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1
Gutperle, Michael. « Dirichlet branes, Dirichlet instantons and string duality ». Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627362.
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2
Beuchler, Sven. « A Dirichlet-Dirichlet DD-pre-conditioner for p-FEM ». Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601329.
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In this paper, a uniformly elliptic second order boundary value problem in 2D is discretized by the p-version of the finite element method. An inexact Dirichlet-Dirichlet domain decomposition pre-conditioner for the system of linear algebraic equations is investigated. The solver for the problem in the sub-domains and a pre-conditioner for the Schur-complement are proposed as ingredients for the inexact DD-pre-conditioner. Finally, several numerical experiments are given.
3
Rodrigues, Guilherme Souza. « Modelos dinâmicos Dirichlet ». reponame:Repositório Institucional da UnB, 2011. http://repositorio.unb.br/handle/10482/10139.
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Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Estatística, 2011.Submitted by Tania Milca Carvalho Malheiros (tania@bce.unb.br) on 2012-03-21T16:17:48Z No. of bitstreams: 1 2011_GuilhermeSouzaRodrigues_Parcial.pdf: 574274 bytes, checksum: 0f38c60daad115aaa5eeeab09a5c59b0 (MD5)
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O interesse central desta dissertação está na modelagem estatística de dados composicionais, que são caracterizados por vetores aleatórios yt definidos no (k − 1)- simplex aberto padrão. Cada coordenada de yt representa a participação, (share), em termos percentuais, de cada uma das k categorias de resposta possíveis em um fenˆomeno. Propomos um modelo dinâmico inédito, batizado como Modelo Dinâmico Dirichlet (MDD), para a descrição de dados composicionais. O MDD é útil tanto no estudo de dados relativos a uma série temporal, quanto no estudo de dados em que não há dinâmica, ou seja, dados estatísticos caracterizando unidades amostrais de um estudo. Apresentamos o modelo em duas estruturas distintas, uma delineada para a estimação recursiva dos parâmetros, dita online, e a outra para a abordagem de estimação via simulação estocástica MCMC (offline), sendo este último método indicado quando há parâmetros desconhecidos na estrutura do modelo. Discutimos a utilização prática do modelo proposto na descrição do comportamento passado da série histórica, assim como no processo de previs˜ao. Abordamos, ainda, a aplicação do Modelo Dinâmico Dirichlet no contexto estático, um importante caso particular no qual o MDD assume a forma de um modelo de regress˜ao Dirichlet. ______________________________________________________________________________ ABSTRACT
The main purpose of this dissertation is on the study of statistical models for compositional data. Such kind of data is characterized by random vectors yt defined on the open standard (k − 1)-simplex. Each coordinate of yt represents the share, in percentage, of each one of the k categories that represent a given phenomena. We propose a new dynamic model, the Dynamic Dirichlet Model (MDD), for describing compositional data. The MDD is useful not only in the study of time series of compositional data but also for analyzing static compositional. We designed both online and offline approaches for the estimation of the parameters in the model. The online version is adequate for recursive estimation while the offline one, which is based on stochastic simulation via MCMC, can be used when there are some specific unknown parameters is the model. We discuss the practical use of the proposed model in describing the past behavior of the series, as well as in the prediction process. We also discuss the application of the Dynamic Dirichlet Model in a static context, an important particular case in which the MDD takes the form of a Dirichlet regression model.
4
Bertoin, Jean. « Processus de Dirichlet ». Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb37602956z.
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5
Scioletti, Francesca. « Il problema di Dirichlet ». Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016.
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Il risultato principale di questa tesi è un risultato di esistenza e unicità della soluzione debole per il problema di Dirichlet associato ad un operatore ellittico in forma di divergenza. Seguendo la presentazione di Gilbarg-Trudinger, la prova utilizza in un primo tempo il Teorema di Lax-Milgram, e successivamente il principio del massimo debole. La prima parte della tesi è dedicata alla presentazione dei risultati di Analisi Funzionale che vengono utilizzati: teoria degli operatori lineari, proprietà degli operatori lineari compatti, teoremi dell'indice, spazi di Sobolev e teoremi di immersione.
6
Song, Yuhyun. « Linkage Based Dirichlet Processes ». Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/74970.
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We live in the era of textit{Big Data} with significantly richer computational resources than the last two decades. The concurrence of computation resources and a large volume of data has boosted researchers' desire for developing feasible Markov Chain Monte Carlo (MCMC) algorithms for large parameter spaces. Dirichlet Process Mixture Models (DPMMs) have become a Bayesian mainstay for modeling heterogeneous structures, namely clusters, especially when the quantity of clusters is not known with the established MCMC methods. As opposed to many ad-hoc clustering methods, using Dirichlet Processes (DPs) in models provide a flexible and probabilistic approach for automatically estimating both cluster structure and quantity. While DPs are not fully parameterized, they depend on both a base measure and a concentration parameter that can heavily impact inferences.
Determining the concentration parameter is critical and essential, since it adjusts the a-priori cluster expectation, but typical approaches for specifying this parameter are rather cavalier. In this work, we propose a new method for automatically and adaptively determining this parameter, which directly calibrates distances between clusters through an explicit link function within the DP. Furthermore, we extend our method to mixture models with Nested Dirichlet Processes (NDPs) that cluster the multilevel data and depend on the specification of a vector of concentration parameters. In this work, we detail how to incorporate our method in Markov chain Monte Carlo algorithms, and illustrate our findings through a series of comparative simulation studies and applications.Ph. D.
7
Narayanan, Sridhar. « Selberg's conjectures on Dirichlet series ». Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=55517.
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In this thesis we introduce the Rankin-Selberg hypothesis in the Selberg Class to obtain a non-vanishing theorem on line $ Re(s)=1$ for a certain sub-class of functions in this class. We also prove that the Selberg's Conjectures imply the $S sb{K}$-primitivity of $ zeta sb{K}.$
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Garousi, Mohammad R. (Mohammad Reza). « Superstring scattering from Dirichlet branes ». Thesis, McGill University, 1996. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=40351.
