Applicatioo of Pade Approximation in Simulating Photonic Crystals

To save finite-difference time-domain(FDTD) computing time, several methods are proposed to convert the time domain FDTD output into frequency domain. The Padé approximation with Baker's algorithm and the program are introduced to simulate photonic crystal structures. For a simple pole system with frequency 160THz and quality factor of 5000,the intensity spectrum obtained by the Padé approximation from a 28-item sequence output is more exact than that obtained by fast Fourier transformation from a 220-item sequence output. The mode frequencies and quality factors are calculated at different wave vectors for the photonic crystal slab from a much shorter FDTD output than that required by the FFT method,and then the band diagrams are obatined. In addition,mode frequencies and Q-factors are calculated for photonic crystal microcavity.

一种基于Pade逼近对短时序列频率和品质因数的估计方法

该文提出了一种基于Pade逼近的谱估计方法。由于Pade逼近能够利用有限项很好地逼近对无限项的求和，文中算法适用于短时序列情况。经过实验仿真并与FFT方法和小波变换谱估计方法进行比较表明，该文算法具有较高的频率分辨率和估计精度，并具有较好的品质因数。

The symbolization of central approximants in the IPA

Approximants that can be considered weaker versions of voiced fricatives (termed here ‘frictionless continuants’) are poorly served by the IPA in terms of symbolization as compared to semi-vowel approximants. In this paper we survey the central approximants and the symbols and diacritics used to transcribe them; we focus on evidence for the use of non-rhotic frictionless continuants in both natural language (by which we mean non-clinical varieties) and disordered speech; and we suggest some possible unitary symbols for those that currently require the use of a hard-to-read lowering diacritic beneath the symbol for the corresponding voiced fricative.

Extracting S-matrix poles for resonances from numerical scattering data: Type-II Pade reconstruction

We present a FORTRAN 77 code for evaluation of resonance pole positions and residues of a numerical scattering matrix element in the complex energy (CE) as well as in the complex angular momentum (CAM) planes. Analytical continuation of the S-matrix element is performed by constructing a type-II Pade approximant from given physical values (Bessis et al. (1994) [421: Vrinceanu et al. (2000) [24]; Sokolovski and Msezane (2004) [23]). The algorithm involves iterative 'preconditioning' of the numerical data by extracting its rapidly oscillating potential phase component. The code has the capability of adding non-analytical noise to the numerical data in order to select 'true' physical poles, investigate their stability and evaluate the accuracy of the reconstruction. It has an option of employing multiple-precision (MPFUN) package (Bailey (1993) [451) developed by D.H. Bailey wherever double precision calculations fail due to a large number of input partial waves (energies) involved. The code has been successfully tested on several models, as well as the F + H-2 -> HE + H, F + HD : HE + D, Cl + HCI CIH + Cl and H + D-2 -> HD + D reactions. Some detailed examples are given in the text.

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

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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."

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

Preliminary phonological analysis of the Limi dialect of Humla Bhotia

The purpose of this research was to analyse the phonological system of the Limi dialect of Humla Bhotia. Humla Bhotia is a Tibeto-Burman language that is spoken by approximately 4000 5000 people in the far northwestern Humla province of the Kingdom of Nepal. The language has not previously been the subject of analysis. The data base for this thesis was collected on two different dialects of Humla Bhotia in Kathmandu, the capital of Nepal, from February to May 2000. I had three language informants who speak Humla Bhotia as their mother tongue. One of the informants speaks the Upper Humla dialect and the other two informants speak the Limi dialect. In this thesis I have concentrated on the phonology of the dialect of Limi but occasionally I also make reference to the Upper Humla dialect. The Limi data base consists of 600 words elicited in isolation, sentences where words have been checked for consonantal and pitch variation, and five texts comprising 117 sentences. Firstly, I have studied the geographical location, population and dialects of Humla Bhotia. Five dialects were identified: Limi, Upper Humla, La Yakba, Nyinba and Humli Khyampa. Information on the dialect areas is based on the accounts of seven mother tongue speakers of the language and on Nancy Levine s (1988) anthropological research of the ethnic group Nyinba. Secondly, I have analysed the phonological system of Limi from the viewpoint of American stucturalism much along the lines followed by Pike 1966 [1947] ja 1967 [1948]. In defining the prosodic elements I have also used acoustic analysis. In the Limi dialect there are 7 vowel phonemes. No vowel clusters occur within the same syllable. In this preliminary analysis 29 contrastive plosives, 8 affricates and 5 6 fricatives were found. The data also revealed 4 nasal phonemes, two rhotic phonemes, one lateral phoneme and two central approximants. Further research is however called for to check the phonemic status of these segments. Four contrastive prosodic elements were encountered: nasalisation, length, phonation type and pitch movement. There are two contrastive types of phonation: tense and lax. Many words were found with a third type of phonation, modal phonation. How modal phonation relates to the prosodic system is unclear at this stage and is therefore left for further research to determine. There are two contrastive pitch movement tonemes: a rising toneme and falling toneme. The falling toneme occurs in free variation with a level pitch contour. Rising appears to be linked with lax phonation and falling with tense phonation.

