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Abstract: This paper presents results of research into the use of the Bellman-Zadeh approach to decision making in a fuzzy environment for solving multiobjective optimization problems. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The use of the Bellman-Zadeh approach has served as a basis for solving a problem of multiobjective allocation of resources (or their shortages) and developing a corresponding adaptive interactive decision-making system (AIDMS1). Its calculating kernel permits one to solve maxmin problems using an algorithm based on a nonlocal search (modification of the Gelfand''s and Tsetlin''s “long valley” method). The AIDMS1 includes procedures for considering linguistic variables to reflect conditions that are difficult to formalize as well as procedures for constructing and correcting vectors of importance factors for goals. The use of these procedures permits one to realize an adaptive approach to processing information of a decision maker to provide successive improving of the solution quality. C++ windows of the AIDMS1 are presented for input, output, and special possibilities related to considering linguistic variables and constructing and correcting vectors of importance factors. The results of the paper are universally applicable and are already being used to solve power engineering problems. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the uniqueness of meromorphic functions in the unit disc that share five distinct meromorphic functions of slow growth in an angular domain. [Copyright &y& Elsevier]

Abstract: In this paper an attempt is made to extend some standard results in set theory on the basis of soft set relations. Antisymmetric relation and transitive closure of a soft set relation are introduced and an analogue of Warshall’s algorithm is proposed for calculating the transitive closure of a soft set relation. Ordering on a soft set is defined and some set theoretical results based on this are proved. [Copyright &y& Elsevier]

Abstract: According to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided. [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: In this paper, an inversion algorithm for a banded matrix is presented. The twisted decompositions of a banded matrix are given first; then the inverse of the matrix is obtained, one column at time. The method is about two times faster than the standard method based on the decomposition, as is shown with the analysis of computing complexity and the numerical experiments. [Copyright &y& Elsevier]

Abstract: The generalized Adams–Bashforth–Moulton method, often simply called “the fractional Adams method”, is a useful numerical algorithm for solving a fractional ordinary differential equation: , where is the first integer not less than , and is the th-order fractional derivative of in the Caputo sense. Although error analyses for this fractional Adams method have been given for (a) , , (b) , , (c) , , (d) , , there are still some unsolved problems—(i) the error estimates for , , (ii) the error estimates for , , (iii) the solution having some special forms. In this paper, we mainly study the error analyses of the fractional Adams method for the fractional ordinary differential equations for the three cases (i)–(iii). Numerical simulations are also included which are in line with the theoretical analysis. [Copyright &y& Elsevier]

Abstract: The covering generalized rough sets are an improvement of traditional rough set model to deal with more complex practical problems which the traditional one cannot handle. It is well known that any generalization of traditional rough set theory should first have practical applied background and two important theoretical issues must be addressed. The first one is to present reasonable definitions of set approximations, and the second one is to develop reasonable algorithms for attributes reduct. The existing covering generalized rough sets, however, mainly pay attention to constructing approximation operators. The ideas of constructing lower approximations are similar but the ideas of constructing upper approximations are different and they all seem to be unreasonable. Furthermore, less effort has been put on the discussion of the applied background and the attributes reduct of covering generalized rough sets. In this paper we concentrate our discussion on the above two issues. We first discuss the applied background of covering generalized rough sets by proposing three kinds of datasets which the traditional rough sets cannot handle and improve the definition of upper approximation for covering generalized rough sets to make it more reasonable than the existing ones. Then we study the attributes reduct with covering generalized rough sets and present an algorithm by using discernibility matrix to compute all the attributes reducts with covering generalized rough sets. With these discussions we can set up a basic foundation of the covering generalized rough set theory and broaden its applications. [Copyright &y& Elsevier]

