Search

Abstract In this paper, we are concerned with the Shamanskii-like self-adaptive Levenberg–Marquardt methods for nonlinear equations. We consider two choices of Levenberg–Marquardt parameter. One of them is the standard self-adaptive Levenberg–Marquardt parameter, the other is nonmonotone self-adaptive Levenberg–Marquardt parameter by using the nonmonotone technique of Grippo, Lampariello and Lucidi. Under the error bound condition which is weaker than nonsingularity, we show that the Shamanskii-like self-adaptive Levenberg–Marquardt methods converge with Q -order (m + 1). Numerical experiments show the new algorithms are efficient and promising. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose two accelerated algorithms for the low-rank approximate method in Wang et al. (0000) for matrix completion. The main idea is to use the successive over-relaxation technique. Based on the successive over-relaxation method for the feasible matrices or projection matrices, the low-rank matrix approximate method is modified and accelerated. Meanwhile, we discuss the convergence of the over-relaxation algorithm for the feasible matrix. Finally, the numerical experiments show them to be effective. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose an efficient method for special least squares solution of the complex matrix equation (A X B , C X D) = (E , F). By using the real representation matrices of complex matrices, the particular structure of the real representation matrices, the Moore–Penrose generalized inverse and the Kronecker product, we obtain the explicit expression of the minimal norm least squares Hermitian solution of the complex matrix equation (A X B , C X D) = (E , F) , which was studied by a product of matrices and vectors in Wang et al. (2016). Our resulting formulas only involve real matrices, and the corresponding algorithm only performs real arithmetic. Therefore our proposed method is more effective and portable. Finally, we give three numerical examples to illustrate the effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider the following nonlinear waveequation with variable exponents: u t t − div (| ∇ u | r (⋅) − 2 ∇ u) + | u t | m (⋅) − 2 u t = 0. By using a lemma by Komornik, we prove the decay estimates for the solution under suitable assumptions on the variable exponents m , r and the initial data. We also give two numerical applications to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study a new kind of vector equilibrium problem and we proved the existence of solutions for this kind of equilibrium problem by using the section theorem and Fan KKM theorem. Then we generalize this kind of vector equilibrium problem to a more general case. Equilibrium problems with lower and upper bounds was an open problem proposed by Isac, Sehgal and Singh in 1999. J. Li, O. Chadli, Y. Chiang and J.C. Yao, Zhang Cong-jun derived some results of the equilibrium problems with lower and upper bounds under certain conditions. In this paper we derive more results of this open problem under certain conditions, constructs an iteration algorithm, and discuses the convergence of the algorithm. [Copyright &y& Elsevier]

In this paper, we construct a new iterative algorithm for set-valued variational inclusions without the compactness condition and study the convergence of the perturbed Ishikawa iterative process for solving a class of the generalized single-valued variational inclusions in Banach spaces. The result obtained in this paper is a generalization and improvement of Noor''s theorem [1]. [Copyright &y& Elsevier]

We prove that the equation x2 − kxy + y2 + x = 0 with k ∊ N+ has an infinite number of positive integer solutions x and y if and only if k = 3. For k = 3 the quotient SHAPE="SOL" ALIGN="C" STYLE="S">xy is asymptotically equal to (3 + √5)/2 or (3 − √5)/2. Results of the paper are based on data obtained via Computer Algebra System (derive 5). Some derive procedures presented in the paper made it possible to discover interesting regularities concerning simple continued fractions of certain numbers. [Copyright &y& Elsevier]

In a recent paper [1] a number of numerical schemes for the shallow water equations based on a conservative linearization are analyzed. In particular, it is established that the schemes are related through the use of a source term. In this paper this technique is applied to the Euler equations, and further analysis suggests a new formulation of an existing scheme having the same key properties. [Copyright &y& Elsevier]

In this paper, we concern over a class of the Wigner–Poisson- X α system introduced and developed by Bao et al. (2003), Mauser (2001) and Stimming (2005), respectively. The model describes the quantum mechanical motion of particles under the influence of the nonlocal Hartree potential and a local power term (exchange potential). The existence and uniqueness of local mild solution to the n -dimensional ( n = 1 , 3 ) Cauchy problems are established on the space of some integrable functions whose inverse Fourier transforms are also integrable. [ABSTRACT FROM AUTHOR]

