In this letter, the time-domain beam propagation method has been formulated and verified to model ultrashort optical pulse propagation in structures containing material dispersion. The nonparaxial time-domain wave equation was used to march the pulsed beams using Pade approximant technique. The method has been tested using three different Lorentzian dispersive profiles. It has been observed that the new ...

Journal: IEEE Photonics Technology Letters - IEEE PHOTONIC TECHNOL LETT, vol. 24, no. 9, pp. 769-771, 2012]]>In this article, we investigate the thermal decomposition of a stockpile of reactive material undergoing a steady-state exothermic chemical reaction inside a long pipe with heat loss characteristics at its surface. It is assumed that the thermal conductivity (k) of the material varies exponentially with temperature and the pipe surface exchanges heat with the ambient following Newton's law ...

Journal: Journal of Energetic Materials - J ENERG MATER, vol. 30, no. 4, pp. 283-298, 2012]]>This paper is devoted to solve the calculation of two special determinants which appear in the construction of generalized inverse vector Padé approximation (GIVPA). Several algorithms are presented to compute [n/2k]-type of GIVPA. An example is given to illustrate the effectiveness of the method.

Conference: International Conference on Computer Science & Education - ICCSE, 2012]]>This paper studies a design method of time-delay systems with communication disturbance observer (CDOB). A time-delay compensation method based on network disturbance (ND) concept and CDOB has been proposed and applied to various control systems. It compensates time-delay effect without using time-delay model and the effectiveness is equivalent to that of Smith predictor. Furthermore, it works ...

Conference: International Workshop on Advanced Motion Control - AMC, 2012]]>Journal: IEEE Transactions on Magnetics - IEEE TRANS MAGN, vol. 47, no. 5, pp. 1150-1153, 2011]]>

A boundary value method for solving a class of nonlinear singularly perturbed two point boundary value problems with a boundary layer at one end is proposed. Using singular perturbation analysis the method consists of solving two problems; namely, a reduced problem and a boundary layer correction problem. We use Pade’ approximation to obtain the solution of the latter problem and ...

Journal: Communications in Nonlinear Science and Numerical Simulation - COMMUN NONLINEAR SCI NUMER SI, vol. 16, no. 9, pp. 3504-3511, 2011]]>In this study, by means of homotopy perturbation method (HPM) an approximate solution of the magnetohydrodynamic (MHD) boundary layer flow is obtained. The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve. HPM produces analytical expressions for the solution to nonlinear differential equations. The obtained analytic solution ...

Journal: Science China-physics Mechanics & Astronomy - SCI CHINA-PHYS MECH ASTRON, vol. 54, no. 2, pp. 342-345, 2011]]>The combination of any series solutions with the Pade approximants provides a powerful tool for handling initial or boundary value problems on infinite or semi-infinite domains. This study apply an integrated Power series- Pade approximants technique (PS - Pade) to solve a system of nonlinear differential equations arising from the similarity solution for the natural convection of Darcian fluid about ...

Journal: Procedia Engineering, vol. 10, pp. 3749-3757, 2011]]>It is "well known" that the interlaced zeros and poles of Pad´ e approximants describe the position of cuts of considered function f. More, the Pade approximants choose automat- icaly this position, "in principal" in the direction joining the point of developpement of f and its ramification point. The "well known" property was studied by J.S.R.Chisholm and ...

Published in 2011]]>Suppose we are given a time series or a signal $x(t)$ for $0\leq t\leq T$. We consider the problem of predicting the signal in the interval $T<t\leq T+t_{f}$ from a knowledge of its history and nothing more. We ask the following question: what is the largest value of $t_{f}$ for which a ...

Published in 2011]]>The question of whether the known virial coefficients are enough to determine the packing fraction &eegr;∞ at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Pade´ approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is ...

Published in 2011]]>The time-domain beam propagation method (TD-BPM) has been implemented and analyzed using several iterative numerical techniques to model the propagation of ultra short pulses in optical structures. The methods depend on one-way non-paraxial time domain propagation that use Pade approximant formulation. Several numerical tests showed that the iterative TD-BPM techniques are very stable and converge ...

Journal: IEEE/OSA Journal of Lightwave Technology - J LIGHTWAVE TECHNOL, vol. 29, no. 16, pp. 2475-2481, 2011]]>In this paper, we construct the exact solution for fluid motion caused by the uniform expansion of a cylindrical or spherical piston into still air. Following Lighthill [1], we introduce velocity potential into the analysis and seek a similarity form of the solution. We find both numerical and analytic solutions of the second order nonlinear differential equation, with the boundary ...

Journal: Applied Mathematical Modelling - APPL MATH MODEL, vol. 35, no. 7, pp. 3434-3442, 2011]]>We consider the two-dimensional problem of steady natural convection in a circular cavity with constant volumetric heat flux filled with viscous fluid subject to constant temperature variation on the boundary. The solution is expanded for low Rayleigh number and extended to 16 terms by computer. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50 ...

