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The paper focuses on the new Multipoint meshless finite difference method, following the original Collatz higher order multipoint concept and the essential ideas of the Meshless FDM. The method was formulated, developed, and tested for various boundary value problems. Generalization of the multipoint method application to nonlinear analysis is the purpose of this research. The first attempt of the multipoint technique application to the geometrically nonlinear problems was successfully done recently. The case of physically nonlinear problem is considered in this paper. Several benefits of the proposed approach are highlighted, numerical algorithm and selected results are presented, and application of the multipoint method to nonlinear analysis is summarized. [ABSTRACT FROM AUTHOR]

We investigate the error of the (semidiscrete) Galerkin method applied to a semilinear subdiffusion equation in the presence of nonsmooth initial data. The diffusion coefficient is allowed to depend on time. We use the energy method to find optimal bounds on the error under weak natural assumptions on the diffusivity. First, we prove the result for the linear problem and then use the "frozen nonlinearity" technique coupled with various generalizations of Grönwall inequality to carry the result to the semilinear case. The paper ends with numerical illustrations supporting the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of ground state sign-changing solutions for a class of Choquard equations − △ u + ( 1 + λ f ( x ) ) u = ( I α ∗ k | u | p ) k ( x ) | u | p − 2 u + | u | 2 ∗ − 2 u , x ∈ R N , where k and f are nonnegative functions, N ≥ 3 , 2 ∗ = 2 N N − 2 , p ∈ 2 , N + α N − 2 , − λ 1 < λ < 0 and λ 1 is the first eigenvalue of the equation − △ u + u = λ f ( x ) u in H 1 ( R N ) . Using the sign-changing Nehari manifold, we prove that the Choquard equation has at least one ground state sign-changing solution. This paper can be regarded as the complementary work of Ghimenti and Van Schaftingen (2016), Van Schaftingen and Xia (2017). [ABSTRACT FROM AUTHOR]

In this paper, by constructing an objective function and using the gradient search, full-rank and reduced-rank gradient-based algorithms are suggested for solving generalized coupled Sylvester matrix equations. It is proved that the reduced-rank iterative algorithm is convergent for proper initial iterative values. By analyzing the spectral radius of the related matrices, the convergence properties are studied and the optimal convergence factor of the reduced-rank algorithm is determined. The relationship between the reduced-rank algorithm and the full-rank algorithm is discussed. Consequently, the computation load can be reduced greatly for solving a class of matrix equation. A numerical example is provided to illustrate the effectiveness of the proposed algorithms and testify the conclusions suggested in this paper. [ABSTRACT FROM AUTHOR]

The spatial fractional diffusion equation can be discretized by employing the implicit finite difference scheme with the shifted Grünwald formula and the given discretized linear systems have a diagonal-plus-Toeplitz structure. In this paper, based on trigonometric transformation splitting (TTS), we study efficient iterative method called GTTS has two parameters. As a focus, we give the simple and effective optimal forms of these two parameters respectively. We carry out some numerical experiments to illustrate the effectiveness and accuracy of this new algorithm. [ABSTRACT FROM AUTHOR]

We are promoting the use of variational principles as some generalizing idea that allows us to create consistent approximations of mathematical models. In this paper, we formulate a computing technology to solve direct and inverse problems of atmospheric dynamics and chemistry. For the implementation, we use functional decomposition methods, splitting techniques, and integrating factors designed as the solutions of some adjoint problems. One of the main purposes of the paper is to relate the theory of approximation with the concept of Eulerian integrating factors that plays the fundamental role in the theory of differential equations. We demonstrate the utility and versatility of the concept applying it to solve the systems of differential equations of convection–diffusion (with dominant convection) and stiff systems of kinetic equations. To identify the prospects of our approach, we briefly introduce how to use integrating factors in the case of unstructured grids. [Copyright &y& Elsevier]