In the past, polynomial particular solutions have been obtained for certain types of partial differential operators without convection terms. In this paper, a closed-form particular solution for more general partial differential operators with constant coefficients has been derived for polynomial basis functions. The newly derived particular solution is further coupled with the method of particular solutions (MPS) for numerically solving a large class of elliptic partial differential equations. In contrast to the use of Chebyshev polynomial basis functions, the proposed approach is more flexible in selecting the collocation points inside the domain. The polynomial basis functions are well-known for yielding ill-conditioned systems when their order becomes large. The multiple scale technique is applied to circumvent the difficulty of ill-conditioning problem. Five numerical examples are presented to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a method for the construction of 8×8 substitution boxes used in the area of cryptography. A symmetric group permutation S8 is applied on Galois field elements that originally belong to GF(28), and as a consequence, 40320 new substitution boxes are synthesized. The Liu J substitution box is used as a seed in the creation process of the new algebraically complex nonlinear components. The core design of this new algorithm relies on the symmetric group permutation operation which is embedded in the algebraic structure of the new substitution box. We study the characteristics of the newly created substitution boxes and highlight the improved performance parameters and their usefulness in practical applications. In particular, we focus on the nonlinear properties and the behavior of input/output bits and determine the suitability of a particular substitution box for a specific type of encryption application. A comparison with some of the prevailing and popular substitution boxes is presented. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the notion of intuitionistic -fuzzy subalgebras in -algebras and study their fundamental properties. We get a fuzzy subalgebra from an intuitionistic -fuzzy subalgebra. Also the notion of intuitionistic -fuzzy (closed) filters of -algebras is introduced. We investigate the relationship between intuitionistic -fuzzy subalgebras and intuitionistic -fuzzy (closed) filters of -algebras. [Copyright &y& Elsevier]

Abstract: In this paper we give a method for peturbation of solutions of linear homogeneous differential equation of the second order. [Copyright &y& Elsevier]

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]

Abstract: In this paper, we study soft hypergroupoids. Firstly, we introduce the notion of soft hypergroupoids, and some examples are given. Also, we show that soft hypergroupoids are closely related to -subhypergroupoid. Secondly, using the notion of soft hypergroupoid, some new properties of soft hypergroupoids are obtained. Lastly, we investigate some properties of soft subhypergroupoids. [Copyright &y& Elsevier]

Abstract: In this paper, we shall study the uniqueness problems of meromorphic functions sharing a small function. Our results improve or generalize many previous results on value sharing of meromorphic functions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we investigate a family of integral operators defined on the space of -valent meromorphic functions. By making use of these novel integral operators, we introduce and investigate several new subclasses of -valent starlike, -valent convex, -valent close-to-convex and -valent quasi-convex meromorphic functions. Also we establish some inclusion relationships associated with the aforementioned integral operators. Several interesting integral-preserving properties are also considered. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a scheduling problem for automated guided vehicles in container terminals is defined and formulated as a Minimum Cost Flow model. This problem is then solved by a novel algorithm, NSA+, which extended the standard Network Simplex Algorithm (NSA). Like NSA, NSA+ is a complete algorithm, which means that it guarantees optimality of the solution if it finds one within the time available. To complement NSA+, an incomplete algorithm Greedy Vehicle Search (GVS) is designed and implemented. The NSA+ and GVS are compared and contrasted to evaluate their relative strength and weakness. With polynomial time complexity, NSA+ can be used to solve very large problems, as verified in our experiments. Should the problem be too large for NSA+, or the time available for computation is too short (as it would be in dynamic scheduling), GVS complements NSA+. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the controllability of a parabolic system with nonlinear memory. Based on the localized estimate of the solution, we prove that the system with a superlinear growth memory is not controllable. Furthermore, two controllability results for some initial data and targets are given as well. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the notions of anti-reflexive kernel, symmetric kernel, reflexive closure, and symmetric closure of a soft set relation are first introduced, respectively. Then, their accurate calculation formulae and some properties are obtained. Finally, soft set relation mappings and inverse soft set relation mappings are proposed, and some related properties are discussed. [ABSTRACT FROM AUTHOR]

Abstract: Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a new set of contiguous function relations are established. Applications of such relations to hypergeometric summation formulas and the theory of Jacobi polynomials are presented. [ABSTRACT FROM AUTHOR]

Abstract: Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we introduce and study soft subrings and soft ideals of a ring by using Molodtsov’s definition of the soft sets. Moreover, we introduce soft subfields of a field and soft submodule of a left -module. Some related properties about soft substructures of rings, fields and modules are investigated and illustrated by many examples. [ABSTRACT FROM AUTHOR]