Published in 2011]]>In this paper, we develop a nonlinear controller to achieve trajectory tracking for a velocity-sensorless vertical take-off and landing (VTOL) aircraft with measurement delays. By applying Pade approximation technique, the original controlled system is approximately transformed into an augmented dimension system without any time delay. After constructing full-order observer, error coordinate transformation, and system decomposition, the tracking ...

Conference: Conference on Decision and Control - CDC, pp. 2499-2504, 2011]]>A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a Pade approximant for approximating accurately a given divergent series. Such series are obtained by summing the partial contribution to the solution coming from trees with arbitrary number of ...

Journal: Journal of Computational Physics - J COMPUT PHYS, vol. 230, no. 21, pp. 7891-7909, 2011]]>The paper addresses numerical time-domain methods for modeling of active and passive dispersive media, needed for simulations of plasmonic metamaterials. The proposed algorithms differ from published results, as our models employ more general formalisms and are more computationally efficient. The frequency dispersion of the permittivity is considered as an arbitrary Pade approximant, its numerical implementation is more universal and ...

Published in 2011]]>In the large eddy simulation (LES) framework for modeling a turbulent flow, when the large scale velocity field is defined by low-pass filtering the full velocity field, a Taylor series expansion of the full velocity field in terms of the large scale velocity field leads (at the leading order) to the nonlinear gradient model for the subfilter stresses. Motivated ...

Journal: Physics of Fluids - PHYS FLUIDS, vol. 23, 2011]]>This paper deals with the design of an Hí-based decentralized power system stabilizer (PSS) controller, which uses selected suitable wide area PMU signals as supplementary inputs to achieve a better damping of specific inter-area modes. The wide area or global signals are taken from network locations where the oscillations are well observable, and the PSS controller uses only...

Published in 2011]]>Extending a Pade approximant method used recently to study the properties of compactons in the Rosenau-Hyman (RH) equation [see B. Mihaila et al. Phys. Rev. E 81, 056708 (2010)], we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS equation has a conserved Hamiltonian which has allowed several ...

Published in 2011]]>In the present paper, we have analysed the pressure dependences of thermal expansivity (α p ) and isothermal compressibility (K T ) for the liquid hexane and chloroform. We have used the formulae based on the pseudospinodal model and the Sanchez et al [1,2] equation of state obtained from the Pade approximation. The thermal expansion coefficient and isothermal compressibility follow a ...

Journal: Indian Journal of Physics - INDIAN J PHYS, vol. 85, no. 3, pp. 421-431, 2011]]>We compare the theoretical predictions for universal thermodynamics of a homogeneous, strongly correlated Fermi gas with the latest experimental measurements reported by the ENS group [S. Nascimbene et al., Nature (London) 463, 1057 (2010)] and the Tokyo group [M. Horikoshi et al., Science 327, 442 (2010)]. The theoretical results are obtained using two diagrammatic theories, together with a virial expansion ...

Journal: Physical Review A - PHYS REV A, vol. 83, no. 6, pp. 063610-063610, 2011]]>The unpolarized longitudinal nucleon structure function FL, measured in the deep inelastic lepton-nucleon scattering, is contained of three parts, singlet, non-singlet and gluon. The aim of this paper is to perform a QCD analysis of the longitudinal heavy and light structure functions FL(x, Q2) in the non-singlet part up to O(alpha s3). We use the ...

Journal: International Journal of Modern Physics A - IJMPA, vol. 26, pp. 686-687, 2011]]>The theory of flute waves (with arbitrary spatial scales compared to the ion Larmor radius) driven by the Rayleigh–Taylor instability (RTI) is developed. Both the kinetic and hydrodynamic models are considered. In this way we have extended the previous analysis of RTI carried out in the long wavelength limit. It is found that complete finite ion Larmor radius stabilization ...

Published in 2011]]>The periodic Green's function in layered media can be expressed as an infinite series in terms of the spectral domain Green's function which can be approximated by complex exponentials through the use of Discrete Complex Image Method (DCIM). During the application of the DCIM, two-level or three- level approximation schemes can be employed. In this work, the ...

Published in 2011]]>Existing fast frequency sweep techniques involve approximations, the application of which is limited to either a finite band width or lossless problems. A new fast frequency sweep algorithm is proposed in this work. This algorithm has no limitation in effective bandwidth. In addition, it is applicable to general electromagnetic problems that involve both lossless and lossy inhomogeneous materials and arbitrarily ...

Conference: Antennas and Propagation Society International Symposium - APSURSI, pp. 2468-2471, 2011]]>Existing fast frequency sweep methods have difficulties in controlling the accuracy and determining the effective bandwidth. In this work, based on the physical understanding of the eigenvalue distribution in integrated circuits, a fast frequency sweep algorithm is developed. In this algorithm, the error and effective bandwidth can be quantitatively analyzed and controlled. Accurate electromagnetic simulation is becoming essential as integrated ...