Abstract: For solving nonsymmetric linear systems, we attempt to establish symmetric structures in nonsymmetric systems and handle them through the methods devised for symmetric cases. A Biconjugate -Orthogonal Residual method based on Biconjugate -Orthonormalization Procedure has been proposed and nominated as BiCOR in [Y.-F. Jing, T.-Z. Huang, Y. Zhang, L. Li, G.-H. Cheng, Z.-G. Ren, Y. Duan, T. Sogabe, B. Carpentieri, Lanczos-type variants of the COCR method for complex nonsymmetric linear systems, J. Comput. Phys. 228 (2009) 6376–6394.]. As many similar characteristics exist between BiCOR and BiCG, the strategies of improved variants of BiCG, such as CGS and BiCGSTAB, can be utilized to enhance the algorithm for BiCOR. Making use of the product of residual polynomials of BiCOR and other polynomials, CORS and BiCORSTAB have been proposed along the same ideas of CGS and BiCGSTAB, respectively in the above-mentioned paper. In this paper, a unified generalized framework of product-type BiCOR, which is epitomized by the product of residual polynomials and other polynomials, is proposed. Numerical examples are selected from the blurring signal cases and the effect of the generalized product-type BiCOR method is prominent in signal deconvolution. [Copyright &y& Elsevier]

Abstract: In this paper, we study the error in the approximation of a convex function obtained via a one-parameter family of approximation schemes, which we refer to as barycentric approximation schemes. For a given finite set of pairwise distinct points in , the barycentric approximation of a convex function is of the form: where is a set of barycentric coordinates with respect to the point set . The main content of this paper is two-fold. The first goal is to derive sharp upper and lower bounds on all barycentric coordinates over the convex polytope . The second objective of the paper is to exploit the convexity assumption heavily and establish a number of upper and lower pointwise bounds on the approximation error for approximating arbitrary convex functions. These bounds depend solely on computable quantities related to the data values of the function, the largest and smallest barycentric coordinates. For convex twice continuously differentiable functions, we derive an optimal error estimate. We show that the Delaunay triangulation gives access to efficient algorithms for computing optimal barycentric approximation. Finally, numerical examples are used to show the success of the method. [Copyright &y& Elsevier]

Abstract: The paper presents a generalized model for quantifying and evaluating the survivability of systems and the services provided by the systems. For this purpose, we consider a multi-server system with infinite buffer, Markovian Arrival Process (MAP) and phase type (PH) service time distribution. The system is subject to the so-called propagated breakdowns. Accordingly, breakdowns arrive in bunches (we call them attacks) according to the MAP. Attacks consist of a random number of failures of different types defined by the required repair time. The process of arrival of different types of server failures within an attack is governed by phase type Markov process. The repair of a server takes an exponentially distributed time with intensity depending on the type of the occurred failure. We analyze the survivability of the system in terms of average time required for its complete recovery after an attack completion conditional no new attack arrives. In this paper, we consider two forms of recovery following the end of failure arrivals based on (1) the length of queue or (2) the number of broken servers reaching a preassigned level. To provide analysis of survivability, we first describe dynamics of the system by the multi-dimensional continuous time Markov chain. Then, we analyze survivability by means of matrix extension of so called method of collective marks. Numerical illustrations are also presented. [Copyright &y& Elsevier]

Abstract: Antirings are an important type of semirings, which generalize Boolean algebra, fuzzy algebra, distributive lattice and incline. In this paper, we study the issue of nilpotent antiring matrices, provide some properties and characterizations of the simultaneous nilpotence for a finite number of antiring matrices, present some methods for calculating the simultaneously nilpotent index of a finite number of antiring matrices. Partial results obtained in this paper generalize and develop the corresponding ones on nilpotent antiring matrices and on simultaneously nilpotent fuzzy matrices (lattice matrices). [Copyright &y& Elsevier]

Abstract: The aim of this paper is to generalize the conic domain defined by Kanas and Wisniowska, and define the class of functions which map the open unit disk onto this generalized conic domain. A brief comparison between these conic domains is the main motivation of this paper. A correction is made in selecting the range interval of order of conic domain. [Copyright &y& Elsevier]

Abstract: This paper generalizes the results for the constructions of explicit bounds and the qualitative properties for the solutions of certain two-dimensional fractional differential systems established in a recent paper of the authors. The main generalizations come from an elementary inequality and by means of the modification of Medveď’s de-singular approach. [Copyright &y& Elsevier]