Abstract: Let denotes the space of almost convergent sequences introduced by Lorentz [G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190] and also be the domain of the generalized difference matrix in the sequence space . In this paper, the - and -duals of the spaces , and are determined. Furthermore, two basic results on the space are proved and the classes and of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where is any given sequence space. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we give some sufficient conditions in terms of regularly generated sequences for a sequence to be subsequentially convergent. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the global behavior of the difference equation with positive parameters and non-negative initial conditions. [ABSTRACT FROM AUTHOR]

Abstract: Given two ellipses, one surrounding the other one, Poncelet introduced a map from the exterior one to itself by using the tangent lines to the interior ellipse. This procedure can be extended to any two smooth, nested and convex ovals and we call these types of maps, Poncelet’s maps. We recall what he proved around 1814 in the dynamical systems language: In the two ellipses’ case and when the rotation number of is rational there exists an such that , or in other words, Poncelet’s map is conjugate to a rational rotation. In this paper we study general Poncelet’s maps and give several examples of algebraic ovals where the corresponding Poncelet’s map has a rational rotation number and is not conjugate to a rotation. Finally, we also provide a new proof of Poncelet’s result based on dynamical and computational tools. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the authors make use of certain analytical techniques for nonlinear algebraic equation systems in order to give another refinement of the Pólya–Szegö inequality in a triangle, which is associated with one of Chen’s theorems (see Chen (1993) and Chen (2000) ). Some remarks and observations, as well as two closely-related open problems, are also presented. [Copyright &y& Elsevier]

Abstract: In this paper, a new kind of intuitionistic fuzzy subgroup theory, which is different from that of Ma, Zhan and Davvaz (2008) , is presented. First, based on the concept of cut sets on intuitionistic fuzzy sets, we establish the neighborhood relations between a fuzzy point and an intuitionistic fuzzy set . Then we give the definitions of the grades of belonging to , quasi-coincident with , belonging to and quasi-coincident with and belonging to or quasi-coincident with , respectively. Second, by applying the 3-valued Lukasiewicz implication, we give the definition of -intuitionistic fuzzy subgroups of a group for , and we show that, in 16 kinds of -intuitionistic fuzzy subgroups, the significant ones are the -intuitionistic fuzzy subgroup, the -intuitionistic fuzzy subgroup and the -intuitionistic fuzzy subgroup. We also show that is a -intuitionistic fuzzy subgroup of if and only if, for any , the cut set of is a 3-valued fuzzy subgroup of , and is a -intuitionistic fuzzy subgroup (or -intuitionistic fuzzy subgroup) of if and only if, for any (or for any ), the cut set of is a 3-valued fuzzy subgroup of . At last, we generalize the -intuitionistic fuzzy subgroup, -intuitionistic fuzzy subgroup and -intuitionistic fuzzy subgroup to intuitionistic fuzzy subgroups with thresholds, i.e., -intuitionistic fuzzy subgroups. We show that is a -intuitionistic fuzzy subgroup of if and only if, for any , the cut set of is a 3-valued fuzzy subgroup of . We also characterize the -intuitionistic fuzzy subgroup by the neighborhood relations between a fuzzy point and an intuitionistic fuzzy set . [Copyright &y& Elsevier]

Abstract: In this paper, we develop a framework to obtain approximate solutions to systems of algebraic–differential equations of fractional order by employing the homotopy analysis method (HAM). The study highlights the efficiency of the method and its dependence on the auxiliary parameter . Numerical examples are examined to highlight the significant features of the HAM method. The method shows improvements over existing analytical techniques [Copyright &y& Elsevier]

Abstract: Molodtsov [D. Molodtsov, Soft set theory–First results, Comput. Math. Appl. 37 (1999) 19–31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Jun [Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408–1413] applied first the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras. In this paper we introduce the notion of soft -ideals and -idealistic soft BCI-algebras, and then investigate their basic properties. Using soft sets, we give characterizations of (fuzzy) -ideals in BCI-algebras. We provide relations between fuzzy -ideals and -idealistic soft BCI-algebras. [Copyright &y& Elsevier]

Abstract: A graph is called -choosable if, for every list assignment with for all , there is an -coloring of such that every vertex has at most neighbors having the same color as itself. Let be a graph embeddable in a surface of nonnegative characteristic. In this paper, we prove: (1) If contains no -cycle with a chord for all , then is -choosable; (2) If contains neither 5-cycle with a chord nor 6-cycle with a chord, then is -choosable. [Copyright &y& Elsevier]