Conference: Antennas and Propagation Society International Symposium - APSURSI, pp. 2476-2479, 2011]]>This paper explores a new numerical strategy for a closed formulation of iterative splitting methods and their embedding in classical waveform-relaxation methods. Since iterative splitting has been developed in several papers, an abstract framework that relates these methods to other classical splitting methods would be useful and is needed. Here, we present an embedding of the iterative splitting method ...

Journal: International Journal of Computer Mathematics - IJCM, vol. ahead-of-p, no. ahead-of-p, pp. 1-20, 2011]]>We set up a new, flexible approach for the tensor reduction of one-loop Feynman integrals. The 5-point tensor integrals up to rank R=5 are expressed by 4-point tensor integrals of rank R-1, such that the appearance of the inverse 5-point Gram determinant is avoided. The 4-point tensor coefficients are represented in terms of ...

Journal: Physical Review D - PHYS REV D, vol. 83, no. 7, pp. 073004-073004, 2011]]>Let f be a germ of an analytic function at infinity that can be analytically continued along any path in the complex plane deprived of a finite set of points, f \in\mathcal{A}(\bar{\C} \setminus A), \sharp A <\infty. J. Nuttall has put forward the important relation between the maximal domain of f where the function has ...

Published in 2011]]>We derive from statistical mechanics the Gibbs free energy of an elastic random-walk chain affected by the presence of an external electric field. Intrachain charge interactions are ignored. In addition, we find two approximations of the Helmholtz potential for this system analogous to the Gaussian and Cohen–Pade´ approximations for an elastic strand without the presence of an electric ...

Published in 2011]]>For unsteady-state diffusion, adsorption and a first-order reaction in a slab, cylinder and sphere catalyst, high-order approximations are developed. A continued fraction is developed as a function of the shape factor and the Thiele modulus in Laplace domain to unify the exact transfer functions of the three catalyst geometries. Inversion of the continued fraction to the time ...

Published in 2011]]>Wide area signals have been suggested to enhance the dynamic performance of large interconnected power systems. Time delays introduced by remote signal transmission and processing may cause stability problems and cannot be neglected in system operation. Pade approximation method is adopted to express the system model with input time delay. Then a phase compensator is proposed for SVC supplementary control ...

Journal: International Journal of Electrical Power & Energy Systems - INT J ELEC POWER ENERG SYST, vol. 32, no. 3, pp. 163-169, 2010]]>K. Mahler introduced the concept of perfect systems in the general theory he developed for the simultaneous Hermite-Pade approximation of analytic functions. We prove that Nikishin systems are perfect providing, by far, the largest class of systems of functions for which this important property holds. As consequences, in the context of Nikishin systems, we obtain: an extension of Markov'...

Published in 2010]]>In this paper, the Emden-Fowler equations are investigated by employing the Adomian decomposition method (ADM) and the Padé approximant. By using the new type of Adomian polynomials proposed by Randolph C. Rach in 2008, our obtained solution series converges much faster than the regular ADM solution of the same order. Meanwhile, we note that the solutions obtained by using...

Journal: Modern Physics Letters B - MOD PHYS LETT B, vol. 24, no. 12, pp. 1237-1254, 2010]]>This study is devoted to investigate the inherent irreversibility and thermal stability in a reactive electrically conducting fluid flowing steadily through a channel with isothermal walls under the influence of a transversely imposed magnetic field. Using a perturbation method coupled with a special type of Hermite-Pade’ approximation technique, the simplified governing non-linear equation is solved and the important ...

Journal: Journal of Thermal Science - J THERM SCI, vol. 19, no. 1, pp. 72-79, 2010]]>It is possible to generalize the fruitful interaction between (real or complex) Jacobi matrices, orthogonal polynomials and Pade approximants at infinity by considering rational interpolants, (bi-)orthogonal rational functions and linear pencils zB-A of two tridiagonal matrices A, B, following Spiridonov and Zhedanov. In the present paper, beside revisiting the underlying generalized Favard theorem, we suggest a new criterion ...

Journal: Journal of Approximation Theory - JAT, vol. 162, no. 6, pp. 1322-1346, 2010]]>The use of Pade approximants for the description of QCD matrix elements is discussed in this talk. We will see how they prove to be an extremely useful tool, specially in the case of resonant amplitudes. It will allow the inclusion of high-energy Euclidian data to improve the determination of low-energy properties, such as the quadratic vector radius. ...

