We consider the problem of integrating and approximating 2D bandlimited functions restricted to a disc by using 2D prolate spheroidal wave functions (PSWFs). We derive a numerical scheme for the evaluation of the 2D PSWFs on a disc, which is the basis for the numerical implementation of the presented quadrature and approximation schemes. Next, we derive a quadrature formula for bandlimited func...

In this paper we generalize the notion of orthogonal Laurent polynomials to orthogonal rational functions. Orthogonality is considered with respect to a measure on the positive real line. From this, Gauss-type quadrature formulas are derived and multipoint Padé approximants for the Stieltjes transform of the measure. Convergence of both the quadrature formula and the multipoint Padé approximant...

We construct a formula for numerical integration of functions over the unit ball in R that uses n Radon projections of these functions and is exact for all algebraic polynomials in R of degree 2n&1. This is the highest algebraic degree of precision that could be achieved by an n term integration rule of this kind. We prove the uniqueness of this quadrature. In particular, we present a quadratur...

This work is devoted to the study of integration with respect to binomial measures. We develop interpolation quadrature rules and study their properties. Applying a local error estimate based on null rules, we test two automatic integrators with local quadrature rules that generalize the five points Newton Cotes formula.

An important problem in geometric compression is to find succinct representations (encoding schemes) for the conectivity of polygonal meshes. In this note, we show that the encoding scheme discussed in [1] for quadrilateral mesh connectivity can be improved from 3.5 bits per vertex to less than 3 bits per vertex. We also show that an easy equivalence between the labelling schemes of King et al ...

This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the W (m,m−1) 2 [0, 1] space for calculating Fourier coefficients. Using S. L. Sobolev’s method we obtain new optimal quadrature formulas of such type for N + 1 ≥ m, where N + 1 is the number of the nodes. Moreover, explicit formulas for the optimal coefficients are obtained. We investigate the...

Zurecht sind die Programme der Gedenkveranstaltungen zum 100. Geburtstag Konrad Zuses gefüllt mit Reden und Vorträgen über seine epochalen Leistungen zur Entwicklung des Digitalrechners, die ihm in den vergangenen Jahrzehnten zwar spät, aber doch noch zu Lebzeiten die Anerkennung als der große Computer-Pionier gebracht haben. Bei diesen hochverdienten Würdigungen wird zumeist vergessen, dass Ko...

where 5 > 0, a is a constant, and F\(p) is analytic and bounded in the half plane Re(j>) > c. We assume that this condition is satisfied. Whether this condition is also sufficient for the convergence of the w-point quadrature formula to the true value of f(t) in (1), when n tends to infinity, has not been determined. The author makes use here of the fact that the convergence occurs whenever F(p...

This paper explores the consequences of creating and improving property rights so that …xed assets can be used as collateral. This has become a cause célèbre of Hernando de Soto whose views are in‡uential in debates about policy reform concerning property rights. Hence, we refer to the economic impact of such reforms as the de Soto e¤ect. We explore the logic of the argument for credit contract...

1 The five BRICS countries are Brazil, Russia, India, China, and South Africa. 2 Ministry of External Affairs of India, “Speech by Foreign Secretary on Building Global Security at the Institute of Peace and Conflict Studies (IPCS) – Konrad Adenauer Stiftung (KAS),” April 16, 2012, http://www.mea.gov.in/Speeches-Statements.htm?dtl/19340/Speech+by+Foreign+Secretary+on+Building+Global+Security+at+...