Dissertations / Theses on the topic 'Cauchy integral'
To see the other types of publications on this topic, follow the link: Cauchy integral.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Cauchy integral.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Oliveira, Saulo Henrique de. "Integral complexa: teorema de Cauchy, fórmula integral de Cauchy e aplicações." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/4981.
Full textAbstract:
Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-12-03T08:37:01Z
No. of bitstreams: 2
Dissertação - Saulo Henrique de Oliveira - 2015.pdf: 1917786 bytes, checksum: 72281ae1c7a550ab53f962bb0da58d07 (MD5)
license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-12-03T08:39:30Z (GMT) No. of bitstreams: 2 Dissertação - Saulo Henrique de Oliveira - 2015.pdf: 1917786 bytes, checksum: 72281ae1c7a550ab53f962bb0da58d07 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)
Made available in DSpace on 2015-12-03T08:39:30Z (GMT). No. of bitstreams: 2 Dissertação - Saulo Henrique de Oliveira - 2015.pdf: 1917786 bytes, checksum: 72281ae1c7a550ab53f962bb0da58d07 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-04-29
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work ...
Este trabalho ...
2
Ruppenthal, Jean. "Zur regularität der Cauchy-Riemannschen Differentialgleichungen auf komplexen Räumen." Bonn : Mathematisches Institut der Universität, 2006. http://catalog.hathitrust.org/api/volumes/oclc/173261836.html.
Full text
3
Cuminato, José Alberto. "Numerical solutions of Cauchy integral equations and applications." Thesis, University of Oxford, 1987. http://ora.ox.ac.uk/objects/uuid:434954bb-bf08-448b-9e02-9948d1287e37.
Full textAbstract:
This thesis investigates the polynomial collocation method for the numerical solution of Cauchy type integral equations and the use of those equations and the related numerical techniques to solve two practical problem in Acoustics and Aerodynamics. Chapters I and II include the basic background material required for the development of the main body of the thesis. Chapter I discusses a number of practical problems which can be modelled as a singular integral equations. In Chapter II the theory of those equations is given in great detail. In Chapter III the polynomial collocation method for singular integral equations with constant coefficients is presented. A particular set of collocation points, namely the zeros of the first kind Chebyshev polynomials, is shown to give uniform convergence of the numerical approximation for the cases of the index K = 0. 1. The convergence rate for this method is also given. All these results were obtained under slightly stronger assumptions than the minimum required for the existence of an exact solution. Chapter IV contains a generalization of the results in Chapter III to the case of variable coefficients. In Chapter V an example of a practical problem which results in a singular integral equation and which is successfully solved by the collocation method is described in substantial detail. This problem consists of the interaction of a sound wave with an elastic plate freely suspended in a fluid. It can be modelled by a system of two coupled boundary value problems - the Helmholtz equation and the beam equation. The collocation method is then compared with asymptotic results and a quadrature method due to Miller. In Chapter VI an efficient numerical method is developed for solving problems with discontinuous right-hand sides. Numerical comparison with other methods and possible extensions are also discussed.
4
Ahmad, Khan Mumtaz, and M. Najmi. "Discrete analogue of Cauchy's integral formula." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96478.
Full text
5
Chunaev, Petr. "Singular integral operators and rectifiability." Doctoral thesis, Universitat Autònoma de Barcelona, 2018. http://hdl.handle.net/10803/663827.
Full textAbstract:
Los problemas que estudiamos en esta tesis se encuentran en el área de Análisis Armónico y Teoría de la Medida Geométrica. En particular, consideramos la conexión entre las propiedades analíticas de operadores integrales singulares definidos en $L^2(\mu)$ y asociados con algunos núcleos de Calderón-Zygmund y las propiedades geométricas de la medida $\mu$. Seamos más precisos.
Sea $E$ un conjunto de Borel en el plano complejo con la medida lineal de Hausdorff $H^1$ finita y distinta de cero, es decir, $0The problems that we study in this thesis lie in the area of Harmonic Analysis and Geometric Measure Theory. Namely, we consider the connection between the analytic properties of singular integral operators defined in $L^2(\mu)$ and associated with some Calderón-Zygmund kernels and the geometric properties of the measure $\mu$. Let us be more precise. Let $E$ be a Borel set in the complex plane with non-vanishing and finite linear Hausdorff measure $H^1$, i.e. such that $0
6
Luther, Uwe. "Approximation Spaces in the Numerical Analysis of Cauchy Singular Integral Equations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200500895.
Full textAbstract:
The paper is devoted to the foundation of
approximation methods for integral equations of
the form (aI+SbI+K)f=g,
where S is the Cauchy singular
integral operator on (-1,1) and K is a weakly
singular integral operator.
Here a,b,g are given functions on (-1,1) and
the unknown function f on (-1,1) is looked for.
It is assumed that a and b are real-valued and
Hölder continuous functions on [-1,1] without
common zeros and that g belongs to some
weighted space of Hölder continuous functions.
In particular, g may have a finite number of
singularities.
Based on known spectral properties of Cauchy
singular integral operators approximation methods
for the numerical solution of the above equation
are constructed, where both aspects the
theoretical convergence and the numerical
practicability are taken into account.
The weighted uniform convergence of these methods
is studied using a general
approach based on the theory of approximation
spaces. With the help of this approach it is
possible to prove simultaneously the stability,
the convergence and results on the order of
convergence of the approximation methods under
consideration.
7
Hanson-Hart, Zachary Aaron. "A Cauchy Problem with Singularity Along the Initial Hypersurface." Diss., Temple University Libraries, 2011. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/126171.
Full textAbstract:
MathematicsPh.D.
We solve a one-sided Cauchy problem with zero right hand side modulo smooth errors for the wave operator associated to a smooth symmetric 2-tensor which is Lorentz on the interior and degenerate at the boundary. The degeneracy of the metric at the boundary gives rise to singularities in the wave operator. The initial data prescribed at the boundary must be modified from the classical Cauchy problem to suit the problem at hand. The problem is posed on the interior and the local solution is constructed using microlocal analysis and the techniques of Fourier Integral Operators.
Temple University--Theses
8
Camargo, Rubens de Figueiredo. "Do teorema de Cauchy ao metodo de Cagniard." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307011.
Full textAbstract:
Orientador: Edmundo Capelas de OliveiraDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-04T02:33:55Z (GMT). No. of bitstreams: 1 Camargo_RubensdeFigueiredo_M.pdf: 815551 bytes, checksum: c2c6d5deb1da34ce6eef3781c5acc1a8 (MD5) Previous issue date: 2005
Resumo: 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 variações
Abstract: 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 variations
Mestrado
Matematica Aplicada
Mestre em Matemática
9
Junghanns, P., and U. Weber. "Local theory of projection methods for Cauchy singular integral equations on an interval." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801281.
Full textAbstract:
We consider a finite section (Galerkin) and a collocation method for Cauchy singular
integral equations on the interval based on weighted Chebyshev polymoninals, where
the coefficients of the operator are piecewise continuous.
Stability conditions are derived using Banach algebra techniques, where
also the system case is mentioned. With the help of
appropriate Sobolev spaces a result on convergence rates is proved.
Computational aspects are discussed in order to develop
an effective algorithm. Numerical results, also
for a class of nonlinear singular integral equations,
are presented.
10
Junghanns, P., and U. Weber. "Local theory of a collocation method for Cauchy singular integral equations on an interval." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801203.
Full textAbstract:
We consider a collocation method for Cauchy singular integral equations on the interval
based on weighted Chebyshev polynomials , where the coefficients of the operator are
piecewise continuous. Stability conditions are derived using Banach algebra methods,
and numerical results are given.
11
Arnold, Rachel Florence. "Complex Analysis on Planar Cell Complexes." Thesis, Virginia Tech, 2008. http://hdl.handle.net/10919/32230.
Full textAbstract:
This paper is an examination of the theory of discrete complex analysis that arises from the
framework of a planar cell complex. Construction of this theory is largely integration-based.
A combination of two cell complexes, the double and its associated diamond complex, allows
for the development of a discrete Cauchy Integral Formula.Master of Science
12
Zhou, Shuang. "Studies on summability of formal solution to a cauchy problem and on integral functions of Mordell’s type." Thesis, Lille 1, 2010. http://www.theses.fr/2010LIL10058/document.
Full textAbstract:
Dans cette Thèse, nous considérons dans le plan complexe l’équation de la chaleur avec la condition initiale singulière u(0,z)=1/(1-exp(z)). Ce problème de Cauchy possède une unique solution formelle série entière, laquelle peut être sommée par des procédés de sommation différents. Le but est d’établir des relations existant entre les différentes sommes ainsi étudiées: d’une part la somme de Borel de celle-ci et, de l’autre, deux versions q-analogues de la somme de Borel qui sont obtenuesrespectivement avec le noyau de la chaleur et la fonction thêta de Jacobi. Notre analyse sur le phénomène de Stokes correspondant nous conduit à une généralisation d’un résultat de Mordell sur le nombre de classes des formes quadratiques binaires définies et positivesIn this thesis, we consider the heat equation with the singular initial condition u(0,z)=1/(1-exp(z)), where z is a complex variable. The aim is to establish relations among three sums of a divergent formal solution to this Cauchy problem: its Borel-sum and two q-Borel-sums obtained by means of heat kernel and theta function respectively. This Stokes analysis allows us to give a generalization to a classical result of Mordell related to the class numbers of the binary positive-definite quadratic forms
13
Ferreira, Marcos Rondiney dos Santos. "Comportamento assintótico de soluções da equação do aerofólio em intervalos disjuntos." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/128043.
