Computing Fresnel integrals via modified trapezium rules

In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis. Our starting point is a method for computation of the error function of complex argument due to Matta and Reichel (J Math Phys 34:298–307, 1956) and Hunter and Regan (Math Comp 26:539–541, 1972). We construct approximations which we prove are exponentially convergent as a function of N , the number of quadrature points, obtaining explicit error bounds which show that accuracies of 10−15 uniformly on the real line are achieved with N=12 , this confirmed by computations. The approximations we obtain are attractive, additionally, in that they maintain small relative errors for small and large argument, are analytic on the real axis (echoing the analyticity of the Fresnel integrals), and are straightforward to implement.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Polinômios de Szegö e análise de frequência

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Polinômios ortogonais e análise de freqüência

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

A Two-Tiered On-Line Server-Side Bandwidth Reservation Framework for the Real-Time Delivery of Multiple Video Streams

The advent of virtualization and cloud computing technologies necessitates the development of effective mechanisms for the estimation and reservation of resources needed by content providers to deliver large numbers of video-on-demand (VOD) streams through the cloud. Unfortunately, capacity planning for the QoS-constrained delivery of a large number of VOD streams is inherently difficult as VBR encoding schemes exhibit significant bandwidth variability. In this paper, we present a novel resource management scheme to make such allocation decisions using a mixture of per-stream reservations and an aggregate reservation, shared across all streams to accommodate peak demands. The shared reservation provides capacity slack that enables statistical multiplexing of peak rates, while assuring analytically bounded frame-drop probabilities, which can be adjusted by trading off buffer space (and consequently delay) and bandwidth. Our two-tiered bandwidth allocation scheme enables the delivery of any set of streams with less bandwidth (or equivalently with higher link utilization) than state-of-the-art deterministic smoothing approaches. The algorithm underlying our proposed frame-work uses three per-stream parameters and is linear in the number of servers, making it particularly well suited for use in an on-line setting. We present results from extensive trace-driven simulations, which confirm the efficiency of our scheme especially for small buffer sizes and delay bounds, and which underscore the significant realizable bandwidth savings, typically yielding losses that are an order of magnitude or more below our analytically derived bounds.

On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

A Relation between the Weyl Group W(e8) and Eight-Line Arrangements on a Real Projective Plane

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.

On the maximal rate of non-square STBCs from complex orthogonal designs

A Linear Processing Complex Orthogonal Design (LPCOD) is a p x n matrix epsilon, (p >= n) in k complex indeterminates x(1), x(2),..., x(k) such that (i) the entries of epsilon are complex linear combinations of 0, +/- x(i), i = 1,..., k and their conjugates, (ii) epsilon(H)epsilon = D, where epsilon(H) is the Hermitian (conjugate transpose) of epsilon and D is a diagonal matrix with the (i, i)-th diagonal element of the form l(1)((i))vertical bar x(1)vertical bar(2) + l(2)((i))vertical bar x(2)vertical bar(2)+...+ l(k)((i))vertical bar x(k)vertical bar(2) where l(j)((i)), i = 1, 2,..., n, j = 1, 2,...,k are strictly positive real numbers and the condition l(1)((i)) = l(2)((i)) = ... = l(k)((i)), called the equal-weights condition, holds for all values of i. For square designs it is known. that whenever a LPCOD exists without the equal-weights condition satisfied then there exists another LPCOD with identical parameters with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1. This implies that the maximum possible rate for square LPCODs without the equal-weights condition is the same as that or square LPCODs with equal-weights condition. In this paper, this result is extended to a subclass of non-square LPCODs. It is shown that, a set of sufficient conditions is identified such that whenever a non-square (p > n) LPCOD satisfies these sufficient conditions and do not satisfy the equal-weights condition, then there exists another LPCOD with the same parameters n, k and p in the same complex indeterminates with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1.

