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Sarkar, Koushik. "Topology of different metric spaces and fixed point theories." Thesis, University of North Bengal, 2021. http://ir.nbu.ac.in/handle/123456789/4380.
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Kreuger, Per. "Computational Issues in Calculi of Partial Inductive Definitions." Doctoral thesis, Decisions, Networks and Analytics lab, 1995. http://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-21196.
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We study the properties of a number of algorithms proposed to explore the computational space generated by a very simple and general idea: the notion of a mathematical definition and a number of suggested formal interpretations ofthis idea. Theories of partial inductive definitions (PID) constitute a class of logics based on the notion of an inductive definition. Formal systems based on this notion can be used to generalize Horn-logic and naturally allow and suggest extensions which differ in interesting ways from generalizations based on first order predicate calculus. E.g. the notion of completion generated by a calculus of PID and the resulting notion of negation is completely natural and does not require externally motivated procedures such as "negation as failure". For this reason, computational issues arising in these calculi deserve closer inspection. This work discuss a number of finitary theories of PID and analyzethe algorithmic and semantical issues that arise in each of them. There has been significant work on implementing logic programming languages in this setting and we briefly present the programming language and knowledge modelling tool GCLA II in which many of the computational prob-lems discussed arise naturally in practice.Also published as SICS Dissertation no. SICS-D-19
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Aziz, Waleed. "Analytic and algebraic aspects of integrability for first order partial differential equations." Thesis, University of Plymouth, 2013. http://hdl.handle.net/10026.1/1468.
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This work is devoted to investigating the algebraic and analytic integrability of first order polynomial partial differential equations via an understanding of the well-developed area of local and global integrability of polynomial vector fields. In the view of characteristics method, the search of first integrals of the first order partial differential equations P(x,y,z)∂z(x,y) ∂x +Q(x,y,z)∂z(x,y) ∂y = R(x,y,z), (1) is equivalent to the search of first integrals of the system of the ordinary differential equations dx/dt= P(x,y,z), dy/dt= Q(x,y,z), dz/dt= R(x,y,z). (2) The trajectories of (2) will be found by representing these trajectories as the intersection of level surfaces of first integrals of (1). We would like to investigate the integrability of the partial differential equation (1) around a singularity. This is a case where understanding of ordinary differential equations will help understanding of partial differential equations. Clearly, first integrals of the partial differential equation (1), are first integrals of the ordinary differential equations (2). So, if (2) has two first integrals φ1(x,y,z) =C1and φ2(x,y,z) =C2, where C1and C2 are constants, then the general solution of (1) is F(φ1,φ2) = 0, where F is an arbitrary function of φ1and φ2. We choose for our investigation a system with quadratic nonlinearities and such that the axes planes are invariant for the characteristics: this gives three dimensional Lotka– Volterra systems x' =dx/dt= P = x(λ +ax+by+cz), y' =dy/dt= Q = y(µ +dx+ey+ fz), z' =dz/dt= R = z(ν +gx+hy+kz), where λ,µ,ν 6= 0. v Several problems have been investigated in this work such as the study of local integrability and linearizability of three dimensional Lotka–Volterra equations with (λ:µ:ν)–resonance. More precisely, we give a complete set of necessary and sufficient conditions for both integrability and linearizability for three dimensional Lotka-Volterra systems for (1:−1:1), (2:−1:1) and (1:−2:1)–resonance. To prove their sufficiency, we mainly use the method of Darboux with the existence of inverse Jacobi multipliers, and the linearizability of a node in two variables with power-series arguments in the third variable. Also, more general three dimensional system have been investigated and necessary and sufficient conditions are obtained. In another approach, we also consider the applicability of an entirely different method which based on the monodromy method to prove the sufficiency of integrability of these systems. These investigations, in fact, mean that we generalized the classical centre-focus problem in two dimensional vector fields to three dimensional vector fields. In three dimensions, the possible mechanisms underling integrability are more difficult and computationally much harder. We also give a generalization of Singer’s theorem about the existence of Liouvillian first integrals in codimension 1 foliations in Cnas well as to three dimensional vector fields. Finally, we characterize the centres of the quasi-homogeneous planar polynomial differential systems of degree three. We show that at most one limit cycle can bifurcate from the periodic orbits of a centre of a cubic homogeneous polynomial system using the averaging theory of first order.
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Han, Zhi. "Applications of stochastic control and statistical inference in macroeconomics and high-dimensional data." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54401.
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This dissertation is dedicated to study the modeling of drift control in foreign exchange reserves management and design the fast algorithm of statistical inference with its application in high dimensional data analysis. The thesis has two parts. The first topic involves the modeling of foreign exchange reserve management as an drift control problem. We show that, under certain conditions, the control band policies are optimal for the discounted cost drift control problem and develop an algorithm to calculate the optimal thresholds of the optimal control band policy. The second topic involves the fast computing algorithm of partial distance covariance statistics with its application in feature screening in high dimensional data. We show that an O(n log n) algorithm for a version of the partial distance covariance exists, compared with the O(n^2) algorithm implemented directly accordingly to its definition. We further propose an iterative feature screening procedure in high dimensional data based on the partial distance covariance. This procedure enjoys two advantages over the correlation learning. First, an important predictor that is marginally uncorrelated but jointly correlated with the response can be picked by our procedure and thus entering the estimation model. Second, our procedure is robust to model mis- specification.
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Leahy, James-Michael. "On parabolic stochastic integro-differential equations : existence, regularity and numerics." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10569.
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In this thesis, we study the existence, uniqueness, and regularity of systems of degenerate linear stochastic integro-differential equations (SIDEs) of parabolic type with adapted coefficients in the whole space. We also investigate explicit and implicit finite difference schemes for SIDEs with non-degenerate diffusion. The class of equations we consider arise in non-linear filtering of semimartingales with jumps. In Chapter 2, we derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by Lévy driven stochastic differential equations (SDEs) with adapted coefficients in weighted Hölder norms using the Sobolev embedding theorem and the change of variable formula. As an application of some basic properties of flows of Weiner driven SDEs, we prove the existence and uniqueness of classical solutions of linear parabolic second order stochastic partial differential equations (SPDEs) by partitioning the time interval and passing to the limit. The methods we use allow us to improve on previously known results in the continuous case and to derive new ones in the jump case. Chapter 3 is dedicated to the proof of existence and uniqueness of classical solutions of degenerate SIDEs using the method of stochastic characteristics. More precisely, we use Feynman-Kac transformations, conditioning, and the interlacing of space inverses of stochastic flows generated by SDEs with jumps to construct solutions. In Chapter 4, we prove the existence and uniqueness of solutions of degenerate linear stochastic evolution equations driven by jump processes in a Hilbert scale using the variational framework of stochastic evolution equations and the method of vanishing viscosity. As an application, we establish the existence and uniqueness of solutions of degenerate linear stochastic integro-differential equations in the L2-Sobolev scale. Finite difference schemes for non-degenerate SIDEs are considered in Chapter 5. Specifically, we study the rate of convergence of an explicit and an implicit-explicit finite difference scheme for linear SIDEs and show that the rate is of order one in space and order one-half in time.