Published in 2010]]>Journal: Applied Radiation and Isotopes - APPL RADIAT ISOTOPES, vol. 68, no. 6, pp. 1177-1179, 2010]]>

A new methodology is proposed in this paper, it is based on Adomian-Pade method and it is used to characterize power system Oscillations. The differential equations of the system are solved using Adomian method and the oscillation characteristics are obtained by applying Pade approximation on this solution. The developed methodology is applied on a single machine - infinite bus system ...

Conference: IEEE/IAS International Conference on Industry Applications - INDUSCON, 2010]]>In this paper we review fourth-order approximations of the biharmonic operator in one, two and three dimensions. In addition, we describe recent developments on second and fourth order finite difference approximations of the two dimensional Navier-Stokes equations. The schemes are compact both for the biharmonic and the Laplacian operators. For the convective term the fourth order scheme invokes ...

Journal: Journal of Scientific Computing, vol. 45, no. 1-3, pp. 238-258, 2010]]>We present a joint theoretical-experimental study on electron scattering by propane (CH) in the low- and intermediate-energy ranges. Calculated elastic differential, integral, and momentum transfer as well as total (elastic + inelastic) and total absorption cross sections are reported for impact energies ranging from 2 to 500 eV. Also, experimental absolute elastic cross sections are reported in the ...

Journal: Physical Review A - PHYS REV A, vol. 82, no. 1, pp. 012709-012709, 2010]]>Journal: Journal of Algorithms & Computational Technology, vol. 4, no. 1, pp. 15-24, 2010]]>

In this work we give an interpretation of a (s(d + 1) + 1)-term recur- rence relation in terms of type II multiple orthogonal polynomials. We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector polynomials with matrix coefficients. We present amatrix interpretation of the type II multi-ortogonality conditions. ...

Journal: Numerical Algorithms, vol. 55, no. 1, pp. 19-37, 2010]]>Disturbance attenuation for a class of time-delay systems is performed by a combined simple adaptive control (SAC) with a new configuration of disturbance observer (DOB). The nominal system results from the Pade approximation, which is in the form of a non-minimum phase LTI system. For the implementation of SAC and DOB, two parallel feedforward compensators (PFC) are designed ...

Published in 2010]]>A Routh-Pade approximation method is presented for obtaining stable reduced order model of 2-D non-separable-denominator discrete-time system. The proposed method preserves initial power-series-expansion-coefficients/Markov-parameters of the system as well as minimizes the errors between a set of subsequent power-series-expansion-coefficients and/or Markov-parameters of the 2-D system ...

Conference: International Conference on Computer and Automation Engineering - ICCAE, 2010]]>Two widely used methods for computing matrix exponentials and matrix logarithms are, respectively, the scaling and squaring and the inverse scaling and squaring. Both methods become effective when combined with Padé approximation. This paper deals with the computation of exponentials of skew-symmetric matrices and logarithms of orthogonal matrices. Our main goal is to improve these two methods by exploiting...

Journal: Journal of Computational and Applied Mathematics - J COMPUT APPL MATH, vol. 233, pp. 2867-2875, 2010]]>Extending a Pade approximant method used for studying compactons in the Rosenau-Hyman (RH) equation, we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS equation has a conserved Hamiltonian which has allowed various approaches for studying analytically the nonlinear stability of the solutions. We study three different compacton ...

Journal: Physical Review E - PHYS REV E, vol. 82, no. 6, pp. 066702-066702, 2010]]>Using a recently presented numerical code for calculating the Lorenz-gauge gravitational self-force (GSF), we compute the O(m) conservative correction to the precession rate of the small-eccentricity orbits of a particle of mass m moving around a Schwarzschild black hole of mass M>>m. Specifically, we study the gauge-invariant function (x), where is defined ...

Journal: Physical Review D - PHYS REV D, vol. 82, no. 8, pp. 084036-084036, 2010]]>We analyze the emission spectrum of a single organic quantum dot coupled to a microcavity in the strong coupling regime. We take into account non-linearities arising from both exciton–exciton interactions and the Pauli exclusion principle. We apply the recently developed Pade approximation for regular truncation of Green functions to calculate the emission spectrum. We show that as the ...

Journal: Superlattices and Microstructures - SUPERLATTICE MICROSTRUCT, vol. 47, no. 1, pp. 139-144, 2010]]>Leaky modes in very deeply etched semiconductor ridge waveguides have been analyzed by the compact 2-D finite-difference time-domain method combined with the uniaxial anisotropic perfectly matched layer absorption boundary condition and the Pade?? approximation transform technique. Results show that instead of continuously dropping, the loss of these leaky modes tends to saturate when the etching depth under ...

Journal: IEEE Photonics Technology Letters - IEEE PHOTONIC TECHNOL LETT, vol. 22, no. 6, pp. 407-409, 2010]]>The paper considers Hermite-Pade approximants to systems of Markov functions defined by means of directed graphs. The minimization problem for the energy functional is investigated for a vector measure whose components are related by a given interaction matrix and supported in some fixed system of intervals. The weak asymptotics of the approximants are obtained in terms of the solution ...

