Search

In this paper, efficient numerical schemes are proposed for solving the fractional water wave models that describe the propagation of surface water wave. By using the weighted and shifted Grünwald–Letnikov (WSGL) formula to approximate the nonlocal fractional operators, we design a series of second order accurate difference schemes for the considered models. The existence, stability and convergence of numerical solutions of the proposed numerical schemes are established rigorously. The analysis shows that the proposed numerical schemes are unconditionally stable with second order accuracy for both temporal and spatial discretizations. Several numerical results are provided to verify the efficiency and accuracy of our theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, a new nonmonotone trust region algorithm with simple quadratic models is proposed. Unlike traditional nonmonotone trust region method, our trust region subproblem is very simple by using a new scale approximation of the minimizing function's Hessian. The global convergence of the proposed algorithm is established under some reasonable conditions. Numerical tests on a set of large scale standard test problems are presented and show that the new algorithm is efficient and robust. [ABSTRACT FROM AUTHOR]

Many different proposals exist for the definition of lower and upper approximation operators in covering-based rough sets and so many different covering rough set models are built correspondingly. It is meaningful to explore the connection of these covering rough set models for their applications in practice. In this paper, we establish relationships between the most commonly used operators in covering rough set models. We investigate the conditions under which two types of upper approximation operations are identical. [ABSTRACT FROM AUTHOR]

In the present paper, we study the existence of approximate fixed point for Reich operator together with the property that the ϵ-fixed points are concentrated in a set with the diameter tends to zero if ϵ → 0. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents and discusses a hybrid-mixed stress finite element model for the dynamic analysis of structures, assuming a physically and geometrically linear behavior. In this model, both the stress and the displacement fields are approximated in the domain of each element. The displacements along the static boundary are also independently approximated. Orthonormal Legendre polynomials are used as approximation functions. The use of these functions enables the use of analytical closed form solutions for the computation of all structural operators and leads to the development of very effective p-refinement procedures. The linear dynamic analysis is performed using time integration procedures. For this purpose, the classical Newmark, Wilson-θ and α-HHT methods are implemented and tested. A recent and promising alternative approach, based on the definition of a mixed approximation in the time domain is also implemented and assessed. The model being discussed is applied to the solution of plane elasticity and Reissner–Mindlin plate bending problems. To validate the model, to illustrate its potential and to assess its accuracy and efficiency, several numerical examples are discussed and comparisons are made with analytical solutions and solutions provided by other numerical techniques. [Copyright &y& Elsevier]

Abstract: The paper describes a multi-objective mathematical model for Dial a Ride Problem (DRP) and an application of Multi-Objective Simulated Annealing (MOSA) to solve it. DRP is to take over the passenger from a place of departure to a place of arrival. In the DRP, customers send transportation requests to an operator. A request consists of a specified pickup location and destination location along with a desired departure or arrival time. The ultimate aim is to offer an alternative to displacement optimized individually and collectively. The DRP is classified as NP-hard problem that''s why most research has been concentrated on the use of approximate methods to solve it. Indeed the DRP is a multi-criteria problem, the proposed solution of which aims to reduce both route duration in response to a certain quality of service provided. In this work, we offer our contribution to the study and solving the DRP in the application using the MOSA algorithm. Tests show competitive results on () benchmark datasets while improving processing times. [Copyright &y& Elsevier]

Abstract: The primitive notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation and satisfying many interesting properties. Many types of generalized rough set models have been proposed in the literature. This paper discusses the rough approximations of Atanassov intuitionistic fuzzy sets in crisp and fuzzy approximation spaces in which both constructive and axiomatic approaches are used. In the constructive approach, concepts of rough intuitionistic fuzzy sets and intuitionistic fuzzy rough sets are defined, properties of rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are examined. Different classes of rough intuitionistic fuzzy set algebras and intuitionistic fuzzy rough set algebras are obtained from different types of fuzzy relations. In the axiomatic approach, an operator-oriented characterization of rough sets is proposed, that is, rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of upper and lower intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of crisp/fuzzy relations which produce the same operators. [Copyright &y& Elsevier]

Abstract: In this paper, using the concept of statistical -convergence which is stronger than statistical convergence, we obtain a statistical approximation theorem for a general sequence of max-product operators, including Shepard type operators, although its classical limit fails. We also compute the corresponding statistical rates of the approximation. [Copyright &y& Elsevier]

Abstract: Multi-window spline-type spaces arise naturally in many areas. Among others they have been used as model spaces in the theory of irregular sampling. This class of shift-invariant spaces is characterized by possessing a Riesz basis which consists of a set of translates along some lattice of a finite family of atoms. Part of their usefulness relies on the explicit knowledge of the structure of the projection operator on such a space using the existence of a finite family of dual atoms. The main goal of this paper is to address the problems arising from the discrepancy between a constructive description and an implementable approximate realization of such concepts. Using function space concepts (e.g. Wiener amalgam spaces) we describe how approximate dual atoms can be computed for any given degree of precision. As an application of our result we describe the best approximation of Hilbert–Schmidt operators by generalized Gabor multipliers, using smooth analysis and synthesis windows. The Kohn–Nirenberg symbols of the rank-one operators formed from analysis and synthesis windows satisfy our general assumptions. Applications to irregular sampling are given elsewhere. [Copyright &y& Elsevier]

We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented to demonstrate the validity and accuracy of these approximate distributions. In terms of the approximate probability distributions, we have also obtained an analytical series expansion of the exact solutions, which can allow us to improve the approximation in a systematic manner. Moreover, we believe that this new approach can be extended to study both (1) the algebraic sum of N lognormals, and (2) the sum and difference of other correlated stochastic processes, for example, two correlated CEV processes, two correlated CIR processes, and two correlated lognormal processes with mean-reversion. [ABSTRACT FROM AUTHOR]