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Mostrando recursos 1 - 20 de 2.211.314
FIVE Applications of Wilf-Zeilberger Theory to Enumeration and Probability - Moa Apagodu; Doron Zeilberger
In the old days, when one had to find some sequence, a(n), there were two extremes. In the lucky case, one had an explicit formula. For example, the probability of tossing a fair coin 2n times and getting exactly n Heads, equals (2n)!/(2 2n n! 2). Sometimes, cheatingly, one considered as ‘explicit’ expressions in terms of sums (or multisums) or integrals (or multi-integrals). The other extreme was to just have a numerical algorithm, that for each (numeric!) input n, found the output. In that case the algorithm was rated by its efficiency. Another compromise was an asymptotic formula, valid (approximately!)...
Bézout Identities With Inequality Constraints - Wayne M. Lawton; Charles A. Micchelli
This paper examines the set B(P ) = fQ : P \Delta Q = 1 ; Q 2 R m g where P 2 R m is unimodular and R is either the algebra PR of algebraic polynomials which are real--valued on the cube I d or the algebra LR of Laurent polynomials which are real--valued on the torus T d : We sharpen previous results for the case m = 2; d = 1 by showing that if P is non-negative, then there exists a positive Q 2 B(P ) whose length is bounded by a function of the...
Von Neumann algebraic H^P Theory - David P. Blecher; Louis E. Labuschagne
Around 1967, Arveson invented a striking noncommutative generalization of classical H ∞ , known as subdiagonal algebras, which include a wide array of examples of interest to operator theorists. Their theory extends that of the generalized Hp spaces for function algebras from the 1960s, in an extremely remarkable, complete, and literal fashion, but for reasons that are ‘von Neumann algebraic’. Most of the present paper consists of a survey of our work on Arveson’s algebras, and the attendant Hp theory, explaining some of the main ideas in their proofs, and including some improvements and short-cuts. The newest results utilize new...
Linearization of . . . interpolating matrix polynomials - Roel Van Beeumen; Wim Michiels; Karl Meerbergen
This paper considers interpolating matrix polynomials P (λ) in Lagrange and Hermite bases. A classical approach to investigate the polynomial eigenvalue problem P (λ)x = 0 is linearization, by which the polynomial is converted into a larger matrix pencil with the same eigenvalues. Since the current linearizations of degree n Lagrange polynomials consist of matrix pencils with n + 2 blocks, they introduce additional eigenvalues at infinity. Therefore, we introduce new linearizations which overcome this. Initially, we restrict to Lagrange and barycentric Lagrange matrix polynomials and give two new and more compact linearizations, resulting in matrix pencils of n +...
THE SPECTRAL SEQUENCE RELATING ALGEBRAIC K-THEORY TO MOTIVIC COHOMOLOGY - Eric M. Friedlander; Andrei Suslin
The purpose of this paper is to establish in Theorem 2.13 a spectral sequence from the motivic cohomology of a smooth variety X over a field F to the algebraic K-theory of X: E p,q 2 = Hp−q (X, Z(−q)) = CH −q (X, −p − q) ⇒ Kp−q(X). (12.13.1) Such a spectral sequence was conjectured by A. Beilinson [Be] as a natural analogue of the Atiyah-Hirzebruch spectral sequence from the singular cohomology to the topological K-theory of a topological space. The expectation of such a spectral sequence has provided much of the impetus for the development of motivic cohomology...
In search for good Chebyshev lattices - Koen Poppe; Ronald Cools
Recently we introduced a new framework to describe some point sets used for multivariate integration and approximation (Poppe Cools, BIT Numerical Mathematics, 2011), which we called Chebyshev lattices. The associated integration rules are equal weight rules, with corrections for the points on the boundary. In this text we detail the development of exhaustive search algorithms for good Chebyshev lattices where the cost of the rules, i.e., the number of points needed for a certain degree of exactness, is used as criterium. Almost loopless algorithms are considered to avoid dependencies on the rank of the Chebyshev lattice and the dimension. Also,...
A combinatorial auctions perspective on min-sum scheduling problems - Yunpeng Pan
In combinatorial auctions, prospective buyers bid on bundles of items for sale, including but not limited to singleton bundles. The bid price given by a buyer on a particular bundle reflects his/her perceived utility of the bundle of items as a whole. After collecting all the bids, the auctioneer determines the revenue-maximizing assignment of winning bidders to bundles subject to nonoverlapping of bundles. To accomplish this, the auctioneer needs to solve a winner determination problem (WDP). The exactly same way of thinking can be taken to the context of min-sum scheduling, where jobs can be viewed as bidders who bid...
SYNTHESIS OF Two-DIMENSIONAL LOSSLESS m-PORTS WITH PRESCRIBED SCATTERING MATRIX - Anton Kummert
Multidimensional lossless networks are of special interest for use as reference structures for multidimensional wave digital filters -. The starting point of the presented synthesis procedure for two-dimensional representatives of the networks mentioned is a scattering matrix description of the desired multiport. This given matrix is assumed to have those properties which have turned out to be necessary , [ 10] for any scattering matrix of a multidimensional lossless network. The method presented for the synthesis of 2-D reactance m-ports is based mainly on known properties of block-companion matrices and the factorization of a univariable rational matrix which is discrete...
Sensing Lena -- Massively Distributed Compression Of Sensor Images - Sergio D. Servetto
We consider the sensor broadcast problem: in our setup, sensors measure each one pixel of an image that unfolds over a field, and broadcast a rate constrained encoding of their measurements to every other sensor---the goal is for all sensors to form an estimate of the entire image. In recent work, we proposed a protocol that uses wavelets to decorrelate sensor data, taking advantage of the compact support of the basis functions to keep costly inter-sensor communication at a minimum. In this paper, we prove an asymptotic optimality result for these protocols: the rate of growth for the traffic they...
The Wave Digital Reed: A Passive Formulation - Stefan Bilbao, et al.
In this short paper, we address the numerical simulation of the single reed excitation mechanism. In particular, we discuss a formalism for approaching the lumped nonlinearity inherent in such a model using a circuit model and the application of wave digital filters (WDFs), which are of interest in that they allow simple stability verification, a property which is not generally guaranteed if one employs straightforward numerical methods. We present first a standard reed model, then its circuit representation, then finally the associated wave digital network. We then enter into some implementation issues, such as the solution of nonlinear algebraic equations,...
Architectonique des formules préférées d’Alain Lascoux - Piotr Pragacz
This article, written in December 2004, is an expanded version of the author’s lecture opening the LascouxFest at the Séminaire Lotharingien de Combinatoire in Domaine Saint-Jacques, Ottrott, March 29-31, 2004. We discuss here some aspects of the work of Alain Lascoux (and some of his coworkers), related to symmetric functions and, more generally, Schubert polynomials. We illustrate some of the techniques he uses: determinants, transformations of alphabets, reproducing kernels, planar displays, divided differences, and vertex operators. The aim of this article is to show to the reader working in Algebraic Combinatorics (and others!) what we can learn from Alain to...