The Lai-Chen algorithm, an extended feedback control scheme of the original Chen- Lai algorithm, was proposed to gradually make an arbitrarily given discrete-time dynamical system chaotic in terms of possessing positive Lyapunov exponents with uniformly bounded orbits. In this paper, based on the Monte Carlo method, we further study the distribution of the controlled Lyapunov exponents generated by the Lai-Chen algorithm. [Copyright &y& Elsevier]

Abstract: A more flexible method of constructing multiwavelet packets with the scale a ≥ 2 from the same set of multiwavelets is discussed in this paper. The properties of these packets are studied. The formulae for performing iterations and decomposition are given. L 2(R) can be further decomposed by these multiwavelet packets and good bases of L 2(R) are given. Finally, we provide the algorithms for the decomposition and reconstruction using these multiwavelet packets. [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: 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: Let F be a set of n × n fuzzy matrices. F is called simultaneously controllable if there exists a permutation matrix P such that for each A ε F, C = [cij ] = P ⊗ A ⊗ P T satisfies cij ≥ cji for i > j, where ⊗ is the max-min composition. In this paper, the necessary and sufficient conditions for a set of n × n fuzzy matrices to be simultaneously controllable will be established. A constructive algorithm which can determine a simultaneously controllable set of n × n fuzzy matrices is presented as well. [Copyright &y& Elsevier]

Abstract: Recently, circulant graphs have received a lot of attention; and a new method was proposed for designing fault-tolerant solutions for any given circulant graph. This method works by partitioning the offsets of the graph in many ways; each leads to one or more solutions. By comparing all these solutions, we can find the one with the least node-degree. In this paper, we shall first review this method; and then re-examine its applications to the design of k-fault-tolerant meshes (for all possible values of k). Our results demonstrate that the solutions obtained (for both two and three-dimensional meshes) are efficient. [Copyright &y& Elsevier]

Abstract: One of the main problems dealing with iterative methods for solving polynomial systemsis the initialization of the iteration. This paper provides an algorithm to initialize the search of solutions of polynomial systems. [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 focus our discussion on the parameterization reduction of soft sets and its applications. First we point out that the results of soft set reductions offered in [1] are incorrect. We also observe that the algorithms used to first compute the reduct-soft-set and then to compute the choice value to select the optimal objects for the decision problems in [1] are not reasonable and we illustrate this with an example. Finally, we propose a reasonable definition of parameterization reduction of soft sets and compare it with the concept of attributes reduction in rough sets theory. By using this new definition of parameterization reduction, we improve the application of a soft set in a decision making problem found in [1]. [Copyright &y& Elsevier]

Abstract: In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is solved and a master direction is obtained, then, an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction. The new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. Finally, some numerical tests are reported. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and study a new system of variational inclusions involving (H, η)-monotone operators in Hilbert space. Using the resolvent operator associated with (H, η)-monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm. [Copyright &y& Elsevier]

Abstract: In the past, the fuzzy shortest path problem in a network has attracted attention from many researchers for its importance to various applications. In this paper, we propose a new algorithm to deal with the fuzzy shortest path problem. It is composed of fuzzy shortest path length procedure and similarity measure. The former is presented to determine the fuzzy shortest path length from source node to the destination node in the network, and the latter is used to measure the similarity degree between fuzzy length sets. This algorithm not only can yield shortest length but also can offer the actual shortest path to decision makers. An illustrative example is also included to demonstrate our proposed algorithm. [Copyright &y& Elsevier]

Abstract: This paper proposes a second-order scheme of precision integration for dynamic analysis with respect to long-term integration. Rather than transforming into first-order equations, a recursive scheme is presented in detail for direct solution of the homogeneous part of second-order algebraic and differential equations. The sine and cosine matrices involved in the scheme are calculated using the so-called 2 N algorithm. Numerical tests show that both the efficiency and the accuracy of homogeneous equations can be improved considerably with the second-order scheme. The corresponding particular solution is also presented, incorporated with the second-order scheme where the excitation vector is approximated by the truncated Taylor series. [Copyright &y& Elsevier]