Preliminary Phonological Analysis of Denjongka of Sikkim

This thesis is a preliminary phonological description of the Tibetan-related Denjongka language of Sikkim, India. Because the language has not been much researched and the previous studies have focused on other issues than phonology, the present paper is the first of its kind. The data for this thesis was gathered in Gangtok, the capital of Sikkim, from March to May 2004. I had four language informants from four different locations in Sikkim who spoke different dialects of Denjongka. One of the informants, from whom I recorded c. 900 words and 530 sentences, was used as the main data source for the analysis. First, I will give some ethnographic background information on the people who speak Denjongka. Next, I will discuss first the segmental and then the suprasegmental phonology of the language, which were analysed much in line with American structuralism. I also used acoustic analysis enabled by the Praat-program. Eight vowel phonemes were found. The phonemic status of /E/, however, is still suspect. I present some preliminary evidence for roundedness, frontness and height assimilation among the vowels. In the interpretation adopted in this analysis, there are no diphthongs in Denjongka. Forty consonant phonemes were found: 17 plosives, 7 affricates, 5 fricatives, 5 nasals, 4 liquids and 2 approximants. Denjongka plosives and affricates have four-way aspiration/voicing distinction: voiceless aspirated, voiceless unaspirated, voiceless slightly aspirated (devoiced), and voiced unaspirated. Two voiceless nasals and two voiceless liquids were found. Two phonation types were found to be contrastive, lax/breathy and tense/creaky. Nasalisation and length in vowels are phonemic. Denjongka is an incipient tone language. Tonal phenomena, which involve mainly pitch and phonation type, are complex. Pitch is most of the time predictable from the initial consonant and the phonation type. In some cases, however, pitch is the only contrastive feature between words. The description of Denjongka in this paper differs from the traditional four-tone system, which has been used in many descriptions of Tibetan-related languages. In the four-tone system, pitch is contrastive both in the high and low register, whereas in the present analysis pitch has been established to contrast only in the high register. Lastly, the appendices include a comparative word list of the four Denjongka dialects studied in this thesis.

Expansion of high pressure gas into air - A more realistic blast wave model

In this paper, we consider a more realistic model of a spherical blast wave of moderate strength. An arbitrary number of terms for the series solution in each of the regions behind the main shock - the expansion region, the nearly uniform region outside the main expansion and the region between the contact surface and the main shock, have been generated and matched across the boundaries. We then study the convergence of the solution by using Pade approximation. It constitutes a genuine analytic solution for a moderately strong explosion, which, however, does not involve a secondary shock. The pressure distribution behind the shock however shows some significant changes in the location of the tail of the rarefaction and the interface, in comparison to the planar problem. The theory developed for the spherical blasts is also extended to cylindrical blasts. The results are compared with the numerical solution.

Chronopotentiometry with power-law perturbation functions at an expanding plane electrode with and without a preceding blank period for systems with a coupled first-order homogeneous chemical reaction

The systems formalism is used to obtain the interfacial concentration transients for power-law current input at an expanding plane electrode. The explicit results for the concentration transients obtained here pertain to arbitrary homogeneous reaction schemes coupled to the oxidant and reductant of a single charge-transfer step and the power-law form without and with a preceding blank period (for two types of power-law current profile, say, (i) I(t) = I0(t−t0)q for t greater-or-equal, slanted t0, I(t) = 0 for t < t0; and (ii) I(t) = I0tq for t greater-or-equal, slanted t0, I(t) = 0 for t < t0). Finally the potential transients are obtained using Padé approximants. The results of Galvez et al. (for E, CE, EC, aC) (J. Electroanal. Chem., 132 (1982) 15; 146 (1983) 221, 233, 243), Molina et al. (for E) (J. Electroanal. Chem., 227 (1987) 1 and Kies (for E) (J. Electroanal. Chem., 45 (1973) 71) are obtained as special cases.