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We derive fully covariant expressions for all two-point scattering amplitudes of two massless closed strings from a Dirichlet p-brane. This construction relies on the observation that there is a simple relation between these D-brane amplitudes in type II superstring theory and four-point scattering amplitudes for type I open superstrings. From the two-point amplitudes, we derive the long range background fields for the D-branes, and verify that as expected they correspond to those of extremally charged p-brane solutions of the low energy effective action.
9
Ponweiser, Martin. « Latent Dirichlet Allocation in R ». WU Vienna University of Economics and Business, 2012. http://epub.wu.ac.at/3558/1/main.pdf.
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Topic models are a new research field within the computer sciences information retrieval and text mining. They are generative probabilistic models of text corpora inferred by machine learning and they can be used for retrieval and text mining tasks. The most prominent topic model is latent Dirichlet allocation (LDA), which was introduced in 2003 by Blei et al. and has since then sparked off the development of other topic models for domain-specific purposes.
This thesis focuses on LDA's practical application. Its main goal is the replication of the data analyses from the 2004 LDA paper ``Finding scientific topics'' by Thomas Griffiths and Mark Steyvers within the framework of the R statistical programming language and the R~package topicmodels by Bettina Grün and Kurt Hornik. The complete process, including extraction of a text corpus from the PNAS journal's website, data preprocessing, transformation into a document-term matrix, model selection, model estimation, as well as presentation of the results, is fully documented and commented. The outcome closely matches the analyses of the original paper, therefore the research by Griffiths/Steyvers can be reproduced. Furthermore, this thesis proves the suitability of the R environment for text mining with LDA. (author's abstract)Series: Theses / Institute for Statistics and Mathematics
10
Laniel, François. « Capacités et espace de Dirichlet ». Thesis, Université Laval, 2013. http://www.theses.ulaval.ca/2013/30186/30186.pdf.
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Choquet influença profondément la théorie du potentiel en démontrant la capacitabilité des ensembles analytiques, en particulier des boréliens. L’abstraction de la capacité newtonienne à des capacités abstraites permit l’introduction de capacités intéressantes à étudier et c’est en partie ce que nous ferons dans ce mémoire. Beurling fut le premier à discuter de l’espace de Dirichlet classique en démontrant dans sa thèse de doctorat un théorème profond liant la capacité logarithmique aux limites non tangentielles des fonctions de cet espace. En compagnie de Carleson, il établit les bases fondamentales de cette théorie. Plusieurs questions restent encore ouvertes concernant l’espace de Dirichlet et c’est ce qui motive l’intérêt de nombreux mathématiciens à son égard. Passant par la démonstration du théorème de Choquet, du théorème de Frostman, du théorème de Beurling et de l’inégalité capacitaire forte, ce mémoire se veut avant tout une introduction aux résultats classiques mais profonds concernant différentes capacités et l’espace de Dirichlet classique.
11
Ortiz, Fernández Alejandro. « El problema de Dirichlet parabólico ». Pontificia Universidad Católica del Perú, 2013. http://repositorio.pucp.edu.pe/index/handle/123456789/95033.
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12
Kis, Ludovic. « Perturbations du problème de Dirichlet ». Metz, 1998. http://docnum.univ-lorraine.fr/public/UPV-M/Theses/1998/Kis.Ludovic.SMZ9832.pdf.
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Dans toute la suite (a) sera un opérateur elliptique du second ordre, (oméga) un domaine de dimension (n), (lp) l'espace des fonctions ayant la p-ième puissance intégrable, (h) l'espace des fonctions ayant des dérivées jusqu'au premier ordre au carré intégrable, (ho) l'espace des fonctions de (h) s'annulant sur le bord, (wp) l'espace des fonctions ayant des dérivées jusqu'au deuxième ordre avec la p-ième puissance intégrable. On met entre parenthèses un symbole mathématique. Le contenu de ce travail est divisé en trois parties. Dans la première partie on étudie des équations semilinéaires de la forme : (f) appartient à (a)(u) + (bêta) ((x), (u)) ou (f) est dans (lp), (u) dans (ho), (bêta) ((x), variable) peut être une perturbation univoque monotone ou non monotone, un graphe maximal monotone, une fonction discontinue, pour presque tout (x) da (oméga). Des travaux en ce sens ont été faits par Brezis et Browder, Amann pour une perturbation univoque. On obtient des résultats du type suivant : lorsque la perturbation dépendante du domaine (beta) sépare deux graphes maximaux monotones indépendants du domaine, on a l'existence d'une solution (u) dans (wp). La technique utilisée repose sur une bonne régularité de la solution lorsque la perturbation monotone est indépendante du domaine et le principe du maximum. Dans le cas multivoque on considère dans un premier temps le problème correspondant à la régularisation de Yosida qui est univoque et ensuite passer à la limite via une méthode de compacité. Notre approche assure une classe entière des sous- et sur-solutions au sens de Amann, elle s'applique aux perturbations monotones multivoques et conduit à des estimations avec un bon contrôle des constantes par rapport aux données du problème. Dans la seconde partie on étudie des perturbations singulières du problème de Dirichlet ayant la forme suivante (epsilon) (a)(ue) + (beta)(ue) = (f) ou (epsilon) est le parametre positif de la perturbation, (ue) est dans (ho), (f) dans (lp), (beta) est une perturbation croissante, continue, univoque. Des travaux sur ce problème ont été faits par Lions, Brauner et Nicolaenko. On montre que la quantité (epsilon)(ue) converge dans wp fort vers la solution d'un problème limité qui est en fait une perturbation par un graphe maximal monotone spécial du problème du Dirichlet. La vitesse de la convergence dépendra du comportement asymptotique de la perturbation monotone (beta) autour de l'infini. On décrit le comportement de la solution pénalisée (ue) dans la partie du domaine ou la solution limite s'annule et on constate qu'il