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Melo, Gustavo Cavalcanti. "Funções parciais recursivas e funções parcialmente Turing-computáveis: uma prova de equivalência." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9586.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In the thirties of the last century, several formal versions for the intuitive notion of algorithmic function were offered. Among them, the version of the recursive functions and the version of the Turing-computable functions. Posteriorly, such versions were extended in order to also include the partial algorithmic functions, giving rise, in this way, to the version of the partial recursive functions and to the version of the partially Turing-computable functions. In this context, this research, located into Computability Theory domain and built in the light of theoretical assumptions of Davis (1982), Mendelson (2009), Dias & Weber (2010), Rogers (1987), Soare (1987), Cooper (2004), among others, is intended to rebuild the proof that the given formal versions referred to the intuitive notion of partial algorithmic function, despite being conceptually distinct, they are extensionally equivalents in the sense that they determine the same set of theoretical-numerical functions. As a part of this rebuilding, we shall prove, in na unprecedented way, using quintuples, that every partial recursive function is partially Turing-computable. In the literature, this theorem is proved by means of a set of quadruples. However, defining a lower cardinality set constructed by quintuples, it is possible to prove it in a smaller time interval, which representes a gain from the computational point of view. Besides presenting this alternative proof, posed by the Church-Turing thesis that the set of partial recursive functions includes all the partial algorithmic functions, we shall investigate if this set itself and its infinite subsets are or are not algorithmic. In this survey, we shall demonstrate, in arithmetical terms, with the aid of Rice‟s theorem, that although the set of partial recursive functions is algorithmic, all its subsets which are different from the empty set are not, among which are the set of recursive functions and the set of primitive recursive functions.
Na década de 30 do século passado, foram oferecidas várias versões formais para a noção intuitiva de função algorítmica. Dentre elas, a versão das funções recursivas e a versão das funções Turing-computáveis. Posteriormente, tais versões foram estendidas a fim de abranger também as funções parciais algorítmicas, dando origem, deste modo, à versão das funções parciais recursivas e à versão das funções parcialmente Turing-computáveis. Nesse contexto, esta pesquisa, situada dentro do domínio da Teoria da Computabilidade e construída à luz dos pressupostos teóricos de Davis (1982), Mendelson (2009), Dias e Weber (2010), Rogers (1987), Soare (1987), Cooper (2004), entre outros, destina-se a reconstruir a prova de que as referidas versões formais dadas para a noção intuitiva de função parcial algorítmica, apesar de conceitualmente distintas, são extensionalmente equivalentes no sentido de que elas determinam o mesmo conjunto de funções numéricas. Como parte desta reconstrução, provaremos, de modo inédito, mediante o uso de quíntuplas, que toda função parcial recursiva é parcialmente Turing-computável. Na literatura especializada, esse teorema é provado por meio de um conjunto de quádruplas. Porém, definindo um conjunto de menor cardinalidade constituído por quíntuplas, é possível prová-lo em um intervalo menor de tempo, o que representa um ganho do ponto de vista computacional. Além de apresentar essa prova alternativa, posto pela Tese de Church-Turing que o conjunto das funções parciais recursivas contém todas as funções parciais algorítmicas, investigaremos se ele próprio e os seus infinitos subconjuntos são ou não algorítmicos. Nesta investigação, demonstraremos, em termos aritméticos, com o auxílio do Teorema de Rice, que embora o conjunto das funções parciais recursivas seja algorítmico, todos os seus subconjuntos diferentes do conjunto vazio não o são, dentre os quais estão o conjunto das funções recursivas e o conjunto das funções recursivas primitivas.
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Yue, Wen. "Absolute continuity of the laws, existence and uniqueness of solutions of some SDEs and SPDEs." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/absolute-continuity-of-the-laws-existence-and-uniqueness-of-solutions-of-some-sdes-and-spdes(2bc80de8-7c36-453f-a7c2-69fa4ee0e705).html.
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This thesis consists of four parts. In the first part we recall some background theory that will be used throughout the thesis. In the second part, we studied the absolute continuity of the laws of the solutions of some perturbed stochastic differential equaitons(SDEs) and perturbed reflected SDEs using Malliavin calculus. Because the extra terms in the perturbed SDEs involve the maximum of the solution itself, the Malliavin differentiability of the solutions becomes very delicate. In the third part, we studied the absolute continuity of the laws of the solutions of the parabolic stochastic partial differential equations(SPDEs) with two reflecting walls using Malliavin calculus. Our study is based on Yang and Zhang \cite{YZ1}, in which the existence and uniqueness of the solutions of such SPDEs was established. In the fourth part, we gave the existence and uniqueness of the solutions of the elliptic SPDEs with two reflecting walls and general diffusion coefficients.
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Barles, Guy. "Contribution à la théorie des solutions de viscosité des équations de Hamilton-Jacobi du premier ordre et applications à des problèmes de contrôle optimal et de perturbations singulières." Paris 9, 1988. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1988PA090004.
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Nous présentons dans ce travail divers résultats concernant les équations de Hamilton-Jacobi du premier ordre ainsi que leurs applications à certains problèmes de contrôle optimal déterministe et de perturbations singulières. La première partie est consacrée à l'étude des solutions continues: nous donnons divers résultats d'existence, d'unicité et de régularité à la fois locale et globale). La deuxième partie décrit une étude systématique des solutions discontinues: elle fournit une approche générale très simple des problèmes de temps de sortie, de contrôle non-borne et de perturbations singulières, avec, en particulier, des applications dans le cadre des grandes déviations
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Santos, Renato Augusto Nascimento. "Existência de soluções para uma classe de problemas elípticos não quadráticos no infinito." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7414.
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Previous issue date: 2014-08-08Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
We study the deformation theorem using the condition introduced by Cerami [8]. Furthermore, we study the following Dirichlet problem: ( u = f(x; u); x 2 u = 0; x 2 @ where is a smooth and bounded domain in RN and f : R ! R is a Caratheodory function with subcritical growth. In the above problem, we use the condition of Cerami [8] again, to ensure the existence of non-trivial solution. For this purpose, we use General Minimax Theorem proved by Bartolo in [12].
Neste trabalho, estudamos o Teorema de Deformação usando a condição introduzida por Cerami [8]. Além disso, estudamos o seguinte problema de Dirichlet: ( u = f(x; u); x 2 u = 0; x 2 @ onde e um domínio suave e limitado em RN e f : R ! R é uma função de Caratheodory com crescimento subcrítico. No problema acima, utilizamos novamente a condição de Cerami [8], para garantir a existência de solução não-trivial, para este propósito, usaremos Teorema Geral de Minimax provado pelo Bartolo em [12].
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Safi, Mohammed. "Stabilité de Lyapunov de systèmes couplés impliquant une équation de transport." Thesis, Toulouse, ISAE, 2018. http://www.theses.fr/2018ESAE0022/document.
