23 research outputs found
Do teorema de Cauchy ao metodo de Cagniard
Orientador: Edmundo Capelas de OliveiraDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Este trabalho versa sobre variaveis complexas, em particular sobre o teorema integral de Cauchy, suas consequencias e aplicações. Como consequencia do teorema integral de Cauchy temos o teorema dos residuos, peça chave para o desenvolvimento deste trabalho. Nas aplicações nos concentramos no estudo das transformadas integrais como metodologia na resolução de equações diferenciais parciais, em particular no calculo da inversão das transformadas de Laplace, Fourier e Hankel, bem como na justa posição das transformadas. Para inversão da justa posição das transformadas nos concentramos no metodo de Cagniard e algumas de suas variaçõesAbstract: This work is about complex variables, in particular about Cauchy¿s integral theorem and its consequences and applications.
We have, as consequences of Cauchy¿s integral theorem, Cauchy¿s theorem and the residue theorem, a keynote to the development of this work. As for the applications, our main objective was to study the integral transforms as a method to solve partial differential equations and, specifically, the inversion of the Laplace, Fourier and Hankel transforms, in the same way, the juxtaposition of transforms. In order to invert the juxtaposition of transforms our main concern was to study Cagniard¿s method and some of its variationsMestradoMatematica AplicadaMestre em Matemátic
Recommended from our members
Climate seasonality limits leaf carbon assimilation and wood productivity in tropical forests
The seasonal climate drivers of the carbon cycle in tropical forests remain poorly known, although these forests account for more carbon assimilation and storage than any other terrestrial ecosystem. Based on a unique combination of seasonal pan-tropical data sets from 89 experimental sites (68 include aboveground wood productivity measurements and 35 litter productivity measurements), their associated canopy photosynthetic capacity (enhanced vegetation index, EVI) and climate, we ask how carbon assimilation and aboveground allocation are related to climate seasonality in tropical forests and how they interact in the seasonal carbon cycle. We found that canopy photosynthetic capacity seasonality responds positively to precipitation when rainfall is < 2000 mm yr⁻¹ (water-limited forests) and to radiation otherwise (light-limited forests). On the other hand, independent of climate limitations, wood productivity and litterfall are driven by seasonal variation in precipitation and evapotranspiration, respectively. Consequently, light-limited forests present an asynchronism between canopy photosynthetic capacity and wood productivity. First-order control by precipitation likely indicates a decrease in tropical forest productivity in a drier climate in water-limited forest, and in current light-limited forest with future rainfall < 2000 mm yr⁻¹
On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator
The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered
On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation
The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations. The so-called generalized Mittag-Leffler function, a function with three-parameter which generalizes the classical ones, appear in the fractional telegraph equation. Here we introduce some integral transforms associated with this generalized Mittag-Leffler function. As particular cases some recent results are recovered.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP
A prelude to the fractional calculus applied to tumor dynamic
In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called Fractional Calculus, i.e., we replace the ordinary derivative of order 1, in one version of the usual equation, by a non-integer derivative of order 0 < α < 1, and recover the classical solution as a particular case. Finally, we analyze the applicability of this model to describe the growth of cancer tumors.Com o intuito de refinar a solução da clássica equação logística e ampliar seu campo de aplicação para o estudo da dinâmica tumoral, propomos e resolvemos a generalização fracionária desta equação, utilizando o assim chamado cálculo fracionário, i.e., substituímos a derivada ordinária da equação usual por uma derivada fracionária de ordem 0 < α < 1, e recuperamos a solução clássica como um caso particular. Por fim, analisamos a aplicabilidade deste modelo para descrever o crescimento de tumores de câncer
One-sided and two-sided Green's functions
We discuss the one-sided Green's function, associated with an initial value problem and the two-sided Green's function related to a boundary value problem. We present a specific calculation associated with a differential equation with constant coefficients. For both problems, we also present the Laplace integral transform as another methodology to calculate these Green's functions and conclude which is the most convenient one. An incursion in the so-called fractional Green's function is also presented. As an example, we discuss the isotropic harmonic oscillator