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Abstract: In this paper, we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max–min and the max–average composition and the max–star composition, respectively. They have been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, Solving a linear programming problem with the convex combination of the max–min and the max–average fuzzy relation equations, Appl. Math. Comput. 180 (2006) 411–418] and Khorram et al. [E. Khorram, A. Ghodousian, A. Abbasi Molai, Solving linear optimization problems with max–star composition equation constraints, Appl. Math. Comput. 179 (2006) 654–661], respectively. Firstly, we show that the “Tabular method algorithm” in the first paper and the “First procedure” in the second paper may not lead to the optimal solutions of the two models in some cases. Secondly, we generalize the proposed algorithm by Abbasi Molai and Khorram [A. Abbasi Molai, E. Khorram, A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian, Appl. Math. Comput. 190 (2007) 1161–1167] to solve the two models. In fact, it modifies the presented algorithms in the two papers. Finally, some numerical examples are given to illustrate the purposes. [Copyright &y& Elsevier]

Abstract: The aim of this short note is to show on a numerical example that one of the two optimization algorithms proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] may not lead to the optimal solution in some cases. Besides it will be pointed out that the other algorithm (correct, but unfortunately ineffective for larger problems) proposed in [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886] can be extended to a wider class of non-convex optimization problems. [Copyright &y& Elsevier]

Given a real number α ∈ (0 , 1) , we define the Webster sequence of density α to be W α = (⌈ (n − 1 / 2) / α ⌉) n ∈ N , where ⌈ x ⌉ is the ceiling function. It is known that if α and β are irrational with α + β = 1 , then W α and W β partition N. On the other hand, an analogous result for three-part partitions does not hold: There does not exist a partition of N into sequences W α , W β , W γ with α , β , γ irrational. In this paper, we consider the question of how close one can come to a three-part partition of N into Webster sequences with prescribed densities α , β , γ. We show that if α , β , γ are irrational with α + β + γ = 1 , there exists a partition of N into sequences of densities α , β , γ , in which one of the sequences is a Webster sequence and the other two are "almost" Webster sequences that are obtained from Webster sequences by perturbing some elements by at most 1. We also provide two efficient algorithms to construct such partitions. The first algorithm outputs the n th element of each sequence in O (1) time and the second algorithm gives the assignment of the m th positive integer to a sequence in O (1) time. We show that the results are best-possible in several respects. Moreover, we describe applications of these results to apportionment and optimal scheduling problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the homogeneous m -machine scheduling problem where unit-time jobs have to be scheduled within their time windows so that, for any subset of machines, the set of the time units at which at least one machine is busy, is an interval. For this problem, a time assignment of the jobs satisfying the time windows constraints is a schedule if it has a pyramidal profile and is a k -schedule if this profile property is satisfied up to level k only. We develop a generic algorithm to solve the problem and show it is correct using a proof that mainly relies on a necessary and sufficient condition for a schedule to exist proved in a previous paper. We finally show that the generic algorithm is polynomial. We conclude by giving the directions of ongoing works and by bringing open questions related to different variants of the basic non-idling m -machine scheduling problem. [ABSTRACT FROM AUTHOR]

Abstract The sensitivity conjecture proposed by Nisan and Szegedy in 1994, which asserts that for any Boolean function, its sensitivity complexity is polynomially related to the block sensitivity complexity, is one of the most important and challenging problems in the study of decision tree complexity. Despite a lot of efforts, the best known upper bound of block sensitivity, as well as the certificate complexity, is still exponential in terms of sensitivity. In this paper, we give a better upper bound for certificate complexity and block sensitivity, b s (f) ≤ C (f) ≤ (8 9 + o (1)) s (f) 2 s (f) − 1 , where b s (f) , C (f) and s (f) are the block sensitivity, certificate complexity and sensitivity, respectively. The proof is based on a deep investigation on the structure of the sensitivity graph. We also provide a tighter relationship between the 0-certificate complexity C 0 (f) and 0-sensitivity s 0 (f) for functions with small 1-sensitivity s 1 (f). [ABSTRACT FROM AUTHOR]