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L’objet de cette thèse est l’étude des propriétés de stabilité et contrôle pour des systèmes linéaires écrits à l’aide d’équations aux dérivées partielles (EDP) ou d’équations à retard. Nous souhaitons exploiter dans cette thèse les liens qui existent entre ces deux classes de systèmes de dimension infinie afin de développer une nouvelle approche permettant leur analyse. En effet dans plusieurs applications, il est possible de choisir l’un ou l’autre de ces deux types de systèmes pour modéliser la dynamique considérée. Par exemple, les phénomènes de congestion dans un réseau routier peuvent être modélisés à l’aide d’EDP de type transport [JKC], mais aussi par un modèle à retard distribué [MMN] ou encore à retard discret [SN]. On peut également renvoyer aux travaux de Krstic [K] sur la formulation d’un système à retard comme un système EDP. Ces deux classes de systèmes sont des cas particuliers de systèmes de dimension infinie, et contrairement aux cas de systèmes de dimension finie, on parle de fonctions d’état plutôt que vecteur d’état. Cela implique que l’analyse associée est plus délicate et fait appel à des outils dédiés. Dans le cadre de la thèse, l’étudiant se focalisera sur les approches basées sur une extension du théorème de Lyapunov pour les systèmes de dimension infinie utilisant des fonctionnelles spécifiques. Comme pour la modélisation, l’analyse de stabilité des systèmes à retard ou de type EDP peut être menée à l’aide de fonctionnelles de Lyapunov très similaires. Nous souhaitons que cette thèse tire parti des travaux existants dans les deux communautés sur les systèmes à retards et de type EDP pour développer une approche novatrice et unifiée pour l’analyse et le contrôle de systèmes de dimension infinie. Pour cela, le candidat s’appuiera sur ses acquis en automatique et en mathématiques ainsi que sur l’expertise des deux encadrants. Plusieurs contributions sont attendues durant la thèse. Dans un premier temps, il sera question d’étendre des résultats récents [SG1,2] développés pour l’analyse de stabilité des systèmes à retards au cas de systèmes régis par des EDP. Ces premiers résultats auront vocation à servir de base pour l’étude de la synthèse de commandes robustes dans le cadre d’applications telles que le contrôle de trafic routier [MMN], le contrôle de vibration [RBPA], etc… Cette thèse en automatique requiert plusieurs compétences parmi lesquelles des connaissances sur la théorie de Lyapunov pour les systèmes avec ou sans retard, sur les inégalités matricielles linéaires tout en s’appuyant sur les outils de mathématiques appliquées pour l’étude des équations aux dérivées partielles (algèbre linéaire, analyse fonctionnelle, espaces de Hilbert, de Sobolev)The purpose of this thesis is the study of stability and control properties for linear systems described by partial differential equations (PDE) or delay differential equations. We wish to use in this thesis the relationship between these two classes of infinite-dimensional systems in view of developing a new paradigm for their analysis. Indeed, in many applications, it is possible to choose one or the other of these two classes of systems to model the dynamics of the system under consideration. For example, traffic flow can be modeled using PDE type of transportation [JKC], but also by a distributed delay model [SMP] or discrete delay [SN]. We may also refer to the work of Krstic [K] on the formulation of a delay system as an PDE system. These two classes of systems are special cases of infinite dimensional systems, unlike the case of finite-dimensional systems, we better called state functions rather than the state vector. This implies that the analysis is more delicate and refers to the use of dedicated tools. As part of the thesis, the student will focus on approaches based on an extension of Lyapunov theorem for infinite dimensional systems using specific functional. As for the modeling process, the stability analysis of delayed or PDE type systems can be conducted using very similar Lyapunov functionals. We hope that this thesis builds on existing work in the two communities on delay systems and PDE to develop an innovative and unified approach to the analysis and control of infinite dimensional systems. To do so, the candidate will build on its skills in automatic and mathematics as well as the on from expertise of both supervisors. Several contributions are expected during the thesis . Initially, we aim at extedning recent results [SG13,14] developed in the context of the stability analysis of delay systems to the case of systems governed by PDE. These first results will provide the basis for the design of robust control laws for various applications including traffic control, vibration control, etc ... Cette thèse portera sur l’étude des propriétés de stabilité et de contrôle des systèmes linéaires de dimension infinie, plus particulièrement écrits à l’aide d’EDP ou d’équations à retard. L’intérêt naturel pour l’étude de cette classe de systèmes à la frontière entre mathématiques appliquées et automatique connaît un succès grandissant de part la large gamme d’applications en contrôle pouvant être décrites par ces modèles : en ingénierie, biologie, informatique… L’émulation scientifique entre systèmes à retard et systèmes de type EDP permettra en outre à cette thèse de tirer parti des méthodes et outils propres à chacun des ces domaines. This PhD proposal in automatic control requires several skills including knowledge on Lyapunov theory for systems with or without delay , on linear matrix inequalities while relying on mathematical tools applied in the study of partial differential equations ( linear algebra functional analysis , Hilbert spaces , Sobolev)
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JANANE, JILALI. "Existence des solutions de certaines equations non-lineaires du type schroedinger." Rennes 1, 1989. http://www.theses.fr/1989REN10041.
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Cette these concerne l'etude de l'existence et la regularite des solutions de certaines equations non lineaires. Les deux premiers chapitres sont consacres a l'etude de l'equation de schroedinger non lineaire stationnaire (premier chapitre) et d'evolution (deuxieme chapitre). On demontre des theoremes d'existence et de regularite. Dans le troisieme chapitre on etudie certaines classes d'operateurs elliptiques degeneres dans les espaces de besov
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Rocha, Suelen de Souza. "Soluções clássicas para uma equação elíptica semilinear não homogênea." Universidade Federal da Paraíba, 2011. http://tede.biblioteca.ufpb.br:8080/handle/tede/8051.
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This work is mainly concerned with the existence and nonexistence of classical solution to the nonhomogeneous semilinear equation Δu + up + f(x) = 0 in Rn, u > 0 in Rn, when n 3, where f 0 is a Hölder continuous function. The nonexistence of classical solution is established when 1 < p n=(n 2). For p > n=(n 2) there may be both existence and nonexistence results depending on the asymptotic behavior of f at infinity. The existence results were obtained by employed sub and supersolutions techniques and fixed point theorem. For the nonexistence of classical solution we used a priori integral estimates obtained via averaging.
Neste trabalho, estamos interessados na existência e não existência de solução clássica para a equação não homogênea semilinear Δu + up + f(x) = 0 em Rn; u > 0 em Rn, n 3 onde f 0 é uma função Hölder contínua. A não existência de solução clássica é estabelecida quando 1 < p n=(n 2). Para p > n=(n 2), temos resultados de existência e não existência de solução clássica, dependendo do comportamento assin- tótico de f no infinito. Os resultados de existência foram obtidos usando o método de sub e supersolução e teoremas de ponto fixo. A não existência de solução clássica é obtida usando-se estimativas integrais a priori via média esférica.
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Velasquez, Castanon Oswaldo. "Sur la répartition des zéros de certaines fonctions méromorphes liées à la fonction zêta de Riemann." Thesis, Bordeaux 1, 2008. http://www.theses.fr/2008BOR13622/document.
