Cubic interaction term for Schnabl's solution using Pade approximants

We evaluate the cubic interaction term in the action of open bosonic string field theory for Schnabl's solution written in terms of Bernoulli numbers. This computation provides us with new evidence for the fact that the string field equation of motion is satisfied when it is contracted with the solution itself.

Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned

The Q-D algorithm for transforming series expansions into a corresponding continued fraction: an extension to cope with zero coefficients

An algorithm for deriving a continued fraction that corresponds to two series expansions simultaneously, when there are zero coefficients in one or both series, is given. It is based on using the Q-D algorithm to derive the corresponding fraction for two related series, and then transforming it into the required continued fraction. Two examples are given. (C) 2003 Elsevier B.V. All rights reserved.

Padé approximants for the acoustical characteristics of rigid frame porous media

In this paper it is shown that a number of theoretical models of the acoustical properties of rigid frame porous media, especially those involving ratios of Bessel functions of complex argument, can be accurately approximated and greatly simplified by the use of Padé approximation techniques. In the case of the model of Attenborough [J. Acoust. Soc. Am. 81, 93–102 (1987)] rational approximations are produced for the characteristic impedance, propagation constant, dynamic compressibility, and dynamic density, as a function of frequency and the material parameters. The model proposed by Stinson and Champoux

Frações contínuas que correspondem a séries de potências em dois pontos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Pure spinor partition function using Padé approximants

In a recent paper, the partition function (character) of ten-dimensional pure spinor worldsheet variables was calculated explicitly up to the fifth mass-level. In this letter, we propose a novel application of Padé approximants as a tool for computing the character of pure spinors. We get results up to the twelfth mass-level. This work is a first step towards an explicit construction of the complete pure spinor partition function.

Direct and Inverse Results on Row Sequences of Hermite-Pad, Approximants

We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of simultaneous rational interpolants with a bounded number of poles. The conditions are expressed in terms of intrinsic properties of the system of functions used to build the approximants. Exact rates of convergence for these denominators and the simultaneous rational approximants are provided.

Iterative and Pade solutions for the water-wave dispersion relation /

"April 1985."

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

On the concept of optimality interval

The approximants to regular continued fractions constitute `best approximations' to the numbers they converge to in two ways known as of the first and the second kind.This property of continued fractions provides a solution to Gosper's problem of the batting average: if the batting average of a baseball player is 0.334, what is the minimum number of times he has been at bat? In this paper, we tackle somehow the inverse question: given a rational number P/Q, what is the set of all numbers for which P/Q is a `best approximation' of one or the other kind? We prove that inboth cases these `Optimality Sets' are intervals and we give aprecise description of their endpoints.

Recueil de pièces historiques et littéraires.

