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Abstract: In this short note, we present a general version of Carlson’s inequality for the Sugeno integral, which generalizes some recent results obtained by others. [Copyright &y& Elsevier]

Abstract: This note is concerned with an efficient computation of integrals of products of a smooth function and Daubechies scale function with partial support by using a one-point quadrature rule. The error estimate is obtained. The rule is illustrated by considering an example from the literature. [Copyright &y& Elsevier]

Abstract: In this paper we generalize classical , , estimates of the gradient to the Orlicz space for weak solutions of a quasilinear parabolic equation of -Laplacian type. [Copyright &y& Elsevier]

Abstract: This work is concerned with Hamiltonian networks of weakly and long-range coupled oscillators with either variable or constant on-site frequencies. We derive an infinite dimensional KAM-like theorem by which we establish that, given any -sites of the lattice, there is a positive measure set of small amplitude, quasi-periodic breathers (solutions of the Hamiltonian network that are quasi-periodic in time and exponentially localized in space) having -frequencies which are only slightly deformed from the on-site frequencies. [Copyright &y& Elsevier]

Abstract: The authors introduce and investigate the various properties and characteristics of two subclasses and of starlike functions of order . In particular, several inclusion relations, Hadamard products, coefficient estimates, distortion theorems and covering theorems are proven here for each of these function classes. Furthermore, some interesting distortion theorems for the Srivastava–Saigo–Owa fractional integral operator are obtained. Some of the results, presented in this paper, generalize and extend the corresponding results of earlier authors. [Copyright &y& Elsevier]

Abstract: Let be an integer and let be the dihedral group of order . It is proved that, if is a sequence of elements in , then there exist distinct indices such that . This result is a sharpening of the famous Erdős–Ginzburg–Ziv theorem for . [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the stability of the trivial solution for impulsive functional differential systems using several Lyapunov functions including partial components coupled with the Razumikhin technique, and obtained some new Razumikhin-type theorems which avoid using the auxiliary function under less restrictive conditions. Our results improve some of the earlier findings, and are suitable for many applications. Some examples are given to illustrate the advantages of the theorems obtained. [Copyright &y& Elsevier]

Abstract: We consider the “minor” and “homeomorphic” analogues of the maximum clique problem, i.e., the problems of determining the largest such that the input graph (on vertices) has a minor isomorphic to or a subgraph homeomorphic to , respectively, as well as the problem of finding the corresponding subgraphs. We term them as the maximum clique minor problem and the maximum homeomorphic clique problem, respectively. We observe that a known result of Kostochka and Thomason supplies an bound on the approximation factor for the maximum clique minor problem achievable in polynomial time. We also provide an independent proof of nearly the same approximation factor with explicit polynomial-time estimation, by exploiting the minor separator theorem of Plotkin et al. Next, we show that another known result of Bollobás and Thomason and of Komlós and Szemerédi provides an bound on the approximation factor for the maximum homeomorphic clique achievable in polynomial time. On the other hand, we show an lower bound (for some constant , unless ) on the best approximation factor achievable efficiently for the maximum homeomorphic clique problem, nearly matching our upper bound. Finally, we derive an interesting trade-off between approximability and subexponential time for the problem of subgraph homeomorphism where the guest graph has maximum degree not exceeding three and low treewidth. [Copyright &y& Elsevier]

Abstract: Theorems about the nonexistence of continuous surjections between continua and related results are extended to almost continuous surjections. Several questions are posed. [Copyright &y& Elsevier]

Abstract: In one of his early papers Claude Berge proved a Helly-type theorem, which replaces the usual “nonempty intersection” condition with a “convex union” condition. Inspired by this we prove a fractional Helly-type result, where we assume that many -tuples of a family of convex sets have a star-shaped union, and the conclusion is that many of the sets have a common point. We also investigate somewhat related art-gallery problems. In particular, we prove a -theorem for guarding planar art galleries with a bounded number of holes, completing a result of Kalai and Matoušek, who obtained such a result for galleries without holes. On the other hand, we show that if the number of holes is unbounded, then no -theorem of this kind holds with . [Copyright &y& Elsevier]

Abstract: Applying a fixed-point theorem of strict-set-contractions, some new criteria are established for the existence of positive periodic solutions of the following neutral differential system with feedback control. [Copyright &y& Elsevier]

Abstract: Several matrix versions of Cochran''s statistical theorem are revisited and some new matrix versions are established. [Copyright &y& Elsevier]

Abstract: In this paper, we consider notion of infine functions and we establish necessary and sufficient optimality conditions for a feasible solution of a multiobjective optimization problem involving mixed constraints (equality and inequality) to be an efficient or properly efficient solution. We also obtain duality theorems for Wolf type and Mond-Weir type duals under the generalized invexity assumptions. [Copyright &y& Elsevier]

Abstract: The Critical Theorem, due to Henry Crapo and Gian-Carlo Rota, has previously been extended or generalised in a number of different ways. The main result of the present paper is a general form of the Critical Theorem that encompasses many of these results. Applications include generalisations of a theorem by Curtis Greene that describes how the weight enumerator of a linear code is determined by the Tutte polynomial of the associated vector matroid, as well as generalisations of the MacWilliams identity for linear codes. [Copyright &y& Elsevier]

Abstract: We present a linear-time algorithm for computing all local periods of a given word. This subsumes (but is substantially more powerful than) the computation of the (global) period of the word and on the other hand, the computation of a critical factorization, implied by the Critical Factorization Theorem. [Copyright &y& Elsevier]

In this paper we develop the basic ideas of Janet by using the theory of D-modules. For the so-called completely integrable systems (Janet Systems), we show that the higher Ext groups are null. [Copyright &y& Elsevier]