Journal: Sbornik Mathematics - SB MATH, vol. 201, no. 2, pp. 183-234, 2010]]>This study is devoted to investigate the inherent irreversibility and thermal stability in a reactive electrically conducting fluid flowing steadily through a channel with isothermal walls under the influence of a transversely imposed magnetic field. Using a perturbation method coupled with a special type of Hermite-Pade' approximation technique, the simplified governing non-linear equation is solved and the important ...

Journal: Journal of Thermal Science - J THERM SCI, vol. 19, pp. 72-79, 2010]]>We present the results of our QCD analysis for nonsinglet unpolarized quark distributions and structure function Fâ(x,QÂ²) up to next-to-next-to-next-to leading order (NÂ³LO). In this regards 4-loop anomalous dimension can be obtained from the Pade approximations. The analysis is based on the Jacobi polynomials expansion of the structure function. New parameterizations a...

Journal: Physical Review D - PHYS REV D, vol. 81, no. 1, pp. 014013-014013, 2010]]>In order to evaluate the energy transfer between Eu-Mn in Ba0.75Al11O17.25-BaMgAl10O17 solid solution, Ba0.75Al11O17.25-BaMgAl10O17:Eu2+,Mn2+ phosphors were prepared by flux method. The crystal structure and the morphology of the solid solution were demonstrated by x-ray dirrfactometer and scanning electron microscopy. The photoluminescence mechanisms were explained by the energy transfer of Eu2+ ...

Journal: Journal of Applied Physics - J APPL PHYS, vol. 108, 2010]]>In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a ...

Published in 2010]]>The method of analytic continuation in the coupling constant in combination with use of the statistical Pade approximation is applied to the determination of resonance energy and width of the ²{sub g} state of N. It is shown that standard quantum chemistry codes provide accurate data which can be used for analytic continuation in the coupling constant, and the ...

Journal: Physical Review A - PHYS REV A, vol. 82, no. 3, pp. 032713-032713, 2010]]>By using the high-temperature series expansion technique, we have analyzed the phase transition and the critical phenomena of a ferromagnetic thin film and ferromagnetic semi-infinite film, through three models: Ising, XY and Heisenberg. The critical reduced temperature tauC(v) is studied as a function of the thickness of the film. In the case of the magnetic film and ...

Journal: International Journal of Modern Physics B - IJMPB, vol. 24, no. 18, pp. 3561-3596, 2010]]>The ferrimagnetic spinels systems CoxFe1-x Cr2S4 has been studied by high-temperature series expansions method in the range 0 <=x <=1. The exchange interactions and exchange energies are calculated by using the probability law. The high-temperature series expansions have been applied in the spinels systems CoxFe1-xCr2S4, combined with the Padé approximants method, to determine the...

Journal: International Journal of Modern Physics B - IJMPB, vol. 24, pp. 6157-6163, 2010]]>Chemical potential and internal energy of a noninteracting Fermi gas at low temperature are evaluated using the Sommerfeld method in the fractional-dimensional space. When temperature increases, the chemical potential decreases below the Fermi energy for any dimension equal to 2 and above due to the small entropy, while it increases above the Fermi energy for dimensions below 2 as ...

Journal: Pramana-journal of Physics - PRAMANA-J PHYS, vol. 75, no. 3, pp. 393-402, 2010]]>We use Pade approximants to study numerically the stability and dynamical properties of K(2,2) Rosenau-Hyman compactons. We present a systematic derivation of Pade approximants for calculating the derivatives of smooth functions on an uniform grid and we illustrate our finding by improving upon traditional fourth-order finite-differences formulas. This study is intended as a stepping block ...

Published in 2010]]>In scale invariant hydrostatic barotropes, the radial evolutionary equation linearly relates the local gravitational and internal energies. From this first-order equation, directly follow all the properties of polytropes and the important mass-radius relation. Quadrature then leads to the regular Lane-Emden functions and their Picard and Pade approximations, which are useful wherever stars are approximately or exactly polytropic. ...

Published in 2010]]>This paper investigates existence of the nonstandard Pade approximants introduced by Cherkaev and Zhang in J. Comp. Phys. 2009 for approximating the spectral function of composites from effective properties at different frequencies. The spectral functions contain microstructure information. Since this reconstruction problem is ill-posed [9], the well-performed Pade approach is noteworthy and requires further investigations. In this paper, ...

Published in 2010]]>In this article, we examine the methodology for extracting the Knudsen number (K) and the ratio of shear viscosity to entropy density (/s) developed by Drescher et al. [1]. The final result for /s turns out to be quite sensitive to Glauber parameters, particularly the parameter x, which controls the balance between N{sub part} and N{sub coll}. We ...