Full textAbstract:
Neste trabalho investigamos, dos pontos de vistas analítico e numérico, o comportamento assintótico da solução da equação do aerofólio, com uma singularidade do tipo Cauchy, de nida sobre um intervalo com uma pequena abertura. Exibimos um modelo matemático com uma solução f" para o intervalo disjunto G" = (−1,−ε) ∪ (ε, 1) e uma solução f0 que corresponde ao limite de f" quando (ε → 0), relacionando esta última com a solução da equação do aerofólio f no intervalo (−1, 1). Além do mais, demonstramos casos particulares de funções ψ = Tm e ψ = Un(onde Tm e Un são os polinômios de Tchebychev do primeiro e segundo tipo respectivamente) em que temos a igualdade f = f0 e conseqüentemente f" ≈ f. Apresentamos e comparamos numericamente as soluções f", f0 e f para diferentes funções ψ e valores de ε no intervalo G". Mostramos ainda soluções quase polinomiais analíticas da equação do aerofólio, e propomos um método espectral para a equação do aerofólio generalizada. Por m, obtemos soluções analíticas das equações do aerofólio para os intervalos G", (−1, 1)\ {0} e (−1, 1) para diferentes funções ψ(t) através da expansão em série da densidade da integral singular com núcleo Cauchy.In this work we investigate, of the analytical and numerical points of views, the asymptotic behavior of the airfoil equation solution with a singularity of the Cauchy type, de ned over a interval with a small opening. We display a mathematical model with a f" solution to the disjoint interval G" = (−1,−ε)∪(ε, 1) and a f0 solution corresponding to limit of f" when (ε → 0), linking the latter with the solution of the airfoil equation f in the interval (−1, 1). Furthermore, we demonstrate particular cases of functions ψ = Tm and ψ = Un (where Tm and Un are the Chebyshev polynomials of the rst and second type respectively) where we have equality f = f0 and then f" ≈ f. We present and compare numerically the solutions f", f0 and f for di erent functions ψ and values of ε in G". We also show almost polynomial analytical solutions for the airfoil equation, and we propose a spectral method for the generalized airfoil equation. Finally, we obtain analytical solutions of the airfoil equations to the interval G", (−1, 1)\ {0} and (−1, 1) for various functions ψ(t) by expanding in series the density of the Cauchy singular integral.
14
Barreiro, Rodrigo Cardoso [UNESP]. "Quatérnios, um ensaio sobre a regularidade e hiperperiodicidade de funções quaterniônicas, e o Teorema de Cauchy." Universidade Estadual Paulista (UNESP), 2009. http://hdl.handle.net/11449/94228.
Full textAbstract:
Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0
Previous issue date: 2009-02-17Bitstream added on 2014-06-13T18:30:54Z : No. of bitstreams: 1
barreiro_rc_me_sjrp.pdf: 585027 bytes, checksum: 039155145a6c7b9e6e1fc03a02180b55 (MD5)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
O objetivo deste trabalho ée estabelecer similaridades entre a análise complexa e os quatérnios. Nele é feito um estudo da regularidade de funções quaterniônicas e são estabelecidas as funções exponencial e logarítmica para os quatérnios sendo feito um estudo da hiperpe- riodicidade dessas funções. Outro resultado apresentado é a generalização quaterniônica da fórmula integral de Cauchy um dos principais teoremas da análise complexa.
The objective of this work is to establish similarities between the complex analysis and the quaternions. In it is made a study of the regularity of quaternionic functions and are established the exponential and logarithmic functions for the quaternions being made a study of the hiperperiodicity of these functions. Another presented result is the quater- nionic generalization of the Cauchy's integral formula one of the main theorems of the complex analysis.
15
Nagamine, Andre. "Solução numérica de equações integro-diferenciais singulares." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-27052009-102500/.
Full textAbstract:
A Teoria das equações integrais, desde a segunda metade do século XX, tem assumido um papel cada vez maior no âmbito de problemas aplicados. Com isso, surge a necessidade do desenvolvimento de métodos numéricos cada vez mais eficazes para a resolução deste tipo de equação. Isso tem como consequência a possibilidade de resolução de uma gama cada vez maior de problemas. Nesse sentido, outros tipos de equações integrais estão sendo objeto de estudos, dentre elas as chamadas equações integro-diferenciais. O presente trabalho tem como objetivo o estudo das equações integro-diferenciais singulares lineares e não-lineares. Mais especificamente, no caso linear, apresentamos os principais resultados necessários para a obtenção de um método numérico e a formulação de suas propriedades de convergência. O caso não-linear é apresentado através de um modelo matemático para tubulações em um tipo específico de reator nuclear (LMFBR) no qual origina-se a equação integro-diferencial. A partir da equação integro-diferencial um modelo numérico é proposto com base nas condições físicas do problemaThe theory of the integral equations, since the second half of the 20th century, has been assuming an ever more important role in the modelling of applied problems. Consequently, the development of new numerical methods for integral equations is called for and a larger range of problems has been possible to be solved by these new techniques. In this sense, many types of integral equations have been derived from applications and been the object of studies, among them the so called singular integro-differential equation. The present work has, as its main objective, the study of singular integrodifferential equations, both linear and non-linear. More specifically, in the linear case, we present our main results regarding the derivation of a numerical method and its uniform convergence properties. The non-linear case is introduced through the mathematical model of boiler tubes in a specific type of nuclear reactor (LMFBR) from which the integro-differential equation originates. For this integro-differential equation a numerical method is proposed based on the physical conditions of the problem
16
Mennouni, Abdelaziz. "Sur la résolution des équations intégrales singulières à noyau de Cauchy." Thesis, Saint-Etienne, 2011. http://www.theses.fr/2011STET4005/document.
Full textAbstract:
L'objectif de ce travail est la résolution des équations intégrales singulières à noyau Cauchy. On y traite les équations singulières de Cauchy de première espèce par la méthode des approximations successives. On s'intéresse aussi aux équations intégrales à noyau de Cauchy de seconde espèce, en utilisant les polynômes trigonométriques et les techniques de Fourier. Dans la même perspective, on utilise les polynômes de Tchebychev de quatrième degré pour résoudre une équation intégro différentielle à noyau de Cauchy. Ensuite, on s'intéresse à une autre équation intégro-différentielle à noyau de Cauchy, en utilisant les polynômes de Legendre, ce qui a donné lieu à développer deux méthodes basées sur une suite de projections qui converge simplement vers l'identité. En outre, on exploite les méthodes de projection pour les équations intégrales avec des opérateurs intégraux bornés non compacts et on a appliqué ces méthodes à l'équation intégrale singulière à noyau de Cauchy de deuxième espèceThe purpose of this thesis is to develop and illustrate various new methods for solving many classes of Cauchy singular integral and integro-differential equations. We study the successive approximation method for solving Cauchy singular integral equations of the first kind in the general case, then we develop a collocation method based on trigonometric polynomials combined with a regularization procedure, for solving Cauchy integral equations of the second kind. In the same perspective, we use a projection method for solving operator equation with bounded noncompact operators in Hilbert spaces. We apply a collocation and projection methods for solving Cauchy integro-differential equations, using airfoil and Legendre polynomials
17
Rogozhin, Alexander. "Approximation Methods for Two Classes of Singular Integral Equations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2003. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200300091.
Full textAbstract:
The dissertation consists of two parts. In the first part approximate methods for multidimensional weakly singular integral operators with operator-valued kernels are investigated. Convergence results and error estimates are given. There is considered an application of these methods to solving radiation transfer problems. Numerical results are presented, too. In the second part we consider a polynomial collocation method for the numerical solution of a singular integral equation over the interval. More precisely, the operator of our integral equation is supposed to be of the form \ $aI + b \mu^{-1} S \mu I $\ with \ $S$\ the Cauchy singular integral operator, with piecewise continuous coefficients \ $a$\ and \ $b,$\ and with a Jacobi weight \ $\mu.$\ To the equation we apply a collocation method, where the collocation points are the Chebyshev nodes of the first kind and where the trial space is the space of polynomials multiplied by another Jacobi weight. For the stability and convergence of this collocation method in weighted \ $L^2$\ spaces, we derive necessary and sufficient conditions. Moreover, the extension of these results to an algebra generated by the sequences of the collocation method applied to the mentioned singular integral operators is discussed and the behaviour of the singular values of the discretized operators is investigatedDie Dissertation beschäftigt sich insgesamt mit der numerischen Analysis singulärer Integralgleichungen, besteht aber aus zwei voneinander unabhängigen Teilen. Der este Teil behandelt Diskretisierungsverfahren für mehrdimensionale schwach singuläre Integralgleichungen mit operatorwertigen Kernen. Darüber hinaus wird hier die Anwendung dieser allgemeinen Resultate auf ein Strahlungstransportproblem diskutiert, und numerische Ergebnisse werden präsentiert. Im zweiten Teil betrachten wir ein Kollokationsverfahren zur numerischen Lösung Cauchyscher singulärer Integralgleichungen auf Intervallen. Der Operator der Integralgleichung hat die Form \ $aI + b \mu^{-1} S \mu I $\ mit dem Cauchyschen singulären Integraloperator \ $S,$\ mit stückweise stetigen Koeffizienten \ $a$\ und \ $b,$\ und mit einem klassischen Jacobigewicht \ $\mu.$\ Als Kollokationspunkte dienen die Nullstellen des n-ten Tschebyscheff-Polynoms erster Art und Ansatzfunktionen sind ein in einem geeigneten Hilbertraum orthonormales System gewichteter Tschebyscheff-Polynome zweiter Art. Wir erhalten notwendige und hinreichende Bedingungen für die Stabilität und Konvergenz dieses Kollokationsverfahrens. Außerdem wird das Stabilitätskriterium auf alle Folgen aus der durch die Folgen des Kollokationsverfahrens erzeugten Algebra erweitert. Diese Resultate liefern uns Aussagen über das asymptotische Verhalten der Singulärwerte der Folge der diskreten Operatoren
18
Barreiro, Rodrigo Cardoso. "Quatérnios, um ensaio sobre a regularidade e hiperperiodicidade de funções quaterniônicas, e o Teorema de Cauchy /." São José do Rio Preto : [s.n.], 2009. http://hdl.handle.net/11449/94228.
Full textAbstract:
Orientador: Manoel Ferreira Borges NetoBanca: Antônio Luís Venezuela
Banca: Sandra Regina Monteiro Masalshiene Roveda
Resumo: O objetivo deste trabalho ée estabelecer similaridades entre a análise complexa e os quatérnios. Nele é feito um estudo da regularidade de funções quaterniônicas e são estabelecidas as funções exponencial e logarítmica para os quatérnios sendo feito um estudo da hiperpe- riodicidade dessas funções. Outro resultado apresentado é a generalização quaterniônica da fórmula integral de Cauchy um dos principais teoremas da análise complexa.
Abstract: The objective of this work is to establish similarities between the complex analysis and the quaternions. In it is made a study of the regularity of quaternionic functions and are established the exponential and logarithmic functions for the quaternions being made a study of the hiperperiodicity of these functions. Another presented result is the quater- nionic generalization of the Cauchy's integral formula one of the main theorems of the complex analysis.
