Abstract It is well known that the interpolation error for $$\left| x\right| ^{\alpha },\alpha &gt;0$$ x ? , &gt; 0 in $$L_{\infty }\left[ -1,1\right] $$ <m...

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...

In this paper we provide three nonparametric tests of independence between continuous random variables based on Bernstein copula and copula density. The first test is constructed based on functional of Cramér-von Mises of the Bernstein empirical copula. The two other tests are based on Bernstein density copula and use Cramér-von Mises and Kullback-Leiber divergencetype respectively. Furthermore...

This paper is devoted to the study of geometric structures modeled on homogeneous spaces G/P , where G is a real or complex semisimple Lie group and P ⊂ G is a parabolic subgroup. We use methods from differential geometry and very elementary finite–dimensional representation theory to construct sequences of invariant differential operators for such geometries, both in the smooth and the holomor...

Time transformation models assume that the survival time is linearly related to covariates through an unknown monotonic transformation function and an error term with known distribution. In this paper the sieve method of maximum likelihood is used to estimate the unknown monotonic transformation of survival time. More specifically a suitable class of Bernstein polynomials is used to estimate th...

Bernstein-Sato polynomial of a hypersurface is an important object with numerous applications. It is known, that it is complicated to obtain it computationally, as a number of open questions and challenges indicate. In this paper we propose a family of algorithms called checkRoot for optimized check of whether a given rational number is a root of BernsteinSato polynomial and the computations of...

We use recently calculated next-to-next-to-leading order (NNLO) anomalous dimension coefficients for the moments of the xF3 structure function in νN scattering, together with the corresponding three-loop Wilson coefficients, to obtain improved QCD predictions for both odd and even moments. To investigate the issue of renormalisation scheme dependence the Complete Renormalization Group Improveme...

Given a matrix A ∈ R, we present a simple, element-wise sparsification algorithm that zeroes out all sufficiently small elements of A and then retains some of the remaining elements with probabilities proportional to the square of their magnitudes. We analyze the approximation accuracy of the proposed algorithm using a recent, elegant non-commutative Bernstein inequality, and compare our bounds...

We survey some recent developments in the theory of b-function, spectrum, and multiplier ideals together with certain interesting relations among them including the case of arbitrary subvarieties. Dedicated to Professor Masaki Kashiwara