Journal: Physical Review C - PHYS REV C, vol. 81, no. 2, pp. 024901-10, 2010]]>This paper investigates existence of the nonstandard Pade approximants introduced by Cherkaev and Zhang in J. Comp. Phys. 2009 for approximating the spectral function of composites from effective properties at different frequencies. The spectral functions contain microstructure information. Since this reconstruction problem is ill-posed [9], the well-performed Pade approach is noteworthy and requires further investigations. In this paper, ...

Published in 2010]]>We present a new approach to exponential functions on time scales and to timescale analogues of ordinary differential equations. We describe in detail the Cayley-exponential function and associated trigonometric and hyperbolic functions. We show that the Cayley-exponential is related to implicit midpoint and trapezoidal rules, similarly as delta and nabla exponential functions are related to Euler numerical schemes. ...

Published in 2010]]>This work re-examines the potential flow theory for a sphere in normal approach to a wall, based on the classical results derived by Lamb [Hydrodynamics (Dover, New York, 1932)] and Milne-Thomson [Theoretical Hydrodynamics, 5th ed. (Dover, New York, 1968)]. These authors generated an expression in which the kinetic energy for a sphere in an unbounded fluid is augmented ...

Published in 2010]]>Quantum Chromodynamics is the fundamental theory of the interactions of quarks and gluons which underlies, among other things, Nuclear Physics. Mathematically, this is a gauge theory based on the "color" quantum number, Nc, following the structure of the SU(Nc) Lie group. Although in the real world Nc = 3, ever since the pioneering work of Ref. (1), it has been ...

Published in 2010]]>The theory of the magnetic Rayleigh-Taylor instability (RTI) is discussed. Modified linear kinetic theory allows us to investigate RTI and flute waves with arbitrary perpendicular spatial scales compared to the ion Larmor radius. It is shown that in the linear limit a Fourier transform of these equations yields the dispersion relation which in the so-called Pade´ approximation corresponds ...

Published in 2010]]>The purpose of this study is to implement Adomian–Pade (Modified Adomian–Pade) technique, which is a combination of Adomian decomposition method (Modified Adomian decomposition method) and Pade approximation, for solving linear and nonlinear systems of Volterra functional equations. The results obtained by using Adomian–Pade (Modified Adomian–Pade) technique, are compared to those obtained by using Adomian decomposition method (...

Journal: Chaos Solitons & Fractals - CHAOS SOLITON FRACTAL, vol. 39, no. 5, pp. 2509-2521, 2009]]>In this paper, we apply the variational iteration method using He’s polynomials for finding the analytical solution of unsteady flow of gas through a porous medium. The proposed method is an elegant combination of He’s variational iteration and the homotopy perturbation methods. The suggested algorithm is quite efficient and is practically well suited for use in such problems. The proposed ...

Journal: Computers & Mathematics With Applications - COMPUT MATH APPL, vol. 58, no. 11-12, pp. 2182-2189, 2009]]>The arithmetical nature of Euler's constant ∞ is still unknown and even getting good rational approximations to it is di-cult. Recently, Aptekarev managed to flnd a third order linear recurrence with polynomial coe-cients which admits two rational solutions an and bn such that an=bn converges sub-exponentially to ∞, viewed as ¡¡0(1), where ¡ is ...

Journal: Transactions of The American Mathematical Society - TRANS AMER MATH SOC, vol. 361, no. 11, pp. 6115-6149, 2009]]>We present a simple analytical description of transient vibrations of forced anharmonic oscillator in terms of periodic non-smooth functions. Such a description (in chosen variables) is similar to that of a vibro-impact process. The main attention is paid to properties of the limiting phase trajectories (LPTs) describing intensive energy exchange between the oscillator and external force. We show ...

Journal: Nonlinear Dynamics, vol. 58, no. 4, pp. 633-642, 2009]]>We present the end-to-end performance of dual-hop wireless communication systems with non-regenerative fixed gain relays operating over independent not necessarily identically generalized-K (KG) fading channels. New closed-form expressions are derived for the moments of the end-to-end signal-to-noise ratio (SNR), while the corresponding moment- generating function (MGF) is accurately approximated with ...

Conference: IEEE International Conference on Communications - ICC, pp. 1-5, 2009]]>This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy ...

Journal: Applied Mathematics and Mechanics-english Edition - APPL MATH MECH-ENGL ED, vol. 30, no. 3, pp. 373-380, 2009]]>The [4/3] Pade approximant for the derivative is modified so that the resulting expression has the required asymptotic behavior. This gives an analytical result which represents the solution of the classical Blasius problem on the whole domain.

Journal: Communications in Nonlinear Science and Numerical Simulation - COMMUN NONLINEAR SCI NUMER SI, vol. 14, no. 4, pp. 1021-1024, 2009]]>The reflection and dispersion characteristics of multilayer structures that involve periodically implanted material blocks are obtained by using the MoM solution of the volume integral equation. The asymptotic waveform evaluation (AWE) technique is utilized to obtain a Pade approximation of the solution in terms of a parameter such as frequency or incident angle. The use of AWE technique enables a ...