Abstract In the current paper, an error estimate has been proposed to find a second-order finite difference scheme for solving the Riesz space distributed-order diffusion equation. The convergence order of the proposed method is O (τ 2 + h 2). The numerical results show the efficiency of the new technique. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we defined the scattering energy intensity based on the Poynting vector to quantitatively study the cloak effect of electromagnetic waves in the time domain. The influences of the effective working frequency bands of four kinds of electromagnetic cloak materials, incidence angle of electromagnetic waves and the number of approximately cloak layers on the cloak effect are studied. To the best of our knowledge, this is the first time to use the time domain method to quantitatively study the effective working frequency band and the scattering energy intensity of cloak materials. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present an integral imaging microscopy, which can achieve continuous depth extraction. The multiple stereo matching algorithm is optimized with data point interpolation and calculation range correction, which can improve the computing efficiency and accuracy. A water suspension of silica-embedded magnetic particles in light-trap environment is used as a specimen. The elementary image array is obtained through sequentially imaging the specimen by the objective lens and microlens array, which contains continuous depth information that can give the optical tweezers a feedback for precise 3-D manipulation. Experimental and calculated results show the feasibility of our method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose a low-overhead equalization algorithm used in the intensity modulation direct detection (IMDD) system with offset-quadrature amplitude modulation orthogonal frequency division multiplexing (OQAM-OFDM) modulation. By utilizing the complex interference approximation (IA) structure and the comb pilot-based frequency domain intra-symbol averaging and intra-subcarrier linear interpolation (CFAL) method, the OQAM-OFDM signal's intrinsic imaginary non-orthogonal distortions can be mitigated and the low overhead of channel estimation with high estimation accuracy can be achieved. The experiment and numerical simulation are constructed to evaluate the proposed IA-CFAL algorithm from the aspects of bit error rate (BER) performance, mean square error (MSE), dispersion tolerance, time jitter tolerance and complexity. Comparison with the previous algorithms are made to prove its robustness to transmission impairments with low training overhead. Highlights • Low pilot overhead. • Simultaneously Estimating Channel and Mitigating Intrinsic imaginary interference. • High estimation accuracy. • Complex interference approximation (IA) structure. • The comb pilot-based frequency domain intra-symbol intra-subcarrier linear interpolation. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present a newfound in the two-dimensional Visible Light Communication (VLC) system, i.e., additional modulation orders are generated in the receiver. Meanwhile, an algorithm named High/Low order Bit Interleaving (HLBI) is proposed in a formulated VLC Multiple-Input-Single-Output (MISO) model, which aims to decrease part of these orders. A data rate of 1.24Gbit/s is achieved in 1.3 m indoor Line-Of-Sight (LOS) scenario with the Bit Error Rate (BER) is under 3.8 × 10−3. Since the algorithm also aids STBC decoding, the Q factor can be improved to 1.92dB. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive fuzzy logic controller (FLC) design technique for controlling an induction motor speed drive using backtracking search algorithm (BSA). This technique avoids the exhaustive traditional trial-and-error procedure for obtaining membership functions (MFs). The generated adaptive MFs are implemented in speed controller design for input and output based on the evaluation results of the fitness function formulated by the BSA. In this paper, the mean absolute error (MAE) of the rotor speed response for three phase induction motor (TIM) is used as a fitness function. An optimal BSA-based FLC (BSAF) fitness function is also employed to tune and minimize the MAE to improve the performance of the TIM in terms of changes in speed and torque. Moreover, the measurement of the real TIM parameters via three practical tests is used for simulation the TIM. Results obtained from the BSAF are compared with those obtained through gravitational search algorithm (GSA) and particle swarm optimization (PSO) to validate the developed controller. Design procedure and accuracy of the develop FLC are illustrated and investigated via simulation tests for TIM in a MATLAB/Simulink environment. Results show that the BSAF controller is better than the GSA and PSO controllers in all tested cases in terms of damping capability, and transient response under different mechanical loads and speeds. [ABSTRACT FROM AUTHOR]

By introducing sign constraints on the weights, this paper proposes sign constrained rectifier networks (SCRNs), whose training can be solved efficiently by the well known majorization–minimization (MM) algorithms. We prove that the proposed two-hidden-layer SCRNs, which exhibit negative weights in the second hidden layer and negative weights in the output layer, are capable of separating any number of disjoint pattern sets. Furthermore, the proposed two-hidden-layer SCRNs can decompose the patterns of each class into several clusters so that each cluster is convexly separable from all the patterns from the other classes. This provides a means to learn the pattern structures and analyse the discriminant factors between different classes of patterns. Experimental results are provided to show the benefits of sign constraints in improving classification performance and the efficiency of the proposed MM algorithm. [ABSTRACT FROM AUTHOR]