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Nous traitons trois problèmes liés à la fonction zêta de Riemann : 1) L'établissement de conditions pour déterminer l'alignement et la simplicité de la quasi-totalité des zéros d'une fonction de la forme f(s)=h(s)±h(2c-s), où h(s) est une fonction méromorphe et c un nombre réel. Cela passe par la généralisation du théorème d'Hermite-Biehler sur la stabilité des fonctions entières. Comme application, nous avons obtenu des résultats sur la répartition des zéros des translatées de la fonction zêta de Riemann et de fonctions L, ainsi que sur certaines intégrales de séries d'Eisenstein. 2) L'étude de la répartition des zéros des sommes partielles de la fonction zêta, et des ses approximations issues de la formule d'Euler-Maclaurin. 3) L'étude du prolongement méromorphe et de la frontière naturelle pour une classe de produits eulériens, qui inclut une série de Dirichlet utilisée dans l'étude de la répartition des valeurs de l'indicatrice d'EulerWe deal with three problems related to the Riemann zeta function: 1) The establishment of conditions to determine the alignment and simplicity of most of the zeros of a function of the form f(s)=h(s)±h(2c-s), where h(s) is a meromorphic function and c a real number. To this end, we generalise the Hermite-Biehler theorem concerning the stability of entire functions. As an application, we obtain some results about the distribution of zeros of translations of the Riemann Zeta Function and L functions, and about certain integrals of Eisenstein series. 2) The study of the distribution of the zeros of the partial sums of the zeta function, and of some approximations issued from the Euler-Maclaurin formula. 3) The study of the meromorphic continuation and the natural boundary of a class of Euler products, which includes a Dirichlet series used in the study of the distribution of values of the Euler totient
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Zanchini, Giulia. "Stochastic local volatility model for fx markets." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7685/.
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Questa tesi verte sullo studio di un modello a volatilità stocastica e locale, utilizzato per valutare opzioni esotiche nei mercati dei cambio. La difficoltà nell'implementare un modello di tal tipo risiede nella calibrazione della leverage surface e uno degli scopi principali di questo lavoro è quello di mostrarne la procedura.
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Sampaio, Júlio César Santos 1983. "Sobre simetrias e a teoria de leis de conservação de Ibragimov." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307216.
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Orientador: Igor Leite FreireTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Neste trabalho estudamos simetrias de Lie e a teoria de leis de conservação desenvolvida por Ibragimov nos últimos 10 anos. Leis de conservação para várias equações sem Lagrangeanas clássicas foram estabelecidas
Abstract: In this work we study Lie point symmetries and the theory on conservation laws developed by Ibragimov in the last 10 years. Conservation laws for several equations without classical Lagrangians were established
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
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Oswald, Luc. "Etude de problemes non lineaires avec singularites." Paris 6, 1987. http://www.theses.fr/1987PA066060.
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Cette these est composee de dix articles que nous avons regroupes en deux parties. La premiere partie est constituee par l'etude et la classification des singularites isolees, premierement, d'une equation elliptique avec diffusion, deuxiemement, de l'equation parabolique correspondante. Dans la seconde partie sont etablis des resultats d'existence pour des problemes elliptiques semi-lineaires. Ces problemes sont caracterises respectivement, par une non-linearite singuliere, une condition de neumann degeneree, une non-linearite sous lineaire et, enfin, des exposants de sobolev critiques
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Busaman, Saofee. "Hyperequational theory for partial algebras." Phd thesis, kostenfrei, 2006. http://opus.kobv.de/ubp/volltexte/2007/1204/.
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Roos, Joakim. "Weighted Potential Theory & Partial Balayage." Thesis, KTH, Matematik (Inst.), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-102809.
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In random matrix theory it is known that the probability measure describing the spectral distribution of certain normal random matrices in the scaling limit tends to the equilibrium measure of an equilibrium problem in weighted potential theory. Motivated by this relation we compare the equilibrium measure of a sample Gaussian background potential perturbed by a point mass with a partial balayage operation of the point mass to a specific set, and get an indication of a general relation between the equilibrium problem of certain background potentials and a specific partial balayage operation. We develop this relation in detail and further discuss the possibility of an even more general method of obtaining the weighted equilibrium measure of a background potential directly through a certain partial balayage operation.
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Lukits, Stefan Hermann. "Information theory and partial belief reasoning." Thesis, University of British Columbia, 2016. http://hdl.handle.net/2429/58193.
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The dissertation investigates the nature of partial beliefs and norms governing their use. One widely accepted (though not uncontested) norm for partial belief change is Bayesian conditionalization. Information theory provides a far-reaching generalization of Bayesian conditionalization and gives it a foundation in an intuition that pays attention principally to information contained in probability distributions and information gained with new evidence. This generalization has fallen out of favour with contemporary epistemologists. They prefer an eclectic approach which sometimes conflicts with norms based on information theory, particularly the entropy principles of information theory. The principle of maximum entropy mandates a rational agent to hold minimally informative partial beliefs given certain background constraints; the principle of minimum cross-entropy mandates a rational agent to update partial beliefs at minimal information gain consistent with the new evidence. The dissertation shows that information theory generalizes Bayesian norms and does not conflict with them. It also shows that the norms of information theory can only be defended when the agent entertains sharp credences. Many contemporary Bayesians permit indeterminate credal states for rational agents, which is incompatible with the norms of information theory. The dissertation then defends two claims: (1) the partial beliefs that a rational agent holds are formally expressed by sharp credences; and (2) when a rational agent updates these partial beliefs in the light of new evidence, the norms used are based on and in agreement with information theory. In the dissertation, I defuse a collection of counter-examples that have been marshaled against entropy principles. More importantly, building on previous work by others and expanding it, I provide a coherent and comprehensive theory of the use of information theory in formal epistemology. Information theory rivals probability theory in formal virtue, theoretical substance, and coherence across intuitions and case studies. My dissertation demonstrates its significance in explaining the doxastic states of a rational agent and in providing the right kind of normativity for them.Arts, Faculty of
Philosophy, Department of
Graduate
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Marquis, Jean-Pierre. "Towards a theory of partial truth." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75841.
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The nature of truth has occupied philosophers since the very beginning of the field. Our goal is to clarify the notion of scientific truth, in particular the notion of partial truth of facts. Our strategy consists to brake the problem into smaller, more manageable, questions. Thus, we distinguish the truth of a scientific theory, what we call the "global" truth value of a theory, from the truth of a particular scientific proposition, what we call the "local" truth values of a theory. We will present a new local theory of partial truth and will have few things to say about the global level. Moreover, we will also introduce some purely formal results, the most important being the introduction of a new class of algebraic structures which have some interesting connections with classical logic.
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Caperna, Giulio. "Partial Order Theory for Synthetic Indicators." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3427242.
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Given a big set of data with several variables, the aim is the evaluation of each unit with a method that produces a synthetic measure describing a complex and non-observable concept; this goal is achieved respecting the characteristics of the variables, specially the measurement scale.
The information gathered with partially ordered sets (poset) reflects this aim, because posets depends only on the order relations among the observations, and allows to handle ordinal and dichotomous variables fairly.
In this setting, the vector of variables observed on a unit is handled as a unique entity called profile and not as a group of different variables that need to be aggregated.
Starting from recent developments in poset theory, this thesis is organized in three parts. The first proposes to obtain a unique indicator combining the values given by the severity measures for evaluation, derived from the fuzzy identification method. The second contribution is the HOGS (Height Of Groups by Sampling) procedure, which is aimed to estimate the average rank of groups of units of a big population. HOGS is a step forward the statistical estimation of the average rank of a profile; furthermore it allows the estimation of the effect of external variables on the synthetic measure.