Journal: IEEE Transactions on Antennas and Propagation - IEEE TRANS ANTENNAS PROPAGAT, vol. 57, no. 9, pp. 2641-2649, 2009]]>This paper presents expressions for the limiting value of the duty cycle and the minimum value of the slope compensation for marginally stable operation as well as for the normalized crossover frequency, the maximum duty cycle, and the value of the slope compensation at a required phase margin. These quantities describe the performance of the inner-current loop in peak ...

Conference: IEEE International Symposium on Circuits and Systems - ISCAS, 2009]]>This paper is devoted to the numerical comparison of methods applied to solve an integro-differential equation. Four numerical methods are compared, namely, the Laplace decomposition method (LDM), the Wavelet–Galerkin method (WGM), the Laplace decomposition method with the Pade approximant (LD–PA) and the homotopy perturbation method (HPM).

Journal: Computers & Mathematics With Applications - COMPUT MATH APPL, vol. 57, no. 9, pp. 1485-1493, 2009]]>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 ...

Journal: Signal Processing, vol. 89, no. 4, pp. 502-509, 2009]]>In this paper, a novel analytical method (DTM-Pade) is proposed for solving nonlinear differential equations, especially for boundary-layer and natural convection problems. This method is based on combination of the differential transform method and the Pade approximant that we use for solve the thermal boundary-layer over a flat plate with a convective surface boundary condition. This technique ...

Conference: International Conference on Signal Processing Systems - ICSPS, 2009]]>First, an abstract scheme of constructing biorthogonal rational systems related to some interpolation problems is proposed. We also present a modification of the famous step-by-step process of solving the Nevanlinna- Pick problems for Nevanlinna functions. The process in question gives rise to three-term recurrence relations with coefficients depending on the spectral parameter. These relations can be rewritten ...

Journal: Journal of Approximation Theory - JAT, vol. 157, no. 1, pp. 70-88, 2009]]>In this paper, the homotopy perturbation method (HPM) and the Padé approximation are employed to investigate the magneto-hydrodynamic (MHD) boundary layer flow over a nonlinear stretching sheet, which occurs in many important engineering applications, such as the power generator, the cooling of reactors and the design of heat exchangers. The validity of results is verified by comparison with exact...

Journal: Modern Physics Letters B - MOD PHYS LETT B, vol. 23, no. 20 & 21, pp. 2541-2556, 2009]]>The purpose of this study is to implement a new analytical method (DTM-Pade technique which is a combination of the differential transform method and the Pade approximant) for solving magnetohydrodynamic boundary-layer flow. We will show that the DTM solutions only valid for small values of independent variable, therefore the DTM not applicable for solving MHD boundary-layer equations. ...

Conference: International Conference on Signal Processing Systems - ICSPS, 2009]]>A fully linearizable single-input-single-output relative-degree n system with an output time delay is considered in this paper. Using the approach of Pade approximation, system center approach, and second-order sliding-mode (SM) control, we have obtained good output tracking results. The Smith predictor is used to compensate the difference between the actual delayed output and its ...

Journal: IEEE Transactions on Industrial Electronics - IEEE TRANS IND ELECTRON, vol. 56, no. 9, pp. 3638-3645, 2009]]>In this paper we approach the design of a class of 2D recursive filters, with an orientation-selective frequency response. We propose an analytical design method based on a given 1D digital prototype filter and a complex frequency transformation which is separable and is determined using Pade or Chebyshev-Pade approximations and the bilinear transform. We also present separately a ...

Published in 2009]]>An alternating direction implicit (ADI), scheme for the wide-angle finite-difference beam propagation method (FD-BPM) based on the wide angled Pade multistep method is presented. The scheme incorporates an iterative technique for correction of the operator splitting error. The resulting equations are efficiently solved by the Thomas algorithm for tri-diagonal band matrices. The dispersion characteristics, accuracy and ...

Journal: IEEE/OSA Journal of Lightwave Technology - J LIGHTWAVE TECHNOL, vol. 27, no. 14, pp. 2595-2604, 2009]]>We construct bivariate polynomial approximations of the Lerch function, which for certain specialisations of the variables and parameters turn out to be Hermite- Pade approximants either of the polylogarithms or of Hurwitz zeta functions. In the former case, we recover known results, while in the latter the results are new and generalise some recent works of Beukers and Prevost. Finally, ...

Journal: Canadian Journal of Mathematics-journal Canadien De Mathematiques - CAN J MATH, vol. 61, no. 6, 2009]]>A class of special solutions of Painleve/Garnier systems arising as the Backlund or Schlesinger transformations of the Riccati solutions is known. In the past several years, the corresponding ¿-functions have been explicitly computed and expressed as certain specialization of the Schur func- tions with rectangle shape partitions. In this note, we will give a simple and direct derivation ...