Abstract: The goal of this paper is to describe an efficient cost-effective mathematical modelfor controlling the Czochralski crystal growth process. We first consider the governing equations for a class of MHD problems. We then choose the use of an externally applied magnetic field as a control mechanism. We examine theoretical and numerical results applicable to the optimal control of evolutionary magnetically conducted flows. The appropriate state equations are derived. First-order necessary conditions are examined. Next, we develop numerical methods for solving the necessary conditions of optimality, and alternative cost-efficient algorithms are discussed. Finally, these results are used to design a control strategy for the Czochralski crystal growth process. [Copyright &y& Elsevier]

Abstract: This paper proves the convergence of some generalized Schwarz algorithms for solvingthe obstacle problems with a T-monotone operator. Numerical results show that the generalized Schwarz algorithms converge faster than the classical Schwarz algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, some new oscillation criteria are obtained for the first-order delay difference equation , where k,l1,l2,, ls are positive integer numbers, f is a function. Our results improve the known results in the literature. And some examples are given to demonstrate the advantage of our results. [Copyright &y& Elsevier]

Abstract: The scheduling problems studied in this paper concern the two-stage no-wait flowshops with parallel machines under the objective function of the minimization of the maximum completion time. A new heuristic algorithm, i.e., the minimum deviation algorithm, is developed to solve the problems. In order to evaluate the average case performance of the algorithm, we design numerical experiments to compare the effectiveness of the algorithm with that of the other approximation algorithms. Extensive simulations are conducted under different shop conditions, and the results statistically show that the minimum deviation algorithm performs well under most of the situations. [Copyright &y& Elsevier]

Abstract: In [l] and [2], two algorithms have been proposed to calculate the output probability of Boolean functions represented by OBDDs, assuming that the input variables are equiprobable and each variable is statistically independent from others. In this paper, we point out that under these assumptions, the output probability calculation is equivalent to counting the number of minterms of the corresponding Boolean functions. An algorithm is proposed to compute the output probability using simple integer arithmetic as opposed to floating point arithmetic involved in [1,2]. To compute output probability of Boolean functions represented by shared OBDI)s and OBDDs with edge negation, we further propose a generalized algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the existence of solutions for first- and second-order nonresonance impulsive functional differential inclusions with variable moments. The proofs make use of the Martelli fixed-point theorem for condensing multivalued maps. [Copyright &y& Elsevier]

Abstract: The notion of convexity and its various generalization is important for quantitative and qualitative studies in operations research or applied mathematics. It has also been considered by many authors in fuzzy set theory. In this paper, we study the concept of Φ-convex and Φ-quasiconvex fuzzy sets which was proposed byChen et al. [1], and develop some useful extrema properties of these fuzzy sets. We prove that any local maximizer of a Φ-convex fuzzy set is also a global maximizer, and that any strict local maximizer of a Φ-quasiconvex fuzzy set is also a global maximizer. We also study the class of strictly Φ-convex (respectively, strictly Φ-quasiconvex) fuzzy sets that is more restricted than the class of Φ-convex (respectively, Φ-quasiconvex) fuzzy sets. We prove for both families of strictly Φ-convex and strictly Φ-quasiconvex fuzzy sets that every local maximizer is also the unique global maximizer. In addition, some applications to fuzzy decision making are discussed. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some oscillation criteria for the neutral difference equation with positive and negative coefficients without the limitation of condition cn + Σn−1i=n−π + α qi ≤ 1, where cn, pn, and qn are nonnegative integers with τ − 1 ≥ maxσ,γ, γ ≥ 1, σ ≥ 0. [Copyright &y& Elsevier]

Abstract: In this paper, we address the problem of the guaranteed cost stabilization for a class of neutral delay-differential systems with a given quadratic cost function. Based on the Lyapunov method, delay-dependent criteria, which are expressed in terms of matrix inequalities, are proposed to guarantee the asymptotic stability of the system. The matrix inequalities can be easily solved by various efficient optimization algorithms. [Copyright &y& Elsevier]

