and Kazancı(2011) [18]. Characterizations for an -fuzzy sublattice (ideal, filter) and -fuzzy sublattice (ideal, filter) are provided. Different classes of lattices are characterized by the properties of these fuzzy sublattices (ideals, filters). Using the notions of a fuzzy sublattice (ideal, filter) with thresholds, characterization of a fuzzy sublattice (ideal, filter), an -fuzzy sublattice (ideal, filter) and -fuzzy sublattice (ideal, filter) are discussed. [Copyright &y& Elsevier]

Abstract: Rank reversal is a phenomenon that occurs when a decision maker, in the process of selecting an alternative from a set of choices, is confronted with new alternatives that were not thought about when the selection process was initiated. It depends on the relationship between this new alternative and the old ones under each criterion. In this paper, we study the rank reversal phenomenon in the TOPSIS method and we propose modifications in the algorithm of Hwang and Yoon in order to solve the problem. Moreover, we present a general demonstration of the proposed modifications in the algorithm, as well as a numerical example to show these modifications. [Copyright &y& Elsevier]

Abstract: Abd-Elfattah et al. suggested a set of estimators for calculating population mean using auxiliary attributes. This paper proposes a family of estimators based on an adaptation of the estimators presented by Koyuncu and Kadilar , and introduces a new family of exponential estimators using auxiliary attributes. The expressions of the mean square errors (MSEs) of the adapted and proposed families are derived in a general form. It is shown that the adapted version of the Koyuncu and Kadilar estimators is always more efficient than that of Abd-Elfattah et al. . Moreover, the new exponential estimators based on auxiliary attributes are more efficient than those of Koyuncu and Kadilar and Abd-Elfattah et al. . The theoretical findings are supported by a numerical example using original data. [Copyright &y& Elsevier]

Abstract: The packing chromatic number of a graph is the smallest integer such that vertices of can be partitioned into disjoint classes where vertices in have pairwise distance greater than . We study the packing chromatic number of infinite distance graphs , i.e., graphs with the set of integers as vertex set and in which two distinct vertices are adjacent if and only if . In this paper we focus on distance graphs with . We improve some results of Togni who initiated the study. It is shown that for sufficiently large odd and for sufficiently large even . We also give a lower bound 12 for and tighten several gaps for with small . [Copyright &y& Elsevier]

Abstract: A connected graph is super edge connected (super- for short) if every minimum edge cut of is the set of edges incident with some vertex. We define a super- graph to be -super- if is still super- for any edge subset with . The maximum integer of such , written as , is said to be the edge fault tolerance of with respect to the super- property. In this paper, we study the bounds for , showing that . More refined bounds are obtained for regular graphs and Cartesian product graphs. Exact values of are obtained for edge transitive graphs. [Copyright &y& Elsevier]

Abstract: In this paper, we prove the following result: let X be a complex manifold, hyperbolic for the Carathéodory distance and let U be an open set relatively compact in X. Then, there exists such that we get, for the Carathéodory infinitesimal metric, . We also get results concerning fixed points of holomorphic mappings from X to U. [Copyright &y& Elsevier]