Abstract CONTENTS Introduction § 1. The function and its properties § 2. Generalized Taylor
series for certain classes of infinitely differentiable functions § 3. Approximation by means of …

Abstract Theory of R-functions [121 provides the methodology for constructing exact implicit
functions for any semianalytic set. This paper systematically explores and compares the …

Финитные бесконечно дифференцируемые функции используются в самых различных
областях математики. Оказывается, существуют финитные бесконечно …

This paper presents a three dimensional interactive sculpting paradigm that employs a
collection of scalar uniform trivariate Bspline functions. The sculpted object is evaluated as …

Continuous and discrete variations in material properties lead to substantial difficulties for
most mesh-based methods for modeling and analysis of physical fields. The meshfree …

A special class of atomic functions, which are compactly supported solutions of linear
functional differential equations with constant coefficients and linear transformations of the …

On the asymptotics of the generalized Fup-functions Page 1 DOI 10.1515/apam-2014-0009 Adv.
Pure Appl. Math. 2014; 5 (3):131–138 Research Article Iryna V. Brysina and Victor A. Makarichev …

Generalized F up-functions are considered. Almost-trigonometric basis theorem is proved.
Spaces of linear combinations of shifts of the generalized F upfunctions are constructed and …

A numerical method for solution of boundary-value problems of mathematical physics is
described that is based on the use of radial atomic basis functions. Atomic functions are …

We study the basis functions φ n, k and ψ n, p of generalized Taylor series for the class H ρ,
2 and obtain asymptotic expansions of the functions φ n, 0 (l) and ψ_n,2⋅4^n-1^(l). We …