Mestre
19
Kaye, Adelina E. "Singular integration with applications to boundary value problems." Kansas State University, 2016. http://hdl.handle.net/2097/32717.
Full textAbstract:
Master of ScienceMathematics
Nathan Albin
Pietro Poggi-Corradini
This report explores singular integration, both real and complex, focusing on the the Cauchy type integral, culminating in the proof of generalized Sokhotski-Plemelj formulae and the applications of such to a Riemann-Hilbert problem.
20
Rogozhin, Alexander. "Approximation methods for two classes of singular integral equations." Doctoral thesis, [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=968783279.
Full text
21
Preciso, Luca. "Perturbation Analysis of the Conformal Sewing Problem and Related Problems." Doctoral thesis, Università degli studi di Padova, 1998. http://hdl.handle.net/11577/3425905.
Full textAbstract:
In this dissertation, we develop two related problems in the nonlinear functional analysis. The first is the analyticity of the Cauchy singular integral in Schauder spaces which is motivated by the second problem, namely the perturbation analysis of the conformal sewing problem in Schauder and Roumieu spaces. In Chapter II, we consider the Cauchy singular integral
f (t)φ0 (t) f ◦ φ(−1) (ξ)
1 1
C[φ, f ]( · ) ≡ p. v. dt = p. v. dξ
2πi ∂D φ(t) − φ(·) 2πi φ ξ − φ(·)
where the oriented simple closed curve φ and the density function f are both defined on the counterclockwise oriented boundary ∂D of the plane unit disk D. Although the linear operator C[φ, ·], for a fixed φ, and the numerical computation of C[φ, f ] have been extensively studied for the last century, in view to several applications to integral equations and boundary value problems (cf. e.g. Muskhelishvili (1953) and Gakhov (1966)), the analysis of the nonlinear functional dependence of C[φ, f ] upon both its arguments seems to be a subject analyzed only more recently (see Introduction Ch. II). This new subject of research finds application in the nonlinear problems of perturbation nature which involve the Cauchy singular integral. In Chapter II we extend the analyticity result for the operator C[·, ·] of Coifman & Meyer (1983b) to a Schauder spaces setting. We assume that both φ and f belong to a Schauder space, say C∗m,α (∂D, C), of complex-valued function of class C m,α on ∂D, with m a positive natural number and α ∈ ]0, 1[. As it is well-known, under such conditions on φ and f , the function C[φ, f ](·) is also of class C m,α . By proving the unique solvability of a boundary value problem of elliptic nature in D and by applying Implicit Function Theorem to a suitable functional equation, we show the real analyticity of C[·, ·]. Then we show the complex analyticity of C[·, ·] and we compute all its differentials. This result of Lanza & Preciso (1998) will be applied in the second part of this dissertation and in another perturbation problem associated to a nonlinear integral equation (cf. Lanza & Rogosin (1997)). In Chapter III, we introduce the conformal sewing problem associated to a shift φ of ∂D, i.e. a homeomorphism of ∂D to itself. It consists in finding a pair of conformal functions (F, G) defined in D and C \ cl D, respectively, such that their continuous extensions to cl D e C \ D, Fe and G e respectively, satisfy Fe(φ(t)) = G(t) for all t ∈ ∂D. A simple normalization condition and well-known results ensure that the sewing problem associated to φ has a unique solution (F, G) and we denote by (F [·], G[·]) the pair of operators which maps φ to the trace on ∂D of such solution. The regularity properties of the operators F [φ] and G[φ] in spaces of regular functions can be used in the study of Teichmüller spaces, which constitute an important subject in geometric function theory (see Nag (1996)). Our aim is to find natural Banach spaces of regular functions where to obtain the analyticity of F [·] and G[·]. First we study the regularity of such operators in Schauder spaces C∗m,α (∂D, C), with m ≥ 1, α ∈ ]0, 1[. By using the classical integral equation approach to the sewing problem, we show that G[φ] and F [φ] = G[φ] ◦ φ(−1) belong to C∗m,α (∂D, C) when φ belongs to C∗m,α (∂D, C). In this setting, by using the analyticity of the Cauchy singular integral (cf. Ch. II) and by applying Implicit Function Theorem to a suitable integral equation, we show that G[·] extends to a complex analytic operator. Then we prove that this Schauder spaces setting is not sufficient in order to obtain an analytic extension of the operator F [·]. Indeed a natural assumption in order to have F [·] analytic, is that φ belongs to a space of real analytic functions of ∂D to C. In Chapter IV we introduce Banach spaces of real analytic functions, namely the Roumieu spaces associated to the differentiation operator. In this setting we show that G[·] and F [·] can be extended to complex analytic operators by employing the regularity results on the composition and on the inversion operator of Lanza (1994 and 1996b).
22
Martins, Camila Aversa [UNESP]. "Existência de solução de equações integrais não lineares em escalas temporais sobre espaços de Banach." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/86515.
Full textAbstract:
Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0
Previous issue date: 2013-06-27Bitstream added on 2014-06-13T19:48:20Z : No. of bitstreams: 1
martins_ca_me_sjrp.pdf: 297081 bytes, checksum: 4a6f13bdad08f9e72c8df07186762615 (MD5)Neste trabalho estabelecemos condições para a existência e unicidade de solução para equações integrais do tipo Volterra–Stieltjes não linear x(t)+ Z [a,t]T DsK(t,s) f (s,x(s)) = u(t), t E [a,b]T em escalas temporais T, usando a integral de Cauchy–Stieltjes à direita sobre funções regradas a valores em espaços de Banach
In this work we establish conditions for the existence and uniqueness of solution a Volterra– Stieltjes integral nonlinear equations x(t)+ Z [a,t]T DsK(t,s) f (s,x(s)) = u(t), t E [a,b]Tin time scales T, using the right Cauchy–Stieltjes integral on regulated functions with values in Banach spaces
23
Martins, Camila Aversa. "Existência de solução de equações integrais não lineares em escalas temporais sobre espaços de Banach /." São José do Rio Preto, 2013. http://hdl.handle.net/11449/86515.
Full textAbstract:
Orientador: Luciano BarbantiCoorientador: Geraldo Nunes Silva
Banca: German Jesus Lozada Cruz
Banca: Márcia Cristina Anderson Braz Federson
Resumo: Neste trabalho estabelecemos condições para a existência e unicidade de solução para equações integrais do tipo Volterra-Stieltjes não linear x(t)+ Z [a,t]T DsK(t,s) f (s,x(s)) = u(t), t E [a,b]T em escalas temporais T, usando a integral de Cauchy-Stieltjes à direita sobre funções regradas a valores em espaços de Banach
Abstract: In this work we establish conditions for the existence and uniqueness of solution a Volterra- Stieltjes integral nonlinear equations x(t)+ Z [a,t]T DsK(t,s) f (s,x(s)) = u(t), t E [a,b]Tin time scales T, using the right Cauchy-Stieltjes integral on regulated functions with values in Banach spaces
Mestre
24
Lladser, Manuel Eugenio. "Asymptotic enumeration via singularity analysis." Connect to this title online, 2003. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1060976912.
Full textAbstract:
Thesis (Ph. D.)--Ohio State University, 2003.Title from first page of PDF file. Document formatted into pages; contains x, 227 p.; also includes graphics Includes bibliographical references (p. 224-227). Available online via OhioLINK's ETD Center
25
Axelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.
Full textAbstract:
The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwells equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwells equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.
26
Balkare, Johan. "Cauchy Integrals Method in the Study of Perturbations of Operators." Thesis, KTH, Matematik (Avd.), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-187351.
Full textAbstract:
We show that functions which are analytic on the open unit disc and fulfil the Hölder condition of order r there, where r lies in the interval (0,1), are operator Hölder of order r on the set of all linear contractions on a Hilbert space. Further, it is known that analytic Lipschitz functions on the unit disc need not be operator Lipschitz. We show that under a certain additional integral condition, these functions are operator Lipschitz. The two results are shown by tools from operator theory including the Spectral theorem and dilations of contractions. We also solve a problem related to theory of dilations which was arisen on a mathematical question- and answer site. More specificaly we show that, for a certain operator-valued polynomial, the von Neumann inequality is false.Vi visar att analytiska funktioner på öppna enhetsskivan som uppfyller Höldervillkoret av ordning r, där r ligger på intervallet (0,1), är operator Hölder av ordning r på mängden av alla linjära kontraktioner på ett Hilbert rum. Vidare så är det känt att analytiska Lipschitzfunktioner på enhetsskivan inte behöver vara operator-Lipschitz. Vi visar att om vi lägger till ett visst integralvillkor så är dessa funktioner operator-Lipschitz. Vi visar de två resultaten med redskap från operatorteori som inkluderar Spektralsatsen och dilationer av kontraktioner. Vi löser även ett problem som är relaterat till teorin om dilationer som uppstod på en matematisk frågor- och svarhemsida. Mer specifikt visar vi att för ett visst polynom som antar operatorvärden så är von Neumanns olikhet falsk.
27
Hui, Hui. "Contribution to a Simulator of Arrays of Atomic Force Microscopes." Thesis, Besançon, 2013. http://www.theses.fr/2013BESA2031/document.
