This thesis consists of studies in the separate fields of operator algebras and non-associative algebras. Two natural operator algebra structures, A ⊗_max B and A ⊗_min B, exist on the tensor product of two given unital operator algebras A and B. Because of the different properties enjoyed by the two tensor products in connection to dilation theory, it is of interest to know when they coincide (completely isometrically). Motivated by earlier work due to Paulsen and Power, we provide conditions relating an operator algebra B and another family {C_i}_i of operator algebras under which, for any operator algebra A, the equality A ⊗_max B = A ⊗_min B either implies, or is implied by, the equalities A ⊗_max C_i = A ⊗_min C_i for every i. These results can be applied to the setting of a discrete group G pre-ordered by a subsemigroup G⁺, where B ⊆ C*_r(G) is the subalgebra of the reduced group C*-algebra of G generated by G⁺, and C_i = A(Q_i) are digraph algebras defined by considering certain pre-ordered subsets Q_i of G. The 16-dimensional algebra A₄ of real sedenions is obtained by applying the Cayley-Dickson doubling process to the real division algebra of octonions. The classification of subalgebras of A₄ up to conjugacy (i.e. by the action of the automorphism group of A₄) was completed in a previous investigation, except for the collection of those subalgebras which are isomorphic to the quaternions. We present a classification of quaternion subalgebras up to conjugacy.

Thèse (D. en études littéraires)--Université du Québec à Montréal, 2004. / En tête du titre: Université du Québec à Montréal. Bibliogr.: f. [357]-373. Publié aussi en version électronique.

Thesis--University of Minnesota, 1926. / Bibliography ; numb. 1, 106-124.

Thesis (M.A.)--Memorial University of Newfoundland, 1999. / Bibliography: leaves 220-238.

Thesis--University of Minnesota, 1926. / Bibliography ; numb. 1, 106-124.

The present work had for objective to verify the relation between growth variability and the interference Dickson Quality Index, to verify the efficiency relation of this /index in the quality indication on seedlings and to identify the behavior of the growth variable during the seedlings development cycle in trays with full and varied competition in Eucalyptus grandis W. Hill ex Maid and Pinus elliottii var. elliottii Engelm seedlings, in the forest nursery of the Universidade Federal de Saint Maria, RS. In this way, for both species, was installed a blank experiment in the greenhouse. The data collection for E. grandis had been to the 60, 75, 90, 105 and 120 days, after the seedling sprout and for P. elliotti to 25, 50, 75, 100, 125, 150, 175 days, after the seedling sprout (DAE). Each species were represented for two trays, being that in one of them was analyzed the diameter of the col (DIAM, in mm), the height of the aerial part (ALT, in cm), the leaf number (NF) (only for E. grandis), dry fitomass of leaves (MSF in gram/plant), dry fitomass of the col (MSC gram/plant), dry fitomass of the radicular system (MSR gram/plant); dry fitomass of the aerial part (MSPA gram/plant), gotten for the sum of MSF and MSC; total dry fitomass(MST), gotten for the sum of MSPA and MSR; the relation of the aerial part/radicular system (RPAR), gotten of the relation between MSPA and MSR; and the relation of the aerial part height /diameter of the col (RAD), gotten from the relation between ALT and DIAM, and the Dickson Quality Index (IQD), gotten from an equation involving the morphologic variable, previously cited, except the NF. For this tray, after each data collection was selected a parcel of seedlings for fitomassas attainment. One proceeded the rearrangement from the remaining seedlings, with the intention of verifying the interference that the seedlings would suffer, giving them a bigger luminosity and aeration. To the other tray were analyzed diameter of col DIAM, ALT, NF (for E. grandis), remaining during all the study, the total number of seedlings. Through statistical methods of Regression Analysis, Pearson Correlation and Pathy Analysis different combinations between the morphologic variables had been studied, with DAE and IQD, using as election criterion for the regression mathematical models: the biggest value of the adjusted determination coefficient (R ² aj), minor variation coefficient (CV%) and minor error average standard (Syx). Dry root Fitomass, was the more related variable with the IQD, however its not viable the attainment because its necessary the destruction of the plantt. The diameter of the col was the most propitious variable to indicate seedling quality, based in its bigger degree of Dickson relation Index(IQD). The varialble height just presented efficient to indicate seedling quality when analyzed together the diameter. The IQD was efficient to indicate seedling quality, therefore it was presented sufficiently related with the studied variables for E. grandis and P. elliotti. The variable col diameter was the one that presented greater relation after sprout, when compared with the seedling height, as much in trays with seedlings in full competition how much in varied competition, for both the studied species / O presente trabalho teve por objetivo verificar a relação entre variáveis de crescimento e a interferência que estas exercem sobre o Índice de Qualidade de Dickson, verificar a relação de eficiência deste na indicação da qualidade de mudas e identificar o comportamento das variáveis de crescimento com o passar do ciclo de mudas em bandejas com competição plena e variada em mudas de Eucalyptus grandis W. Hill ex Maid e Pinus elliottii var. elliottii - Engelm, no viveiro florestal da Universidade Federal de Santa Maria, RS. Nesse sentido, para ambas espécies, se instalou um experimento em branco em casa de vegetação. A coleta dos dados para E. grandis foram aos 60, 75, 90, 105 e 120 dias, após a emergência das mudas e para P. elliottii aos 25, 50, 75, 100, 125, 150, 175 dias, após emergência das mudas (DAE). Cada espécie era representada por duas bandejas, sendo que em uma delas analisou-se o diâmetro do colo (DIAM, em mm), a altura da parte aérea (ALT, em cm), o número de folhas (NF) (somente para E. grandis), a fitomassa seca de folhas (MSF em grama/planta), fitomassa seca do colo (MSC grama/planta), fitomassa seca do sistema radicular (MSR grama/planta); a fitomassa seca da parte aérea (MSPA grama/planta), obtida pela soma da MSF e MSC; a fitomassa seca total (MST), obtida pela soma do MSPA e MSR; a relação da parte aérea/sistema radicular (RPAR), obtida da relação entre MSPA e MSR; e a relação da altura da parte aérea/diâmetro do coleto (RAD), obtida da relação entre ALT e DIAM, e Índice de Qualidade de Dickson (IQD), obtido a partir de uma equação envolvendo as variáveis morfológicas, anteriormente citadas, com exceção do NF. Para essa bandeja, após cada coleta dos dados selecionou-se uma parcela de mudas para obtenção das fitomassas. Procedeu-se o rearranjo das mudas remanescentes, com o intuito de assim se verificar interferência que as mudas sofreriam, disponibilizando de maior luminosidade e aeração. Para a outra bandeja analisou-se diâmetro do colo DIAM, ALT, NF (para E. grandis), mantendo-se, durante todo o estudo, o número total de mudas. Através de métodos estatísticos como Análise de Regressão, Correlação de Pearson e Análise de Trilha estudaram-se diferentes combinações entre as variáveis morfológicas, com DAE e IQD, usando-se como critérios de seleção para os modelos matemáticos de regressão: o maior valor do coeficiente de determinação ajustado (R²aj), menor coeficiente de variação (CV%) e menor erro padrão médio (Syx). A fitomassa seca de raiz, foi a variável mais relacionada com o IQD, porém não é viável sua obtenção por ser necessária a destruição da muda. O diâmetro do colo foi a variável mais propícia para indicar qualidade de muda, baseado no seu maior grau de relação com Índice de Qualidade de Dickson (IQD). A variável altura só se apresentou eficiente para indicar qualidade de mudas quando analisada juntamente com o diâmetro. O IQD foi eficiente para indicar qualidade de mudas, pois se apresentou bastante relacionado com as variáveis estudadas para E. grandis e P. elliottii. A variável diâmetro do colo foi a que apresentou maior relação com os dias após emergência, quando comparada com a altura da muda, tanto em bandejas com mudas em competição plena quanto em variada, para ambas as espécies estudadas

