Liouville's theorem and power series for quaternionic functions

In recent years quaternionic functions have been an intense and prosperous object of research, and important results were determined [1]-[6]. Some of these results are similar to well known cases in one complex variable, op. cit. [5], [6]. In this paper the hypercomplex expansion of a function in a power series as well as determination of a Liouville's type theorem have been investigated to the quaternionic functions. In this case, it is observed that the Liouville's type theorem is true for second order derivatives, which differs from its classical version. © 2011 Academic Publications, Ltd.

Fourier series for quaternions and the square of the error theorem

In this paper we introduce a type of Hypercomplex Fourier Series based on Quaternions, and discuss on a Hypercomplex version of the Square of the Error Theorem. Since their discovery by Hamilton (Sinegre [1]), quaternions have provided beautifully insights either on the structure of different areas of Mathematics or in the connections of Mathematics with other fields. For instance: I) Pauli spin matrices used in Physics can be easily explained through quaternions analysis (Lan [2]); II) Fundamental theorem of Algebra (Eilenberg [3]), which asserts that the polynomial analysis in quaternions maps into itself the four dimensional sphere of all real quaternions, with the point infinity added, and the degree of this map is n. Motivated on earlier works by two of us on Power Series (Pendeza et al. [4]), and in a recent paper on Liouville’s Theorem (Borges and Mar˜o [5]), we obtain an Hypercomplex version of the Fourier Series, which hopefully can be used for the treatment of hypergeometric partial differential equations such as the dumped harmonic oscillation.

Schur-SzegA composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Orbital perturbations using geopotential coefficients up to high degree and order: Highly eccentric orbits

Several methods have been proposed for calculations of the eccentricity function for a high value of the eccentricity, however they cannot be used when the high degree and order coefficients of gravity fields are taken into account. The method proposed by Wnuk(1) is numerically stable in this case, but when is used. a large number of terms occurs in formulas for geopotential perturbations. In this paper we propose an application of expansions of some functions of the eccentric anomaly E as well as Hansen coefficients in power series of (e - e*), where e* is a fixed value of the eccentricity derived by da Silva Fernandes(2,3,4). These series are convergent for all e < 1.

Error function approximations of interest in electrochemistry.

The error function is present in several equations describing eletrode processes. But, only approximations of this function are used. In this work, these and other approximations are studied and evaluated according to precision.

Negative dimensional integration: Lab testing at two loops

Negative dimensional integration method (NDIM) is a technique to deal with D-dimensional Feynman loop integrals. Since most of the physical quantities in perturbative Quantum Field Theory (pQFT) require the ability of solving them, the quicker and easier the method to evaluate them the better. The NDIM is a novel and promising technique, ipso facto requiring that we put it to test in different contexts and situations and compare the results it yields with those that we already know by other well-established methods. It is in this perspective that we consider here the calculation of an on-shell two-loop three point function in a massless theory. Surprisingly this approach provides twelve non-trivial results in terms of double power series. More astonishing than this is the fact that we can show these twelve solutions to be different representations for the same well-known single result obtained via other methods. It really comes to us as a surprise that the solution for the particular integral we are dealing with is twelvefold degenerate.

Um estudo sobre sequências e séries

Pós-graduação em Matemática em Rede Nacional - IBILCE

Modelos de regressão aplicado no absenteísmo em uma empresa do setor sucroalcooleiro

Pós-graduação em Engenharia de Produção - FEB

Cálculo e análise de efeitos de campo magnético nos estados eletrônicos de impurezas rasas em materiais semicondutores

Pós-graduação em Ciência e Tecnologia de Materiais - FC

Schur-Szegö composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fluxo do grupo de renormalização dos modelos-'alfa' e as álgebras de Lie contínuas

Pós-graduação em Física - IFT

Time-series-based maximization of distributed wind power generation integration

Energy policies and technological progress in the development of wind turbines have made wind power the fastest growing renewable power source worldwide. The inherent variability of this resource requires special attention when analyzing the impacts of high penetration on the distribution network. A time-series steady-state analysis is proposed that assesses technical issues such as energy export, losses, and short-circuit levels. A multiobjective programming approach based on the nondominated sorting genetic algorithm (NSGA) is applied in order to find configurations that maximize the integration of distributed wind power generation (DWPG) while satisfying voltage and thermal limits. The approach has been applied to a medium voltage distribution network considering hourly demand and wind profiles for part of the U.K. The Pareto optimal solutions obtained highlight the drawbacks of using a single demand and generation scenario, and indicate the importance of appropriate substation voltage settings for maximizing the connection of MPG.

Melhora da estabilidade dinâmica de sistemas elétricos de potência multimáquinas usando o dispositivo facts thyristor-controlled series capacitor - TCSC

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The gradually truncated Levy flight for systems with power-law distributions

Power-law distributions have been observed in various economical and physical systems. Levy flights have infinite variance which discourage a physical approach. We introduce a class of stochastic processes, the gradually truncated Levy flight in which large steps of a Levy flight are gradually eliminated. It has finite variance and the system can be analyzed in a closed form. We applied the present method to explain the distribution of a particular economical index. The present method can be applied to describe time series in a variety of fields, i.e. turbulent flow, anomalous diffusion, polymers, etc. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Dimmable electronic ballast with high power-factor SEPIC preregulator, for multiple tubular fluorescent lamps

An electronic ballast for multiple tubular fluorescent lamps is presented in this paper. The proposed structure features high power-factor, dimming capability, and soft-switching to the semiconductor devices operated in high frequencies. A Zero-Current-Switching - Pulse-Width-Modulated (ZCS-PWM) SEPIC converter composes the rectifying stage, controlled by the instantaneous average input current technique, performing soft-commutations and high input power factor. Regarding the inverting stage, it is composed by a classical resonant Half-Bridge converter, associated to Series Parallel-Loaded Resonant (SPLR) filters. The dimming control technique employed in this Half-Bridge inverter is based on the phase-shift in the current processed through the sets of filter + lamp. In addition, experimental results are shown in order to validate the developed analysis.