Linear feedback shift registers (LFSRs) play a significant role in communications security and we investigate design of a selected class of word-based LFSRs known as σ -LFSRs. Both the search algorithm and the construction algorithm generate efficient primitive σ -LFSRs. The search algorithm first constructs the σ -polynomial and then checks the primitiveness of the σ -polynomial, whereas the construction algorithm for the σ -LFSR, first finds a primitive polynomial f ( x ) and then constructs the primitive σ -LFSR from f ( x ) . In this paper, we present some novel results pertaining to the search algorithm for primitive σ -LFSR along with the exhaustive search space complexity of the search algorithm for σ -LFSRs. Then we investigate and compare the performance of the construction algorithm with the search algorithm for the primitive σ -LFSR. Finally, the number of σ -LFSRs similar to the σ -LFSRs generated by the construction algorithm is provided. [ABSTRACT FROM AUTHOR]

In Gordon (1998), Gordon presented alternate proofs of several well known results in elementary real analysis using tagged partitions. In this paper, we provide a set of alternative proofs based on the dyadic partitions. An important difference between tagged and dyadic partitions is that the results based on the dyadic partition can be obtained constructively, i.e. an algorithm is supplied to reach the conclusion of each proof. In addition, the construction involves only concepts and results presented in a first course real analysis, which is the reason why, comparing tagged partition and its theory, the proofs based on dyadic partition are more straightforward and accessible to a wide range of audience. [ABSTRACT FROM AUTHOR]

Successful classification of questioned footwear has tremendous evidentiary value; the result can minimize the potential suspect pool and link a suspect to a victim, a crime scene, or even multiple crime scenes to each other. With this in mind, several different automated and semi-automated classification models have been applied to the forensic footwear recognition problem, with superior performance commonly associated with two different approaches: correlation of image power (magnitude) or phase, and the use of local interest points transformed using the Scale Invariant Feature Transform (SIFT) and compared using Random Sample Consensus (RANSAC). Despite the distinction associated with each of these methods, all three have not been cross-compared using a single dataset, of limited quality (i.e., characteristic of crime scene-like imagery), and created using a wide combination of image inputs. To address this question, the research presented here examines the classification performance of the Fourier-Mellin transform (FMT), phase-only correlation (POC), and local interest points (transformed using SIFT and compared using RANSAC), as a function of inputs that include mixed media (blood and dust), transfer mechanisms (gel lifters), enhancement techniques (digital and chemical) and variations in print substrate (ceramic tiles, vinyl tiles and paper). Results indicate that POC outperforms both FMT and SIFT+RANSAC, regardless of image input (type, quality and totality), and that the difference in stochastic dominance detected for POC is significant across all image comparison scenarios evaluated in this study. [ABSTRACT FROM AUTHOR]

Let P be a set of n points in general position in the plane which is partitioned into color classes. The set P is said to be color-balanced if the number of points of each color is at most [n/2] . Given a color-balanced point set P, a balanced cut is a line which partitions P into two color-balanced point sets, each of size at most 2n/3+1 . A colored matching of P is a perfect matching in which every edge connects two points of distinct colors by a straight line segment. A plane colored matching is a colored matching which is non-crossing. In this paper, we present an algorithm which computes a balanced cut for P in linear time. Consequently, we present an algorithm which computes a plane colored matching of P optimally in Θ(nlog n) time. [ABSTRACT FROM AUTHOR]

The Small Exponent Test (SET) for exponentiation is an essential batch-verification technique that is widely applied. In this paper, we propose a simplified SET that can securely batch-verify n instances with only n − 1 randomizing exponents. We show that the structure of the proposed batch test is compact in the sense that it works with a minimal number of randomizing exponents for the SET. Thus, our test offers various advantages. Overall, compared to the original SET, the proposed simplified SET is more efficient for any sized batch instance. In particular, unlike the SET, our proposal performs well even when the size of a batch instance is small, e.g., n = 1 , 2 , 3 , and 4. This feature can be also used to significantly reduce pairing computations in a signature scheme where several pairing equations are verified. In addition, our test can be combined easily and generically with existing batch techniques such as the use of sparse exponents, the bucket test for large batch sizes, or an automated tool to generate a batch algorithm. Finally, with our simplified test, an efficient identification algorithm can be constructed to discover incorrect instances in a batch. [ABSTRACT FROM AUTHOR]

In this paper, we propose a blind Volterra series based nonlinear equalization (VNLE) with low complexity for the nonlinear distortion mitigation in short reach optical carrierless amplitude and phase (CAP) modulation system. The principle of the blind VNLE is presented and the performance of its blind adaptive algorithms including the modified cascaded multi-mode algorithm (MCMMA) and direct detection LMS (DD-LMS) are investigated experimentally. Compared to the conventional VNLE using training symbols before demodulation, it is performed after matched filtering and downsampling, so shorter memory length is required but similar performance improvement is observed. About 1 dB improvement is observed at BER of 3.8×10 −3 for 40 Gb/s CAP32 signal over 40 km standard single mode fiber. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new framework for managing congestion during emergency evacuations. The algorithm allows a long link of the network to be used as a buffer to keep the traffic flow moving in. Concurrently, a detour trigger time is estimated to keep the traffic under-saturated in the buffer zone and minimize the total travel time. The integration algorithm presented in this paper is an efficient mathematical solution for travel time cost calculation. A case study is presented to demonstrate the efficacy of the traffic demand buffering strategy developed in this research for managing the evacuation flow. [Copyright &y& Elsevier]