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<p>For "Subject Categories" I entered "European Law". I think that it is the best description, unless there is a category "Legal Philosophy".</p> / <p>In this work I address a number of important theoretical questions that the institutional order of the European Union (EU) poses for legal theory. I examine Raz’s approach to theorizing legality and several elements of his theory of law, arguing that the institutional structures of the EU resist the Razian theoretical framework. I also explore the inter-institutional theory of law developed by Culver and Giudice, arguing that its conceptual framework needs further development but that the conception of the ordinary law subject it employs is more robust than Raz’s. A significant portion of my work relies on the framework of <em>the indirectly evaluative approach</em> for evaluation of these theories, which was developed by Julie Dickson.</p> / Master of Philosophy (MA)

We first introduce the octonions as an eight dimensional vector space over a field of characteristic zero with a multiplication defined using a table. We also show that the multiplication rules for octonions can be derived from a special graph with seven vertices call the Fano Plane. Next we explain the Cayley-Dickson construction, which exhibits the octonions as the set of ordered pairs of quaternions. This approach parallels the realization of the complex numbers as ordered pairs of real numbers. The rest of the thesis is devoted to following a paper by N. Jacobson written in 1939 entitled "Cayley Numbers and Normal Simple Lie Algebras of Type G". We prove that the algebra of derivations on the octonions is a Lie algebra of type G_2. The proof proceeds by showing the set of derivations on the octonions is a Lie algebra, has dimension fourteen, and is semisimple. Next, we complexify the algebra of derivations on the octonions and show the complexification is simple. This suffices to show the complexification of the algebra of derivations is isomorphic to g_2 since g_2 is the only semisimple complex Lie algebra of dimension fourteen. Finally, we conclude the algebra of derivations on the octonions is a simple Lie algebra of type G_2. / Master of Science

The focus of this thesis is to provide an introduction to Lie groups—the study of continuous symmetries—and related concepts. Starting with topology and geometry, progressing through the construction of Cayley-Dickson algebras, the thesis ultimately explores a few of the most common Lie groups. Finally, geometric and visual interpretations of SO(3) and SU(2), as well as the relations between them, are investigated.