Full textAbstract:
Dans cette thèse, nous établissons un modèle à deux échelles à la fois pour desmatrices de cantilevers unidimensionnels et bidimensionnels en régime de fonctionnementélastodynamique avec des applications possibles aux réseaux de microscopesà force atomique (AFM). Son élaboration est basée sur une analyseasymptotique pour les structures minces élastiques, une approximation à deuxéchelles et une mise à l’échelle utilisée pour l’homogénéisation des milieux fortementhétérogènes. Nous complétons la théorie de l’approximation à deux échellespour les problèmes aux limites du quatrième ordre posés dans des domaines mincespériodiques connexes seulement dans certaines directions. Notre modèle reproduitla dynamique globale du support ainsi que les mouvements locaux des cantilevers.Pour simplifier la suite du travail, nous concentrons nos travaux à l’étude de matricesde leviers constituées de lignes découplées en régime dynamique. Comme lesupport des leviers est élastique, l’effet du couplage entre levier est pris en compte.La vérification du modèle est soigneusement réalisée. Nous montrons que chaquemode propre peut être décomposé en produits d’un mode de base avec un modede levier. Nous présentons une méthode de discrétisation du modèle et effectuonssa vérification numérique en la comparant avec des résultats de simulation paréléments finis du problème d’élasticité tridimensionnel. Par ailleurs, nous avonsélaboré de nouveaux outils d’aide à la conception de réseaux d’AFM. Une boîte àoutils d’optimisation robuste est interfacée avec le modèle permettant d’optimiserun design avant micro-Fabrication. Un algorithme d’estimation de l’état statiquecombinant la mesure de déplacements mécaniques par interférométrie et le modèlea été introduit. Nous avons également synthétisé un régulateur quadratiquelinéaire (LQR) pour un réseau de cantilevers en mode dynamique comprenant actionneurset capteurs régulièrement espacées. Dans le but de mettre en oeuvre lecontrôle en temps réel, nous proposons une approximation semi-Décentralisée quipeut être réalisé par un circuit électronique distribué analogique. Plus précisément,notre processeur analogique peut être réalisé par un réseau périodique derésistances (PNR). La méthode d’approximation de commande est basée sur deuxconcepts généraux, à savoir sur un calcul fonctionnel (c’est-À-Dire des fonctionsd’opérateurs) et sur la formule de représentation d’une fonction d’opérateur deDunford-Schwartz. Cette méthode d’approximation est étendue pour la résolutiond’un problème de filtrage optimal robuste de type H∞ de la dynamique d’un réseaude leviers couplés avec sources aléatoires de bruitIn this dissertation, we establish a two-Scale model both for one-Dimensionaland two-Dimensional Cantilever Arrays in elastodynamic operating regime withpossible applications to Atomic Force Microscope (AFM) Arrays. Its derivationis based on an asymptotic analysis for thin elastic structures, a two-Scale approximationand a scaling used for strongly heterogeneous media homogenization. Wecomplete the theory of two-Scale approximation for fourth order boundary valueproblems posed in thin periodic domains connected in some directions only. Ourmodel reproduces the global dynamics as well as each of the cantilever motion. Forthe sake of simplicity, we present a simplified model of mechanical behavior of largecantilever arrays with decoupled rows in the dynamic operating regime. Since thesupporting bases are assumed to be elastic, cross-Talk effect between cantileversis taken into account. The verification of the model is carefully conducted. Weexplain not only how each eigenmode is decomposed into products of a base modewith a cantilever mode but also the method used for its discretization, and reportresults of its numerical validation with full three-Dimensional Finite Element simulations.We show new tools developed for Arrays of Microsystems and especiallyfor AFM array design. A robust optimization toolbox is interfaced to aid for designbefore the microfabrication process. A model based algorithm of static stateestimation using measurement of mechanical displacements by interferometry ispresented. We also synthesize a controller based on Linear Quadratic Regulator(LQR) methodology for a one-Dimensional cantilever array with regularly spacedactuators and sensors. With the purpose of implementing the control in real time,we propose a semi-Decentralized approximation that may be realized by an analogdistributed electronic circuit. More precisely, our analog processor is made by PeriodicNetwork of Resistances (PNR). The control approximation method is basedon two general concepts, namely on functions of operators and on the Dunford-Schwartz representation formula. This approximation method is extended to solvea robust H∞ filtering problem of the coupled cantilevers for time-Invariant systemwith random noise effects
28
LY, KIM HA. "ON TWO APPROACHES FOR PARTIAL DIFFERENTIAL EQUATIONS IN SEVERAL COMPLEX VARIABLES." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3423534.
Full textAbstract:
The aim of this thesis is to present influence of notations of ''type" on partial differential equations in several complex variables. The notations of "type" here include the finite and the infinite type in the sense of Hormander, and D'Angelo. In particular, in the first part, under the finite type condition, we will consider the existence and uniqueness of solutions for the initial value problem associated to the heat operator δs+□b on CR manifolds. The finite type m is the critical condition to provide pointwise estimates of the heat kernel via theory of singular integral operators developed by E. Stein and A. Nagel, D.H. Phong and E. Stein. Next, in the second part, we will introduce a new method to investigate the Cauchy-Riemann equations δu = φ. The solutions are constructed via the integral representation method. Moreover, we will show that the new method here is also applied well to the complex Monge-Ampère operator (ddc)n inCn. The main point is that our method can pass some well-known results from the case of finite type to infinite type.Lo scopo di questa tesi è quello di presentare l'influenza di notazioni di " tipo'' su equazioni differenziali alle derivate parziali in più variabili complesse. Le notazioni di "tipo" qui includono il finito e il tipo di infinito, nel senso di Hormander, e D'Angelo. In particolare, nella prima parte, a condizione tipo finito, prenderemo in considerazione l'esistenza e l'unicità delle soluzioni per il problema del valore iniziale associato ai operatore calore δs+□b su varietà CR. Il tipo finito m è la condizione fondamentale per fornire stime puntuali del nucleo del calore attraverso la teoria degli operatori integrali singolari sviluppate da E. Stein e A. Nagel, D.H. Phong e E. Stein. Prossimo, nella seconda parte, introdurremo un nuovo metodo per indagare la equazioni Cauchy-Riemann δu = φ. Le soluzioni sono costruite con via metodo rappresentazione integrale. Inoltre, mostreremo che il nuovo metodo qui viene applicato anche ben al complesso operatore Monge-Ampère (ddc)n inCn. Il punto principale è che il nostro metodo può passare alcuni risultati noti dal caso di tipo finito al tipo di infinito.
29
Poltoratski, Alexei G. Makarov Nicolai G. "Boundary behavior of Cauchy integrals and rank one perturbations of operators /." Diss., Pasadena, Calif. : California Institute of Technology, 1995. http://resolver.caltech.edu/CaltechETD:etd-10122007-080912.
Full text
30
Judd, Kristin N. "An extension of green's theorem with application." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/5638.
Full textAbstract:
Thesis (M.S.)--University of Missouri-Columbia, 2008.The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on September 5, 2008) Includes bibliographical references.
31
Kaiser, Robert. "Polynomiale Kollokations-Quadraturverfahren für singuläre Integralgleichungen mit festen Singularitäten." Doctoral thesis, Universitätsbibliothek Chemnitz, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-229930.
Full textAbstract:
Viele Probleme der Riss- und Bruchmechanik sowie der mathematischen Physik lassen sich auf Lösungen von singulären Integralgleichungen über einem Intervall zurückführen. Diese Gleichungen setzen sich im Wesentlichen aus dem Cauchy'schen singulären Integraloperator und zusätzlichen Integraloperatoren mit festen Singularitäten in den jeweiligen Kernen zusammen. Zur numerischen Lösung solcher Gleichungen werden polynomiale Kollokations-Quadraturverfahren betrachet. Als Ansatzfunktionen und Kollokationspunkte werden dabei gewichtete Polynome und Tschebyscheff-Knoten gewählt. Die Gewichte sind so gewählt, dass diese das asymptotische Verhalten der Lösung in den Randpunkten widerspiegeln. Mit Hilfe von C*-Algebra Techniken, werden in dieser Arbeit notwendige und hinreichende Bedingungen für die Stabilität der Kollokations-Quadraturverfahren angegeben. Die theoretischen Resultate werden dabei durch numerische Berechnungen anhand des Problems der angerissenen Halbebene und des angerissenen Loches überprüft.
32
Chung, Kwok-Chiu. "Computing oscillatory integrals by complex methods." Thesis, Loughborough University, 1998. https://dspace.lboro.ac.uk/2134/33239.
Full textAbstract:
The research is concerned with the proposal and the development of a general method for computing rapidly oscillatory integrals with sine and cosine weight integrands of the form f(x) exp(iωq(x)). In this method the interval (finite or infinite) of integration is transformed to an equivalent contour in the complex plane and consequently the problem of evaluating the original oscillatory integral reduces to the evaluation of one or more contour integrals. Special contours, called the optimal contours, are devised and used so that the resulting real integrals are non-oscillatory and have rapidly decreasing integrands towards one end of the integration range. The resulting real integrals are then easily computed using any general-purpose quadrature rule.
33
BONNEAU, PIERRE. "Solutions integrales de l'operateur de cauchy-riemann dans les domaines pseudoconvexes : applications a des problemes de division." Toulouse 3, 1987. http://www.theses.fr/1987TOU30034.
Full textAbstract:
Depuis 1970, on sait obtenir -et estimer- dans les domaines strictement pseudoconvexes, des solutions integrales de l'operateur de cauchy-riemann. L'objet essentiel de cette these est, d'une part, d'utiliser ces resultats pour resoudre certains problemes de division, d'autre part, de construire des solutions integrales de l'operateur de cauchy-riemann dans les domaines faiblement pseudoconvexes. Tout d'abord, dans un domaine strictement convexe, on ecrit une fonction meromorphe, a croissance connue, comme le quotient de deux fonctions holomorphes de croissance comparable. Dans un domaine strictement pseudoconvexe, etant donnee une fonction holomorphe dans un ideal, on l'ecrit en fonction des generateurs de l'ideal, et l'on etudie la regularite des quotients en fonction de la regularite de la donnee. Ensuite, dans certains domaines faiblement convexes, on construit une fonction support holomorphe que l'on controle bien et on estime la solution de henkin associee pour l'operateur d". Enfin, dans les domaines faiblement pseudoconvexes, malgre l'absence de fonction support holomorphe, on construit une solution integrale de l'operateur de cauchy-riemann et l'on estime cette solution
34
Querze, Sara. "Le funzioni olomorfe e il loro collegamento con le funzioni armoniche." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7876/.
Full textAbstract:
Questo elaborato si propone di analizzare il collegamento tra olomorfia e armonicità. La prima parte della tesi tratta le funzioni olomorfe, mentre la seconda parte tratta le funzioni armoniche. Per quanto riguarda la seconda parte, inizialmente ci limiteremo a studiare le funzioni armoniche in R^2, sottolineando il legame tra queste e le funzioni olomorfe. Considereremo poi il caso generale, ovvero estenderemo la nozione di funzione armonica ad R^N e osserveremo che molte delle proprietà viste per le funzioni olomorfe valgono anche per le funzioni armoniche. In particolare, vedremo che le formule di media per le funzioni armoniche svolgono un ruolo analogo alla formula integrale di Cauchy per le funzioni olomorfe. Vedremo anche che il Teorema di Liouville per le funzioni armoniche è l’analogo del Teorema di Liouville per le funzioni intere (funzioni olomorfe su tutto C) e, infine, osserveremo che il Principio del massimo forte non è altro che il trasferimento alle funzioni armoniche del Principio del massimo modulo visto nella teoria delle funzioni olomorfe.