Abstract: With a transformation matrix of B-spline bases (abbreviated to BSBT matrix), a B-spline basis can be represented by another B-spline basis. In this paper, we first give the existence conditions and some useful properties of BSBT matrices. Then we propose a recursive formula for BSBT matrices and an efficient method for the computation of BSBT matrices. Based on these results, we further probe into the applications of BSBT matrices in knot insertion and degree elevation of B-spline curves. Using BSBT matrices, we develop a new uniform algorithm for knot insertion and degree elevation of B-spline curves. This algorithm is efficient, general-purpose, and simple to implement. It can be used to insert one knot or multiple knots, raise one degree or multiple degrees, or to insert knot and raise degree simultaneously. Several examples are given to illustrate the stability of the algorithm. The results in the paper show that BSBT matrices can be applied to establish a uniform mathematical model for knot insertion, degree elevation, knot removal and degree reduction of B-spline curves and surfaces, and to provide a general tool for the conversions between different representations of B-spline curves and surfaces. [Copyright &y& Elsevier]

Abstract: Rigid sub-chain detection and isomorphism identification are two of the most difficult problems in the computer-aided structure synthesis of kinematic chains. This paper aims to find an efficient solution which can be fulfilled within the computer itself to the problem of rigid sub-chain detection of planar kinematic chains, especially for complex planar mechanisms. Based on the array representation of the loops of kinematic chains, this paper first introduces two operations of loops, the “Θ” and “⊕” operations. Then a new theory of structure decomposition of kinematic chains is proposed on the basis of the concept of the independent loop set. After that a new method grounded on the theory is proposed for rigid sub-chain detection. Finally, the optimized algorithm for structure decomposition is presented and the corresponding program for rigid sub-chain detection is developed as well. [Copyright &y& Elsevier]

Abstract: This paper presents a survey of error-free algorithms to solve various systems of linear equations. The presented algorithms do not introduce computational errors into the solution and thus they are well suited to solve ill-conditioned linear systems. The error-free algorithms are based on modulo arithmetic. Two basic approaches have been investigated in the paper. The first one is based on iterative scheme using one modulus only. The other one is parallel and uses several moduli and the Chinese theorem. It is based on polynomial algebra operations that allow to express the operation of deconvolution as a sequence of convolutions of both response and output signals. [Copyright &y& Elsevier]

Abstract: This paper develops a novel computational technique to define and construct manifold splines with only one singular point by employing the rigorous mathematical theory of Ricci flow. The central idea and new computational paradigm of manifold splines are to systematically extend the algorithmic pipeline of spline surface construction from any planar domain to an arbitrary topology. As a result, manifold splines can unify planar spline representations as their special cases. Despite its earlier success, the existing manifold spline framework is plagued by the topology-dependent, large number of singular points (i.e.,  for any genus- surface), where the analysis of surface behaviors such as continuity remains extremely difficult. The unique theoretical contribution of this paper is that we devise new mathematical tools so that manifold splines can now be constructed with only one singular point, reaching their theoretic lower bound of singularity for real-world applications. Our new algorithm is founded upon the concept of discrete Ricci flow and associated techniques. First, Ricci flow is employed to compute a special metric of any manifold domain (serving as a parametric domain for manifold splines), such that the metric becomes flat everywhere except at one point. Then, the metric naturally induces an affine atlas covering the entire manifold except this singular point. Finally, manifold splines are defined over this affine atlas. The Ricci flow method is theoretically sound, and practically simple and efficient. We conduct various shape experiments and our new theoretical and algorithmic results alleviate the modeling difficulty of manifold splines, and hence, promote the widespread use of manifold splines in surface and solid modeling, geometric design, and reverse engineering. [Copyright &y& Elsevier]

Abstract: In this paper, we formulate a new robust two-species nonautonomous predator–prey model with multi-delays and impulsive effects and perform a systematic mathematical and ecological study. Our results in this paper indicate that under the appropriate linear periodic impulsive perturbations, the system is permanent and has a unique positive globally attractive semi-trivial periodic solution. By using the Brouwer fixed point theorem, we prove that if the periodic system is permanent, then there is at least one positive periodic solution of the system. We show that the conditions for global attractivity of the positive semi-trivial periodic solution and permanence of the population of the model depend on time delay, so, we call it “profitless”. In this paper, the main feature is that we introduce multi-delays and impulses into the predator–prey model, exhibit a new modeling method which is applied to investigate multi-species impulsive multi-delays differential equations. [Copyright &y& Elsevier]