Abstract: In this paper, we prove that the operations and of effect algebras are continuous with respect to their ideal topology, and if the effect algebras are lattice effect algebras, then under some conditions, the lattice operations and are also continuous with respect to their ideal topology. [Copyright &y& Elsevier]

Abstract: In this paper, two sharp inequalities are derived. The first is a sharp Simpson inequality and the second is a sharp inequality of Ostrowski type in two independent variables. [Copyright &y& Elsevier]

Abstract: In this paper, by using the concept of -accretive mappings and the new resolvent operator technique associated with -accretive mappings, we introduce and study a system of general mixed quasivariational inclusions involving -accretive mappings in Banach spaces, and construct a new perturbed iterative algorithm with mixed errors for this system of nonlinear -accretive variational inclusions in -uniformly smooth Banach spaces. Our results improve and generalize the corresponding results of recent works. [Copyright &y& Elsevier]

Abstract: A simplified model that studies stimuli representation and the set of algorithms that let us analyze associative learning in some particular cases with predetermined values of the salience of the stimuli is presented. We simulate an experiment where rats were trained in a Morris pool to find a hidden platform in the presence of a single landmark. The results obtained agree with a previous study where it was found that the control acquired by a single landmark is different depending on its relative distance from the hidden platform. In this paper, some simplified equations of the associative learning model have been used. [Copyright &y& Elsevier]

Abstract: In this paper, we obtained rich solutions for the discrete complex cubic Ginzburg–Landau equation by means of the extended tanh-function approach. These solutions include chirpless bright soliton, chirpless dark soliton, triangular function solutions and some solutions with alternating phases, and so on. Meanwhile, the range of parameters where some exact solution exists is given. [Copyright &y& Elsevier]

Abstract: Day and Tripathi [K. Day, A. Tripathi, Unidirectional star graphs, Inform. Process. Lett. 45 (1993) 123–129] proposed an assignment of directions on the star graphs and derived attractive properties for the resulting directed graphs. Cheng and Lipman [E. Cheng, M.J. Lipman, On the Day–Tripathi orientation of the star graphs: Connectivity, Inform. Process. Lett. 73 (2000) 5–10; E. Cheng, M.J. Lipman, Connectivity properties of unidirectional star graphs, Congr. Numer. 150 (2001) 33–42] studied the connectivity properties of these unidirectional star graphs. The class of star graphs is a special case of Cayley graphs generated by transposition trees. In this paper, we give directions on these graphs and study the connectivity properties of the resulting unidirectional graphs. [Copyright &y& Elsevier]

Abstract: In this paper we consider the total domination number and the total bondage number for digraphs. The total bondage number, defined as the minimum number of edges whose removal enlarges the total domination number, measures to some extent the robustness of a network where a minimum total dominating set is required. We determine the total domination number and total bondage number of the extended de Burijn digraph and the extended Kautz digraph, proposed by Shibata and Gonda in 1995, which generalize the classical de Bruijn digraph and the Kautz digraph. [Copyright &y& Elsevier]

This paper develops and demonstrates a guaranteed a-priori error bound for the Taylor polynomial approximation of any degree to the solution of initial value ordinary differential equations. The error bound is explicit and does not require upper bounds on the potentially complicated and intrinsically unknown right-hand side nor on any of its higher-order derivatives as with existing bounds, and thus it provides a valuable tool for the numerous applications in which initial value ode problems arise and for which approximate solutions must be sought. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a continuous-time level-dependent QBD process with a continuous phase variable. We extend the censoring technique to be able to deal with the QBD process. We define a new version for the R- and G-measures, and provide two types of RG-factorizations in terms of these measures. If the matrix of generalized density functions of the QBD process is in L 2([0,+∞)2), which is a space of square integrable bivariate real functions, then we provide orthonormal representations for the R- and G-measures, which lead to the matrix structure of the RG-factorizations. Based on this, we can provide an algorithmic framework for computing main performance measures of the QBD process. Furthermore, we introduce a continuous phase type (CPH) distribution, and then analyze a CPH/CPH/1 queue as an interesting example. [Copyright &y& Elsevier]

Abstract: In this paper, we use the coincidence degree theory to establish new results on the existence of w-periodic solutions for a two-neuron network model. [Copyright &y& Elsevier]

