This paper investigates the convergence condition for the polynomial approximation of rational functions and rational curves. The main result, based on a hybrid expression of rational functions (or curves), is that two-point Hermite interpolation converges if all eigenvalue moduli of a certain r_r matrix are less than 2, where r is the degree of the rational function (or curve), and where the e...

This survey is devoted to necessary and suffcient conditions for a rational number be representable by Cantor series. Necessary are formulated the case of an arbitrary sequence $(q_k)$.

Oxidative stress resulting from metal-ion misregulation plays a role in the development of Alzheimer's disease (AD). This process includes the production of tissue-damaging reactive oxygen species and amyloid aggregates. Herein we describe the synthesis, characterization and protective capacity of the small molecule, lipoic cyclen, which has been designed to target molecular features of AD. Thi...

Funding information National Science Foundation, Grant/Award Number: 1453218, 1506605; Department of Energy, Grant/Award Number: DE-NA0002509 Abstract Glass is in general brittle and therefore usually cannot sustain large deformation. Recent advances in glass material development as well as micro-mechanical designs, however, are set to defy the conventional wisdom through the demonstration of f...

Cooperation is the foundation of many protocols in wireless networks. Without cooperation, the performance of a network significantly decreases. Hence, all nodes in traditional networks are required to cooperate with each other. In this paper, instead of traditional networks, a network of rational and autonomous nodes is considered. Which means that each node itself can decide whether to cooper...

The aim of this paper is to determine generators of the rational cohomology algebras of moduli spaces of parabolic vector bundles on a curve, under some ‘primality’ conditions (see Assumptions 1.1 and 1.2) on the parabolic datum. These generators are canonical in a sense which will be made precise below. Our results are new even for usual vector bundles (i.e., vector bundles without parabolic s...

This paper posits that developers cannot sustain extensive customisation of software without clear software product line architecture, modular subsystem platforms, and disciplined interfaces among these platforms. To explore this proposition, we initially define the basic principles of desirable software architecture and then apply these definitions to the development of software and the busine...

Let G be a semisimple Lie group without compact factors, Γ be an irreducible lattice in G. In the first part of the article we give the necessary and sufficient condition under which a sequence of translates of probability “horospherical measures” is convergent. And the limiting measure is also determined when it is convergent (see Theorems 1 and 2 for the precise statements). In the second par...

We focus on the implicitization of parametric CAGD entities which are supposed to be of tensor product type. The presented approach is featured by its ability to treat polynomial or rational splines having a great number of control points. For B-splines, we describe a method of exactly obtaining the Fourier coefficients without using quadrature rules. As for NURBS, a preprocessing step is neces...