Abstract: This paper deals with existence theorems of positive solutions for singular elliptic boundary value problems in a ball. The results of this paper are generalizations of those proved by authors cited in the references. [Copyright &y& Elsevier]

Abstract: Learning and job deterioration co-exist in many realistic scheduling situations. This paper introduces a general scheduling model with the effects of learning and deterioration simultaneously which is a significant generalization of some existing models in the literature. By the effects of learning and deterioration, we mean that job processing times are defined by functions of their start times and positions in the sequence. This paper shows that the single-machine scheduling problems to minimize the makespan, sum of the th power of completion times, total lateness and sum of earliness penalties (with a common due date) are polynomially solvable under the proposed model. It further shows that the problems to minimize the total weighted completion time, discounted total weighted completion time, maximum lateness, maximum tardiness, total tardiness and total weighted earliness penalties (with a common due date) are polynomially solvable under certain conditions. [ABSTRACT FROM AUTHOR]

Abstract: Fuzzy n-ary hypergroups were introduced as suitable generalizations of fuzzy polygroups and a special case of fuzzy n-ary hyper groups. The aim of this paper is to introduce the notion of fuzzy n-ary factor polygroups of a polygroup. Based on the fuzzy n-ary factor group, we also study the product structures of the generating fuzzy factor n-ary groups. At the end of the paper, we prove the fundamental theorem of isomorphism of fuzzy n-ary groups. [Copyright &y& Elsevier]

Abstract: In this article, we will show that (1) the results about the triple I method for fuzzy reasoning obtained in the paper “Computers and Mathematics with Applications 44 (2002) 1567–1579” are correct; (2) Example 2.1 in the paper “Notes on triple I method of fuzzy reasoning” presented by Hua-wen Liu is incorrect; (3) -triple I method presented by Liu is a generalization of -triple I method. [Copyright &y& Elsevier]

A generalized element-free Galerkin (GEFG) method is developed in this paper for solving Stokes problem in primitive variable form. To obtain stable numerical results for both velocity and pressure, extended terms are only introduced into the approximate space of velocity in a special way as that in the generalized finite element method. Theoretical analysis shows that the GEFG method implies a stabilized formulation similar to that in the variational multiscale element-free Galerkin (VMEFG) method. Numerical results show the efficiency of the present method and reveal that both computational errors and CPU times of the present method are less than those of the VMEFG and the finite element methods. [ABSTRACT FROM AUTHOR]

In this paper, an iterative algorithm for solving a generalized coupled Sylvester-conjugate matrix equations over Hermitian R -conjugate matrices given by A 1 V B 1 + C 1 W D 1 = E 1 V ¯ F 1 + G 1 and A 2 V B 2 + C 2 W D 2 = E 2 V ¯ F 2 + G 2 is presented. When these two matrix equations are consistent, the convergence theorem shows that a solution can be obtained within finite iterative steps in the absence of round-off error for any initial arbitrary Hermitian R -conjugate solution matrices V 1 , W 1 . Some lemmas and theorems are stated and proved where the iterative solutions are obtained. A numerical example is given to demonstrate the behavior of the proposed method and to support the theoretical results. [ABSTRACT FROM AUTHOR]

We study the blowup for a type of generalized Zakharov system in this paper. It is proved that the solution of such system either blows up in finite time or blows up in infinite time provided that the initial energy is negative. [ABSTRACT FROM AUTHOR]

In this paper, we will present a new (3+1)-dimensional KP-like nonlinear partial differential equation, and construct the rational solutions to this new (3+1)-dimensional KP-like equation. The proposed method in this work is based on a generalized bilinear differential equation, which implies that we can build the rational solutions to the presented KP-like equation from polynomial solutions to the aforementioned generalized bilinear equation. Moreover, for y = z , this new model reduces to the new (2+1)-dimensional KP-like nonlinear partial differential equation, which will be studied as well herein. [ABSTRACT FROM AUTHOR]

This paper considers the existence and uniqueness of the global smooth solution for the initial value problem of generalized Zakharov equations in dimension two. By means of a priori integral estimates, Galerkin method and compactness theory, one has the existence and uniqueness for small initial data. [ABSTRACT FROM AUTHOR]