The last results are two new R functions: the first computes the approximated average rank for large data sets overcoming the usual sample sizes considered by the software usually used until now, the second implements the information given by the frequency of profiles in the computation of approximated average rank, making its use more profitable for social sciences.Data una grande popolazione osservata su diverse variabili, ci si pone l'obiettivo di valutare le singole unità con un metodo che sia in grado di produrre una informazione sintetica per la descrizione di un concetto complesso e non osservabile; in questa tesi si vuole raggiungere questo scopo rispettando le caratteristiche dei dati, specialmente la scala di misura di questi. Gli insiemi parzialmente ordinati (poset) si adattano a questo scopo; questo tipo di insiemi sono costruiti unicamente sulle relazioni d'ordine tra le osservazioni e quindi consentoto di trattare le variabili ordinali e dicotomiche in modo adeguato alle loro caratteristiche. Nella letteratura dei poset, il vettore di variabili osservate su una unità è chiamato profilo e trattato come un oggetto unico senza procedure di aggregazione. Questa tesi si connette ai più recenti sviluppi nella teoria dei poset ed è organizzata in tre parti principali. La prima propone una sintesi dell'informazione fornita dalle misure di severity, derivate dal metodo di fuzzy identification. Il secondo e principale contributo è la procedura HOGS (Height OF Groups by Sampling), che ha lo scopo di stimare l'average rank di gruppi di unità da grandi popolazioni. HOGS permette di avvicinarsi alla stima statistica dell'average rrank dei singoli profili ed inoltre fornisce un metodo per studiare l'effetto di variabili esterne sulla misura sintetica. L'ultima parte contiene le funzioni che sono state sviluppate in R: la prima calcola l'average rank approssimato per grandi moli di dati, la seconda implementa l'informazione data dalle frequenze dei signoli profili nella popolazione osservata, rendendo questo metodo più spendibile nelle scienze sociali.
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Sanomiya, Thais Akemi Tokubo. "Sobre o teorema de Campbell-Magaard e o problema de Cauchy na relatividade." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9542.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
After the formulation of general relativity differential geometry has become an increasing important tool in theoretical physics. This is even more clear in the investigation of the so-called embedding space-time theories. In this work we focus our attention in the Cauchy problem. These have played a crucial role in our understanding of the mathematical structure of general relativity and embedding theories. We investigate the similarities and differences between the two approaches. We also study an extension of the Campbell-Magaard theorem and give two examples of both formalisms.
A geometria diferencial passou a ser uma ferramenta fundamental na fisica com o surgimento da relatividade geral. Em particular, destacamos sua importância na investigado das chamadas teorias de imersdo do espaco-tempo. Neste trabalho analisamos dois grandes formalismos fundamentados de forma direta ou indireta na teoria de imersões: o teorema de Campbell-Magaard e o problema de Cauchy para a relatividade geral. Tendo como principal objetivo tracar um paralelo entre esses dois formalismos, estudamos, nesta dissertacdo, o problema de valor inicial (pvi) para a relatividade geral mostrando que alem de admitir a formulae-do de pvi, a mesma é bem posta. Ademais, aplicamos este formalismo para o caso de uma metrica do tipo Friedmann-Robertson-Walker em (3+1). Estudamos tambem o teorema de Campbell-Magaard e sua extensdo para o espaco-tempo de Einstein e aplicamos este teorema para uma metrica do tipo de Sitter em (2+1).
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Easton, Todd William. "On partial completion problems." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/25478.
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Nornes, Nils Melvær. "Partial Orders in Representation Theory of Algebras." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9689.
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In this paper we investigate some partial orders used in representation theory of algebras. Let $K$ be a commutative ring, $Lambda$ a finitely generated $K$-algebra and $d$ a natural number. We then study partial orders on the set of isomorphism classes of $Lambda$-modules of length $d$. The orders degeneration, virtual degeneration and hom-order are discussed. The main purpose of the paper is to study the relation $leq_n$ constructed by considering the ranks of $ntimes n$-matrices over $Lambda$ as $K$-endomorphisms on $M^n$ for a $Lambda$-module $M$. We write $Mleq_n N$ when for any $ntimes n$-matrix the rank with respect to $M$ is greater than or equal to the rank with respect to $N$. We study these relations for various algebras and determine when $leq_n$ is a partial order.
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Shipley, Adrian. "Theory of partial discharge and arc formation." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/55280/.
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The demand for electrical power has consistently risen over time, whether it be to support the development and expansion of cities or because traditional approaches to societies solutions are being replaced by their electrical equivalent. The automotive industry is beginning to introduce more electric, greener vehicles. The aviation industry is also being challenged with the same issues. Whatever the motivation, this rising demand for power is always facilitated by employing higher and higher voltage levels. It is well understood that if the voltage is too high for a given air gap, electric breakdown will occur. this effect is exacerbated by increases in altitude, resulting in constant challenges in aviation to satisfy the contradictory demands for smaller/lighter compact solutions against the biggest possible air gaps necessary to prevent electric breakdown. An experimental curve by Louis Karl Heinrich Friedrich Paschen was developed, which relates the voltage at which electric breakdown would be expected to that of the product of gas pressure (p) and distance (d). The aviation industry does not use this curve directly as alternate guidance documents are used. These documents are extremely conservative, sometimes overly so, as will be seen in the thesis. Mathematical attempts have been provided to try and explain the Paschen curve, based on Townsend Primary and secondary ionisation. However, the variable 'pd' does not get explicitly linked and a type of mathematical fudge becomes incorporated. This thesis attempts to provide a theory of the minimum electric breakdown curve and fundamentally link he 'pd' product. by experimental validation of the theory, with the accepted standards included. A basis for challenging these standards may result and prevent potential over engineering in the future in this continually challenging environment. This theory will then go on to explain arc formation by providing a treatment to a paradox that occurs at the point of breakdown.
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McEwen, Peter A. "Trellis coding for partial response channels /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1999. http://wwwlib.umi.com/cr/ucsd/fullcit?p9968170.
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Chulkov, Sergei. "Topics in analytic theory of partial differential equations /." Stockholm : Dept. of mathematics, Stockholm university, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-782.
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Alfadhli, Amani Mohammad. "Some representation theory of decorated partial Brauer algebra." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/20943/.
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In this thesis we introduce a new family of finite dimensional diagram algebras over a commutative ring with identity, the decorated partial Brauer algebras. These algebras are unital, associative and have a basis consisting of decorated partial Brauer diagrams which are partial Brauer diagrams with possibly decorated edges and decorated isolated vertices. We show that this algebra is a cellular algebra by applying Theorem of Green and Paget to iterated construction . Subsequently, we give an indexing set for the simple modules. Over a field of characteristic different from 2, we determine when the decorated partial Brauer algebra is quasi-hereditary. Finally, we give a complete description of the restriction rule for the cell modules over C.
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Knapp, Cory. "Partial functions and recursion in univalent type theory." Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8448/.