Abstract: Replication is a key technology of distributed storage systems. In this paper, an indirect replication algorithm is proposed following the intrinsic characteristic of distributed storage systems and the peer-to-peer model. In the indirect replication algorithm, the data object is partitioned into several data blocks. These data blocks are encoded in order that there is data redundancy between data blocks. Comparing with the traditional replication algorithm, the indirect replication algorithm has less granularity of replication, less bandwidth and storage costs, and provides higher availability, durability, and security. The performance evaluation shows that the encoding and decoding times are proportional to the data size, and that the irregular cascade bipartite graphs are of great advantage in improving the success ratio of data recovery. Finally, if the number of data blocks used to recover the data object is larger than a certain value, the success ratio of data recovery approaches 100%. [Copyright &y& Elsevier]

Abstract: In this paper, the authors establish some explicit formulas and representations for the Nörlund polynomial B n (χ) and b n (χ) Several identities involving Bernoulli numbers, Nörlund numbers, Stirling numbers and the associated Stirling numbers are also presented. [Copyright &y& Elsevier]

Abstract: Until now, only nonoscillatory radial basis functions (RBFs) have been considered in the literature. It has recently been shown that a certain family of oscillatory RBFs based on J-Bessel functions gives rise to nonsingular interpolation problems and seems to be the only class of functions not to diverge in the limit of flat basis functions for any node layout. This paper proves another interesting feature of these functions: exact polynomial reproduction of arbitrary order on an infinite lattice in ℝ n . First, a closed form expression is derived for calculating the expansion coefficients for any order polynomial in any dimension. Then, a proof is given showing that the resulting interpolant, using this class of oscillatory RBFs, will give exact polynomial reproduction. Examples in one and two dimensions are presented. It is specifically noted that such closed form expressions cannot be derived for other classes of RBFs due to the fact that J-Bessel RBFS reproduce polynomials via a different mechanism. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the bondage number b(G) for a digraph G, which is defined as the minimum number of edges whose removal results in a new digraph with larger domination number. This parameter measures to some extent the robustness of an interconnection network with respect to link failures. By constructing a family of minimum dominating sets, we compute the bondage numbers of the extended de Bruijn digraph and the extended Kautz digraph. As special cases, we obtain for the de Bruijn digraph B(d, n) and the Kautz digraph K(d, n) that b(B(d, n)) = d if n is odd and d ⩽ b(B(d, n)) < 2d if n is even, and b(K(d, n)) = d + 1. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of a reflexive, with respect to the generalized reflection matrix P, solution of the matrix equation AX B = C. For the special case when B = I, we get the result of Peng and Hu [1]. [Copyright &y& Elsevier]

Abstract: The dual Phase-1 algorithm using the most-obtuse-angle row pivot rule is very efficient for providing a dual feasible basis, in either the classical or the basis-deficiency-allowing context. In this paper, we establish a basis-deficiency-allowing Phase-I algorithm using the so-called most-obtuse-angle column pivot rule to produce a primal (deficient or full) basis. Our computational experiments with the smallest test problems from the standard NETLIB set show that a dense projected-gradient implementation largely outperforms that of the variation of the primal simplex method from the commercial code MATLAB LINPROG v1.17, and that a sparse projected-gradient implementation of a normalized revised version of the proposed algorithm runs 34% faster than the sparse implementation of the primal simplex method included in the commercial code TOMLAB LPSOLVE v3.0. [Copyright &y& Elsevier]

Abstract: In the early 1990s, Yau developed a new class of nonlinear filters, called the Yau Filterswhich contain the Kalman-Bucy filters and the Benes filters as special cases. It has been shown that, from the Lie algebraic point of view, the Yau filters are the most general finite-dimensional filters. Yau and Hu proved that the DMZ equation for a Yau filter can be reduced to a Kolmogorov type partial differential equation and a system of linear differential equations. They noticed that the PDE is independent of the observed data and hence can be solved off-line. An efficient parallel algorithm for the system of ODEs would lead to fast solutions of Yau filters and hence their suitability for real-life applications. In this paper, we have proposed several parallel methods suitable for this system of ODEs. [Copyright &y& Elsevier]

Abstract: We propose a “fast” algorithm for the construction of a data-sparse inverse of a generalToeplitz matrix. The computational cost for inverting an N × N Toeplitz matrix equals the cost of four length-N FFTs plus an O(N)-term. This cost should be compared to the O(N log2 N) cost of previously published methods. Moreover, while those earlier methods are based on algebraic considerations, the procedure of this paper is analysis-based; as a result, its stability does not depend on the symmetry and positive-definiteness of the matrix being inverted. The performance of the scheme is illustrated with numerical examples. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with a model for the survival of red blood cells with periodic coefficients, . Some new sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the equation. [Copyright &y& Elsevier]