The algebra of matrices M with entries in an abelian von Neumann algebra is a C*-module. C*-modules were originally defined and studied by Kaplansky and we outline the foundations of the theory and particular properties of M. Furthermore, we prove a structure theorem for ultraweakly closed submodules of M, using techniques from the theory of type I finite von Neumann algebras. By analogy with the classical join in topology, the join for operator algebras A and B acting on Hilbert spaces H and K, respectively, was defined by Gilfeather and Smith. Assuming that K is finite dimensional, Gilfeather and Smith calculated the Hochschild cohomology groups of the join. We assume that M is the algebra of matrices with entries in a maximal abelian von Neumann algebra U, A is an operator algebra acting on a Hilbert space K, and B is an ultraweakly closed subalgebra of M containing U. In this new context, we redefine the join, generalize the calculations of Gilfeather and Smith, and calculate the cohomology groups of the join.

Dans ce mémoire, je démontre que la distribution de probabilités de l'état quantique Greenberger-Horne-Zeilinger (GHZ) sous l'action locale de mesures de von Neumann indépendantes sur chaque qubit suit une distribution qui est une combinaison convexe de deux distributions. Les coefficients de la combinaison sont reliés aux parties équatoriales des mesures et les distributions associées à ces coefficients sont reliées aux parties réelles des mesures. Une application possible du résultat est qu'il permet de scinder en deux la simulation de l'état GHZ. Simuler, en pire cas ou en moyenne, un état quantique comme GHZ avec des ressources aléatoires, partagées ou privées, et des ressources classiques de communication, ou même des ressources fantaisistes comme les boîtes non locales, est un problème important en complexité de la communication quantique. On peut penser à ce problème de simulation comme un problème où plusieurs personnes obtiennent chacune une mesure de von Neumann à appliquer sur le sous-système de l'état GHZ qu'il partage avec les autres personnes. Chaque personne ne connaît que les données décrivant sa mesure et d'aucune façon une personne ne connaît les données décrivant la mesure d'une autre personne. Chaque personne obtient un résultat aléatoire classique. La distribution conjointe de ces résultats aléatoires classiques suit la distribution de probabilités trouvée dans ce mémoire. Le but est de simuler classiquement la distribution de probabilités de l'état GHZ. Mon résultat indique une marche à suivre qui consiste d'abord à simuler les parties équatoriales des mesures pour pouvoir ensuite savoir laquelle des distributions associées aux parties réelles des mesures il faut simuler. D'autres chercheurs ont trouvé comment simuler les parties équatoriales des mesures de von Neumann avec de la communication classique dans le cas de 3 personnes, mais la simulation des parties réelles résiste encore et toujours. / In this Master's thesis, I show that the probability distribution of the Greenberger-Horne-Zeilinger quantum state (GHZ) under local action of independent von Neumann measurements follows a convex distribution of two distributions.The coefficients of the combination are related to the equatorial parts of the measurements, and the distributions associated with those coefficients are associated with the real parts of the measurements. One possible application of my result is that it allows one to split into two pieces the simulation of the GHZ state. Simulating, in worst case or in average, a quantum state like the GHZ state with random resources, shared or private, as well as with classical communication resources or even odd resources like nonlocal boxes is a very important in the theory of quantum communication complexity. We can think of this simulation problem as a problem in which many people get the description of a von Neumann measurement. Each party does not know the description of any other measurements belonging to the other parties. Each party after having applied his measurement on the subsystem of the state that he shares with the others gets a classical outcome. The joint distribution of the outcomes of every parties follows the distribution studied in this thesis in the case of the GHZ state. My result indicates that in order to simulate the distribution, we can first simulate the equatorial parts of the measurements in order to know which distribution associated to the real parts of the measurements to simulate. Other researchers have found how to simulate the equatorial parts of the von Neumann measurements with classical resources in the case of 3 parties, but it is still unknown how to simulate the real parts.

Thesis (Ph. D.)--University of Adelaide, Dept. of Pure Mathematics, 1984. / Includes bibliographical references.

Thesis (Ph. D.)--University of California, Riverside, 2009. / Includes abstract. Includes bibliographical references (leaves 67-68). Issued in print and online. Available via ProQuest Digital Dissertations.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2011. / Submitted by Max Lee da Silva (bruce1415@hotmail.com) on 2011-06-28T14:12:42Z No. of bitstreams: 1 2011_WesleyFerreiraLopes.pdf: 365403 bytes, checksum: 9327932f47211edd41e584221a505cd9 (MD5) / Approved for entry into archive by Guilherme Lourenço Machado(gui.admin@gmail.com) on 2011-06-30T15:46:59Z (GMT) No. of bitstreams: 1 2011_WesleyFerreiraLopes.pdf: 365403 bytes, checksum: 9327932f47211edd41e584221a505cd9 (MD5) / Made available in DSpace on 2011-06-30T15:46:59Z (GMT). No. of bitstreams: 1 2011_WesleyFerreiraLopes.pdf: 365403 bytes, checksum: 9327932f47211edd41e584221a505cd9 (MD5) / Neste trabalho estudamos a continuidade dos atratores para problemas parabólicos semilineares com condição de fronteira de Neumann. Veremos que se as perturbações nos domínios são tais que a convergência dos autovalores e autofunções do laplaciano com condição de fronteira de Neumann é garantida, teremos a semicontinuidade superior dos atratores. Além disso, se todo ponto de equilíbrio for hiperbólico, teremos a continuidade dos atratores. _________________________________________________________________________________ ABSTRACT / In this work we study the continuity of attractors for semilinear parabolic problems with Neumann boundary condition. We will see that if the perturbations on the domain are such that the convergence of eigenvalues and eigenfunctions of the Neumann Laplacian is granted, we have the upper semicontinuity of the attractors. Moreover, if every equilibrium point is hyperbolic, we have the continuity of the attractors.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2016-10-07T20:27:12Z No. of bitstreams: 2 Dissertação - Thiago Mureebe Carrijo - 2012.pdf: 1256435 bytes, checksum: 9e11cc08523726144554b4aac51c6949 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-10-10T15:51:39Z (GMT) No. of bitstreams: 2 Dissertação - Thiago Mureebe Carrijo - 2012.pdf: 1256435 bytes, checksum: 9e11cc08523726144554b4aac51c6949 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-10-10T15:51:40Z (GMT). No. of bitstreams: 2 Dissertação - Thiago Mureebe Carrijo - 2012.pdf: 1256435 bytes, checksum: 9e11cc08523726144554b4aac51c6949 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2012-04-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work has the goal to treat the concept of correlation on both classical and quantum, addressing what already exists about the matter and giving a new perspective about it. Beyond this, we propose a new manner to calculate the amount of information of a quantum system. For this, the EPR paradox, Bell theorem, entanglement concept, Shannon and von Neumann entropies, code theory and the quantum correlation measure so-called quantum discord will be discussed. From those subjects, two generalizations will be proposed: of the von Neumann entropy and the quantum correlation concept. Some features e properties will be discussed about these new definitions, however there is still much to be investigated about its implications. / Este trabalho tem por objetivo tratar o conceito de correlação, tanto clássica quanto quântica, abordando o que já existe sobre o assunto e fornecendo uma nova perspectiva sobre o tema e, além disso, propor uma nova maneira de calcular a quantidade de informação de um sistema quântico. Para isso, será discutido o paradoxo de EPR, o teorema de Bell, o conceito de emaranhamento, as entropias de Shannon e von Neumann, a teoria de códigos e a medida de correlação conhecida como discórdia quântica. A partir desses temas, será proposta duas generalizações: da entropia de von Neumann e do conceito de correlação quântica. Alguns aspectos e propriedades serão discutidos sobre essas novas definições, porém ainda há muito o que ser investigado sobre suas implicações.

En este trabajo se estudia la existencia y unicidad de solución de la ecuación de la onda con condiciones de frontera del tipo Neumann, con disipación localmente distribuida usando el método de Faedo Galerkin. Además analiza el decaimiento no exponencial de la energía asociado al sistema planteado. Se hacen las estimativas correspondientes basándose en propiedades del espacio donde se encuentra la solución de la ecuación, así como los teoremas correspondientes al sistema estudiado. / Tesis

In Part I, we investigate the principal series representations of the n-fold covering groups of the special linear group over a p-adic field. Such representations are constructed via the Stone-von Neumann theorem. We have three interrelated results. We first compute the K-types of these representations. We then give a complete set of reducibility points for the unramified principal series representations. Among these are the unitary unramified principal series representations, for which we further investigate the distribution of the K-types among its irreducible components. In Part II, we demonstrate another application of the Stone-von Neumann theorem. Namely, we present a lower bound for the minimal degree of a faithful representation of an adjoint Chevalley group over a quotient ring of a non-Archimedean local field.

Through von Neumann's reduction theory, the classification of injective von Neumann algebras acting on separable Hilbert spaces translates into the classification of injective factors. In his proof of the uniqueness of the injective type II₁ factor, Connes showed an alternate characterization of the approximately inner automorphisms of type II₁ factors. Moreover, he conjectured that this characterization could be extended to all types of factors acting on separable Hilbert spaces. In this thesis, we present a general toolbox containing the basic notions needed to study von Neumann algebras, before describing our work concerning Connes' conjecture in the case of type IIIλ factors. We have obtained partial results towards the proof of a modified version of this conjecture.

This dissertation studies the immediate reception of von Neumann and Morgenstern\'s Theory of Games and Economic Behavior. It focuses on how economists (and other scientists, such as mathematicians) reacted to von Neumann and Morgenstern\'s axiomatization of expected utility theory. Such study employs book reviews the Theory of Games received, articles authored by mathematically-proficient readers who followed von Neumann and Morgenstern\'s lead of axiomatizing choice under uncertainty, and articles that cited the later. The main conclusions are threefold. First, to understand the history of the Theory of Games\' reception it is unavoidable to consider how secondary sources acted as disseminators of its premises, results, and method. Second, many skilled authors reflected on von Neumann and Morgenstern\'s book. Most economists who used that literature in an axiomatic framework cited such contributions to borrow and adapt assumptions. Those who applied results directly generally used less-sophisticated mathematical tools and were not proof-driven. Third, while the independence axiom is a necessary condition for expected utility theory, economists struggled to understand how von Neumann and Morgenstern used it. It was not clear where the Theory of Games hid that assumption. After economists discovered the independence axiom, they did not find an immediate use for it / Esta dissertação estuda a recepção imediata do Theory of Games and Economic Behavior, de von Neumann e Morgenstern. Seu foco reside em como economistas (e outros cientistas, tais como matemáticos) reagiram à axiomatização da teoria de utilidade esperada composta por von Neumann e Morgenstern. Tal estudo se vale de resenhas do Theory of Games, artigos autorados por leitores proficientes em matemática que seguiram a deixa dos autores de axiomatizar teoria de escolha sob incerteza e, por fim, artigos cujas citações incluem trabalhos destes leitores habilidosos. Há três conclusões principais. Primeiro, para entender a história de recepção do Theory of Games, é importante considerar que fontes secundárias agiram como disseminadores de premissas, resultados e o próprio método do Theory of Games. Segundo, muitos leitores capazes refletiram sobre o livro de von Neumann e Morgenstern. A maioria dos que usaram tal literatura a fizeram de acordo com o método axiomático, citanto aqueles artigos para reproduzir ou adaptar hipóteses. Dentre os que os citaram para aplicar seus resultados diretamente usaram ferramentas matemáticas menos sofisticadas e não tinham como objetivo a produção de demonstrações formais, em geral. Terceiro, enquanto o axioma de independência é uma condição necessária para a teoria de utilidade esperada, economistas tiveram dificuldades em compreender como von Neumann e Morgenstern usaram-no. Não estava claro para eles onde o Theory of Games o havia escondido. Uma vez que os economistas descobriram o axioma, não encontraram uso imediato para ele