dépend de la nature coercive de (beta), du comportement asymptotique de (beta) autour de l'infini et de la régularité de la solution (uo) du problème (beta)(uo) = (f). On distingue les situations ou la perturbation monotone (beta) est bornée et non bornée. Nous élaborons une méthode de monotonie spécifique aux espaces (lp) qui généralise une méthode similaire de Lions pour (p) = 2. Le principe du maximum est un outil indispensable : il peut s'appliquer dans des situations ou le paramètre (epsilon) de la pénalisation est suffisamment petit ou pour dominer la suite pénalisée qui est susceptible de converger ponctuellement donc le théorème de convergence dominée de Lebesgue peut s'appliquer. La méthode de compacité sera souvent utilisée car on travaille dans des espaces réflexifs. Nos techniques s'appliquent aussi bien dans le cas ou la contrainte sur la solution pénalisée nulle sur le bord est remplacée par la contrainte constante inconnue sur le bord et l'intégrale de (beta)(ue) est une constante donnée. Pour ce problème on donne une approche analytique basée sur le principe du maximum avec caractérisation du comportement de la solution pénalisée dans la partie du domaine ou la solution limite s'annule. Dans certains travaux de Hilhorst et Diekmann on trouve une approche variationnelle avec l'étude de (epsilon)(ue) seulement. La troisième partie traite des inégalités variationnelles non locales de la forme : (u) dans (k), l'intégrale du produit ((a)(u) (f))((v) (u)) est positive pour tout (v) dans (k) un ensemble des fonctions de (ho) soumises à une contrainte convexe (j) telles que respectivement la différence (j)((x), (v)) (alpha) positive dans le domaine, la différence j((x),(v))(alpha) positive sur la frontière du domaine, la différence (j)((x), gradient (v)) (alpha) positive ou (alpha) est une constante positive. On continue certains travaux de Brezis et Stampacchia, Chipot. Nous développons une méthode de continuité qui consiste en plusieurs étapes : pénalisation, estimation à priori, stabilité de la solution pénalisée, continuité de la contrainte et existence via continuité. Cette approche permet de capter aussi à la limite les versions locales des problèmes étudiés notamment le problème du double obstacle. Dans certaines situations on utilise aussi les multiplicateurs de Lagrange. En général on obtient l'existence et l'unicité d'une solution (u) dans (wp). On étudie aussi des inégalités variationnelles du quatrième ordre de la forme : (u) dans (k), l'intégrale du produit ((a)(u) (f)) ((a)(v)(a)(u)) est positive pour tout (v) dans (k) un ensemble des fonctions de (ho) et (w2) soumises à une contrainte convexe (j) telles que respectivement : la différence (j)((x),(v))(alpha) positive, la différence (j)((x),(a)(v)) (alpha) positive. On obtient aussi que le problème du double obstacle pour l'opérateur biharmonique avec une fonction générique (f) dans (lp) admet une solution (u) dans (wp). On améliore des résultats de régularité obtenus par Brezis et Stampacchia, Caffare. . .
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KIS, LUDOVIC Chipot Michel. « PERTURBATIONS DU PROBLEME DE DIRICHLET / ». [S.l.] : [s.n.], 1998. ftp://ftp.scd.univ-metz.fr/pub/Theses/1998/Kis.Ludovic.SMZ9832.pdf.
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Arnekvist, Isac, et Ludvig Ericson. « Finding competitors using Latent Dirichlet Allocation ». Thesis, KTH, Skolan för datavetenskap och kommunikation (CSC), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-186386.
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Identifying business competitors is of interest to many, but is becoming increasingly hard in an expanding global market. The aim of this report is to investigate whether Latent Dirichlet Allocation (LDA) can be used to identify and rank competitors based on distances between LDA representations of company descriptions. The performance of the LDA model was compared to that of bag-of-words and random ordering by evaluating then comparing them on a handful of common information retrieval metrics. Several different distance metrics were evaluated to determine which metric had best correspondence between representation distance and companies being competitors. Cosine similarity was found to outperform the other distance metrics. While both LDA and bag-of-words representations were found to be significantly better than random ordering, LDA was found to perform worse than bag-of-words. However, computation of distance metrics was considerably faster for LDA representations. The LDA representations capture features that are not helpful for identifying competitors, and it is suggested that LDA representations could be used together with some other data source or heuristic.Det finns ett intresse av att kunna identifiera affärskonkurrenter, men detta blir allt svårare på en ständigt växande och alltmer global marknad. Syftet med denna rapport är att undersöka om Latent Dirichlet Allocation (LDA) kan användas för att identifiera och rangordna konkurrenter. Detta genom att jämföra avstånden mellan LDA-representationerna av dessas företagsbeskrivningar. Effektiviteten av LDA i detta syfte jämfördes med den för bag-of-words samt slumpmässig ordning, detta med hjälp av några vanliga informationsteoretiska mått. Flera olika avståndsmått utvärderades för att bestämma vilken av dessa som bäst åstadkommer att konkurrerande företag hamnar nära varandra. I detta fall fanns Cosine similarity överträffa andra avståndsmått. Medan både LDA och bag-of-words konstaterades vara signifikant bättre än slumpmässig ordning så fanns att LDA presterar kvalitativt sämre än bag-of-words. Uträkning av avståndsmått var dock betydligt snabbare med LDA-representationer. Att omvandla webbinnehåll till LDA-representationer fångar dock vissa ospecifika likheter som inte nödvändigt beskriver konkurrenter. Det kan möjligen vara fördelaktigt att använda LDA-representationer ihop med någon ytterligare datakälla och/eller heuristik.
15
Balčiūnas, Aidas. « Mellin transforms of Dirichlet L-functions ». Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20141209_112534-52265.
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In the thesis moromorphic continuation of modified Mellin transforms of Dirichlet L-functions to the whole complex plane have been obtained.Disertacijoje gauta modifikuotosios Melino transformacijos L- funkcijai meromorfinis pratęsimas į visą kompleksinę plokštumą.
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Choubey, Rahul. « Tag recommendation using Latent Dirichlet Allocation ». Thesis, Kansas State University, 2011. http://hdl.handle.net/2097/9785.
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Master of ScienceDepartment of Computing and Information Sciences
Doina Caragea
The vast amount of data present on the internet calls for ways to label and organize this data according to specific categories, in order to facilitate search and browsing activities. This can be easily accomplished by making use of folksonomies and user provided tags. However, it can be difficult for users to provide meaningful tags. Tag recommendation systems can guide the users towards informative tags for online resources such as websites, pictures, etc. The aim of this thesis is to build a system for recommending tags to URLs available through a bookmark sharing service, called BibSonomy. We assume that the URLs for which we recommend tags do not have any prior tags assigned to them. Two approaches are proposed to address the tagging problem, both of them based on Latent Dirichlet Allocation (LDA) Blei et al. [2003]. LDA is a generative and probabilistic topic model which aims to infer the hidden topical structure in a collection of documents. According to LDA, documents can be seen as mixtures of topics, while topics can be seen as mixtures of words (in our case, tags). The first approach that we propose, called topic words based approach, recommends the top words in the top topics representing a resource as tags for that particular resource. The second approach, called topic distance based approach, uses the tags of the most similar training resources (identified using the KL-divergence Kullback and Liebler [1951]) to recommend tags for a test untagged resource. The dataset used in this work was made available through the ECML/PKDD Discovery Challenge 2009. We construct the documents that are provided as input to LDA in two ways, thus producing two different datasets. In the first dataset, we use only the description and the tags (when available) corresponding to a URL. In the second dataset, we crawl the URL content and use it to construct the document. Experimental results show that the LDA approach is not very effective at recommending tags for new untagged resources. However, using the resource content gives better results than using the description only. Furthermore, the topic distance based approach is better than the topic words based approach, when only the descriptions are used to construct documents, while the topic words based approach works better when the contents are used to construct documents.
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Sánchez, Vera Juan Carlos. « Un problema de Dirichlet no local ». Bachelor's thesis, Universidad Nacional Mayor de San Marcos, 2017. https://hdl.handle.net/20.500.12672/9313.
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Se prueba que un problema de Dirichlet no local posee una solución débil. La demostración se realiza mediante el uso de un corolario del Teorema de Weierstrass Generalizado. Así mismo, se prueba un resultado de unicidad bajo una condición de pequeñez y se presenta la solución numérica del problema.Tesis
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Sargent, Ethan. « Radial Solutions to Semipositone Dirichlet Problems ». Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/hmc_theses/229.
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We study a Dirichlet problem, investigating existence and uniqueness for semipositone and superlinear nonlinearities. We make use of Pohozaev identities, energy arguments, and bifurcation from a simple eigenvalue.
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Chalmoukis, Nikolaos <1993>. « Interpolation problems in Dirichlet type spaces ». Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amsdottorato.unibo.it/9540/1/PhD_Thesis_AMS_Submission.pdf.
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This thesis deals with interpolation problems in spaces of analytic functions of Dirichlet type, that is spaces in which the corresponding norm is defined in terms of some integral involving (partial) derivatives of the function. These problems can be categorized roughly into two categories. The first one is problems of interpolation by sequences where one tries to find a function in a given space such that on prescribed points assumes prescribed values. The second is boundary interpolation where one prescribes the values of the function on a set that sits in the boundary of the natural domain of definition. In the first part we explore simply interpolating sequences for the Dirichlet space. We manage to give a partial answer to a problem first raised by Bishop. We prove that for sequences which satisfy the so called Shapiro–Shields condition there exists a potential theoretic characterization of when they are simply interpolating. In the second part we study random interpolating sequences for the standard weighted Dirichlet spaces. We are able to prove 0–1 Kolmogorov type characterizations for universally interpolating, zero and separated sequences for this class of spaces. Our results generalize and improve upon previous results of Rudowicz Bogdan and Cochran. Finally, in the last part we work with Hardy–Sobolev spaces in the unit ball of n complex variables. Our results concern the equivalence of two notions of “negligibility”of sets on the boundary of the ball. One notion is classical and is that of capacity zero sets and the second notion is that of a totally null set. Our main result shows that at least for compact sets these two notions coincide. Our result can be applied to improve a result on boundary interpolation of Cohn & Verbitsky.
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Maciulevičienė, Irmutė. « Dvimatė ribinė teorema Dirichlė L-funkcijoms ». Master's thesis, Lithuanian Academic Libraries Network (LABT), 2006. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2006~D_20060605_123853-83240.
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Dobilienė, Irmina. « Kai kurių Dirichlė eilučių nuliai ». Master's thesis, Lithuanian Academic Libraries Network (LABT), 2007. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2007~D_20070816_160419-10199.
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Nagrinėjamos dvi funkcijos. Darbe nustatyta, kad esant papildomiems reikalavimams, šios funkcijos turi be galo daug nulių atitinkamoje juostoje ir pusplokštumoje.The two functions are analytically continuable to the whole complex plane. It is prove that the functions have infinitely many zeros in the strop and in the half-plane.
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Hassanpour, Mehran. « Sufficient Conditions for Uniqueness of Positive Solutions and Non Existence of Sign Changing Solutions for Elliptic Dirichlet Problems ». Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc279227/.
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In this paper we study the uniqueness of positive solutions as well as the non existence of sign changing solutions for Dirichlet problems of the form $$\eqalign{\Delta u + g(\lambda,\ u) &= 0\quad\rm in\ \Omega,\cr u &= 0\quad\rm on\ \partial\Omega,}$$where $\Delta$ is the Laplace operator, $\Omega$ is a region in $\IR\sp{N}$, and $\lambda>0$ is a real parameter. For the particular function $g(\lambda,\ u)=\vert u\vert\sp{p}u+\lambda$, where $p={4\over N-2}$, and $\Omega$ is the unit ball in $\IR\sp{N}$ for $N\ge3$, we show that there are no sign changing solutions for small $\lambda$ and also we show that there are no large sign changing solutions for $\lambda$ in a compact set. We also prove uniqueness of positive solutions for $\lambda$ large when $g(\lambda,\ u)=\lambda f(u)$, where f is an increasing, sublinear, concave function with f(0) $<$ 0, and the exterior boundary of $\Omega$ is convex. In establishing our results we use a number of methods from non-linear functional analysis such as rescaling arguments, methods of order, estimation near the boundary, and moving plane arguments.