Contient : 1 Traité d'Arras, entre Charles VII et Philippe le Bon, duc de Bourgogne. 21 septembre 1435 ; 2 Petit mémoire de ce qui fut résolu par Philippe le Bon, duc de Bourgogne, et Charles le Téméraire, comte de Charolais, sur le sort des villes de Dinan et de Liège. 25 août 1466 ; 3 « Ordonnances faictes en l'eschiquier de Normendie tenu à Rouen, au terme de Pasques, l'an 1463 » ; 4 Ratification faite à Paris, le 27 octobre 1465, par LOUIS XI, du traité conclu avec son frère Charles, duc de Guyenne, et autres seigneurs du royaume, qui avaient été cause de la ligue dite du Bien public. Cette ratification est suivie des noms des « trente six personnes ordonnées pour la cause dessus dite », et de la publication de ladite paix ; 5 Sommation faite par PHILIPPE LE BON, duc DE BOURGOGNE, aux Gantois de se remettre sous son obéissance, en acceptant les conditions qu'il leur avait fait proposer. « Donné en nostre host, le mardi XXIIIe jour de fevrier, l'an mil CCCCLIII » ; 6 Lettre de PHILIPPE LE BON, duc DE BOURGOGNE, à Louis XI. 25 juillet 1463 ; 7 Offres des Gantois à Philippe le Bon, « à fin de paix et avoir sa bonne grace ». 30 juillet 1453 ; 8 Version en prose du roman des Sept Sages ; 9 Histoire de Barlaam et Joasaph ; 10 Le Miroir de l'âme ; 11 « La Vie de saint Anthoine de Pade » ; 12 « C'est la complainte des trois estaz de France de la mort du roy Charles dernier passé[Charles VII], avec ses epitaphes » ; 13 « Les Fainctes du monde » ; 14 « Significacions moult notables et beaulx de la messe » ; 15 Arrêt du parlement de Paris, prononcé, le 19 décembre 1475, contre Louis de Luxembourg, comte de Saint-Pol ; 16 L'Échelle de charité ; 17 Trépassement Notre-Dame ; 18 « Incipit compassio beate Marie circa crucem, sicut ab ipsa revelatum fuit beato Augustino » ; 19 Conte dévot en quatrains monorimes d'une « dame... de Boullenoiz et d'un chevalier, qui allèrent en pèlerinage à Saint-Jacques de Galice ; 20 « Exemologesis, seu confessio generalis peccatorum valde pia, cum aliquot devotis orationibus » ; 21 Poésies latines en l'honneur : 1° de la sainte Vierge : a. « Laudes et oratio de beata virgine Maria. Salve, sancta mater Dei, radix vite, robur spei... » (fol. 230-232) ; b. « O miserum, cur valeo, cur non amore langueo... » (fol. 232 v°) ; c. « Oratio ad beatam virginem Mariam. O predulcis creatura, Majestatis scrinium... » (fol. 232 v°-233 v°) ; 2° du saint Sacrement : a. « Laudes et oratio de sacramento altaris. Ave, vivens hostia, veritas et vita... » (fol. 233 v° -234 v° ) ; b. « Oratio ad sacramentum altaris. Ad te suspirat anxius pauperculus inutilis... » (fol. 235) ; 22 Le Jeu des échecs moralisés ; 23 Histoire d'Hérode, de Judas et de Pilate ; 24 « Informacion envoyée par Francisco de Trane » (Traona) au « cardinal d'Avignon », Alain de Coëtivy, sur la prise de Constantinople par les Turcs, en 1453 ; 25 Lettre des Vénitiens au pape Nicolas V, faisant mention de la prise de Constantinople par les Turcs. 30 juin 1453 ; 26 Lettres « envoyées par le Turc à nostre saint père le pape... anno Machometi VIIIC.XL... », à l'occasion de la croisade que l'on faisait publier contre les Turcs. En latin ; 27 Lettres patentes de LOUIS XI, déchargeant les habitants de Rouen de l'impôt de 12 deniers par livre sur les marchandises déclarées, 29 août 1465, avec la vérification par les généraux et conseillers des finances, 14 septembre 1465 ; 28 Articles présentés par les ambassadeurs de Charles VII, roi de France, assemblés à Arras, aux ambassadeurs de Henri VI, roi d'Angleterre, et Philippe le Bon, duc de Bourgogne, pour parvenir à la paix générale, 7 septembre 1435, avec les lettres de pouvoir données par CHARLES VII à ses ambassadeurs, 6 juillet 1435 ; 29 Traité d'Arras. 20 septembre 1435

A new algorithm for OFDM joint data detection and phase noise cancellation

This paper proposes a new iterative algorithm for OFDM joint data detection and phase noise (PHN) cancellation based on minimum mean square prediction error. We particularly highlight the problem of "overfitting" such that the iterative approach may converge to a trivial solution. Although it is essential for this joint approach, the overfitting problem was relatively less studied in existing algorithms. In this paper, specifically, we apply a hard decision procedure at every iterative step to overcome the overfitting. Moreover, compared with existing algorithms, a more accurate Pade approximation is used to represent the phase noise, and finally a more robust and compact fast process based on Givens rotation is proposed to reduce the complexity to a practical level. Numerical simulations are also given to verify the proposed algorithm.

An on-line algorithm of uncertain time delay estimation in a continuous system

In this paper, we present an on-line estimation algorithm for an uncertain time delay in a continuous system based on the observational input-output data, subject to observational noise. The first order Pade approximation is used to approximate the time delay. At each time step, the algorithm combines the well known Kalman filter algorithm and the recursive instrumental variable least squares (RIVLS) algorithm in cascade form. The instrumental variable least squares algorithm is used in order to achieve the consistency of the delay parameter estimate, since an error-in-the-variable model is involved. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.

OFDM joint data detection and phase noise cancellation based on minimum mean square prediction error

This paper proposes a new iterative algorithm for orthogonal frequency division multiplexing (OFDM) joint data detection and phase noise (PHN) cancellation based on minimum mean square prediction error. We particularly highlight the relatively less studied problem of "overfitting" such that the iterative approach may converge to a trivial solution. Specifically, we apply a hard-decision procedure at every iterative step to overcome the overfitting. Moreover, compared with existing algorithms, a more accurate Pade approximation is used to represent the PHN, and finally a more robust and compact fast process based on Givens rotation is proposed to reduce the complexity to a practical level. Numerical Simulations are also given to verify the proposed algorithm. (C) 2008 Elsevier B.V. All rights reserved.