35
Громик, Андрій Петрович, Андрей Петрович Громик, and A. P. Hromyk. "Математичне моделювання процесів теплопереносу в тонких пластинах." Thesis, Тернопільський національний технічний університет ім. Івана Пулюя, 2012. http://elartu.tntu.edu.ua/handle/123456789/1849.
Full textAbstract:
Роботу виконано в Кам’янець-Подільському національному університеті імені Івана Огієнка Міністерства освіти і науки, молоді та спорту України.Захист відбувся “30” листопада 2012 р. о “14” год. “00” хв. на засіданні спеціалізованої вченої ради К 58.052.01 у Тернопільському національному технічному університеті імені Івана Пулюя (46001, м. Тернопіль, вул. Руська, 56, аудиторія 79).
З дисертацією можна ознайомитись у науково-технічній бібліотеці Тернопільського національного технічного університету імені Івана Пулюя (46001, м. Тернопіль, вул. Руська, 56).Дисертація присвячена питанням математичного моделювання процесів теплопереносу в тонких пластинах різної геометричної форми, що описуються декартовою чи циліндричною системою координат, та побудові й дослідженню моделі випікання тонких плоских тістових заготовок. У роботі за найбільш загальних припущень у межах феноменологічної теорії теплопровідності вперше розроблено математичні моделі стаціонарного й нестаціонарного процесів теплопереносу в тонких пластинах у випадку, коли задача теплопереносу несиметрична відносно серединної площини пластини і коефіцієнти теплообміну з бічних поверхонь пластини різні. Методом головних розв’язків (фундаментальних функцій, функцій Коші та функцій Гріна) одержано у замкнутому вигляді точні розв’язки модельних крайових задач стаціонарного та нестаціонарного процесів теплопереносу для пластин різної конструкції. Для побудови головних розв’язків залучено відповідні інтегральні перетворення, породжені диференціальним оператором Фур’є чи диференціальним оператором Бесселя. Виконано аналітичне та комп’ютерне моделювання стаціонарного й нестаціонарного теплопереносу в процесах випікання тонких плоских тістових заготовок прямокутної та кругової форми. Досліджено вплив конструктивних і частотних (густинних) характеристик теплових джерел плити нагріву для забезпечення рівномірного нагріву тістових заготовок різних розмірів та отримання просторово-розподілених температурних розподілів заготовок з рівномірною інтенсивністю розподілу температур на їх поверхні.
Диссертационная работа посвящена вопросам математического моделирования процессов теплопереноса в тонких пластинах различной геометрической формы, описываемых декартовой или цилиндрической системами координат, а также построению и исследованию модели выпекания тонких плоских тестовых заготовок. В работе при наиболее общих предположениях в пределах феноменологической теории теплопроводности впервые разработано математические модели стационарного и нестационарного процессов теплопереноса для тонких изотропных пластин различной геометрии в декартовой и цилиндрической системах координат. Рассмотрен наиболее общий случай, когда задача теплопередачи асимметрична относительно срединной плоскости пластины и коэффициенты теплообмена с боковых поверхностей пластины разные. Как следствия выписаны решения для случаев, когда задача теплопередачи асимметрична или симметрична относительно срединной плоскости пластины и коэффициенты теплообмена с боковых поверхностей пластины равные. Методом главных решений (фундаментальных функций, функций Коши и функций Грина) в замкнутом виде получено точные решения модельных краевых задач стационарного и нестационарного процессов теплопереноса для пластин разной конструкции (прямоугольный клин, полоса-пластина, полуполоса-пластина, прямоугольная пластина; неограниченная цилиндрически-изотропная пластина с круговым вырезом и неограниченная клиновидная цилиндрически-изотропная пластина с вырезом в виде кругового сектора, цилиндрически-изотропная круговая пластина и цилиндрически-изотропная пластина в виде кругового сектора, цилиндрически-изотропная кольчатая пластина и кольчатая клиновидная цилиндрически-изотропная пластина). Для построения главных решений привлечены соответствующие интегральные преобразования для однородных сред, порожденные дифференциальным оператором Фурье (ось, полуось, сегмент), интегральные преобразования Фурье относительно угловой переменной, интегральные преобразования, порожденные дифференциальным оператором Бесселя (интегральные преобразования Вебера, Ганкеля 1-го и 2-го рода относительно радиальной переменной). Как следствия из общих решений получены наиболее часто встречаемые в инженерной практике случаи модельных задач для задания на границе пластины: распределения температуры по поверхности пластины в любой момент времени; плотности теплового потока; температуры окружающей среды и закона теплообмена между поверхностью тела и окружающей средой, а также их возможных комбинаций. Выполнено аналитическое и компьютерное моделирование стационарного и нестационарного теплопереноса в процессах выпекания тонких плоских тестовых заготовок прямоугольной и круговой формы. В результате компьютерного моделирования получено пространственно-распределенные температурные распределения заготовок с равномерной интенсивностью распределения температур на их поверхностях, на основании которых исследовано влияние конструктивных и частотных (плотностных) характеристик тепловых источников плиты нагревания для обеспечения равномерного нагревания тестовых заготовок разных размеров. Проведенный анализ дает возможность осуществлять обоснование более равномерных режимов нагревания и теплопереноса, что в целом существенно влияет на энерго- и ресурсосберегательные показатели теплоэнергетических и теплонагревательных установок.
The thesis is devoted to mathematical modeling of heat transfer in thin plates of different geometry described by Cartesian or cylindrical coordinate system, and the construction and study of models of thin flat baking dough preparations. In this dissertation, the most common assumptions within the phenomenological theory of heat was first formed mathematical models of stationary and non-stationary processes of heat transfer in thin plates where heat transfer problem is asymmetric relative to the median plane of the plate and the heat transfer coefficients of the lateral surfaces of the plate are different. The method of principal solutions (basic functions, Cauchy functions and Green's functions) are obtained in closed form exact solutions of boundary value problems modeling stationary and non-stationary processes of heat transfer to plates of various designs. To construct the main solutions involving the generation of the corresponding integral transformations differential operator Fourier or Bessel differential operator. Done the analytical and computer modeling of steady and unsteady heat transfer in the process of baking dough thin flat pieces of rectangular and circular shapes. The influence of structural and frequency (density) characteristics of thermal sources of heating plate to ensure uniform heating of the dough pieces in different sizes and a spatially distributed temperature distributions billets with uniform intensity distribution of temperature at the surface.
36
Bladé, Ernest. "Modelación del flujo en lámina libre sobre cauces naturales. Análisis integrado con esquemas en volúmenes finitos en una y dos dimensiones." Doctoral thesis, Universitat Politècnica de Catalunya, 2005. http://hdl.handle.net/10803/6394.
Full textAbstract:
El conocimiento del funcionamiento hidráulico de un río en avenida es fundamental para la resolución de gran variedad de problemas de ingeniería hidráulica y dinámica fluvial, como delimitación de zonas inundables, diseño de encauzamientos y estructuras hidráulicas, estabilización de márgenes, estudios de rotura de presa, proyectos de rehabilitación de ríos, o determinación del riesgo asociado a episodios extraordinarios de lluvia. Para ello es necesario el estudio del flujo de agua en lámina libre en régimen variable y con geometrías irregulares. En este trabajo se aborda este estudio mediante la puesta a punto de herramientas de modelación numérica. El objetivo es la puesta a punto de una herramienta para la modelación matemática del flujo de agua en lámina libre, en régimen variable, con geometrías irregulares como son los cauces naturales. Los esquemas que se desarrollan permiten modelar con precisión flujos de agua discontinuos o con singularidades (cambios de régimen, frentes de onda, resaltos hidráulicos), como ocurre en la realidad durante el transcurso de una avenida en gran parte de los ríos, sobretodo en los cauces torrenciales. Se desarrollan esquemas numéricos para la resolución de las ecuaciones de Saint Venant en forma conservativa, explícitos en volúmenes finitos. Este tipo de esquemas shock capturing son los más adecuados para la simulación de flujos con singularidades. Los esquemas desarrollados son de alta resolución, con segundo orden de precisión fuera de las discontinuidades mientras que en éstas no se producen oscilaciones espurias ni más disipación de la debida.
La geometría de los ríos condiciona las características del flujo hidráulico. Cuando existe una dirección del flujo predominante se puede utilizar una aproximación unidimensional, pero en ocasiones (confluencias de ríos, flujos alrededor de estructuras, cauces compuestos, curvas, desbordamiento de cauces) esto no es así debiéndose recurrir a una aproximación bidimensional, más costosa en información, complejidad del modelo y tiempo de cálculo. Se desarrollan nuevas metodologías para la modelación en una y en dos dimensiones y se realiza la integración de ambas para disponer de modelos que permitan simular grandes áreas considerando una aproximación unidimensional donde ésta sea suficiente, y en dos dimensiones donde las características geométricas o del flujo así lo aconsejen, mejorando la eficiencia de las metodologías existentes actualmente.
Las características de las ecuaciones de Saint Venant determinan que las metodologías válidas para otros sistemas de ecuaciones hiperbólicos presenten problemas que conducen a errores importantes en la solución. En una dimensión, y para geometrías irregulares, las ecuaciones presentan una variación espacial del vector de flujo debido a los cambios geométricos. Se desarrolla una metodología para considerar dicha variación que, junto con un correcto tratamiento del término independiente, permite desarrollar un esquema de alta resolución en una dimensión de aplicación a ríos con convergencia a la solución estacionaria correcta.
Para la aproximación bidimensional también se consigue un correcto balance del término independiente discretizado, así como el mojado y secado del dominio, y se permite la incorporación de agua de lluvia al modelo. Así se dispone de un modelo hidrológico distribuido de transformación lluvia - escorrentía totalmente integrado en un modelo hidráulico. En la discretización se pueden utilizar tanto elementos triangulares como cuadriláteros. El sistema se ha implementado en una interfaz amigable de preproceso y postproceso.
Se realiza una exhaustiva verificación de la metodología desarrollada, mediante la comparación con problemas con solución analítica, otros modelos numéricos, y experiencias de laboratorio. Se presentan también aplicaciones de la herramienta desarrollada, para la resolución de problemas reales de ingeniería y dinámica fluvial.