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Daghighi, Abtin. « The Dirichlet problem for certain discrete structures ». Thesis, Uppsala University, Department of Mathematics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121384.
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Faires, Hafedh. « Modèles hiérarchiques de Dirichlet à temps continu ». Phd thesis, Université d'Orléans, 2008. http://tel.archives-ouvertes.fr/tel-00466503.
Texte intégralRésumé :
Nous étudions les processus de Dirichlet dont le paramètre est une mesure proportionnelle à la loi d'un processus temporel, par exemple un mouvement Brownien ou un processus de saut Markovien. Nous les utilisons pour proposer des modèles hiérarchiques bayésiens basés sur des équations différentielles stochastiques en milieu aléatoire. Nous proposons une méthode pour estimer les paramètres de tels modèles et nous l'illustrons sur l'équation de Black-Scholes en milieu aléatoire.
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Brevig, Ole Fredrik. « The Sidon Constant for Ordinary Dirichlet Series ». Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-20688.
Texte intégralRésumé :
We obtain the asymptotic formula of the Sidon constant for ordinary Dirichlet series using the Bohnenblust--Hille inequality and estimates on smooth numbers. We moreover give precise estimates for the error term.
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Vougalter, Vitali. « Diamagnetic behavior of sums of Dirichlet eigenvalues ». Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/28034.
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Stefański, Bogdan. « String theory, dirichlet branes and K-theory ». Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621023.
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Murugiah, S. « Bayesian nonparametric clustering based on Dirichlet processes ». Thesis, University College London (University of London), 2010. http://discovery.ucl.ac.uk/20467/.
Texte intégralRésumé :
Following a review of some traditional methods of clustering, we review the Bayesian nonparametric framework for modelling object attribute differences. We focus on Dirichlet Process (DP) mixture models, in which the observed clusters in any particular data set are not viewed as belonging to a fixed set of clusters but rather as representatives of a latent structure in which clusters belong to one of a potentially infinite number of clusters. As more information about attribute differences is revealed, the number of inferred clusters is allowed to grow. We begin by studying DP mixture models for normal data and show how to adapt one of the most widely used conditional methods for computation to improve sampling efficiency. This scheme is then generalized, followed by an application to discrete data. The DP’s dispersion parameter is a critical parameter controlling the number of clusters. We propose a framework for the specification of the hyperparameters for this parameter, using a percentile based method. This research was motivated by the analysis of product trials at the magazine Which?, where brand attributes are usually assessed on a 5-point preference scale by experts or by a random selection of Which? subscribers. We conclude with a simulation study, where we replicate some of the standard trials at Which? and compare the performance of our DP mixture models against various other popular frequentist and Bayesian multiple comparison routines adapted for clustering.
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Risch, Johan. « Detecting Twitter topics using Latent Dirichlet Allocation ». Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-277260.
Texte intégralRésumé :
Latent Dirichlet Allocations is evaluated for its suitability when detecting topics in a stream of short messages limited to 140 characters. This is done by assessing its ability to model the incoming messages and its ability to classify previously unseen messages with known topics. The evaluation shows that the model can be suitable for certain applications in topic detection when the stream size is small enough. Furthermoresuggestions on how to handle larger streams are outlined.
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Carvalho, Ana Marcia Fernandes Tucci de. « O problema de Dirichlet : metodos de resolução ». [s.n.], 1994. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306629.
Texte intégralRésumé :
Orientador: Syairo Guedes de FigueiredoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica
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Resumo: Não informado.
Abstract: Not informed.
Mestrado
Mestre em Matemática
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Presoto, Adilson Eduardo 1983. « Criterios de solubilidade do problema de Dirichlet ». [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306980.
Texte intégralRésumé :
Orientadores: Djairo Guedes de Figueiredo, Francisco Odair de PaivaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Abordaremos diferentes métodos da Teoria do Potencial desenvolvidos no fim do século XIX e no começo do século XX para solucionar o Problema de Dirichlet. Iniciamos o primeiro capítulo com o Método da Varredura de Poincaré que transcendeu os anteriores e focalizou o problema sob uma nova óptica. Neste método, uma função harmônica, num domínio geral, era obtida, uma vez que condição de contorno fosse dada. Então condições na fronteira eram analizadas afim de que a função harmônica fosse, de fato, a solução do Problema de Dirichlet. Até então, as principais resoluções se baseavam no Princípio de Dirichlet que admitia soluções minimizantes para integrais de energia, se fundamentando em argumentos físicos. Contudo, tais argumentos continham alguns deslizes matemáticos como a admissão do mínimo para essas integrais. Posteriormente, surgiram os métodos de Perron e de Wiener dentro do espírito o Método do Poincaré. Ainda no primeiro capítulo, apresentamos um antecessor do método de Poincaré: o "Método de Schwarz. O segundo capítulo é dedicado ao Método das Equações Intregrais de Fredholm, no qual a Análise FUncional e as Equações Diferenciais Parciais caminharam lado a lado. Por fim, no último capítulo temos um resultado devido a Wiener que caracteriza os pontos regulares em termos de convergência de uma série envolvendo a capacidade de alguns conjuntos
Abstract: We will present different methods of Potential Theory developed at the end of the nineteenth century and the beginning of the twentieth century to solve the Dirichlet Problem. We start in the first chapter, with the Poincaré's Sweepping out Method, which transcended the former ones and focused the problem in a new insight. In this method, a harmonic function in a general domain is obtained, once a boundary condition is given. Then, conditions in the boundary are discussed so that this harmonic function is indeed the solution of the Dirichlet Problem. Until then, the key results were based on Dirichlet PrincipIe which admitted minimizing solutions to energy integraIs, by using some physical arguments. However, such arguments contained a few Mathematical gaps like the admission of a minimun to these integrals. Later, it appeared the Perron and Wiener Methods in the spirit of the Poincaré Method. Even in the first chapter, we discuss a predecessor of Poincaré's Method: the Schwarz's Method. The second chapter is devoted to the Integral Equations Method, where the Functional Analysis and Differential Equations walked side by side. Finally, the last chapter is a result due to Wiener that characterizes the regular points in terms of covergence of a series involving the capacity of some sets
Mestrado
Matematica - Analise- Equações Diferenciais e Parciais
Mestre em Matemática
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Caballero, Cantú José Jeremías. « Solución de una ecuación diferencial tipo Dirichlet ». Bachelor's thesis, Universidad Nacional Mayor de San Marcos, 2008. https://hdl.handle.net/20.500.12672/12713.
Texte intégralRésumé :
Expone la solución numérica de la ecuación diferencial con condiciones de frontera, resolviendo por el método de elementos finitos con funciones de base lineales. La forma clásica se pasará a la forma variacional o débil, luego se discretiza, de la cuál sale un sistema de n ecuaciones lineales y resolviendo mediante este sistema se obtiene la solución aproximada.Trabajo de suficiencia profesional
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Silva, José Eduardo Jesus da. « Propriedade Alternada do Operador de Dirichlet-Neumann ». Universidade Federal da Paraíba, 2010. http://tede.biblioteca.ufpb.br:8080/handle/tede/7455.
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Previous issue date: 2010-07-22Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
In this work we talk about properties of the Dirichlet-to-Neumann map for the conductivity equation in a smooth manifold with boundary of R2. We use several times the Maximum Principle to conclude a Alternating Property of the Dirichlet-to- Neumann map. Using this property, we and that the Kernel satises a given set of inequalities. Finally, we note that these inequalities imply the Alternating Property of the Kernel of the Dirichlet-to-Neumann map.
Neste trabalho dissertamos sobre Propriedades do Funcional de Dirichlet-Neumann para uma equação de condutividade numa variedade diferenciavel bidimensional com bordo. Utilizamos varias vezes o Principio do Maximo para concluir que esse Funcional tem uma Propriedade Alternada. A partir dessa propriedade, verificamos que o Nucleo do Funcional satisfaz um conjunto especifico de desigualdades. Porém, verificamos que essas desigualdades implicam na Propriedade Alternada do Nucleo do Funcional.
34
Nawaz, Daud. « The Dirichlet Series To The Riemann Hypothesis ». Thesis, Högskolan i Gävle, Avdelningen för elektronik, matematik och naturvetenskap, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-27028.
Texte intégralRésumé :
This paper examines the Riemann zeta-function and its relation to the prime distribution. In this work, I present the journey from the Dirichlet series to the Riemann hypothesis. Furthermore, I discuss the prime counting function, the Riemann prime counting function and the Riemann explicit function for distribution of primes. This paper explains that the non-trivial zeros of the zeta-function are the key to understand the prime distribution.
35
Xiong, Jue. « The Dirichlet operator and its mapping properties ». The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1554944747702051.
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Laadnani, Idriss. « Approximation du semi-groupe de Dirichlet-Neumann ». Poitiers, 2005. http://www.theses.fr/2005POIT2333.
Texte intégralRésumé :
Dans cette thèse nous considérons l'opérateur de Dirichet-Neumann Lambda-gamma qui à toute donnée f sur le bord d'un domaine régulier borné D, associe le flux sortant à travers le bord du domaine, qui représente la dérivée normale de la solution de l'équation de conductivité électrique. Nous montrons que cet opérateur engendre un semigroupe S(t) analytique, compact, irréductible de Markov et à contraction. Nous étudions le comportement asymptotique de ce semigroupe dans l'espace des fonctions continues. Puis en généralisant la construction explicite du semigroupe de P. D. Lax, nous définissons une famille d'opérateurs V(t) qui converge au sens de Chernoff vers S(t). Nous démontrons les caractères régularisant et compact de V(t). Finalement, nous présentons des résultats numériques sur les valeurs propres de l'opérateur Lambda -gamma, par les méthodes de Prony et "Matrix Pencil"In this thesis we consider the Dirichet-Neumann operator lambda-gamma which, to every datum f on the edge of a bounded smooth domain D, associates a current flux across a boundary, where represent a normal derivative of solution of the electrical conductivity equation. We show that lambda-gamma generates a semigroup S (t) analytic, compact, irreducible of Markov and contractive. We study the asymptotic behaviour of this semigroup in a space of continuous functions. Then, by a generalization of the Lax semigroup, we define the family of operators V (t) which converges in the sense of Chernoff to S (t). We show the compactness and regularizing characters of V (t). Finally, we present numerical results on the eigenvalues of lambda-gamma by methods of Prony and "Matrix Pencil"
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Gruppioni, Sara. « Il problema di Dirichlet per il Laplaciano ». Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2012. http://amslaurea.unibo.it/4575/.
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Soares, da Silva Gomes Gecynalda. « Análise de influência para a distribuição Dirichlet ». Universidade Federal de Pernambuco, 2005. https://repositorio.ufpe.br/handle/123456789/6455.
Texte intégralRésumé :
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Previous issue date: 2005Modelagem de dados restritos ao intervalo (0,1) é muito comum na prática. Para modelar dados desta natureza podemos fazer uso da distribuição beta. Contudo, quando o interesse é estudar conjuntamente variáveis que estão compreendidas no intervalo (0,1) e trabalhar com modelos multivariados, uma distribuição útil é a Dirichlet, que é uma generalização da distribuição beta. Nesta dissertação avaliamos a influência local através da curvatura normal conforme para dados correspondentes a variáveis independentes e identicamente distribuídas (i.i.d.) segundo a distribuição Dirichlet. A metodologia da curvatura normal conforme foi proposta por Poon & Poon (1999) para avaliar medidas de influência segundo pequenas perturbações nos dados ou no modelo é considerada no contexto da distribuição Dirichlet. Consideramos dois esquemas de perturbação, um em que uma das componentes é modificada através das formas aditiva e multiplicativa e outro em que perturbamos a log-verossimilhança de forma multiplicativa. Após analisarmos as observações influentes através de tais medidas, comparamos as estimativas dos parâmetros da distribuição Dirichlet quando todas as observações estão presentes nos dados com as estimativas desses parâmetros ao retirarmos uma observação influente com o intuito de verificar o impacto causado nas estimativas
39
Mota, Adalgisa Mendonça. « O problema de Dirichlet em domínios limitados ». Universidade Federal de Alagoas, 2011. http://repositorio.ufal.br/handle/riufal/1046.
Texte intégralRésumé :
In this work we use two approach to prove the existence of solutions for the Classical Dirichlet Problem on bounded domains. The first method is applied to domains with smooth boundary and is based on the Single and Double Layer Potentials Theory. The second method uses the Variational Dirichlet Principle to solve the Dirichlet Problem in plane domains with boundary less regular than the previous case; more precisely, boundary satisfying the property of the outer triangle.Fundação de Amparo a Pesquisa do Estado de Alagoas
Nesta dissertação usamos duas abordagens diferentes para provar a existência de soluções para o Problema de Contorno de Dirichlet Clássico em domínios limitados. Aplicamos o primeiro método quando estamos trabalhando com domínios cuja fronteira é duas vezes continuamente diferenciável. Essa abordagem baseia-se na Teoria dos Potenciais de Camadas Simples e Dupla, onde a teoria de operadores compactos tem um papel fundamental. O segundo método usa o Princípio Variacional de Dirichlet para resolver o problema em domínios do plano com fronteiras menos regulares que no caso anterior; a saber, fronteiras que satisfazem a condição do triângulo exterior.
40
Mattioli, Federico. « Problema di Cauchy-Dirichlet per l'equazione del calore ». Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12042/.
Texte intégralRésumé :
In quest'elaborato si risolve il problema di Cauchy-Dirichlet per l'equazione del calore, prendendo come oggetto d'esame una sbarra omogenea. Nel primo capitolo si studiano le serie di Fourier reali a partire dalle serie trigonometriche; vengono dati, poi, i principali risultati di convergenza puntuale, uniforme ed in L^2 e si discute l'integrabilità termine a termine di una serie di Fourier.
Il secondo capitolo tratta la convergenza secondo Cesàro, le serie di Fejèr ed i principali risultati di convergenza di queste ultime. Nel terzo, ed ultimo, capitolo si risolve il Problema di Cauchy-Dirichlet, distinguendo i casi in cui il dato iniziale sia di classe C^1 o solo continuo; nel secondo caso si propone una risoluzione basata sulle serie di Fejér e sul concetto di barriera ed una utilizzando il nucleo di Green per l'equazione del calore.
41
Cappelli, Federico. « Il problema di Dirichlet per le funzioni armoniche ». Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14115/.
Texte intégralRésumé :
Questa tesi ha come argomento principale le funzioni olomorfe e le funzioni armoniche. Obbiettivo: quello di mostrare i collegamenti tra queste due classi di funzioni e le loro principali proprietà. Grande importanza verrà data al Problema di Dirichlet per il Laplaciano, e alla ricerca di una soluzione su un disco qualsiasi del piano reale. In questo modo potremo arrivare ad alcuni dei risultati più importanti sulle funzioni armoniche: formule di media, disuguaglianza di Harnack, teorema di massimo e minimo forte; che hanno un equivalente per le funzioni olomorfe.
42
Ruppen, Hans-Jörg. « Le problème de Dirichlet non-linéaire sur RN / ». Lausanne, 1985. http://library.epfl.ch/theses/?nr=593.
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Karlsson, Jonas. « Modular forms and converse theorems for Dirichlet series ». Thesis, Linköping University, Applied Mathematics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-19446.
Texte intégralRésumé :
This thesis makes a survey of converse theorems for Dirichlet series. A converse theo-rem gives sufficient conditions for a Dirichlet series to be the Dirichlet series attachedto a modular form. Such Dirichlet series have special properties, such as a functionalequation and an Euler product. Sometimes these properties characterize the modularform completely, i.e. they are sufficient to prove the proper transformation behaviourunder some discrete group. The problem dates back to Hecke and Weil, and has morerecently been treated by Conrey et.al. The articles surveyed are:
- "An extension of Hecke's converse theorem", by B. Conrey and D. Farmer
- "Converse theorems assuming a partial Euler product", by D. Farmer and K.Wilson
- "A converse theorem for ¡0(13)", by B. Conrey, D. Farmer, B. Odgers and N.Snaith
The results and the proofs are described. The second article is found to contain anerror. Finally an alternative proof strategy is proposed.
44
MATSUMOTO, Kohji, et Hirofumi TSUMURA. « Generalized multiple Dirichlet series and generalized multiple polylogarithms ». Institute of Mathematics Polish Academy of Sciences, 2006. http://hdl.handle.net/2237/9366.
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Bouchard, Hugues. « Systèmes de diffusion-réaction avec conditions Dirichlet-périodiques ». Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0018/NQ56991.pdf.
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Maier, Marco J. « DirichletReg : Dirichlet Regression for Compositional Data in R ». WU Vienna University of Economics and Business, 2014. http://epub.wu.ac.at/4077/1/Report125.pdf.
Texte intégralRésumé :
Dirichlet regression models can be used to analyze a set of variables lying
in a bounded interval that sum up to a constant (e.g., proportions, rates,
compositions, etc.) exhibiting skewness and heteroscedasticity, without
having to transform the data.