Abstract: Neighborhoods and neighborhood sequences play important roles in several branches of pattern analysis. In earlier papers in only certain special (e.g. periodic or octagonal) sequences were investigated. In this paper we study neighborhood sequences which are either ultimately periodic or allow at every neighborhood to do nothing at no cost. We give finite procedures and descriptive theoretical criteria for certain important (e.g. metrical) properties of the sequences. Our results are valid for several types of classical neighborhood sequences and for generated distance functions (e.g. octagonal and chamfer distances) which are widely applied in digital image processing. We conclude the paper by showing how our results contribute to the theory of distance transformations. [Copyright &y& Elsevier]

Abstract: This paper describes a generic software designed to implement meshing algorithms based on the Delaunay refinement paradigm. Such a meshing algorithm is generally described through a set of rules guiding the refinement of mesh elements. The central item of the software design is a generic class, called a mesher level, that is able to handle one of the rules guiding the refinement process. Several instantiations of the mesher level class can be stacked and tied together to implement the whole refinement process. As shown in this paper, the design is flexible enough to implement all currently known mesh generation algorithms based on Delaunay refinement. In particular it can be used to generate meshes approximating smooth or piecewise smooth surfaces, as well as to mesh three dimensional domains bounded by such surfaces. It also adapts to algorithms handling small input angles and various refinement criteria. This design highly simplifies the task of implementing Delaunay refinement meshing algorithms. It has been used to implemented several meshing algorithms in the Cgal library. [Copyright &y& Elsevier]

Abstract: In this paper, a filled function with one-parameter is proposed for solving unconstrained global optimization problems. This filled function is modified from the previously reported one (see paper [Y.J. Yang, Y.L. Shang, A new filled function method for unconstrained global optimization, Applied Mathematics and Computations 173 (1) (2006) 501–512]). The properties of the filled function are discussed in this paper. An algorithm for unconstrained global optimization is developed from this new filled function. The computational results show that this algorithm is efficient and reliable. [Copyright &y& Elsevier]

Abstract: In this paper, we focus on the proposed algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition that it has been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, An algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition, Appl. Math. Comput. 178 (2006) 502–509]. Firstly, we show that the algorithm may not lead to the optimal solution in some cases. Secondly, we propose a new algorithm for solving the presented model by Ghodousian and Khorram (2006), as mentioned above. In fact, it modifies the presented algorithm in the Ghodousian and Khorram’s paper. Also, this algorithm is extended to the presented model by Khorram and Ghodousian [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886.] with max-av composition. Finally, some numerical examples are given for illustrating the purposes. [Copyright &y& Elsevier]

Abstract: This paper presents the new convergence analysis for the Newton-like method proposed by [Xinyuan Wu, A new continuation Newton-like method and its deformation, Appl. Math. Comput. 112 (2000) 75–78.] Compared with the original version of the convergence analysis, the restriction imposed on f″(x) is removed thoroughly. In order to guarantee the quadratic convergence of the Newton-like method, it is suffices to suppose that f′(x ∗)≠0 and f′(x) is local Lipschitz near x ∗, where x ∗ is a solution of nonlinear equation f(x)=0. Moreover, some comments are given with examples for the Newton-like method, in comparison with Newton’s method. It can be concluded that the new algorithm is more feasible, effective than Newton’s method. In particularly, when it happens that, the derivative of the function f(x) at an iterate is singular or almost singular, the Newton-like method is vast superior to the classical Newton method. The numerical results of the paper strongly support the conclusion. [Copyright &y& Elsevier]

Radial basis functions are a popular basis for interpolating scattered data during the image reconstruction process in graphic analysis. In this context, the solution of a linear system of equations represents the most time-consuming operation. In this paper an efficient preconditioning technique is proposed to solve these linear systems of equations. This algorithm consists of an iterative method which enforces at each iteration a projection of the residual onto a suitable subspace called coarse space. This constraint is ensured by solving an auxiliary problem at each iteration without regularisation. As increasing the number of the coarse space basis functions increases the computational cost of the algorithm, correct selection of coarse space basis is addressed in the paper. Numerical results illustrate the convergence properties of the proposed method with wavelet-like basis functions and regular distributed radial basis functions for image reconstruction. [Copyright &y& Elsevier]

