The maximal minors of a matrix indeterminates are universal Gröbner basis by theorem Bernstein, Sturmfels and Zelevinsky. On the other hand it is known that they not always Sagbi basis. By an experimental approach we discuss their behavior under varying monomial orders extensions to bases. These experiments motivated new implementation algorithm which organized in Singular script falls back on ...

Recently, Kim’s work in press introduced q-Bernstein polynomials which are different Phillips’ q-Bernstein polynomials introduced in the work by Phillips, 1996; 1997 . The purpose of this paper is to study some properties of several type Kim’s q-Bernstein polynomials to express the p-adic q-integral of these polynomials on Zp associated with Carlitz’s q-Bernoulli numbers and polynomials. Finall...

Mixture models for density estimation provide a very useful set up for the Bayesian or the maximum likelihood approach. For a density on the unit interval, mixtures of beta densities form a flexible model. The class of Bernstein densities is a much smaller subclass of the beta mixtures defined by Bernstein polynomials, which can approximate any continuous density. A Bernstein polynomial prior i...

In this paper we construct new operators of Bernstein type with a better approximation than the classical Bernstein operator for some classes of functions on the whole interval [0,1]. Convergence of these operators and their shape preserving properties are discussed. We determine the subintervals in [0,1] in which the approximation order of constructed operators is better than that of the Berns...

In this study, we introduce a new kind of nonlinear Bernstein-Chlodowsky operators based on q-integers. Firstly, define the q?Bernstein-Chlodowsky max-product kind. Then, give an error estimation for q?Bernstein Chlodowsky by using suitable generalizition Shisha-Mond Theorem. There follows upper estimates approximation some subclasses functions.

In this paper, we discuss properties of convergence for a modification of the q-Bernstein operators. Using the notion of A-statistical approximation, where A is a nonnegative regular summability matrix, we investigate the Korovkin type statistical approximation properties of this modification via A-statistical approximation. For 0 < q ≤ 1, we obtain that the q-Bernstein operators is A-statistic...

We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems.