- About
-
The Global ETD Search service is a free service for researchers
to find electronic theses and dissertations. This service is
provided by the
Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
Search results
Showing 241 to 250 of 275 (0.079 seconds)Spelling suggestions: "subject:"regularity"" "subject:"dregularity""
| 241 |
Estimation de régularité locale / Local regularity estimationServien, Rémi 12 March 2010 (has links)
L'objectif de cette thèse est d'étudier le comportement local d'une mesure de probabilité, notamment à l'aide d'un indice de régularité locale. Dans la première partie, nous établissons la normalité asymptotique de l'estimateur des kn plus proches voisins de la densité. Dans la deuxième, nous définissons un estimateur du mode sous des hypothèses affaiblies. Nous montrons que l'indice de régularité intervient dans ces deux problèmes. Enfin, nous construisons dans une troisième partie différents estimateurs pour l'indice de régularité à partir d'estimateurs de la fonction de répartition, dont nous réalisons une revue bibliographique. / The goal of this thesis is to study the local behavior of a probability measure, using a local regularity index. In the first part, we establish the asymptotic normality of the nearest neighbor density estimate. In the second, we define a mode estimator under weakened hypothesis. We show that the regularity index interferes in this two problems. Finally, we construct in a third part various estimators of the regularity index from estimators of the distribution function, which we achieve a review.
|
| 242 |
Théorie des opérateurs sur les espaces de tentes / Operator theory on tent spacesHuang, Yi 12 November 2015 (has links)
Nous donnons un mécanisme de type Calderón-Zygmund concernant la théorie de l’extrapolationpour des opérateurs d’intégrale singulière sur les espaces de tentes. Pour des opérateursde régularité maximale sur les espaces de tentes, nous donnons des résultats optimaux enexploitant la structure des opérateurs intégraux de convolution et en utilisant des estimationsde la décroissance hors-diagonale du semi-groupe ou de la famille résolvante sous-jacente.Nous appliquons des techniques précédentes d’analyse harmonique et fonctionnelle pourestimer sur les espaces de tentes certains opérateurs d’intégrale évolutionnelle, nées de l’étudedes problèmes aux limites elliptiques et des systèmes non-autonomes du premier ordre. / We give a Calderón-Zygmund type machinery concerning the extrapolation theory for thesingular integral operators on tent spaces. For maximal regularity operators on tent space, wegive some optimal results by exploiting the structure of convolution integral operators and byusing the off-diagonal decay estimates of the underlying semigroup or resolvent family.We apply the previous harmonic and functional analysis techniques to estimate on tentspaces certain evolutionary integral operators arisen from the study of boundary value ellipticproblems and first order non-autonomous systems.
|
| 243 |
Régularité des solutions de problèmes elliptiques ou paraboliques avec des données sous forme de mesure / Regularity of the solutions of elliptic or parabolic problems with data measureAriche, Sadjiya 25 June 2015 (has links)
Dans cette thèse on étudie la régularité de problèmes elliptiques (Laplace, Helmholtz) ou paraboliques (équation de la chaleur) avec donnée mesure dans divers cadres géométriques. Ainsi, on considère pour les seconds membres des masses de Dirac en un point, sur une ligne infinie, semi-infinie ou finie, et également sur une courbe régulière. Les solutions de ces problèmes étant singulières sur la fracture (modélisée par la masse de Dirac dans le second membre), on étudie la régularité dans des espaces de Sobolev avec poids. Dans le cas d'une fracture droite, on utilise une technique classique qui consiste à appliquer une transformée de Fourier ou de Mellin à l'équation de Laplace. Ceci nous amène à étudier l'équation de Helmholtz en 2D. Pour ce dernier, on montre des estimations uniformes qui permettent ensuite de prendre la transformée inverse et d'obtenir le résultat de régularité attendu. De même, la transformée de Laplace transforme l'équation de la chaleur dans la même équation de Helmholtz en 2D. Dans le cas d'une fracture courbe régulière, grâce aux résultats de [D'angelo:2012], en utilisant un argument de localisation et un recouvrement dyadique, on obtient une régularité améliorée de la solution toujours dans les espaces de Sobolev avec poids. / In this thesis, we study the regularity of elliptic problems (Laplace, Helmholtz) or parabolic problems (heat equation) with measure data in different geometric frames. Thus, we consider for the second members, Dirac masses at a point, on a line, on a half-line, or on a bounded segment, and also on a regular curve. As the solutions of these problems are singular on the fracture (modeled by Dirac mass in the second member), we study their regularity in weighted Sobolev spaces. In the case of a straight fracture, using Fourier or Mellin technique reduces the problem in dimension three to a Helmholtz problem in dimension two. For the latter, we prove uniform estimates, which are then used to apply the inverse transform and to obtain the expected regularity result. Similarly, the Laplace transformation transforms the heat equation into the same Helmholtz equation in 2D. In the case of a smooth curve fracture, thanks to the results of [D'angelo:2012], using a localization argument and a dyadic recovery we get an improved smoothness of the solution always in weighted Sobolev spaces.
|
| 244 |
The complexity of unavoidable word patternsSauer, Paul Van der Merwe 12 1900 (has links)
Bibliography: pages 192-195 / The avoidability, or unavoidability of patterns in words over finite alphabets has
been studied extensively. The word α over a finite set A is said to be unavoidable
for an infinite set B+ of nonempty words over a finite set B if, for all but finitely
many elements w of B+, there exists a semigroup morphism φ ∶ A+ → B+ such that
φ(α) is a factor of w.
In this treatise, we start by presenting a historical background of results that are
related to unavoidability. We present and discuss the most important theorems
surrounding unavoidability in detail.
We present various complexity-related properties of unavoidable words. For words
that are unavoidable, we provide a constructive upper bound to the lengths of
words that avoid them. In particular, for a pattern α of length n over an alphabet
of size r, we give a concrete function N(n, r) such that no word of length N(n, r)
over the alphabet of size r avoids α.
A natural subsequent question is how many unavoidable words there are. We show
that the fraction of words that are unavoidable drops exponentially fast in the
length of the word. This allows us to calculate an upper bound on the number of
unavoidable patterns for any given finite alphabet.
Subsequently, we investigate computational aspects of unavoidable words. In
particular, we exhibit concrete algorithms for determining whether a word is
unavoidable. We also prove results on the computational complexity of the problem
of determining whether a given word is unavoidable. Specifically, the
NP-completeness of the aforementioned problem is established. / Decision Sciences / D. Phil. (Operations Research)
|
| 245 |
On Partial Regularities and Monomial PreordersNguyen, Thi Van Anh 28 June 2018 (has links)
My PhD-project has two main research directions. The first direction is on partial regularities which we define as refinements of the Castelnuovo-Mumford regularity. Main results are: relationship of partial regularities and related invariants, like the a-invariants or the Castelnuovo-Mumford regularity of the syzygy modules; algebraic properties of partial regularities via a filter-regular sequence or a short exact sequence; generalizing a well-known result for the Castelnuovo-Mumford regularity to the case of partial regularities of stable and squarefree stable monomial ideals; finally extending an upper bound proven by Caviglia-Sbarra to partial regularities. The second direction of my project is to develop a theory on monomial preorders. Many interesting statements from the classical theory of monomial orders generalize to monomial preorders. Main results are: a characterization of monomial preorders by real matrices, which extends a result of Robbiano on monomial orders; secondly, leading term ideals with respect to monomial preorders can be studied via flat deformations of the given ideal; finally, comparing invariants of the given ideal and the leading term ideal with respect to a monomial preorder.
|
| 246 |
Refinements of the Solution Theory for Singular SPDEsMartin, Jörg 14 August 2018 (has links)
Diese Dissertation widmet sich der Untersuchung singulärer stochastischer partieller Differentialgleichungen (engl. SPDEs). Wir entwickeln Erweiterungen der bisherigen Lösungstheorien, zeigen fundamentale Beziehungen zwischen verschiedenen Ansätzen und
präsentieren Anwendungen in der Finanzmathematik und der mathematischen Physik.
Die Theorie parakontrollierter Systeme wird für diskrete Räume formuliert und eine schwache Universalität für das parabolische Anderson Modell bewiesen.
Eine fundamentale Relation zwischen Hairer's modellierten Distributionen und Paraprodukten wird bewiesen: Wir zeigen das sich der Raum modellierter Distributionen durch Paraprodukte beschreiben lässt. Dieses Resultat verallgemeinert die Fourierbeschreibung von Hölderräumen mittels Littlewood-Paley Theorie.
Schließlich wird die Existenz von Lösungen der stochastischen Schrödingergleichung auf dem ganzen Raum bewiesen und eine Anwendung Hairer's Theorie zur Preisermittlung von Optionen aufgezeigt. / This thesis is concerned with the study of singular stochastic partial differential equations
(SPDEs). We develop extensions to existing solution theories, present fundamental interconnections between different approaches and give applications in financial mathematics
and mathematical physics.
The theory of paracontrolled distribution is formulated for discrete systems, which allows us to prove a weak universality result for the parabolic Anderson model.
This thesis further shows a fundamental relation between Hairer's modelled distributions and paraproducts: The space of modelled distributions can be characterized completely by using paraproducts. This can be seen a generalization of the Fourier description of Hölder spaces.
Finally, we prove the existence of solutions to the stochastic Schrödinger equation on the full space and provide an application of Hairer's theory to option pricing.
|
| 247 |
[en] A CHARACTERIZATION OF TESTABLE GRAPH PROPERTIES IN THE DENSE GRAPH MODEL / [pt] UMA CARACTERIZAÇÃO DE PROPRIEDADES TESTÁVEIS NO MODELO DE GRAFOS DENSOSFELIPE DE OLIVEIRA 19 June 2023 (has links)
[pt] Consideramos, nesta dissertação, a questão de determinar se um grafo
tem uma propriedade P, tal como G é livre de triângulos ou G é 4-
colorível. Em particular, consideramos para quais propriedades P existe um
algoritmo aleatório com probabilidades de erro constantes que aceita grafos que
satisfazem P e rejeita grafos que são epsilon-longe de qualquer grafo que o satisfaça.
Se, além disso, o algoritmo tiver complexidade independente do tamanho
do grafo, a propriedade é dita testável. Discutiremos os resultados de Alon,
Fischer, Newman e Shapira que obtiveram uma caracterização combinatória de
propriedades testáveis de grafos, resolvendo um problema em aberto levantado
em 1996. Essa caracterização diz informalmente que uma propriedade P de
um grafo é testável se e somente se testar P pode ser reduzido a testar a
propriedade de satisfazer uma das finitas partições Szemerédi. / [en] We consider, in this thesis, the question of determining if a graph has a
property P such as G is triangle-free or G is 4-colorable. In particular,
we consider for which properties P there exists a random algorithm with
constant error probabilities that accept graphs that satisfy P and reject graphs
that are epsilon-far from any graph that satisfies it. If, in addition, the algorithm
has complexity independent of the size of the graph, the property is called
testable. We will discuss the results of Alon, Fischer, Newman, and Shapira
that obtained a combinatorial characterization of testable graph properties,
solving an open problem raised in 1996. This characterization informally says
that a graph property P is testable if and only if testing P can be reduced to
testing the property of satisfying one of finitely many Szemerédi-partitions.
|
| 248 |
[pt] TEORIA DE REGULARIDADE PARA MODELOS COMPLETAMENTE NÃO-LINEARES / [en] TOWARDS A REGULARITY THEORY FOR FULLY NONLINEAR MODELSPEDRA DARICLEA SANTOS ANDRADE 28 December 2020 (has links)
[pt] Neste trabalho examinamos equações completamente não-lineares em dois contextos distintos. A princípio, estudamos jogos de campo médio completamente não-lineares. Aqui, examinamos ganhos de regularidade para as soluções do problema, existência de soluções, resultados de relaxação e aspectos particulares de um example explícito. A segunda metade da tese dedica-se à regularidade ótima das soluções de um modelo completamente não-linear que degenera-se com respeito ao gradiente das soluções. A pergunta fundamental subjacente a ambos os tópicos diz respeito aos efeitos da elipticidade sobre propriedades intrínsecas das soluções de equações não-lineares. Mais precisamente, no caso dos jogos de campo médio, a elipticidade parece magnificada pelos efeitos do acoplamento, enquanto no caso dos problemas degenerados, esta quantidade colapsa em sub-regiões do domínio, dando origem a delicados fenômenos. Nossa análise inclui um
breve contexto da inserção do trabalho. / [en] In this thesis, we examine fully nonlinear problems in two distinct contexts. The first part of our work focuses on fully nonlinear mean-field games. In this context, we examine gains of regularity, the existence of solutions, relaxation results, and particular aspects of a one-dimensional problem. The second half of the thesis concerns a (sharp) regularity theory for fully nonlinear equations degenerating with respect to the gradient of the solutions. The fundamental question underlying both topics regards the effects of ellipticity on the intrinsic properties of solutions to nonlinear equations. To be more precise, in the case of mean-field game systems, ellipticity seems to be magnified through the coupling structure. On the other hand, in the degenerate setting, ellipticity collapses, giving rise to intricate regularity phenomena. Our analysis is preceded by some context on both topics.
|
| 249 |
Application of the Duality TheoryLorenz, Nicole 15 August 2012 (has links) (PDF)
The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning.
First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature.
In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above.
The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization.
We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem.
|
| 250 |
Application of the Duality Theory: New Possibilities within the Theory of Risk Measures, Portfolio Optimization and Machine LearningLorenz, Nicole 28 June 2012 (has links)
The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning.
First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature.
In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above.
The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization.
We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem.
|
Page generated in 0.0872 seconds