Evolution of the long water waves and small-amplitude surface waves with the weak nonlinearity, weak dispersion and weak perturbation in fluid mechanics in three spatial dimensions can be described by a generalized ( 3 + 1 )-dimensional variable-coefficient Kadomtsev–Petviashvili equation, which is studied in this paper with symbolic computation. Via the truncated Painlevé expansion, an auto-Bäcklund transformation is derived, based on which, under certain variable-coefficient constraints, one-soliton, two-soliton, homoclinic breather-wave and rouge-wave solutions are respectively obtained via the Hirota method. Graphic analysis shows that the soliton propagates with the varying soliton direction. Change of the value of any one of g ( t ) , m ( t ) , n ( t ) , h ( t ) , q ( t ) and l ( t ) in the equation can cause the change of the soliton shape, while the soliton amplitude cannot be affected by that change, where g ( t ) represents the dispersion, m ( t ) and n ( t ) respectively stand for the disturbed wave velocities along the y and z directions, h ( t ) , q ( t ) and l ( t ) are the perturbed effects, y and z are the scaled spatial coordinates, and t is the temporal coordinate. Soliton direction and type of the interaction between the two solitons can vary with the change of the value of g ( t ) , while they cannot be affected by m ( t ) , n ( t ) , h ( t ) , q ( t ) and l ( t ) . Homoclinic breather wave and rouge wave are respectively displayed, where the rouge wave comes from the extreme behaviour of the homoclinic breather wave. [ABSTRACT FROM AUTHOR]

Recently, a class of generalized shift-splitting iteration methods were proposed for solving nonsingular nonsymmetric saddle point problems (Cao et al., 2015). In this paper, the generalized shift-splitting iteration method is extended to solve singular nonsymmetric saddle point problems. Semi-convergence of the generalized shift-splitting iteration method is carefully analyzed, which shows that the iterative sequence generated by the generalized shift-splitting iteration method converges to a solution of the singular saddle point problem unconditionally. Numerical results verify the robustness and efficiency of the generalized shift-splitting iteration method. [ABSTRACT FROM AUTHOR]

In this paper, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the exp-function method, the ( G ′ G ) -expansion method and the generalized Kudryashov method are used to construct exact solutions for ( 3 + 1 ) -dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation. This fractional equation can be turned into another nonlinear ordinary differential equation by fractional complex transformation and then these three methods are applied to solve it. As a result, some new exact solutions are obtained. The three methods demonstrate power, reliability and efficiency. [ABSTRACT FROM AUTHOR]

In this paper we study a ( 2 + 1 ) -dimensional Haˇraˇgus-Courcelle–Il’ichev equation (HCI) that models gravity–capillary and flexural-gravity waves. This equation is a generalization of the Kadomtsev–Petviashvili equation, and is obtained due to the presence of certain surface effects. We obtain analytic solutions of the HCI equation by using the Lie symmetry method along with the auxiliary equation method. The solutions obtained are the solitary, cnoidal and snoidal wave solutions. In addition to this we derive the conservation laws of the underlying equation by using the multiplier approach. [ABSTRACT FROM AUTHOR]

The extended homoclinic test approach (EHTA) is a straightforward and efficient method to solve nonlinear partial differential equations. In this paper, new exact solutions including kinky periodic solitary-wave solutions, periodic soliton solutions and periodic kink solutions for the ( 3 + 1 ) -dimensional generalized Kadomtsev–Petviashvili (KP) and B-type Kadomtsev–Petviashvili (BKP) equations are obtained. Moreover, the strangely mechanical features of these wave solutions are investigated. These solutions enrich the variety of the dynamics of higher-dimensional nonlinear wave field. [ABSTRACT FROM AUTHOR]