Understanding the hydraulic behaviour of rivers during floods is crucial for the resolution of a variety of problems of hydraulic engineering and river dynamics as flood areas mapping, embankments and hydraulic structures design, streambank stabilization, dam break studies, river rehabilitation, or risk assessment in extraordinary precipitation events. That is the reason for studying unsteady open channel flow in irregular geometries through the development of numerical simulation tools.
The main objective of this work is generating mathematical modelling tools for unsteady open channel flow in irregular geometries, as natural rivers are. The developed numerical schemes are aimed to be able to properly simulate discontinuous flows (front waves, hydraulic jumps, transcritical flows) as occurs during a real flood in most rivers, especially those in Mediterranean areas. Explicit numerical schemes, based on the finite volumes technique, for the resolution of the Saint Venant equations in conservative form, are developed. This shock capturing schemes are most suitable for the simulation of flows with discontinuities. The developed schemes are high resolution schemes: second order precision away from flow discontinuities, no spurious oscillations and no extra dissipation (as with first order schemes) around them.
Flow patterns in rivers depend on their geometry. When there exists a predominant flow direction a one dimensional approach can be used, but other times (river confluences, flow around structures, compound channels, river channel overflow) a two dimensional approach is needed. This last one is more expensive as needs more topographic information, model development is complex, and computational time is greater. New methodologies for one and two dimensional modelling are developed, but also both approaches have been integrated in order to be able to model big areas using a one dimensional approach when it is enough, and a two dimensional one when it is required by flow or geometry characteristics. In that way the efficiency of existing modelling methodologies is improved.
Due to the special characteristics of Saint Venant equations, modelling methods that work for other hyperbolic equations can lead to important errors. In one dimension and irregular geometries, the flux vector of the equations has a spatial dependency on the geometry variations. A methodology that takes into account that dependency is developed. That, together with a correct treatment of the equations source term, allows a correct balance with the discretised term of the rest of the equations, leading to one dimensional high resolution schemes for irregular geometries. Similar schemes in known previous works were not able to converge to steady state solutions or, if they did, they did not converge to the correct one.
A correct balance of the discrtetised source term is also achieved in two dimensions. Also, wetting and drying of the domain and precipitation inputs are implemented. In such way, the developed model can also be seen as a hydrological distributed rainfall-runoff transformation model fully integrated in a hydraulic model. The domain discretisation can be done using triangles or quadrilaterals, and the whole system has been integrated in a user friendly pre-process and post-process interface.
High resolution schemes are based in a mathematical theory which is only valid for hyperbolic equations much simpler than Saint Venant equations. For that reason an exhaustive verification of the methodology is carried out. Verification is done with comparison against problems with analytical solution, other numerical models and laboratory experiments. Finally, some real applications of the methodology to engineering and river dynamics problems are presented.
37
Bladé, Castellet Ernest. "Modelación del flujo en lámina libre sobre cauces naturales. Análisis integrado con esquemas en volúmenes finitos en una y dos dimensiones." Doctoral thesis, Universitat Politècnica de Catalunya, 2005. http://hdl.handle.net/10803/6394.
Full textAbstract:
El conocimiento del funcionamiento hidráulico de un río en avenida es fundamental para la resolución de gran variedad de problemas de ingeniería hidráulica y dinámica fluvial, como delimitación de zonas inundables, diseño de encauzamientos y estructuras hidráulicas, estabilización de márgenes, estudios de rotura de presa, proyectos de rehabilitación de ríos, o determinación del riesgo asociado a episodios extraordinarios de lluvia. Para ello es necesario el estudio del flujo de agua en lámina libre en régimen variable y con geometrías irregulares. En este trabajo se aborda este estudio mediante la puesta a punto de herramientas de modelación numérica. El objetivo es la puesta a punto de una herramienta para la modelación matemática del flujo de agua en lámina libre, en régimen variable, con geometrías irregulares como son los cauces naturales. Los esquemas que se desarrollan permiten modelar con precisión flujos de agua discontinuos o con singularidades (cambios de régimen, frentes de onda, resaltos hidráulicos), como ocurre en la realidad durante el transcurso de una avenida en gran parte de los ríos, sobretodo en los cauces torrenciales. Se desarrollan esquemas numéricos para la resolución de las ecuaciones de Saint Venant en forma conservativa, explícitos en volúmenes finitos. Este tipo de esquemas shock capturing son los más adecuados para la simulación de flujos con singularidades. Los esquemas desarrollados son de alta resolución, con segundo orden de precisión fuera de las discontinuidades mientras que en éstas no se producen oscilaciones espurias ni más disipación de la debida.La geometría de los ríos condiciona las características del flujo hidráulico. Cuando existe una dirección del flujo predominante se puede utilizar una aproximación unidimensional, pero en ocasiones (confluencias de ríos, flujos alrededor de estructuras, cauces compuestos, curvas, desbordamiento de cauces) esto no es así debiéndose recurrir a una aproximación bidimensional, más costosa en información, complejidad del modelo y tiempo de cálculo. Se desarrollan nuevas metodologías para la modelación en una y en dos dimensiones y se realiza la integración de ambas para disponer de modelos que permitan simular grandes áreas considerando una aproximación unidimensional donde ésta sea suficiente, y en dos dimensiones donde las características geométricas o del flujo así lo aconsejen, mejorando la eficiencia de las metodologías existentes actualmente.Las características de las ecuaciones de Saint Venant determinan que las metodologías válidas para otros sistemas de ecuaciones hiperbólicos presenten problemas que conducen a errores importantes en la solución. En una dimensión, y para geometrías irregulares, las ecuaciones presentan una variación espacial del vector de flujo debido a los cambios geométricos. Se desarrolla una metodología para considerar dicha variación que, junto con un correcto tratamiento del término independiente, permite desarrollar un esquema de alta resolución en una dimensión de aplicación a ríos con convergencia a la solución estacionaria correcta.Para la aproximación bidimensional también se consigue un correcto balance del término independiente discretizado, así como el mojado y secado del dominio, y se permite la incorporación de agua de lluvia al modelo. Así se dispone de un modelo hidrológico distribuido de transformación lluvia - escorrentía totalmente integrado en un modelo hidráulico. En la discretización se pueden utilizar tanto elementos triangulares como cuadriláteros. El sistema se ha implementado en una interfaz amigable de preproceso y postproceso.Se realiza una exhaustiva verificación de la metodología desarrollada, mediante la comparación con problemas con solución analítica, otros modelos numéricos, y experiencias de laboratorio. Se presentan también aplicaciones de la herramienta desarrollada, para la resolución de problemas reales de ingeniería y dinámica fluvial.Understanding the hydraulic behaviour of rivers during floods is crucial for the resolution of a variety of problems of hydraulic engineering and river dynamics as flood areas mapping, embankments and hydraulic structures design, streambank stabilization, dam break studies, river rehabilitation, or risk assessment in extraordinary precipitation events. That is the reason for studying unsteady open channel flow in irregular geometries through the development of numerical simulation tools.The main objective of this work is generating mathematical modelling tools for unsteady open channel flow in irregular geometries, as natural rivers are. The developed numerical schemes are aimed to be able to properly simulate discontinuous flows (front waves, hydraulic jumps, transcritical flows) as occurs during a real flood in most rivers, especially those in Mediterranean areas. Explicit numerical schemes, based on the finite volumes technique, for the resolution of the Saint Venant equations in conservative form, are developed. This shock capturing schemes are most suitable for the simulation of flows with discontinuities. The developed schemes are high resolution schemes: second order precision away from flow discontinuities, no spurious oscillations and no extra dissipation (as with first order schemes) around them.Flow patterns in rivers depend on their geometry. When there exists a predominant flow direction a one dimensional approach can be used, but other times (river confluences, flow around structures, compound channels, river channel overflow) a two dimensional approach is needed. This last one is more expensive as needs more topographic information, model development is complex, and computational time is greater. New methodologies for one and two dimensional modelling are developed, but also both approaches have been integrated in order to be able to model big areas using a one dimensional approach when it is enough, and a two dimensional one when it is required by flow or geometry characteristics. In that way the efficiency of existing modelling methodologies is improved.Due to the special characteristics of Saint Venant equations, modelling methods that work for other hyperbolic equations can lead to important errors. In one dimension and irregular geometries, the flux vector of the equations has a spatial dependency on the geometry variations. A methodology that takes into account that dependency is developed. That, together with a correct treatment of the equations source term, allows a correct balance with the discretised term of the rest of the equations, leading to one dimensional high resolution schemes for irregular geometries. Similar schemes in known previous works were not able to converge to steady state solutions or, if they did, they did not converge to the correct one.A correct balance of the discrtetised source term is also achieved in two dimensions. Also, wetting and drying of the domain and precipitation inputs are implemented. In such way, the developed model can also be seen as a hydrological distributed rainfall-runoff transformation model fully integrated in a hydraulic model. The domain discretisation can be done using triangles or quadrilaterals, and the whole system has been integrated in a user friendly pre-process and post-process interface.High resolution schemes are based in a mathematical theory which is only valid for hyperbolic equations much simpler than Saint Venant equations. For that reason an exhaustive verification of the methodology is carried out. Verification is done with comparison against problems with analytical solution, other numerical models and laboratory experiments. Finally, some real applications of the methodology to engineering and river dynamics problems are presented.
38
CRUZ, Thamires Santos. "Resultados de existência para um sistema acoplado de equações diferenciais fracionárias não lineares com condições de fronteira em três pontos." Universidade Federal de Pernambuco, 2012. https://repositorio.ufpe.br/handle/123456789/7611.
Full textAbstract:
Made available in DSpace on 2014-06-12T18:33:55Z (GMT). No. of bitstreams: 2
arquivo9590_1.pdf: 550592 bytes, checksum: f39c06a39449cf3e4286c5bc1c417dbe (MD5)
license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5)
Previous issue date: 2012Conselho Nacional de Desenvolvimento Científico e Tecnológico
Neste trabalho, foi mostrado a existência de solucão para um sistema acoplado de equações diferenciais fracionarias não lineares com condicões de fronteira em três pontos, onde algumas condições são satisfeitas. Para isto, precisou-se de um estudo sobre integrais e derivadas fracion arias e teoremas de ponto fixo. Estudou-se ainda a existência e unicidade da solucão do problema de Cauchy para funcões lipschitzianas, com condicões iniciais de ordem fracionaria. Alem disso, foi analisada uma aplicacão de derivadas fracionarias, a viscoelasticidade linear
39
Gómez, Cardona Luz Adriana, and Jaramillo Andrés Felipe Motta. "Mecanismos para la generación de ingresos de las víctimas de conflicto armado contemplados en la Política Pública para la atención y reparación integral, para el periodo 2013-2015 en el Bajo Cauca Antioqueño." Master's thesis, Pontificia Universidad Católica del Perú, 2021. http://hdl.handle.net/20.500.12404/19882.
