In 1967 Durrmeyer introduced a modiication of the Bernstein polynomials as a selfadjoint polynomial operator on L 2 0; 1] which proved to be an interesting and rich object of investigation. Incorporating Jacobi weights Berens and Xu obtained a more general class of operators, sharing all the advantages of Durrmeyer's modiication, and identiied these operators as de la Vall ee{Poussin means with...

In this work G'/G-expansion method has been employed to solve (2+1)-dimensional dispersive long wave equation. It is shown that G'/G-expansion method, with the help of symbolic computation, provides a very effective and powerful mathematical tool, for solving this equation.

We apply the holonomic gradient method introduced by Nakayama et al. [19] to the evaluation of the exact distribution function of the largest root of a Wishart matrix, which involves the hypergeometric function 1F1 of a matrix argument. Compared to methods based on infinite series expansion in terms of zonal polynomials, whose convergence is slow, the proposed method is more practical for compu...

The two dimensional with a triangular-lattice cross sectional pattern of elliptic air holes photonic crystal fiber (PCF) is investigated in detail by use of plan wave expansion (PWE) method. Using PWE method, the dependence of dispersion on structure parameters is calculated. We compared the dispersion relations between the circular air holes PCF and the elliptic one. We find that the flatter d...

This paper presents a new method for the fast evaluation of univariate radial basis functions of the form s(x) = ∑N n=1 dnφ(|x− xn|) to within accuracy . The method can be viewed as a generalization of the fast multipole method in which calculations with far field expansions are replaced by calculations involving moments of the data. The method has the advantage of being adaptive to changes in ...

We report on experience with an investigation of the analytic structure of the solution of certain algebraic complex equations. In particular the behavior of their series expansions around the origin is discussed. The investigation imposes the need for an analysis of the singularities and the Riemann sheets of the solution, in which numerical methods are used. [email protected] [email protected]

We develop the theory of Abelian functions defined using a tetragonal curve of genus six, with the specific example of the cyclic curve, y = x + λ4x + λ3x + λ2x + λ1x + λ0 discussed in detail. We define generalisations of the Weierstrass σ and ℘ functions, along with additional classes of Abelian functions. In addition, we present the associated partial differential equations satisfied by the f...

The SMERP 2017 data challenge track given a set of tweets posted during Italy earthquake. For retrieving more relevance information respect to user interest profile in this paper provide BM25 and word2vec techniques for retrieving relevance information from twitter stream. This techniques aim is to find real-world and most relevance information respect to the query. For retrieving most relevant...

Using transfer matrix method to solve 3D Ising model is generalized straightforwardly from 2D case. We follow the B.Kaufman's approach. No approximation is made except the largest eigenvalue cannot be identified. This problem comes from the fact that we follow the choice of directions of 2-dimensional rotations in direct product space of 2D Ising model such that all eigenvalue equations reduce ...