In the paper, we show a law of the iterated logarithm for rescaled R/S statistics without second moment. [Copyright &y& Elsevier]

Most collision detection algorithms are ones of a discrete type which utilize convexity and local coherence to verify the closest points. However, the incremental algorithms have such critical drawbacks like failure to detect high-speed collisions and dependence on the time complexity on the time step size of animation. In this paper, in order to find a new method which can resolve the drawbacks, we are concerned with a more restricted but nontrivial version of the problem: given a fixed infinite plane H and a moving convex polyhedron P, compute their collision time. Our algorithm utilizes the spherical extreme vertex diagram that is the embedding of the dual graph P onto the Gauss sphere. Exploiting the diagram, we are able to efficiently compute the sequence of the extreme vertices vis, i = 1, …, m and find the time interval [ti, ti+1] during which vi is the extreme vertex of P. With the sequences of the consecutive time intervals and extreme vertices, we construct a distance function between P and H. Hence, we can compute their collision time within a given tolerance by applying the interval Newton method to the distance function. Moreover, the total time complexity is independent of the time step size of animation. [Copyright &y& Elsevier]

This paper studies the problem of control for a class of fuzzy system models by using a linear output controller. The system under consideration is described by a continuous-time fuzzy system model under sampled output measurements. The premise variables of the fuzzy system model are assumed unmeasurable. We develop a technique for designing an output feedback control law which globally stabilises this class of fuzzy system models. A design algorithm for constructing the linear output controller is given. A numerical simulation example is given to show the potential of the proposed techniques. [Copyright &y& Elsevier]

In this paper, we analyse the stability of parallel algorithms for the evaluation of polynomials written as a finite series of orthogonal polynomials. The basic part of the computation is the solution of a triangular tridiagonal linear system. This fact allows us to present a more detailed analysis. The theoretical results show that the parallel algorithms are almost as stable as their sequential counterparts for practical applications. Extensive numerical experiments confirm the theoretical conclusions. [Copyright &y& Elsevier]

This paper presents some new techniques in designing finite-difference domain decomposition algorithm for the heat equation. The basic procedure is to define the finite-difference schemes at the interface grid points with smaller time step Δt = SHAPE="SOL" ALIGN="C" STYLE="S">Δtm (m is a positive integer) by Saul''yev asymmetric schemes. The algorithm can increase the stability bounds of the classical explicit method by 2m times, and the prior error estimates for the numerical solutions are obtained for some algorithms when m = 2 or m = 3. Numerical experiments on stability and accuracy are also presented. [Copyright &y& Elsevier]

One of the most common data structures, at least in scientific computing, is the multidimensional array. Some numerical algorithms may conveniently be expressed as a generalized matrix multiplication, which computes a multidimensional array from two other multidimensional arrays. By adopting index notation with the Einstein summation convention, an elegant tool for expressing generalized matrix multiplications is obtained. Index notation is the succinct and compact notation primarily used in tensor calculus.In this paper, we develop computer support for index notation as a domain specific language. Grammar and semantics are proposed, yielding an unambiguous interpretation algorithm. An object-oriented implementation of a C++ library that supports index notation is described.A key advantage with computer support of index notation is that the notational gap between a mathematical index notation algorithm and its implementation in a computer language is avoided. This facilitates program construction as well as program understanding. Program examples that demonstrate the close resemblance between code and the original mathematical formulation are presented. [Copyright &y& Elsevier]

In this paper, we present feasibility conditions for mathematical programs with affine equilibrium constraints (MPECs) where additional joint constraints are present that must be satisfied by the state and design variables of the problems. We show that these conditions are also sufficient for quadratic programming subproblems arising from the penalty interior point algorithm (PIPA) and the smooth sequential quadratic programming (SQP) algorithm for solving MPECs to be consistent. [Copyright &y& Elsevier]