This paper considers an approximate factorisation of three bivariate Bernstein basis polynomials that are defined in a triangular domain. problem is important for the computation intersection points curves computer-aided design systems, and it reduces to determination greatest common divisor (AGCD) d(y) polynomials. The Sylvester matrix its subresultant matrices these formed shown there four fo...

We prove weighted Markov–Bernstein inequalities of the form

This paper is aimed at studying sensitivity of parameters α and β appearing in the operators introduced by D.D. Stancu [11] in 1969. Results are established on the behavior the nodes used in Bernstein-Stancu polynomials and the nodes used in Bernstein polynomials and graphical presentations of them are generated. Alternate proof of uniform convergence of Bernstein-Stancu operators and an upper ...

The finite element method and its application to the simulation of static linear elasticity has a long research history. The same applies for Bernstein–Bézier representations of curves and surfaces in computer aided geometric design. However, the combination of both to build tetrahedral Bernstein–Bézier finite elements presents an inspiring and fruitful challenge. The theory and implementation ...

In the present note, we introduce a Bezier variant of a new type of Bernstein Durrmeyer operator, which was introduced by Gupta [3]. We estimate the rate of convergence by using the decomposition technique of functions of bounded variation and applying the optimum bound. It is observed that the analysis for our Bezier variant of new Bernstein Durrmeyer operators is different from the usual Bern...

In embryonic stem cells (ESCs), silent genes with major developmental functions display a unique epigenetic state in which strong and broad binding by Polycomb repressive complexes (PRCs) is accompanied by the presence of poised RNA polymerase II (RNAPII) and activating histone marks (e.g. H3K4me3) (Azuara et al, 2006; Bernstein et al, 2006; Stock et al, 2007; Brookes et al, 2012). It has been ...