Full textAbstract:
El presente proyecto de tesis para la Maestría en Gerencia Social es un estudio
de caso, que, desde el enfoque cualitativo de la investigación, analiza la Política
Pública para la atención y reparación integral de víctimas del conflicto armado, para
el periodo 2013-2015, en el Bajo Cauca antioqueño. Para lograrlo se determinó
pertinente realizar una revisión documental sobre la norma desde la generalidad
(Colombia) y en relación con el contexto del Bajo Cauca antioqueño. Posteriormente
se asume para la investigación un solo componente de la política integral - generación
de ingresos - que pretende ser profundizada en términos de ocurrencia, desarrollo,
eficiencia e impacto.
Con este fin y entendiendo a las víctimas como población objetivo, se hace uso
del muestreo no probabilístico aleatorio estratificado con la intención de formar grupos
focales en cada uno de los seis municipios que constituyen el Bajo Cauca.
Finalmente, a través de la observación directa, la entrevista semiestructurada y la
historia de vida, se hizo la recolección de información necesaria que permitiera dar
cumplimiento al objetivo general y objetivos específicos de la investigación.
Como conclusiones trascendentales del proceso pueden plantearse,
inicialmente que La ley 1448 de 2011 tiene una profunda dicotomía, desde su
inspirada redacción hasta su necesaria, vital e innegociable ejecución, esta situación
puede estar antecedida, al hecho que la política no fue concertada con los grupos de
víctimas organizados a nivel territorial y en estos términos no corresponde a una
subsanación real de sus necesidades. Adicionalmente, desde un escenario de
reparación de víctimas, que aún está en conflicto, son difíciles elementos como el
control del territorio y la participación, situaciones que ponen en entredicho los
principios vectores de la política: la reparación, la justicia y la paz.
La intención del documento, además de su carácter analítico de la norma, es
también la de asumir una postura reflexiva de influencia real sobre la realidad de las
víctimas en el Bajo Cauca en particular, y en Colombia, en términos generales. Pues
el ejercicio de investigar debe y tiene que cumplir una función de transformación de
los fenómenos problemáticos que impiden a los seres humanos alcanzar el “desarrollo
de sus capacidades”, mejorar su “calidad de vida” y propender por su felicidad. Sea
cual sea la idea que se tiene de ella.
Se proponen dos modelos de intervención a la problemática, teniendo en
cuenta las organizaciones, “índice de capacidad organizacional” y la capacidad
empresarial a través del “fortalecimiento empresarial para víctimas”.
El índice de capacidad organizacional tiene como objetivo fundamental el
“fortalecimiento de capacidades gerenciales, administrativas, financieras, de
relacionamiento y de gestión de las organizaciones de las víctimas”.
Para lograrlo, es necesario realizar un acercamiento diagnóstico a través del
Índice de capacidad organizacional, herramienta de medición cuantitativa, que de 1 a
3 mide el nivel gerencial, administrativo, financiero, de gestión y de relacionamiento
interno. Una vez obtenida la base diagnóstica, se identificará con ella el área a
fortalecer y las temáticas que deberían ser tratadas, este fortalecimiento empresarial,
se llevará a cabo a través de una estrategia participativa, lúdica, reflexiva y
experiencial.
La propuesta de fortalecimiento empresarial para víctimas fusiona servicios
financieros y no financieros, contrastando la oferta del crédito con formación en
desarrollo empresarial y autonomía personal. Los servicios financieros se desarrollan
a través de los créditos individuales y grupales, cada uno con sus respectivos
procesos de formación, finalmente, la oferta de servicios no financieros está
enmarcado dentro del programa de desarrollo humano y el programa de desarrollo
empresarial con enfoque de víctimas y estrategias de sostenibilidad.
40
CRUZ, Thamires Santos. "Resultados de exist^encia para um sistema acoplado de equa c~oes diferenciais fracion arias n~ao lineares com condi c~oes de fronteira em tr^es pontos." Universidade Federal de Pernambuco, 2012. https://repositorio.ufpe.br/handle/123456789/11701.
Full textAbstract:
Submitted by Etelvina Domingos (etelvina.domingos@ufpe.br) on 2015-03-10T17:34:15Z
No. of bitstreams: 2
license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5)
TSC.pdf: 550592 bytes, checksum: f39c06a39449cf3e4286c5bc1c417dbe (MD5)Made available in DSpace on 2015-03-10T17:34:15Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TSC.pdf: 550592 bytes, checksum: f39c06a39449cf3e4286c5bc1c417dbe (MD5) Previous issue date: 2012
CAPES CNPq
Neste trabalho, foi mostrado a exist^encia de solu c~ao para um sistema acoplado de equa c~oes diferenciais fracion arias n~ao lineares com condi c~oes de fronteira em tr^es pontos, onde algumas condi c~oes s~ao satisfeitas. Para isto, precisou-se de um estudo sobre integrais e derivadas fracion arias e teoremas de ponto xo. Estudou-se ainda a exist^encia e unicidade da solu c~ao do problema de Cauchy para fun c~oes lipschitzianas, com condi c~oes iniciais de ordem fracion aria. Al em disso, foi analisada uma aplica c~ao de derivadas fracion arias, a viscoelasticidade linear.
41
Hamdi, Tarek. "Calcul stochastique commutatif et non-commutatif : théorie et application." Thesis, Besançon, 2013. http://www.theses.fr/2013BESA2015/document.
Full textAbstract:
Mon travail de thèse est composé de deux parties bien distinctes, la première partie est consacrée à l’analysestochastique en temps discret des marches aléatoires obtuses quant à la deuxième partie, elle est liée aux probabili-tés libres. Dans la première partie, on donne une construction des intégrales stochastiques itérées par rapport à unefamille de martingales normales d-dimentionelles. Celle-ci permet d’étudier la propriété de représentation chaotiqueen temps discret et mène à une construction des opérateurs gradient et divergence sur les chaos de Wiener correspon-dant. [...] d’une EDP non linéaire alors que la deuxième est de nature combinatoire.Dans un second temps, on a revisité la description de la mesure spectrale de la partie radiale du mouvement Browniensur Gl(d,C) quand d ! +¥. Biane a démontré que cette mesure est absolument continue par rapport à la mesurede Lebesgue et que son support est compact dans R+. Notre contribution consiste à redémontrer le résultat de Bianeen partant d’une représentation intégrale de la suite des moments sur une courbe de Jordon autour de l’origine etmoyennant des outils simples de l’analyse réelle et complexeMy PhD work is composed of two parts, the first part is dedicated to the discrete-time stochastic analysis for obtuse random walks as to the second part, it is linked to free probability. In the first part, we present a construction of the stochastic integral of predictable square-integrable processes and the associated multiple stochastic integrals ofsymmetric functions on Nn (n_1), with respect to a normal martingale.[...] In a second step, we revisited thedescription of the marginal distribution of the Brownian motion on the large-size complex linear group. Precisely, let (Z(d)t )t_0 be a Brownian motion on GL(d,C) and consider nt the limit as d !¥ of the distribution of (Z(d)t/d)⋆Z(d)t/d with respect to E×tr
42
Dannawi, Ihab. "Contributions aux équations d'évolutions non locales en espace-temps." Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS007/document.
Full textAbstract:
Dans cette thèse, nous nous intéressons à l'étude de quatre équations d'évolution non-locales. Les solutions de ces quatre équations peuvent exploser en temps fini. Dans la théorie des équations d'évolution non-linéaires, une solution est qualifiée de globale si elle est définie pour tout temps positif. Au contraire, si une solution existe seulement sur un intervalle de temps [0; T) borné, elle est dite locale. Dans ce dernier cas et quand le temps maximal d'existence est relié à une alternative d'explosion, on dit aussi que la solution explose en temps fini. Dans un premier travail, nous considérons l'équation de Schrödinger non-linéaire avec une puissance fractionnaire du laplacien, et nous obtenons l'explosion de la solution en temps fini Tmax > 0 pour toute condition initiale positive et non-triviale dans le cas d'exposant sous-critique. Ensuite, nous étudions une équation des ondes amorties avec un potentiel d'espace-temps et un terme non-linéaire et non-local en temps. Nous obtenons un résultat d'existence locale d'une solution dans l'espace d'énergie sous des conditions restrictives sur les données initiales, la dimension de l'espace et la croissance du terme non-linéaire. De plus, nous obtenons l'explosion de la solution en temps fini pour toute condition initiale de moyenne strictement positive. De plus, nous étudions un problème de Cauchy pour l'équation d'évolution avec un p- Laplacien avec une non linéarité non-locale en temps. Dans ce cadre, nous nous intéressons à l'étude de l'existence locale d'une solution de cette équation ainsi qu'un résultat de non-existence de solution globale. Finalement, nous étudions l'intervalle maximal d'existence des solutions de l'équation des milieux poreux avec un terme non-linéaire non-local en tempsIn this thesis, we study four non-local evolution equations. The solutions of these four equations can blow up in finite time. In the theory of nonlinear evolution equations, a solution is qualified as global if it isdefined for any time. Otherwise, if a solution exists only on a bounded interval [0; T), it is called local solution. In this case and when the maximum time of existence is related to a blow up alternative, we say that the solution blows up in finite time. First, we consider the nonlinear Schröodinger equation with a fractional power of the Laplacien operator, and we get a blow up result in finite time Tmax > 0 for any non-trivial non-negative initial condition in the case of sub-critical exponent. Next, we study a damped wave equation with a space-time potential and a non-local in time non-linear term. We obtain a result of local existence of a solution in the energy space under some restrictions on the initial data, the dimension of the space and the growth of nonlinear term. Additionally, we get a blow up result of the solution in finite time for any initial condition positive on average. In addition, we study a Cauchy problem for the evolution p-Laplacien equation with nonlinear memory. We study the local existence of a solution of this equation as well as a result of non-existence of global solution. Finally, we study the maximum interval of existence of solutions of the porous medium equation with a nonlinear non-local in time term
43
Luther, Uwe. "Approximation Spaces in the Numerical Analysis of Cauchy Singular Integral Equations." Doctoral thesis, 2004. https://monarch.qucosa.de/id/qucosa%3A17285.