Fixed point iterations are still the most common approach to dealing with a variety of numerical problems such as coupled problems (multi-physics, domain decomposition, …) or nonlinear problems (electronic structure, heat transfer, nonlinear mechanics, …). Methods to accelerate fixed point iteration convergence or more generally sequence convergence have been extensively studied since the 1960’s. For scalar sequences, the most popular and efficient acceleration method remains the Δ 2 of Aitken. Various vector acceleration algorithms are available in the literature, which often aim at being multi-dimensional generalizations of the Δ 2 method. In this paper, we propose and analyse a generic residual-based formulation for accelerating vector sequences. The question of the dynamic use of this residual-based transformation during the fixed point iterations for obtaining a new accelerated fixed point method is then raised. We show that two main classes of such iterative algorithms can be derived and that this approach is generic in that various existing acceleration algorithms for vector sequences are thereby recovered. In order to illustrate the interest of such algorithms, we apply them in the field of nonlinear mechanics on a simplified “point-wise” solver used to perform mechanical behaviour unit testings. The proposed test cases clearly demonstrate that accelerated fixed point iterations based on the elastic operator (quasi-Newton method) are very useful when the mechanical behaviour does not provide the so-called consistent tangent operator. Moreover, such accelerated algorithms also prove to be competitive with respect to the standard Newton–Raphson algorithm when available. [ABSTRACT FROM AUTHOR]

In this paper we establish the regularity criteria of solutions to the three space dimensions generalized viscous Hall-magnetohydrodynamics. Moreover, we also prove that there exist classical solutions globally in time to the generalized viscous Hall-MHD if the initial data is small enough or the fractional Laplacian dissipation powers α and β are suitably large. These results are some improvements of very recent work (Chae and Lee, 2014) established by Chae and Lee. [ABSTRACT FROM AUTHOR]

In this paper we consider a von Karman equation of memory type u t t + Δ 2 u − ∫ 0 t g ( t − s ) Δ 2 u ( s ) d s = [ u , F ( u ) ] with clamped boundary condition. We establish a decay result of solutions without imposing the usual relation between a kernel function g and its derivative. This result generalizes earlier ones to an arbitrary rate of decay, which is not necessarily of an exponential or polynomial decay. [ABSTRACT FROM AUTHOR]

The weighted Minkowski inverse A M , N ⊕ ∈ M n , m ​related to the positive definite matrices M ∈ M m and N ∈ M n of an arbitrary matrix A ∈ M m , n (including singular and rectangular) is one of the important generalized inverses for solving matrix equations in Minkowski space μ . In this paper, the results are introduced in the following three ways. First, we establish some new and attractive properties of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ . Second, new representations and conditions for the continuity of the weighted Minkowski inverse A M , N ⊕ in a Minkowski space μ are discussed. Finally, some illustrated counterexamples are also studied to show that some well-known properties of the weighted Moore–Penrose inverse A M , N + in a Hilbert space H are not valid in the Minkowski inverse A M , N ⊕ in a Minkowski space μ . [ABSTRACT FROM AUTHOR]

In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics, namely the time fractional KdV–Zakharov–Kuznetsov (KdV–ZK) and space–time fractional modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equations by using improved fractional sub equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie’s modified Riemann–Liouville sense. [ABSTRACT FROM AUTHOR]

The author of the commented paper applies the Exp-function method for the derivation of generalized solitary solutions to a system of nonlinear partial differential equations. We argue that the derived solution does not exist for all initial conditions and use operator techniques to derive the conditions of existence of the solitary solution. [ABSTRACT FROM AUTHOR]

Recently, some authors (Darvishi and Hessari, 2011; Zhang et al., 2012) discussed the generalized modified symmetric successive over relaxation (GMSSOR) method for saddle point problems. In this paper, we further study the GMSSOR method for solving singular saddle point problems. We prove the semi-convergence of the GMSSOR method without the assumption that the (1, 1)-block sub-matrix A should be symmetric, and analyze the spectral property of the corresponding preconditioned matrix. Numerical experiments are given to illustrate the efficiency of GMSSOR with appropriate parameters. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the iteration solutions of generalized coupled Sylvester-transpose matrix equations: , . When the coupled matrix equations are consistent, we propose a modified conjugate gradient method to solve the equations and prove that a solution can be obtained within finite iterative steps in the absence of roundoff-error for any initial value. Furthermore, we show that the minimum-norm solution can be got by choosing a special kind of initial matrices. When the coupled matrix equations are inconsistent, we present another modified conjugate gradient method to find the least-squares solution with the minimum-norm. Finally, some numerical examples are given to show the behavior of the considered algorithms. [Copyright &y& Elsevier]