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We investigate partial functions and computability theory from within a constructive, univalent type theory. The focus is on placing computability into a larger mathematical context, rather than on a complete development of computability theory. We begin with a treatment of partial functions, using the notion of dominance, which is used in synthetic domain theory to discuss classes of partial maps. We relate this and other ideas from synthetic domain theory to other approaches to partiality in type theory. We show that the notion of dominance is difficult to apply in our setting: the set of �0 1 propositions investigated by Rosolini form a dominance precisely if a weak, but nevertheless unprovable, choice principle holds. To get around this problem, we suggest an alternative notion of partial function we call disciplined maps. In the presence of countable choice, this notion coincides with Rosolini’s. Using a general notion of partial function,we take the first steps in constructive computability theory. We do this both with computability as structure, where we have direct access to programs; and with computability as property, where we must work in a program-invariant way. We demonstrate the difference between these two approaches by showing how these approaches relate to facts about computability theory arising from topos-theoretic and typetheoretic concerns. Finally, we tie the two threads together: assuming countable choice and that all total functions N - N are computable (both of which hold in the effective topos), the Rosolini partial functions, the disciplined maps, and the computable partial functions all coincide. We observe, however, that the class of all partial functions includes non-computable partial functions.
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Roos, Joakim. "Partial Balayage and Related Concepts in Potential Theory." Doctoral thesis, KTH, Matematik (Avd.), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-186367.
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This thesis consists of three papers, all treating various aspects of the operation partial balayage from potential theory. The first paper concerns the equilibrium measure in the setting of two dimensional weighted potential theory, an important measure arising in various mathematical areas, e.g. random matrix theory and the theory of orthogonal polynomials. In this paper we show that the equilibrium measure satisfies a complementary relation with a partial balayage measure if the weight function is of a certain type. The second paper treats the connection between partial balayage measures and measures arising from scaling limits of a generalisation of the so-called divisible sandpile model on lattices. The standard divisible sandpile can, in a natural way, be considered a discrete version of the partial balayage operation with respect to the Lebesgue measure. The generalisation that is developed in this paper is essentially a discrete version of the partial balayage operation with respect to more general measures than the Lebesgue measure. In the third paper we develop a version of partial balayage on Riemannian manifolds, using the theory of currents. Several known properties of partial balayage measures are shown to have corresponding results in the Riemannian manifold setting, one of which being the main result of the first paper. Moreover, we utilize the developed framework to show that for manifolds of dimension two, harmonic and geodesic balls are locally equivalent if and only if the manifold locally has constant curvature.Denna avhandling består av tre artiklar som alla behandlar olika aspekter av den potentialteoretiska operationen partiell balayage. Den första artikeln betraktar jämviktsmåttet i tvådimensionell viktad potentialteori, ett viktigt mått inom flertalet matematiska inriktningar såsom slumpmatristeori och teorin om ortogonalpolynom. I denna artikel visas att jämviktsmåttet uppfyller en komplementaritetsrelation med ett partiell balayage-mått om viktfunktionen är av en viss typ. Den andra artikeln behandlar relationen mellan partiell balayage-mått och mått som uppstår från skalningsgränser av en generalisering av den så kallade "delbara sandhögen", en diskret modell för partikelaggregation på gitter. Den vanliga delbara sandhögen kan på ett naturligt sätt betraktas som en diskret version av partiell balayage-operatorn med avseende på Lebesguemåttet. Generaliseringen som utarbetas i denna artikel är väsentligen en diskret version av partiell balayage-operatorn med avseende på mer allmänna mått än Lebesguemåttet. I den tredje artikeln formuleras en version av partiell balayage på riemannska mångfalder utifrån teorin om strömmar. Åtskilliga tidigare kända egenskaper om partiella balayage-mått visas ha motsvarande formuleringar i formuleringen på riemannska mångfalder, bland annat huvudresultatet från den första artikeln. Vidare så utnyttjas det utarbetade ramverket för att visa att tvådimensionella riemannska mångfalder har egenskapen att harmoniska och geodetiska bollar lokalt är ekvivalenta om och endast om mångfalden lokalt har konstant krökning.
QC 20160524
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Fiore, Marcelo P. "Axiomatic domain theory in categories of partial maps." Thesis, University of Edinburgh, 1994. http://hdl.handle.net/1842/406.
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This thesis is an investigation into axiomatic categorical domain theory as needed for the denotational semantics of deterministic programming languages. To provide a direct semantic treatment of non-terminating computations, we make partiality the core of our theory. Thus, we focus on categories of partial maps. We study representability of partial maps and show its equivalence with classifiability. We observe that, once partiality is taken as primitive, a notion of approximation may be derived. In fact, two notions of approximation, contextual approximation and specialisation, based on testing and observing partial maps are considered and shown to coincide. Further we characterise when the approximation relation between partial maps is domain-theoretic in the (technical) sense that the category of partial maps Cpo-enriches with respect to it. Concerning the semantics of type constructors in categories of partial maps, we present a characterisation of colimits of diagrams of total maps; study order-enriched partial cartesian closure; and provide conditions to guarantee the existence of the limits needed to solve recursive type equations. Concerning the semantics of recursive types, we motivate the study of enriched algebraic compactness and make it the central concept when interpreting recursive types. We establish the fundamental property of algebraically compact categories, namely that recursive types on them admit canonical interpretations, and show that in algebraically compact categories recursive types reduce to inductive types. Special attention is paid to Cpo-algebraic compactness, leading to the identification of a 2-category of kinds with very strong closure properties. As an application of the theory developed, enriched categorical models of the metalanguage FPC (a type theory with sums, products, exponentials and recursive types) are defined and two abstract examples of models, including domain-theoretic models, are axiomatised. Further, FPC is considered as a programming language with a call-by-value operational semantics and a denotational semantics defined on top of a categorical model. Operational and denotational semantics are related via a computational soundness result. The interpretation of FPC expressions in domain-theoretic Poset-models is observed to be representation-independent. And, to culminate, a computational adequacy result for an axiomatisation of absolute non-trivial domain-theoretic models is proved.
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Huang, Guan. "An averaging theory for nonlinear partial differential equations." Palaiseau, Ecole polytechnique, 2014. http://pastel.archives-ouvertes.fr/docs/01/00/25/27/PDF/these.pdf.
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Cette thèse se consacre aux études des comportements de longtemps des solutions pour les EDPs nonlinéaires qui sont proches d'une EDP linéaire ou intégrable hamiltonienne. Une théorie de la moyenne pour les EDPs nonlinéaires est presenté. Les modèles d'équations sont les équations Korteweg-de Vries (KdV) perturbées et quelques équations aux dérivées partielles nonlinéaires faiblementThis Ph. D thesis focuses on studying the long-time behavior of solutions for non-linear PDEs that are close to a linear or an integrable Hamiltonian PDE. An averaging theory for nonlinear PDEs is presented. The model equations are the perturbed Korteweg-de Vries (KdV) equations and some weakly nonlinear partial differential equations
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Chang, Charles Chung 1962. "Partial discharge pattern analysis." Monash University, Dept. of Electrical and Computer Systems Engineering, 2001. http://arrow.monash.edu.au/hdl/1959.1/8400.
