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Abstract: Uniform resampling is the easiest to apply and is a general recipe for all problems, but it may require a large replication size . To save computational effort in uniform resampling, balanced bootstrap resampling is proposed to change the bootstrap resampling plan. This resampling plan is effective for approximating the center of the bootstrap distribution. Therefore, this paper applies it to neural model selection. Numerical experiments indicate that it is possible to considerably reduce the replication size . Moreover, the efficiency of balanced bootstrap resampling is also discussed in this paper. [Copyright &y& Elsevier]

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]

Abstract: Smoking is one of the main causes of health problems and continues to be one of the world’s most significant health challenges. In this paper, the dynamics of a giving up smoking model containing fractional derivatives is studied numerically. The multistep generalized differential transform method (for short MSGDTM) is employed to compute accurate approximate solutions to a giving up smoking model of fractional order. The unique positive solution for the fractional order model is presented. A comparative study between the new algorithm and the classical Runge–Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically. [Copyright &y& Elsevier]

Abstract: The multidimensional Itô–Volterra integral equations arise in many problems such as an exponential population growth model with several independent white noise sources. In this paper, we obtain a stochastic operational matrix of block pulse functions on interval to solve m-dimensional stochastic Itô–Volterra integral equations. By using block pulse functions and their stochastic operational matrix of integration, -dimensional stochastic Itô–Volterra integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. We prove that the rate of convergence is . Furthermore, a 95% confidence interval of the errors’ mean is made, the results shows that the approximate solutions have a credible degree of accuracy. [Copyright &y& Elsevier]

Abstract: Rough set theory, initiated by Pawlak, is a mathematical tool in dealing with inexact and incomplete information. Various types of uncertainty measure such as accuracy measure, roughness measure, etc, which aim to quantify the imprecision of a rough set caused by its boundary region, have been extensively studied in the existing literatures. However, a few of these uncertainty measures are explored from the viewpoint of formal rough set theory, which, however, help to develop a kind of graded reasoning model in the framework of rough logic. To solve such a problem, a framework of uncertainty measure for formulae in rough logic is presented in this paper. Unlike the existing literatures, we adopt an axiomatic approach to study the uncertainty measure in rough logic, concretely, we define the notion of rough truth degree by some axioms, such a notion is demonstrated to be adequate for measuring the extent to which any formula is roughly true. Then based on this fundamental notion, the notions of rough accuracy degree, roughness degree for any formula, and rough inclusion degree, rough similarity degree between any two formulae are also proposed. In addition, their properties are investigated in detail. These obtained results will be used to develop an approximate reasoning model in the framework of rough logic from the axiomatic viewpoint. [Copyright &y& Elsevier]

Abstract: In this paper, the approximate solutions of the mathematical model of a mass attached to a stretched elastic wire are presented. At the beginning of the study, the equation of motion is derived in a detailed way. He’s max–min approach, He’s frequency–amplitude method and the parameter-expansion method are implemented to solve the established model. The numerical results are further compared with the approximate analytical solutions for both a small and large amplitude of oscillations, and a very good agreement is observed. The relative errors are computed to illustrate the strength of agreement between the numerical and approximate analytical results. [ABSTRACT FROM AUTHOR]