Abstract: In the present paper the method of successive approximations and Faber polynomials are used to derive the approximate solution of a generalized boundary value problem of linear conjugation on the Lyapunov curve. The conditions for the existence and uniqueness of the solution are presented in the and spaces. [Copyright &y& Elsevier]

Abstract: In this paper, we study the parabolic Monge–Ampère equations in exterior domains for . Using the Perron method, we establish the existence and uniqueness of viscosity solutions with asymptotic behavior. We generalize the results of elliptic Monge–Ampère equations in dimension two. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new preconditioned generalized local Hermitian and skew-Hermitian splitting (GLHSS) iteration method for solving the non-Hermitian saddle point problems. The semi-convergence of this method is discussed. Theoretical analysis shows that the semi-convergence of this new method can be guaranteed by suitable choices of the parameters and parameter matrices. Numerical examples are used to illustrate the theoretical results and examine the numerical effectiveness of the GLHSS iteration method served either as a preconditioner for GMRES or as a solver. [Copyright &y& Elsevier]

Abstract: In this paper, we have carried out a global stability analysis of the flow inside a two sided staggered lid-driven cavity for both the parallel and anti-parallel motions of the lids. A fourth order spatially accurate and second order temporally accurate compact scheme is used to discretize the two-dimensional Navier–Stokes equations governing the flow as well as the perturbed equations leading to the generalized eigenvalue problem. Estimates of the critical parameters are found for several grids and extensive grid convergence study is performed to accurately identify them. Computation is performed for a wide range of Reynolds numbers (Re) on either side of the critical values in the range . For flows below the critical Reynolds number , our numerical results are compared with established steady-state results and an excellent agreement is obtained in all the cases. For Reynolds numbers above , phase plane and spectral density analysis confirmed the existence of periodic and chaotic flow patterns. [Copyright &y& Elsevier]

Abstract: Our current paper is devoted to studying the numerical and analytical solutions for a class of Generalized Fractional Diffusion Equations (GFDEs) with new Generalized Time-Fractional Derivative (GTFD). The GTFD we propose here is defined in the Caputo sense. We consider the GFDEs on a bounded domain. The numerical solutions are obtained by using the Finite Difference Method (FDM) of full discretization. The stability of FDM is discussed and the order of convergence is evaluated numerically. Numerical experiments are given, which illustrate that the FDM is simple and effective for solving the GFDEs with different coefficients and source functions. An interesting phenomenon is that we can observe the period-like solution in GFDEs with a particular positive periodic weight function. Using the method of separation of variables, we convert the homogeneous GFDE into two ordinary differential equations, and solve them via the help of solutions of the initial value problem with Caputo derivative. In the analytical solution, we observe that the weight function in the denominator, and scale function mapping the response domain differently. Since the derivative considered in this article is new, many existing results of FDEs are generalized. [Copyright &y& Elsevier]

Abstract: Generalized Multiple Kernel Learning (GMKL) has been proposed in the literature for feature selection. GMKL learns linear, product and exponential combinations of given base kernels which makes it more robust and efficient than traditional Multiple Kernel Learning (MKL). GMKL has been shown to be a good tool for feature selection as well. Time taken for the convergence of GMKL depends upon the initialization of kernel weights. Optimization schemes in GMKL initialize kernel weights randomly. This produces variability in convergence time. In this paper, we propose a Fuzzy Rough Set based kernel weight initialization for GMKL (FR-GMKL). We show that this results in faster convergence than that obtained by random initialization in GMKL while retaining same level of accuracy. We also show that the computation time of our proposed method is lower than that obtained through Quadratic Programming Feature Selection (QPFS) based as well as Maximal Relevance (MaxRel) based initialization of the regularization parameter. The performance of our proposed method is evaluated using five benchmark binary classification datasets and three benchmark multi-class classification datasets from the UCI repository. [Copyright &y& Elsevier]

Abstract: We consider a linear algebraic system , where the elements of the matrix and the right-hand side vector are linear functions of uncertain parameters varying within given intervals. The linear tolerance problem for the so-called parametric tolerable solution set requires an inner estimation of this solution set, that is an interval vector , such that . In this paper we consider the first methods for finding inner estimation of the parametric tolerable solution set, namely, we propose parametric generalization of the so-called centered approach and of the vertex approach. The results obtained by the two approaches are compared on some numerical examples. The advantages of the parametric approach are demonstrated on problems with independent nonparametric entries and in controllability analysis of linear dynamical systems involving interval uncertainties. [Copyright &y& Elsevier]