Abstract: In this paper, we consider completely generalized nonlinear quasi-variational-like inclusions in Banach spaces and propose an Ishikawa type iterative algorithm for computing their approximate solutions by applying the new notion of -proximal mapping given in [R. Ahmad, A.H. Siddiqi, Z. Khan, Proximal point algorithm for generalized multi-valued nonlinear quasi-variational-like inclusions in Banach spaces, Appl. Math. Comput. 163 (2005) 295–308]. We prove that the approximate solutions obtained by the proposed algorithm converge to the exact solution of our quasi-variational-like inclusions. The results presented in this paper extend and improve the corresponding results of [R. Ahmad, A.H. Siddiqi, Z. Khan, Proximal point algorithm for generalized multi-valued nonlinear quasi-variational-like inclusions in Banach spaces, Appl. Math. Comput. 163 (2005) 295–308; X.P. Ding, F.Q. Xia, A new class of completely generalized quasi-variational inclusions in Banach spaces, J. Comput. Appl. Math. 147 (2002) 369–383; N.J. Huang, Generalized nonlinear variational inclusions with non-compact valued mappings, Appl. Math. Lett. 9(3) (1996) 25–29; A. Hassouni, A. Moudafi, A perturbed algorithm for variational inclusions, J. Math. Anal. Appl. 185(3) (1994) 706–712]. Some special cases are also discussed. [Copyright &y& Elsevier]

Abstract: A Cramer rule for solving a kind of restricted matrix equationsis presented in [G. Wang, Jie Sun, A Cramer rule for solution of the general restricted matrix equation, Appl. Math. Comput. 154 (2004) 415–422]. This paper gives a more condensed Cramer rule for the solution of the matrix equations. The results in [G. Wang, Z.L. Xu, Solving a kind of restricted matrix equations and Cramer rule, Appl. Math. Comput. 162 (2005) 329–338, Chao Gu, G.R. Wang, Z.L. Xu, PCR Algorithm for the Parallel Computation of the Solution of a class of Singular linear Systems, Appl. Math. Comput. 176 (2006) 237–244] are partially the special cases in our paper. [Copyright &y& Elsevier]

Abstract: In this paper we consider the Nonnegative Matrix Factorization (NMF) problem: given an (elementwise) nonnegative matrix find, for assigned k, nonnegative matrices and such that V = WH. Exact, nontrivial, nonnegative factorizations do not always exist, hence it is interesting to pose the approximate NMF problem. The criterion which is commonly employed is I-divergence between nonnegative matrices. The problem becomes that of finding, for assigned k, the factorization WH closest to V in I-divergence. An iterative algorithm, EM like, for the construction of the best pair (W, H) has been proposed in the literature. In this paper we interpret the algorithm as an alternating minimization procedure à la Csiszár–Tusnády and investigate some of its stability properties. NMF is widespreading as a data analysis method in applications for which the positivity constraint is relevant. There are other data analysis methods which impose some form of nonnegativity: we discuss here the connections between NMF and Archetypal Analysis. [Copyright &y& Elsevier]

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 a finite dataset consisting of positive and negative observations represented as real valued -vectors, a positive (negative) pattern is an interval in with the property that it contains sufficiently many positive (negative) observations, and sufficiently few negative (positive) ones. A pattern is spanned if it does not include properly any other interval containing the same set of observations. Although large collections of spanned patterns can provide highly accurate classification models within the framework of the Logical Analysis of Data, no efficient method for their generation is currently known. We propose in this paper, an incrementally polynomial time algorithm for the generation of all spanned patterns in a dataset, which runs in linear time in the output; the algorithm resembles closely the Blake and Quine consensus method for finding the prime implicants of Boolean functions. The efficiency of the proposed algorithm is tested on various publicly available datasets. In the last part of the paper, we present the results of a series of computational experiments which show the high degree of robustness of spanned patterns. [Copyright &y& Elsevier]

Abstract: In this paper, a new definition of the filled function is given, it is different from the primary definition which was given by Ge in paper [R.P. Ge, A filled function method for finding a global minimzer of a function of several variables, Math. Program. 46 (1990) 191–204]. Based on the definition, a new filled function is proposed, and it has better properties. An algorithm for unconstrained global optimization is developed from the new filled function. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. [Copyright &y& Elsevier]

Abstract: The present paper describes an efficient algorithm to integrate the equations of motion implicitly in the frequency domain. The standard FEM displacement model (Galerkin formulation) is employed to perform space discretization, and the time-marching process is carried out through an algorithm based on the Green’s function of the mechanical system in nodal coordinates. In the present formulation, mechanical system Green’s functions are implicitly calculated in the frequency domain. Once the Green’s functions related matrices are computed, a time integration procedure, which demands low computational effort when applied to non-linear mechanical systems, becomes available. At the end of the paper numerical examples are presented in order to illustrate the accuracy of the present approach. [Copyright &y& Elsevier]