Full textAbstract:
The paper is devoted to the foundation of
approximation methods for integral equations of
the form (aI+SbI+K)f=g,
where S is the Cauchy singular
integral operator on (-1,1) and K is a weakly
singular integral operator.
Here a,b,g are given functions on (-1,1) and
the unknown function f on (-1,1) is looked for.
It is assumed that a and b are real-valued and
Hölder continuous functions on [-1,1] without
common zeros and that g belongs to some
weighted space of Hölder continuous functions.
In particular, g may have a finite number of
singularities.
Based on known spectral properties of Cauchy
singular integral operators approximation methods
for the numerical solution of the above equation
are constructed, where both aspects the
theoretical convergence and the numerical
practicability are taken into account.
The weighted uniform convergence of these methods
is studied using a general
approach based on the theory of approximation
spaces. With the help of this approach it is
possible to prove simultaneously the stability,
the convergence and results on the order of
convergence of the approximation methods under
consideration.
44
Hay, Todd. "The analytic edge - image reconstruction from edge data via the Cauchy Integral." Thesis, 2015. https://hdl.handle.net/2144/16055.
Full textAbstract:
A novel image reconstruction algorithm from edges (image gradients) follows from the
Sokhostki-Plemelj Theorem of complex analysis, an elaboration of the standard Cauchy
(Singular) Integral. This algorithm demonstrates the use of Singular Integral Equation
methods to image processing, extending the more common use of Partial Differential
Equations (e.g. based on variants of the Diffusion or Poisson equations). The Cauchy Integral approach has a deep connection to and sheds light on the (linear and non-linear) diffusion equation, the retinex algorithm and energy-based image regularization. It extends the commonly understood local definition of an edge to a global, complex analytic structure - the analytic edge - the contrast weighted kernel of the Cauchy Integral. Superposition of the set of analytic edges provides a "filled-in" image which is the piece-wise analytic image corresponding to the edge (gradient data) supplied. This is a fully parallel operation which avoids the time penalty associated with iterative solutions and thus is compatible with the short time (about 150 milliseconds) that is biologically available for the brain to construct a perceptual image from edge data. Although this algorithm produces an exact reconstruction of a filled-in image from the gradients of that image, slight modifications of it produce images which correspond to perceptual reports of human observers when presented with a wide range of "visual contrast illusion" images.
45
Prescott, Richard Warren. "A necessary condition for supporting sets of measures with cauchy integral in H²(Bn)." 1987. http://catalog.hathitrust.org/api/volumes/oclc/16270249.html.
Full textAbstract:
Thesis (Ph. D.)--University of Wisconsin--Madison, 1987.Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 47).
46
Luther, Uwe [Verfasser]. "Approximation spaces in the numerical analysis of Cauchy singular integral equations / vorgelegt von Uwe Luther." 2005. http://d-nb.info/976581167/34.
Full text
47
Lee, Jia-Wei, and 李家瑋. "Application of the Clifford algebra valued boundary integral equations with Cauchy-type kernels to some engineering problems." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/02351203973629353925.
Full textAbstract:
博士國立臺灣海洋大學
河海工程學系
104
The conventional complex variable boundary integral equation (CVBIE) based on the conventional Cauchy integral formula is powerful and suitable to solve two-dimensional problems. In particular, the unknown function is a complex-valued holomorphic function. In other words, the unknown function satisfies the Cauchy-Riemann equations. However, the most part of practical engineering problems are three-dimensional problems and do not necessarily satisfies Cauchy-Riemann equations. Therefore, there are two targets in this dissertation. One is to extend the conventional CVBIE to solve two-dimensional problems for which the unknown function is not a complex-valued holomorphic function. The other is to extend to three-dimensions and derive an extended BIE still preserving some properties of complex variables in the three-dimensional state. For the extension of the conventional CVBIE, we employ the Borel-Pompeiu formula to derive the generalized CVBIE. In this way, the torsion problems can be solved in the state of two shear stress fields directly. In addition, the torsional rigidity can also be determined simultaneously. Since the theory of complex variables has a limitation that is only suitable for 2-dimensional problems, we introduce Clifford algebra and Clifford analysis to replace complex variables to deal with 3-dimensional problems. Clifford algebra can be seen as an extension of complex or quaternionic algebras. Clifford analysis is also known as hypercomplex analysis. We apply the Clifford algebra valued Stokes' theorem to derive Clifford algebra valued BIEs with Cauchy-type kernels. In this way, some three-dimensional problem with multiple unknown fields may be solved straightforward. Finally, several electromagnetic scattering problems are considered to check the validity of the derived Clifford algebra valued BIEs.
48
Lee, Cheuk Yu. "Fundamental solution based numerical methods for three dimensional problems: efficient treatments of inhomogeneous terms and hypersingular integrals." Phd thesis, 2016. http://hdl.handle.net/1885/117204.
Full textAbstract:
In recent years, fundamental solution based numerical methods
including the meshless method of fundamental solutions (MFS), the
boundary element method (BEM) and the hybrid fundamental solution
based finite element method (HFS-FEM) have become popular for
solving complex engineering problems. The application of such
fundamental solutions is capable of reducing computation
requirements by simplifying the domain integral to the boundary
integral for the homogeneous partial differential equations. The
resulting weak formulations, which are of lower dimensions, are
often more computationally competitive than conventional
domain-type numerical methods such as the finite element method
(FEM) and the finite difference method (FDM).
In the case of inhomogeneous partial differential equations
arising from transient problems or problems involving body
forces, the domain integral related to the inhomogeneous
solutions term will need to be integrated over the interior
domain, which risks losing the competitive edge over the FEM or
FDM. To overcome this, a particular treatment to the
inhomogeneous term is needed in the solution procedure so that
the integral equation can be defined for the boundary. In
practice, particular solutions in approximated form are usually
applied rather than the closed form solutions, due to their
robustness and readiness. Moreover, special numerical treatment
may be required when evaluating stress directly on the domain
surface which may give rise to hypersingular integral
formulation. This thesis will discuss how the MFS and the BEM can
be applied to the three-dimensional elastic problems subjected to
body forces by introducing the compactly supported radial basis
functions in addition to the efficient treatment of hypersingular
surface integrals. The present meshless approach with the MFS and
the compactly supported radial basis functions is later extended
to solve transient and coupled problems for three-dimensional
porous media simulation.
49
Abdeljawad, Ahmed. "Global microlocal analysis on Rd with applications to hyperbolic partial differential equations and modulation spaces." Doctoral thesis, 2019. http://hdl.handle.net/2318/1718409.
Full textAbstract:
This thesis treats different aspects of microlocal and time-frequency analysis, with particular emphasis on techniques involving multi-products of Fourier integral operators and one-parameter group properties for pseudodifferential operators. In the first part, we study a class of hyperbolic Cauchy problems, associated with linear operators and systems with polynomially bounded coefficients, variable multiplicities and involutive characteristics, globally defined on Rd. We prove well-posedness in Sobolev-Kato spaces, with loss of smoothness and decay at infinity. We also obtain results about propagation of singularities, in terms of wave-front sets describing the evolution of both smoothness and decay singularities of temperate distributions. In the second part, we deduce lifting property for modulation spaces and construct explicit isomorpisms between them. To prove such results, we study one-parameter group properties for pseudo-differential operators with symbols in some Gevrey-Hörmander classes. Furthermore, we focus on some classes of pseudo-differential operators with symbols admitting anisotropic exponential growth at infinity. We deduce algebraic and invariance properties of these classes. Moreover, we prove mapping properties for these operators on Gelfand-Shilov spaces of type S and modulation spaces.
50
Бабак, Тетяна Юріївна. "Розв’язання характеристичного сингулярного інтегрального рівняння на замкненому контурі." Магістерська робота, 2020. https://dspace.znu.edu.ua/jspui/handle/12345/3075.
Full textAbstract:
Бабак Т. Ю. Розв’язання характеристичного сингулярного інтегрального рівняння на замкненому контурі : кваліфікаційна робота магістра спеціальності 111 "Математика" / наук. керівник Н. М. Д’яченко. Запоріжжя : ЗНУ, 2020. 59 с.UA : Робота викладена на 59 сторінках друкованого тексту, містить 8 рисунків, 15 джерел. Об’єкт дослідження: характеристичні сингулярні інтегральні рівняння і крайові задачі теорії аналітичних функцій, до яких вони зводяться. Мета роботи: вивчити теоретичні відомості щодо розв’язання характеристичних сингулярних інтегральних рівнянь методом зведення їх до крайових задач Рімана; розв’язати конкретні приклади для рівнянь на зімкненому контурі і на дійсній осі. Методи дослідження: зведення характеристичних сингулярних інтегральних рівнянь до крайових задач Рімана, метод Гахова розв’язання крайових задач Рімана. У роботі вивчено основні поняття, пов’язані з характеристичними сингулярними інтегральними рівняннями. Викладено метод Гахова Ф.Д. розв’язання рівнянь такого типу зведенням їх до крайових задач Рімана. Наведено приклади розв’язання характеристичних сингулярних інтегральних рівнянь на замкненому контурі та на дійсній осі, деякі із запропонованих в підручнику Гахова Ф.Д., а деякі – авторські.
EN : The work is presented on 59 pages of printed text, 8 figures, 15 references. The object of the study is the characteristic singular integral equations and the boundary value problems of the theory of analytic functions to which they are reduced. The aim of the study is to study theoretical information about solving characteristic singular integral equations by reducing them to Riemann boundary problems; to solve some examples of the equations for closed contour and real axis. The methods of research are the reduction of the characteristic singular integral equations to the Riemann boundary-value problems, the Gakhov method for solving of the Riemann boundary-value problems. The basic concepts related to the characteristic singular integral equations are studied. The F. Gakhov method for solving equations of this type by reducing them to Riemann boundary-value problems. The examples of solving characteristic singular integral equations on a closed circuit and on a real axis are presented, some of them are proposed in the F. Gakhov textbook, and some are author's.