Abstract: For computing the smallest eigenvalues and their corresponding eigenvectors of symmetric generalized eigenproblems simultaneously, Quillen and Ye have introduced a block inverse-free preconditioned Krylov subspace method (Quillen and Ye, 2010) [14]. To accelerate convergence and compute interior eigenpairs, in this paper we present a refined shifted block inverse-free Krylov subspace algorithm based on the block Arnoldi process that generates a -orthogonality basis of the matrix Krylov subspace. It is proved that this algorithm can guarantee the convergence if the corresponding Ritz values converge. Numerical experiments show that the refined algorithm is more efficient than the original approach. [Copyright &y& Elsevier]

Abstract: In this paper, we execute elementary row and column operations on the partitioned matrix into to compute generalized inverse of a given complex matrix , where is a matrix such that and . The total number of multiplications and divisions operations is and the upper bound of is less than when . A numerical example is shown to illustrate that this method is correct. [Copyright &y& Elsevier]

Abstract: Monogenic orthogonal polynomials over 3D prolate spheroids were previously introduced and shown to have some remarkable properties. In particular, the underlying functions take values in the quaternions (identified with ), and are generally assumed to be nullsolutions of the well known Moisil–Théodoresco system. In this paper, we show that these polynomial functions play an important role in defining the Szegö kernel function over the surface of 3D (prolate) spheroids. As a concrete application, we prove an explicit expression of the monogenic Szegö kernel function over 3D (prolate) spheroids and present two numerical examples. [Copyright &y& Elsevier]

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

Abstract: Maji et al. introduced the concept of intuitionistic fuzzy soft sets which is a generalization of fuzzy soft sets and standard soft sets. In this paper, we further discuss the operation properties and algebraic structure of intuitionistic fuzzy soft sets. The lattice structures of intuitionistic fuzzy soft sets are derived. The notions of -intuitionistic fuzzy soft equalities are introduced and their basic properties are investigated. The relationships between -intuitionistic fuzzy soft equalities and soft equalities introduced by Qin and Hong are developed. The notion of a mapping on intuitionistic fuzzy soft classes is introduced and several properties of the image and inverse image of intuitionistic fuzzy soft sets are presented. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a generalized edge-weighted centroidal Voronoi tessellation (GEWCVT) model and corresponding solution algorithms, then apply them for geometry processing such as curve/surface smoothing and reconstruction. The main idea of the method is to seek a good way to discretize the similarity and regularity measures of the objective functional in the context of centroidal Voronoi tessellation methodology, so that its minimization can be done by clustering-type algorithms. Through various numerical examples, the proposed GEWCVT-based method is shown to be an effective and robust tool for such applications. [Copyright &y& Elsevier]

Abstract: In this paper, the concept of -fuzzy soft sets based on complete Boolean lattices, which can be seen as a generalization of fuzzy soft sets, is introduced. The topological and lattice structure of -fuzzy soft sets are obtained. Some operations on -fuzzy soft sets are discussed, and new types of -fuzzy soft sets such as full, keeping intersection and keeping union -fuzzy soft sets are defined and supported by some illustrative examples. A pair of -fuzzy soft rough approximations is proposed and their properties are given. Based on -fuzzy soft rough approximations, the concept of -fuzzy soft rough sets is introduced and their structures are studied. The fact that every finite -fuzzy topological space is an -fuzzy soft approximation space is revealed. In addition, we obtain two one-to-one correspondence relationships associated with -fuzzy soft sets, which expounds the broad application prospect of -fuzzy soft sets. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to give a generalization of Szasz operators defined by means of the Brenke type polynomials. We obtain convergence properties of our operators with the help of Korovkin’s theorem and the order of convergence by using a classical approach, the second modulus of continuity and Peetre’s -functional. An explicit example with our operators including Gould–Hopper polynomials which generalize Szasz operators in a natural way is given. [Copyright &y& Elsevier]