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31
Beppo Levi’s theorem for vector valued McShane integral and applications
 Bull. Belg. Math. Soc
, 1997
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On Multipower Equations: Some Iterative Solutions and Applications
, 1996
"... A generalization of McFarland's iterative scheme [12] for solving quadratic equations in Banach spaces is reported. The notion of a uniformly contractive system is introduced and subsequently employed to investigate the convergence of a new iterative method for approximating solutions to this w ..."
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A generalization of McFarland's iterative scheme [12] for solving quadratic equations in Banach spaces is reported. The notion of a uniformly contractive system is introduced and subsequently employed to investigate the convergence of a new iterative method for approximating solutions to this wider class of multipower equations. Existence and uniqueness of solutions are addressed within the framework of a uniformly contractive system. To illustrate the use of the new iterative scheme, we employ it when approximating solutions to a Hammerstein equation and a Chandrashekar equation. Due to the nature of the examples, we have found that wavelet/scaling function bases are a natural choice for the implementation of our iterative method. AMS(MOS) Subject Classification (1991 Revision): 47H17,46N20,47N20,65J15. Keywords and Phrases: Multipower equation, klinear equation, uniformly contractive system, Hammerstein equations, Chandrashekar equations, wavelets. 1 Introduction We seek the soluti...
Adaptive Wavelet Control of Nonlinear Systems
"... This paper considers the design and analysis of adaptive wavelet control algorithms for uncertain nonlinear dynamical systems. The Lyapunov synthesis approach is used to develop a statefeedback adaptive control scheme based on nonlinearly parametrized wavelet network models. Semiglobal stability r ..."
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This paper considers the design and analysis of adaptive wavelet control algorithms for uncertain nonlinear dynamical systems. The Lyapunov synthesis approach is used to develop a statefeedback adaptive control scheme based on nonlinearly parametrized wavelet network models. Semiglobal stability results are obtained under the key assumption that the system uncertainty satisfies a "matching" condition. The localization properties of adaptive networks are discussed and formal definitions of interference and localization measures are proposed. Keywordswavelets, neural networks, adaptive nonlinear control, Lyapunov stability theory, localization. 1 Introduction The analytical study of adaptive nonlinear control systems involving online approximation structures has evolved considerably during the last five years [1][6]. The design of online approximation based controllers can be broken up into two stages: first, the unknown nonlinearity is represented by some online approximator....
A new exclusion test for finding the global minimum �
, 2006
"... www.elsevier.com/locate/cam Exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain. These algorithms are based on a minimization condition that can be applied to each cell in the domain. ..."
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www.elsevier.com/locate/cam Exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain. These algorithms are based on a minimization condition that can be applied to each cell in the domain. In this paper, we consider Lipschitz functions of order � and give a new minimization condition for the exclusion algorithm. Furthermore, convergence and complexity results are presented for such algorithm.
Monetary Trading: An Optimal Exchange System
, 2002
"... We show that monetary trading is simple, selfenforcing, symmetric, and irreducible in a natural framework. Furthermore, we will show that the utility for each economic agent is at least as big under the monetary system as under any other simple, selfenforcing, symmetric, and irreducible trading sy ..."
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We show that monetary trading is simple, selfenforcing, symmetric, and irreducible in a natural framework. Furthermore, we will show that the utility for each economic agent is at least as big under the monetary system as under any other simple, selfenforcing, symmetric, and irreducible trading system of the same complexity. Thus, we rationalize the monetary nature of realworld trade as being an efficient way to achieve those properties.
On the Utility of Laguerre Series for the Envelope PDF in Multipath Fading Channels
"... Abstract — It is well known that multipath fading significantly affects the performance of communication systems. In order to incorporate the impact of this random phenomenon on system analysis and design, in many cases we need to calculate the probability density function (PDF) of the received sign ..."
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Abstract — It is well known that multipath fading significantly affects the performance of communication systems. In order to incorporate the impact of this random phenomenon on system analysis and design, in many cases we need to calculate the probability density function (PDF) of the received signal envelope in multipath fading channels. In this paper, we consider a general multipath fading channel with arbitrary number of paths, where the amplitudes of multipath components are arbitrary correlated positive random variables, independent of phases, whereas the phases are independent and identically distributed random variables with uniform distributions. Since the integral form of the envelope PDF for such a general channel model is too complicated to be used for analytic calculations, we propose two infinite expansions for the PDF, a Laguerre series and a power series. Based on the tight uniform upper bounds on the truncation error of these two infinite series, we show that the Laguerre series is superior to the power series due to the fact that for a fixed number of terms, it yields a smaller truncation error. This Laguerre series with a finite number of terms, which expresses the envelope PDF just in terms of simple polynomialexponential kernels, is particularly useful for mathematical performance prediction of communication systems in those indoor and outdoor multipath propagation environments, where the number of strong multipath components is small.
BMC Cardiovascular Disorders BioMed Central
, 2005
"... Research article Characteristic wave detection in ECG signal using morphological transform ..."
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Research article Characteristic wave detection in ECG signal using morphological transform
Integre Technical Publishing Co., Inc. American Mathematical Monthly 108:6 February 15, 2001 9:01 a.m. reviews.tex page 573 REVIEWS
"... First and foremost: This book is wonderful. Written as a text for a required course for students who will not take higher mathematics courses, it can also entertain and instruct mathematics majors and mathematicians in general. Here’s a quick run through the table of contents: numbers (pigeonhole pr ..."
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First and foremost: This book is wonderful. Written as a text for a required course for students who will not take higher mathematics courses, it can also entertain and instruct mathematics majors and mathematicians in general. Here’s a quick run through the table of contents: numbers (pigeonhole principle, Fibonacci, primes, modular arithmetic, irrationals, finite and infinite decimals), everything you wanted to know about infinity but didn’t think to ask (Cantor’s cardinals made accessible to all—but, no, they don’t go into inaccessible cardinals!), Geometric Gems (Pythagoras, the art gallery problem, the golden mean, tilings, Platonic solids, nonEuclidean and higherdimensional geometries), nonmetric geometry (“equivalence by distortion”, Möbius and Klein, V − E + F, knots and links, fixed points, and hot loops), chaos and fractals, and finally, Risky Business (probability, including the likelihood of coincidences and statistical pitfalls). At first I didn’t quite pay attention to, or believe the claim of, the title. Living up to it is, after all, a tall order. However, this book does seem to me to capture “the heart of mathematics”, taking “heart ” in the senses of both “essence ” and “spirit”. And by