Journal: Funkcialaj Ekvacioj-serio Internacia - FUNKC EKVACIOJ-SER INT, vol. 52, no. 1, pp. 83-92, 2009]]>A recently observed connection between some Pade approximants for the exponen- tial series and the convergents of the simple continued fraction for e is established, leading to an alternative proof of the latter. Similar results for the simple continued fraction e2,e1/M and e2/M,

Journal: Ramanujan Journal - RAMANUJAN J, vol. 19, no. 1, pp. 95-105, 2009]]>For every odd integer N we give an explicit construction of a polynomial curve C(t) = (x(t), y(t)), where deg x = 3, deg y = N + 1 + 2 � N4 � that has exactly N crossing points C(ti) = C(si) whose parameters satisfy s1 < ··· < sN < t1 < ··· < tN. Our proof makes use ...

Journal: Applicable Algebra in Engineering, Communication and Computing - AAECC, vol. 20, no. 5-6, pp. 361-377, 2009]]>We use a version of the Fair-Luke algorithm to find the Padé approximate solutions of the Painlevé I and II equations. We find the distributions of poles for the well-known Ablowitz-Segur and Hastings-McLeod solutions of the Painlevé II equation. We show that the Boutroux tritronquée solution of the Painleé I equation has poles only in...

Journal: Theoretical and Mathematical Physics - THEOR MATH PHYS-ENGL TR, vol. 159, no. 3, pp. 853-862, 2009]]>The purpose of this paper is to give sharp error estimates for reg- ularized versions of A-stable rational approximations of C-regularized semi- groups such as the Backward Euler and Crank-Nicolson scheme among oth- ers. The main tools used are those developed by P. Brenner and V. Thomee for strongly continuous semigroups together with a regularized version of ...

Journal: Proceedings of The American Mathematical Society - PROC AMER MATH SOC, vol. 137, no. 11, pp. 3885-3885, 2009]]>The main goal of this paper is to propose a methodology to determine the minimum number of measurement points in an indoor environment for a 2.4 GHz Wireless Local Area Network (WLAN) project. For validate this methodology, measurement campaigns was accomplished in two buildings (indoor environments), using an access point as signal transmitter, and a notebook computer as receiver, ...

Conference: Microwave and Optoelectronics SBMO/IEEE MTT-S International Conference - IMOC, pp. 330-334, 2009]]>The design of PID controller for unstable processes is always difficult due to instability and non-minimum phase. The design procedures for unstable processes involve compensation of unstable zeros or poles. In most of the cases PID controllers are used to control the stable processes, however less common for unstable processes. In this paper, a simple controller design rule and ...

Conference: International Conference on Advances in Computing, Control, & Telecommunication Technologies - ACT, 2009]]>The use of Pade Approximants for the analysis of the pion vector form-factor is discussed and justified in this talk. The method is tested first in a theoretical model and applied then on real experimental data. It is shown how the Pade Approximants provide a convenient and reliable framework to incorporate both low and high energy information in the ...

Journal: Nuclear Physics B-proceedings Supplements - NUCL PHYS B-PROC SUPPL, vol. 186, pp. 157-160, 2009]]>Resonance Saturation in QCD can be understood in the large-Nc limit from the mathematical theory of Pade Approximants to meromorphic functions.

Journal: Nuclear Physics B-proceedings Supplements - NUCL PHYS B-PROC SUPPL, vol. 186, pp. 149-152, 2009]]>We use the Linear Sigma Model to test the convergence of different sequences of Pade Approximants when used to unitarize the low energy pi-pi scattering amplitude. We find that, in this particular case, diagonal sequences reproduce the sigma pole with high accuracy, as opposed to other sequences that have been discussed extensively.

Journal: Nuclear Physics B-proceedings Supplements - NUCL PHYS B-PROC SUPPL, vol. 186, pp. 161-164, 2009]]>Diagonal Pade approximants of elliptic functions are studied. It is known that the absence of uniform convergence of such approximants is related to them having spurious poles that do not correspond to any singularities of the function being approximated. A sequence of piecewise rational functions is proposed, which is constructed from two neighbouring Pade approximants and approximates an elliptic function ...

Journal: Sbornik Mathematics - SB MATH, vol. 200, no. 6, pp. 923-941, 2009]]>The current theory of Pade approximation emphasises results of an inverse character, when conclusions about the properties of the approximated function are drawn from information about the behaviour of the approximants. In this paper Gonchar's conjecture is proved; it states that analogues of Fabry's classical 'ratio' theorem hold for rows of the table of Pade approximants for orthogonal ...

Journal: Sbornik Mathematics - SB MATH, vol. 200, no. 7, pp. 981-1050, 2009]]>