Abstract: The goal of this paper is to prove that the implementation of Taylor models in COSY, based on floating-point arithmetic, computes results satisfying the “containment property”, i.e. guaranteed results. First, Taylor models are defined and their implementation in the COSY software by Makino and Berz is detailed. Afterwards IEEE-754 floating-point arithmetic is introduced. Then the core of this paper is given: the algorithms implemented in COSY for multiplying a Taylor model by a scalar, for adding or multiplying two Taylor models are given and are proven to return Taylor models satisfying the containment property. [Copyright &y& Elsevier]

Abstract: In this paper, we present a comprehensive method consisting of efficient state minimization and a comprehensive method of state assignment techniques to synthesize finite state machines (FSMs) to optimize power, area, and delay for “next-state” logic network design. The goal is to reduce the number of gates and literals relevant to power and area, and simultaneously to shorten the critical-path delay in FSM optimization. In the first step, we try to reduce the complexity of state minimization by applying (i) compatible graph to target one of optimal solutions in efficiency, (ii) conflict graph to determine the lower bound of the number of states and possible optimal solutions, (iii) Boolean expression effects due to alternative ways of minimized states, such that the required number of flip–flops is minimum for completely (or incompletely) specified FSMs. Next, a comprehensive method of state assignment techniques consisting of (i) edge-covering algorithm, (ii) block-reordering algorithm, (iii) cost calculation, (iv) ping-pong Gray-codes assignment, and (iv) design space exploration, is developed to choose the best state assignment. Finally, Espresso is run to determine the Boolean expressions and choose the best state assignment with the minimal sum-of-product (SOP) terms and literals from those optimal solutions. At last, the performance metrics in power, area, and delay are calculated based on the developed cell libraries for those optimal solutions with same minimized terms and literals. Our solutions provide engineers and designers to choose the best state assignment having less power, area, and delay to meet their system specification. Again this paper provides a comprehensive method of FSM synthesis and optimization for large FSMs in terms of power, area, and delay. Our experiments show that the derived optimal state assignment results in less power, area, and delay in FSM MCNC benchmarks. [Copyright &y& Elsevier]

Some new concepts (rank of a loop, degree of freedom of a graph, path unit and ordered path arrangement, constraint degree of path, coupling degree of a graph, basic graph, etc.), formulas, and algorithms, are proposed in this paper. Based on these concepts, a new systematic theory and practical method for the design of topological structure, kinematics and dynamics of mechanical systems is established. Some conjectures and problems needed to be researched are also put forward. The concepts, formulae and algorithms presented in this paper will find wide potential applications. [ABSTRACT FROM AUTHOR]

In this paper, we consider the convergence criteria for iterative algorithms of Uzawa type for solving linear saddle point problems. Theoretically weaker convergence criteria than before are established for the general case and these are used to deduce conditions for convergence of two special cases: the exact Uzawa algorithm and the linear one-step method. The conclusions given here hold for both symmetric and nonsymmetric saddle point problems. These new sufficient conditions are compared with some known results and illustrated by two examples. Numerical experiments to verify the conclusions in this paper for the preconditioned exact Uzawa algorithm are provided. [Copyright &y& Elsevier]

In this paper, we introduce the concept of generalized mixed quasivariational inclusions and generalized mixed resolvent equations for fuzzy mappings. By using the resolvent operator technique for maximal monotone mapping, we obtain that the generalized mixed quasivariational inclusions for fuzzy mappings are equivalent to the fuzzy fixed-point problems and the generalized mixed resolvent equations for fuzzy mappings, respectively. We suggest a number of iterative algorithms, establish the existence results of solutions for the generalized mixed quasivariational inclusions for fuzzy mappings and prove the convergence of the algorithms. The results presented in this paper are improvements of previously known results. [Copyright &y& Elsevier]

This paper describes a method to make multiple hypotheses with high cumulative recognition rate using SVMs. To make just a single hypothesis by using SVMs, it has been shown that Directed Acyclic Graph Support Vector Machines (DAGSVM) is very good with respect to recognition rate, learning time and evaluation time. However, DAGSVM is not directly applicable to make multiple hypotheses. In this paper, we propose a hybrid method of DAGSVM and Max-Win algorithm. Based on the result of DAGSVM, a limited set of classes are extracted. Then, Max-Win algorithm is applied to the set. We also provide the experimental results to show that the cumulative recognition rate of our method is as good as the Max-Win algorithm, and that the execution time is almost as fast as DAGSVM. [Copyright &y& Elsevier]

