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On convex Bézier triangles

H. Prautzsch (1992)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

On Müntz rational approximation in multivariables

S. Zhou (1995)

Colloquium Mathematicae

The present paper shows that for any s sequences of real numbers, each with infinitely many distinct elements, λ n j , j=1,...,s, the rational combinations of x 1 λ m 1 1 x 2 λ m 2 2 . . . x s λ m s s are always dense in C I s .

On regularization in superreflexive Banach spaces by infimal convolution formulas

Manuel Cepedello-Boiso (1998)

Studia Mathematica

We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-Hölder derivatives (for some 0 < α≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function f which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of Δ-convex C 1 , α functions converging to f uniformly on bounded sets and...

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

Oskolkov, K. (2002)

Serdica Mathematical Journal

* The author was supported by NSF Grant No. DMS 9706883.Let P be a bi-variate algebraic polynomial of degree n with the real senior part, and Y = {yj }1,n an n-element collection of pairwise noncolinear unit vectors on the real plane. It is proved that there exists a rigid rotation Y^φ of Y by an angle φ = φ(P, Y ) ∈ [0, π/n] such that P equals the sum of n plane wave polynomials, that propagate in the directions ∈ Y^φ .

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