Studies on the Japanese long-line fishery for tuna and marlin in the Eastern Tropical Pacific Ocean during 1963

ENGLISH: During 1963, the area of operation of the Japanese long-line fishery in the eastern Pacific further expanded, and total fishing effort increased. Charts are presented showing the distribution of effort and of catch-rates, by species, for major fishing areas; and showing catch-rates by species, by quarters of the year, by areas of one-degree of latitude and longitude. In the newly-exploited region north of 10°N, yellowfin and striped marlin are principal elements of the catch, while in the newly-fished region south of the former fishing areas, south of about 20°S, albacore dominate in the catch. Continued decline in catch rates of bigeye tuna, associated with increased fishing effort, indicates that there has been a real decrease in abundance of this species, and that it may have resulted from effects of the fishery on the stock. Changes in catch rates of yellowfin tuna seem to be associated with effects on the stock by both the long-line fishery and by the near-surface fishery by purse-seiners and bait-boats. Over the short series of years for which data are available, there are no discernible trends in apparent abundance of striped marlin or albacore. Information is presented concerning seasonal and geographical distributions of spawning yellowfin tuna, based on examination of gonads. Analysis of data on size composition of yellowfin tuna for 1958-1964 indicates that the long-line fishery is becoming increasingly dependent on the most recently recruited year class, further confirming the effect of the fishery on the stock. The long-line fishery now takes nearly all of its catch of yellowfin tuna from two year-classes each year, during their third and fourth years of life. SPANISH: Durante 1963 el área de operación de la pesca palangrera japonesa en el Pacífico oriental se extendió más y se incrementó el esfuerzo total de pesca. Se presentan cartas indicando la distribución del esfuerzo y las tasas de captura por especies, para las áreas principales de pesca; y se muestran las tasas de captura por especies y por trimestres del año en áreas de un grado de latitud y longitud. En la región recientemente explotada al norte de los 10°N, los principales elementos de la captura son el atún aleta amarilla y el marlín rayado, mientras aproximadamente al sur de los 20°S en la región recientemente pescada al sur de las primeras áreas de pesca la albacora predomina en la captura. La continua merma en las tasas de captura del patudo en asociación con el incremento en el esfuerzo de pesca, indica que ha habido una real reducción en la abundancia de esta especie y que puede ser el resultado de los efectos de la pesquería sobre el stock. Los cambios en las tasas de captura del atún aleta amarilla parecen estar asociados con los efectos sobre el stock tanto de la pesquería palangrera como de la pesca de superficie por barcos rederos y de carnada. No hay tendencias perceptibles en la abundancia aparente del marlín rayado o la albacora en el corto período de años de los que se disponen datos. Se presenta información referente a la distribución estacional y geográfica del desove del atún aleta amarilla basado en el examen de las gónadas. El análisis de los datos sobre la composición de tallas del atún aleta amarilla correspondiente a 1958-1964 indica que la pesca palangrera depende cada vez más de las clases anuales recientemente reclutadas, confirmando aún más el efecto que tiene la pesquería sobre el stock. La pesquería palangrera coge casi toda su pesca de atún aleta amarilla de dos clases anuales cada año, durante su tercer y cuarto año de vida. (PDF contains 70 pages.)

On linear combinations of L-orthogonal polynomials associated with distributions belonging to symmetric classes

This paper deals with the classes S-3(omega, beta, b) of strong distribution functions defined on the interval [beta(2)/b, b], 0 < beta < b <= infinity, where 2 omega epsilon Z. The classification is such that the distribution function psi epsilon S-3(omega, beta, b) has a (reciprocal) symmetry, depending on omega, about the point beta. We consider properties of the L-orthogonal polynomials associated with psi epsilon S-3(omega, beta, b). Through linear combination of these polynomials we relate them to the L-orthogonal polynomials associated with some omega epsilon S-3(1/2, beta, b). (c) 2004 Elsevier B.V. All rights reserved.

Behavior of overhead transmission line parameters on the presence of ground-wires

Initially this paper shows the ground wire reduction process for generic multiphase transmission lines and after, the ground wire reduction process for a specilic 440-kV three-phase overhead transmission line. Following this, the influence of the ground wire reduction process considering two situations is shown: first, considering frequency independence and second, when these parameters are considered as frequency dependent. This paper presents analytical results for generic multiphase transmission lines. For a specific 440-kV three-phase overhead transmission line, analytical and graphic results are shown considering real data for every frequency between 10 Hz and 1 MHz.

Interlacing of zeros of orthogonal polynomials under modification of the measure

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ (x), supported on the interval (a, b) and the other with respect to the measure |x -c|τ|x -d|γdμ (x), where c and d are outside (a, b) We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0 < τ, γ ≤ 1 or γ = 0 and 0 < τ ≤ 2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones. © 2013 Elsevier Inc.