Related papers: A de Casteljau Algorithm for Bernstein type Polyno…
By identifying a family of corner cutting schemes as a dimension elevation process of Gelfond-Bezier curves, we give a Muntz type condition for the convergence of the generated control polygons to the underlying curve. The surprising…
In this paper we investigate some properties for the q-Euler numbers ans polymials. From these properties we give some identities on the Bernstein polymials and q-Euler polynpmials.
We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form k[x,y]/<q>, where q is a homogeneous quadric. We also provide a finite algorithm for decomposing Betti diagrams, including…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…
In this note, we present a new method for computing fundamental groups of curve complements using a variation of the Zariski-Van Kampen method on general ruled surfaces. As an application we give an alternative (computation-free) proof for…
In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite…
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and differential equations using this generating…
We prove various theorems on approximation using polynomials with integer coefficients in the Bernstein basis of any given order. In the extreme, we draw the coefficients from $\{ \pm 1\}$ only. A basic case of our results states that for…
In the past few decades polynomial curves with Pythagorean Hodograph (for short PH curves) have received considerable attention due to their usefulness in various CAD/CAM areas, manufacturing, numerical control machining and robotics. This…
Recently, Kim-Kim Introduced some interesting identities of symmetry for q-Bernoulli polynomials under symmetry group of degree n. In this paper, we study the degenerate q-Euler polynomials and derive some identities of symmetry for these…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…
We present a new algorithm for computing integral bases in algebraic function fields of one variable, or equivalently for constructing the normalization of a plane curve. Our basic strategy makes use of the concepts of localization and…
We provide an algorithm for computing the Euler characteristic of the curves $S_p$ in the space of cubic polynomials, consisting of all polynomials with a periodic critical point of period $p$. The curves were introduced in [Milnor,…
In this paper, we study some properties of Changhee's q-Bernou lli polynomials which are derived from p-adic invariant integral on Zp. By using these properties, we give some interesting identities related to higher- order q-Bernoulli…
We propose a novel approach to the problem of polynomial approximation of rational B\'ezier triangular patches with prescribed boundary control points. The method is very efficient thanks to using recursive properties of the bivariate dual…
We present some notes on the definition of mathematical design as well as on the methods of mathematical modeling which are used in the process of the artistic design of the environment and its components. For the first time in the field of…
We use Berezin's quantization procedure to obtain a formal $U_q su_{1,1}$-invariant deformation of the quantum disc. Explicit formulae for the associated q-bidifferential operators are produced.
In order to construct quantum trigonometric B\'ezier curves with shape parameter, one parameter family of trigonometric Bernstein basis functions are introduced. We study the total positivity of the basis functions to analyze the shape…
The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…
A class P_{n,m,p}(x) of polynomials is defined. The combinatorial meaning of its coefficients is given. Chebyshev polynomials are the special cases of P_{n,m,p}(x). It is first shown that P_{n,m,p}(x) may be expressed in terms of…