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Zhang, Nien-fan. "Estimating partial group delay." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/74721.
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Partial group delay is a spectral parameter, which measures the time lag between two time series in a system after the spurious effects of the other series in the system have been eliminated.
For weakly-stationary processes, estimators for partial group delay are proposed based on indirect and direct approaches. Conditions for weak consistency and asymptotic normality of the proposed estimators are obtained. Applications to a multiple test of partial group delay are investigated.
The time lag interpretation of partial group delay is justified, which provides insight into the nature of linear relationships among weakly-stationary processes.
Extensions are made to group delay estimation and partial group delay estimation for non-stationary "oscillatory" processes.Ph. D.
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Seck, Ousmane. "Sur un modèle de diffusion non linéaire en dynamique des populations." Nancy 1, 1986. http://www.theses.fr/1986NAN10162.
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Les équations d'évolution. Étude dans L**(1) de solutions particulières. Les résultats d'existence connus. Estimations à priori. Relaxation des hypothèses de régularité et de compatibilité. Relaxation des hypothèses de stricte positivité
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Moose, Phillip J. "Approximate signal reconstruction from partial information." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06102009-063326/.
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Kwon, Myung-Joong. "Partial vertical integration and competition policy." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357525.
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Kan, Kin-fai, and 簡健輝. "Maintenance of partial-sum-based histograms." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B26635197.
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Luo, Yong [Verfasser], and Guofang [Akademischer Betreuer] Wang. "Some topics from submanifold theory and geometric partial differential equations = Einige Themen aus Untermannigfaltigkeit Theorie und geometrischen partiellen Differentialgleichungen." Freiburg : Universität, 2013. http://d-nb.info/1114887412/34.
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Temple-Raston, Mark Renwick. "Monopole motions." Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.276584.
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Anna, Slivková. "Partial closure operators and applications in ordered set theory." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2018. https://www.cris.uns.ac.rs/record.jsf?recordId=107201&source=NDLTD&language=en.
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In this thesis we generalize the well-known connections between closure operators, closure systems and complete lattices. We introduce a special kind of a partial closure operator, named sharp partial closure operator, and show that each sharp partial closure operator uniquely corresponds to a partial closure system. We further introduce a special kind of a partial clo-sure system, called principal partial closure system, and then prove the representation theorem for ordered sets with respect to the introduced partial closure operators and partial closure systems.Further, motivated by a well-known connection between matroids and geometric lattices, given that the notion of matroids can be naturally generalized to partial matroids (by dening them with respect to a partial closure operator instead of with respect to a closure operator), we dene geometric poset, and show that there is a same kind of connection between partial matroids and geometric posets as there is between matroids and geometric lattices. Furthermore, we then dene semimod-ular poset, and show that it is indeed a generalization of semi-modular lattices, and that there is a same kind of connection between semimodular and geometric posets as there is betweensemimodular and geometric lattices.Finally, we note that the dened notions can be applied to im-plicational systems, that have many applications in real world,particularly in big data analysis.U ovoj tezi uopštavamo dobro poznate veze između operatora zatvaranja, sistema zatvaranja i potpunih mreža. Uvodimo posebnu vrstu parcijalnog operatora zatvaranja, koji nazivamo oštar parcijalni operator zatvaranja, i pokazujemo da svaki oštar parcijalni operator zatvaranja jedinstveno korespondira parcijalnom sistemu zatvaranja. Dalje uvodimo posebnu vrstu parcijalnog sistema zatvaranja, nazvan glavni parcijalni sistem zatvaranja, a zatim dokazujemo teoremu reprezentacije za posete u odnosu na uvedene parcijalne operatore zatvaranja i parcijalne sisteme zatvaranja. Dalje, s obzirom na dobro poznatu vezu između matroida i geometrijskih mreža, a budući da se pojam matroida može na prirodan nacin uopštiti na parcijalne matroide (definišući ih preko parcijalnih operatora zatvaranja umesto preko operatora zatvaranja), definišemo geometrijske uređene skupove i pokazujemo da su povezani sa parcijalnim matroidima na isti način kao što su povezani i matroidi i geometrijske mreže. Osim toga, definišemo polumodularne uređene skupove i pokazujemo da su oni zaista uopštenje polumodularnih mreža i da ista veza postoji između polumodularnih i geometrijskih poseta kao što imamo između polumodularnih i geometrijskih mreža. Konačno, konstatujemo da definisani pojmovi mogu biti primenjeni na implikacione sisteme, koji imaju veliku primenu u realnom svetu, posebno u analizi velikih podataka.
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Heinz, Sebastian. "Preservation of quasiconvexity and quasimonotonicity in polynomial approximation of variational problems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2008. http://dx.doi.org/10.18452/15808.
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Die vorliegende Arbeit beschäftigt sich mit drei Klassen ausgewählter nichtlinearer Probleme, die Forschungsgegenstand der angewandten Mathematik sind. Diese Probleme behandeln die Minimierung von Integralen in der Variationsrechnung (Kapitel 3), das Lösen partieller Differentialgleichungen (Kapitel 4) und das Lösen nichtlinearer Optimierungsaufgaben (Kapitel 5). Mit deren Hilfe lassen sich unterschiedlichste Phänomene der Natur- und Ingenieurwissenschaften sowie der Ökonomie mathematisch modellieren. Als konkretes Beispiel werden mathematische Modelle der Theorie elastischer Festkörper betrachtet. Das Ziel der vorliegenden Arbeit besteht darin, ein gegebenes nichtlineares Problem durch polynomiale Probleme zu approximieren. Um dieses Ziel zu erreichen, beschäftigt sich ein großer Teil der vorliegenden Arbeit mit der polynomialen Approximation von nichtlinearen Funktionen. Den Ausgangspunkt dafür bildet der Weierstraßsche Approximationssatz. Auf der Basis dieses bekannten Satzes und eigener Sätze wird als Hauptresultat der vorliegenden Arbeit gezeigt, dass im Übergang von einer gegebenen Funktion zum approximierenden Polynom wesentliche Eigenschaften der gegebenen Funktion erhalten werden können. Die wichtigsten Eigenschaften, für die dies bisher nicht bekannt war, sind: Quasikonvexität im Sinne der Variationsrechnung, Quasimonotonie im Zusammenhang mit partiellen Differentialgleichungen sowie Quasikonvexität im Sinne der nichtlinearen Optimierung (Theoreme 3.16, 4.10 und 5.5). Schließlich wird gezeigt, dass die zu den untersuchten Klassen gehörenden nichtlinearen Probleme durch polynomiale Probleme approximiert werden können (Theoreme 3.26, 4.16 und 5.8). Die dieser Approximation zugrunde liegende Konvergenz garantiert sowohl eine Approximation im Parameterraum als auch eine Approximation im Lösungsraum. Für letztere werden die Konzepte der Gamma-Konvergenz (Epi-Konvergenz) und der G-Konvergenz verwendet.In this thesis, we are concerned with three classes of non-linear problems that appear naturally in various fields of science, engineering and economics. In order to cover many different applications, we study problems in the calculus of variation (Chapter 3), partial differential equations (Chapter 4) as well as non-linear programming problems (Chapter 5). As an example of possible applications, we consider models of non-linear elasticity theory. The aim of this thesis is to approximate a given non-linear problem by polynomial problems. In order to achieve the desired polynomial approximation of problems, a large part of this thesis is dedicated to the polynomial approximation of non-linear functions. The Weierstraß approximation theorem forms the starting point. Based on this well-known theorem, we prove theorems that eventually lead to our main result: A given non-linear function can be approximated by polynomials so that essential properties of the function are preserved. This result is new for three properties that are important in the context of the considered non-linear problems. These properties are: quasiconvexity in the sense of the calculus of variation, quasimonotonicity in the context of partial differential equations and quasiconvexity in the sense of non-linear programming (Theorems 3.16, 4.10 and 5.5). Finally, we show the following: Every non-linear problem that belongs to one of the three considered classes of problems can be approximated by polynomial problems (Theorems 3.26, 4.16 and 5.8). The underlying convergence guarantees both the approximation in the parameter space and the approximation in the solution space. In this context, we use the concepts of Gamma-convergence (epi-convergence) and of G-convergence.