There are two parametrization for the presented model, one using the common
Dirichlet distribution's alpha parameters, and a reparametrization of the
alpha's to set up a mean-and-dispersion-like model.
By applying appropriate link-functions, a GLM-like framework is set up that
allows for the analysis of such data in a straightforward and familiar way,
because interpretation is similar to multinomial logistic regression.
This paper gives a brief theoretical foundation and describes the
implementation as well as application (including worked examples) of
Dirichlet regression methods implemented in the package DirichletReg (Maier,
2013) in the R language (R Core Team, 2013). (author's abstract)Series: Research Report Series / Department of Statistics and Mathematics
47
McGillivray, Ivor Edward. « Some applications of Dirichlet forms in probability theory ». Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.241102.
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Scotti, Simone. « Applications of the error theory using Dirichlet forms ». Phd thesis, Université Paris-Est, 2008. http://tel.archives-ouvertes.fr/tel-00349241.
Texte intégralRésumé :
This thesis is devoted to the study of the applications of the error theory using Dirichlet forms. Our work is split into three parts. The first one deals with the models described by stochastic differential equations. After a short technical chapter, an innovative model for order books is proposed. We assume that the bid-ask spread is not an imperfection, but an intrinsic property of exchange markets instead. The uncertainty is carried by the Brownian motion guiding the asset. We find that spread evolutions can be evaluated using closed formulae and we estimate the impact of the underlying uncertainty on the related contingent claims. Afterwards, we deal with the PBS model, a new model to price European options. The seminal idea is to distinguish the market volatility with respect to the parameter used by traders for hedging. We assume the former constant, while the latter volatility being an erroneous subjective estimation of the former. We prove that this model anticipates a bid-ask spread and a smiled implied volatility curve. Major properties of this model are the existence of closed formulae for prices, the impact of the underlying drift and an efficient calibration strategy. The second part deals with the models described by partial differential equations. Linear and non-linear PDEs are examined separately. In the first case, we show some interesting relations between the error and wavelets theories. When non-linear PDEs are concerned, we study the sensitivity of the solution using error theory. Except when exact solution exists, two possible approaches are detailed: first, we analyze the sensitivity obtained by taking "derivatives" of the discrete governing equations. Then, we study the PDEs solved by the sensitivity of the theoretical solutions. In both cases, we show that sharp and bias solve linear PDE depending on the solution of the former PDE itself and we suggest algorithms to evaluate numerically the sensitivities. Finally, the third part is devoted to stochastic partial differential equations. Our analysis is split into two chapters. First, we study the transmission of an uncertainty, present on starting conditions, on the solution of SPDE. Then, we analyze the impact of a perturbation of the functional terms of SPDE and the coefficient of the related Green function. In both cases, we show that the sharp and bias verify linear SPDE depending on the solution of the former SPDE itself
49
Liu, Zelong. « High performance latent dirichlet allocation for text mining ». Thesis, Brunel University, 2013. http://bura.brunel.ac.uk/handle/2438/7726.
Texte intégralRésumé :
Latent Dirichlet Allocation (LDA), a total probability generative model, is a three-tier Bayesian model. LDA computes the latent topic structure of the data and obtains the significant information of documents. However, traditional LDA has several limitations in practical applications. LDA cannot be directly used in classification because it is a non-supervised learning model. It needs to be embedded into appropriate classification algorithms. LDA is a generative model as it normally generates the latent topics in the categories where the target documents do not belong to, producing the deviation in computation and reducing the classification accuracy. The number of topics in LDA influences the learning process of model parameters greatly. Noise samples in the training data also affect the final text classification result. And, the quality of LDA based classifiers depends on the quality of the training samples to a great extent. Although parallel LDA algorithms are proposed to deal with huge amounts of data, balancing computing loads in a computer cluster poses another challenge. This thesis presents a text classification method which combines the LDA model and Support Vector Machine (SVM) classification algorithm for an improved accuracy in classification when reducing the dimension of datasets. Based on Density-Based Spatial Clustering of Applications with Noise (DBSCAN), the algorithm automatically optimizes the number of topics to be selected which reduces the number of iterations in computation. Furthermore, this thesis presents a noise data reduction scheme to process noise data. When the noise ratio is large in the training data set, the noise reduction scheme can always produce a high level of accuracy in classification. Finally, the thesis parallelizes LDA using the MapReduce model which is the de facto computing standard in supporting data intensive applications. A genetic algorithm based load balancing algorithm is designed to balance the workloads among computers in a heterogeneous MapReduce cluster where the computers have a variety of computing resources in terms of CPU speed, memory space and hard disk space.
50
Bouchard, Hugues. « Systèmes de diffusion-réaction avec conditions Dirichlet-périodiques ». Thèse, Université de Sherbrooke, 1998. http://savoirs.usherbrooke.ca/handle/11143/4983.
Texte intégralRésumé :
La présente thèse étudie l'existence et le calcul de solutions deux fois dérivables dans L2 de systèmes de diffusion-réaction avec conditions Dirichlet-périodiques. La méthode utilisée pour résoudre le problème consiste à ajouter une nouvelle inconnue et un problème adjoint au problème original. La partie linéaire du système est alors auto-adjointe et la partie non-linéaire est un potentiel. Ensuite, on associe au problème augmenté une fonctionnelle φ, définie sur un espace de Sobolev adéquat, dont les points critiques seront les solutions du système de diffusion-réaction augmenté. Pour montrer l'existence et calculer les points critiques de la fonctionnelle φ, on utilise une base Hilbertienne bien choisie pour l'espace de Hilbert sur lequel la fonctionnelle φ est définie; on montre que la restriction de φ au sous-espace engendré par un sous ensemble fini de la base possède toujours au moins un point critique; on montre finalement que les points critiques des restrictions en dimension finie de φ possèdent des points d'accumulation (selon une certaine topologie) et que ces points d'accumulation sont des points critiques de la fonctionnelle non restreinte.