This paper considers the simultaneous fault detection and control (SFDC) problem. This problem is formulated as a mixed H2/H∞ optimization problem and its solution is presented in terms of two coupled Riccati equations. This solution yields controller/detector systems of modest complexity. An easily implementable design algorithm summarizes the methodology presented in the paper. [Copyright &y& Elsevier]

Isometric subgraphs of hypercubes, or partial cubes as they are also called, are a rich class of graphs that include median graphs, subdivision graphs of complete graphs, and classes of graphs arising in mathematical chemistry and biology. In general, one can recognize whether a graph on n vertices and m edges is a partial cube in O(mn) steps, faster recognition algorithms are only known for median graphs. This paper exhibits classes of partial cubes that are not median graphs but can be recognized in O(m log n) steps. On the way relevant decomposition theorems for partial cubes are derived, one of them correcting an error in a previous paper (Eur. J. Combin. 19 (1998) 677). [Copyright &y& Elsevier]

The development of a novel second-order accurate both in time and space kinetic scheme, called the Kinetic Wave/Particle Split (KWPS) scheme is reported in this paper. It is demonstrated that the first-order KWPS algorithm, while computationally efficient and robust, is very diffusive on a reasonable mesh. The KWPS scheme is derived by employing the following steps: the molecular velocity in the Boltzmann equation is split as a sum of fluid velocity and thermal (peculiar) velocity, thus the flux vector in the Boltzmann equation is divided into a convective part and an acoustic part. The Boltzmann equation is then discretized using an upwind differencing. Moments of the discretized Boltzmann equation with the collision invariant vector and Maxwellian distribution function then yield the KWPS scheme for the Euler equations. The second-order formulation is obtained through the application of a Taylor series expansion of the Maxwellian distribution function to include the first-order derivatives. Numerical test cases, both in 1-D and 2-D, are computed to demonstrate the improved accuracy of the second-order KWPS scheme, while maintaining both the efficiency and robustness of the first-order scheme. It should be noted that the new second-order KWPS formulation cannot be obtained using the standard numerical approach employed in the literature for second-order extension. The methodology employed in this paper can be easily extended to formulate a KWPS scheme to any order of accuracy. [Copyright &y& Elsevier]

Hydraulic fracturing of rocks has various engineering applications. However, there has been limited research into crack propagation prediction by three dimensional analytical techniques. This paper discusses such a technique for predicting the propagation surface of a pressurized circular crack subjected to various loading conditions. The propagation surfaces predicted from the proposed crack front propagation algorithm align well with published results. The suggested method consumes only a fraction of the time needed for a numerical simulation, and therefore it could be useful in assisting the design of hydraulic fracturing operations. [ABSTRACT FROM AUTHOR]

A frequency offset estimation (FOE) algorithm based on fast Fourier transform (FFT) of the signal's argument is investigated, which does not require removing the modulated data phase. In this paper, we analyze the flaw of the argument-FFT algorithm and propose a combined FOE algorithm, in which the absolute of frequency offset (FO) is accurately calculated by argument-FFT algorithm with a relatively large number of samples and the sign of FO is determined by FFT-based interpolation discrete Fourier transformation (DFT) algorithm with a relatively small number of samples. Compared with the previous algorithms based on argument-FFT, the proposed one has low complexity and can still effectively work with a relatively less number of samples. [ABSTRACT FROM AUTHOR]

Suppose a measurand can be computed by two different but consistent measurement models. Then, the output of one of the models would serve as prior knowledge to the other. In this paper, two alternative methods to produce a PDF for the measurand that take into account both models are presented. The first method proceeds by propagating the PDFs for the input quantities through the corresponding models in the usual way and then merging the resulting PDFs using the logarithmic or linear pooling techniques. The result is a kind of ‘compromise distribution’ of the pooled PDFs. The second method starts by propagating the PDFs for all input quantities except one, say X 1 , through the model that relates the former quantities to the latter. In this way the PDF for X 1 is obtained, which is then updated using its likelihood. The resulting PDF, which encodes all information available, is finally propagated through the model that relates X 1 to the measurand. This second method is the preferred way of analysis, because it results in a PDF that is narrower than the one obtained with the first method. [ABSTRACT FROM AUTHOR]

We can define the adjacency algebra of an association scheme over an arbitrary field. It is not always semisimple over a field of positive characteristic. The structures of adjacency algebras over a field of positive characteristic have not been sufficiently studied. In this paper, we consider the structures of adjacency algebras of dual polar schemes over a field of positive characteristic and determine them when their algebras are local algebras. [ABSTRACT FROM AUTHOR]