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Souvignier, Thomas Victor. "Turbo decoding for partial response channels /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1999. http://wwwlib.umi.com/cr/ucsd/fullcit?p9938584.
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Van, Delden Sebastian Alexander. "Larger-first partial parsing." Doctoral diss., University of Central Florida, 2003. http://digital.library.ucf.edu/cdm/ref/collection/RTD/id/2038.
Full textAbstract:
University of Central Florida College of Engineering ThesisLarger-first partial parsing is a primarily top-down approach to partial parsing that is opposite to current easy-fzrst, or primarily bottom-up, strategies. A rich partial tree structure is captured by an algorithm that assigns a hierarchy of structural tags to each of the input tokens in a sentence. Part-of-speech tags are first assigned to the words in a sentence by a part-of-speech tagger. A cascade of Deterministic Finite State Automata then uses this part-of-speech information to identify syntactic relations primarily in a descending order of their size. The cascade is divided into four specialized sections: (1) a Comma Network, which identifies syntactic relations associated with commas; (2) a Conjunction Network, which partially disambiguates phrasal conjunctions and llly disambiguates clausal conjunctions; (3) a Clause Network, which identifies non-comma-delimited clauses; and (4) a Phrase Network, which identifies the remaining base phrases in the sentence. Each automaton is capable of adding one or more levels of structural tags to the tokens in a sentence. The larger-first approach is compared against a well-known easy-first approach. The results indicate that this larger-first approach is capable of (1) producing a more detailed partial parse than an easy first approach; (2) providing better containment of attachment ambiguity; (3) handling overlapping syntactic relations; and (4) achieving a higher accuracy than the easy-first approach. The automata of each network were developed by an empirical analysis of several sources and are presented here in detail.
Ph.D.
Doctorate;
Department of Electrical Engineering and Computer Science
Engineering and Computer Science
Electrical Engineering and Computer Science
215 p.
xiv, 212 leaves, bound : ill. ; 28 cm.
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Seiler, Werner Markus. "Analysis and application of the formal theory of partial differential equations." Thesis, Lancaster University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.238979.
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Lattimer, Timothy Richard Bislig. "Singular partial integro-differential equations arising in thin aerofoil theory." Thesis, University of Southampton, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243192.
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Surnachev, Mikhail. "On qualitative theory of solutions to nonlinear partial differential equations." Thesis, Swansea University, 2010. https://cronfa.swan.ac.uk/Record/cronfa42611.
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In this work I study certain aspects of qualitative behaviour of solutions to nonlinear PDEs. The thesis consists of introduction and three parts. In the first part I study solutions of Emden-Fowler type elliptic equations in nondivergence form. In this part I establish the following results; 1. Asymptotic representation of solutions in conical domains; 2. A priori estimates for solutions to equations with weighted absorption term; 3. Existence and nonexistence of positive solutions to equations with source term in conical domains. In the second part I study regularity properties of nonlinear degenerate parabolic equations. There are two results here: A Harnack inequality and the H51der continuity for solutions of weighted degenerate parabolic equations with a time-independent weight from a suitable Muckenhoupt class; A new proof of the Holder continuity of solutions. The third part is propedeutic. In this part I gathered some facts and simple proofs relating to the Harnack inequality for elliptic equations. Both divergent and nondivergent case are considered. The material of this chapter is not new, but it is not very easy to find it in the literature. This chapter is built entirely upon the so-called "growth lemma" ideology (introduced by E.M. Landis).
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Bagri, Gurjeet S. "Existence theorems for periodic solutions to partial differential equations with applications in hydrodynamics." Thesis, Loughborough University, 2010. https://dspace.lboro.ac.uk/2134/6724.
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The thesis looks at a number of existence theorems that prove the existence of small-amplitude periodic solutions to systems of partial differential equations. The existence theorems we consider are the Hopf bifurcation theorem, the Lyapunov centre theorem, the Weinstein-Moser theorem, and extensions of these theorems; the Hopf-Iooss bifurcation theorem, the Lyapunov-Iooss centre theorem and the Weinstein-Moser-Iooss theorem, respectively. The theorems have been derived so that they are applicable to functional analytical problems, and have been represented in a coherent and uniform manner in order to bridge the fundamental structure common to them all. Applications of these theorems, in this standardised form, are then applied in a systematic way to two particular hydrodynamical problems; the water wave problem and the Navier-Stokes equations. The classic water wave problem concerns the irrotational flow of a perfect fluid of unit density, subject to the forces of gravity and surface tension. We apply the Lyapunov-Iooss centre theorem to prove the existence of doubly-periodic waves; a doubly-periodic wave is a travelling wave that possess spatially periodic profiles in two different horizontal directions. Fundamental to our approach is the spatial dynamics formulation. The spatial dynamics formulation involves formulating a system of partial differential equations, defined on some spatial domain, as a dynamical system where one of the unbounded spatial variables plays the role of time. We catalogue a variety of parameter values for which it is possible to obtain doubly periodic waves, and we conclude with an existence result for doubly periodic waves under specific parameter restrictions. The Navier-Stokes equations in an exterior domain models the flow of an incompressible, viscous fluid past an obstacle. We apply the Hopf-Iooss bifurcation theorem to the defining equations to determine the existence of time-periodic waves. Our approach involves a careful examination of the Oseen problem to which we apply a 'cut-off' technique. This technique is used to constructs a solution to the Oseen problem using the respective solutions to the Oseen problem on a bounded domain and free space (the existence of which are well established). Time-periodic solutions are established using the Hopf-Iooss bifurcation theorem provided certain spectral conditions are met. The verification of the conditions may only be possible numerically, and so beyond the scope of our investigation.
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Sarkar, Koushik. "Topology of different metric spaces and fixed point theories." Thesis, University of North Bengal, 2021. http://ir.nbu.ac.in/handle/123456789/4235.
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Bryant, Ross. "A Computation of Partial Isomorphism Rank on Ordinal Structures." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5387/.
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We compute the partial isomorphism rank, in the sense Scott and Karp, of a pair of ordinal structures using an Ehrenfeucht-Fraisse game. A complete formula is proven by induction given any two arbitrary ordinals written in Cantor normal form.