The enhanced (G′/G)-expansion method is highly effective and competent mathematical tool to examine exact traveling wave solutions of nonlinear evolution equations (NLEEs) arising in mathematical p...

In this paper CR-warped product submanifolds of a generalized complex space form are studied and a characterizing inequality for existence of CR-warped product submanifolds is established. Moreover, some special cases are also discussed.

This paper presents a new approach and methodology to solve the second-order one-dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method. The usual finite difference scheme is used to discretize the time derivative. The cubic trigonometric B-spline basis functions are utilized as an interpolating function in the space dimension, with a θ weighted scheme. The scheme is shown to be unconditionally stable for a range of θ values using the von Neumann (Fourier) method. Several test problems are presented to confirm the accuracy of the new scheme and to show the performance of trigonometric basis functions. The proposed scheme is also computationally economical and can be used to solve complex problems. The numerical results are found to be in good agreement with known exact solutions and also with earlier studies.

In this paper, we introduce the method for solving fuzzy transportation problem (FTP) using Robust’s ranking technique for the representative value of the fuzzy number. In addition we are using allocation table method (ATM) to find an initial basic feasible solution (IBFS) for the FTP. Moreover, this method is also good optimal solution in the literature and illustrated with numerical examples.

It is well known that generating functions play an important role in theory of the classical orthogonal polynomials. In this paper, we deal with systems of polynomials defined by generating functions and the following problems for them. (A) Derive a differential equation that each polynomial satisfies. (B) Derive the general solution for the differential equation obtained in (A). (C) Is the general solution obtained in (B) written as a linear combination of functions that are expressed by making use of generalized hypergeometric functions? The purpose of this paper is to give two examples that the problem (C) can be affirmatively solved. One is related to the Humbert polynomials, and its general solution is written by $ _{k}F_{k-1} $-type hypergeometric functions. The other is related to a genelarization of the Hermite polynomials, and its general solution is written by $ _{k}F_{\\ell } $-type $ (k\\le \\ell ) $ hypergeometric functions.

In this paper, the definition of the Toeplitz autocorrelation matrix is used to derive a kernel-based portmanteau test statistic for ARMA models. Under the null hypothesis of no serial correlation, the distribution of the test statistic is approximated by a standard normal using the kernel-based normalized spectral density estimator, without having to specify any alternative model. Unlike most existing portmanteau test statistics, the proposed test is defined for all lags. Simulation studies are conducted to assess the performance of the proposed test. A real application is given to demonstrate the usefulness of this goodness-of-fit test statistic.

In this paper, we numerically study a dynamic viscoelastic problem. The variational formulation is written as a linear parabolic variational equation for the velocity field. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced using the implicit Euler scheme and the finite element method, for which some a priori error estimates are derived, leading to the linear convergence of the algorithm under suitable additional regularity conditions. Finally, some one- and three-dimensional numerical simulations are presented to show the accuracy of the algorithm and the behaviour of the solution, including a comparison with an experimental study.

We first give an alternative proof of a theorem originally presented by E. R. van Dam. Then we show a generalization of the van Dam matrix inequality.

Abstract In clinical study, calculation for sample size is often done using the frequentist framework. However, several methods of calculation using the Bayesian framework have been proposed. In this paper, we propose a method for the determination of sample sizes using the index θ=Pπ1>π2|X1,X2, where X1 and X2 denote the binomial random variables for trials n1 and n2 and parameters π1 and π2, respectively. In this paper, we propose a new method of calculation, by which we determine in advance the estimated difference between the posterior proportions and the value to be derived at the end of the test to obtain the necessary sample size. We provide the lists of necessary sample sizes with various assumptions and the calculation program using Mathematica.