This licentiate thesis consists of one paper about unitary representationtheory of ample groupoids and semigroups together with generalizationsto étale and non-Hausdorff groupoids. In the paper we study algebraically the type I and CCR properties forample Hausdorff groupoids. Clarke and Van Wyk proved that both ofthese properties admit a topological characterization for Hausdorff second countable groupoids in terms of separation properties of their orbitspace and the isotropy groups. Using a Stone type duality between ample groupoids and Boolean inverse semigroups with meets, we exploit thischaracterization to get a purely algebraic statement. We also apply thoseresults to get characterizations of the type I and CCR properties for inverse semigroups using their Boolean inverse completions. The generalization is about characterizing the same properties for both étale and ample non-necessarily Hausdorff groupoids which nonethelesshave Hausdorff unit spaces. In this setup, we first give a direct proofof the topological characterization for the CCR property which doesn't rely on the disintegration theory. The argument cannot be adapted toget an easier proof in the type I case, but we rather explain how to geta proof following the original ideas of Clark and Van Wyk in that case.Finally, we state for both étale and ample groupoids algebraic conditionsequivalent to the CCR and GCR properties on their pseudogroup of openand compact open bisections respectively.

While many school districts in the state of Florida have achieved unitary status and are no longer under court jurisdiction, evidence that school districts continue to practice discipline policies that result in the disproportionate suspension of Black students can be found. Despite decades of desegregation, Black students continue to experience the devastating consequences of suspension and expulsion from school. The overrepresentation of Black students in the administration of school discipline is a serious concern for school districts. This study investigated if the attainment of unitary status resulted in equity in school discipline for Black students. Additionally, the study investigated the overrepresentation of Black students in the administration of school discipline as measured by out-of-school suspensions in the secondary schools of the 67 Florida public school districts in 2005-2006. The study compared the representation of Hispanic and Multiracial students to Black students in the administration of school discipline. The study also examined the effects of grade level (6, 7, 8, and 9) on Black, Hispanic, and Multiracial students in the administration of school discipline. Analysis of the data derived from the Florida Department of Education database for school year 2005-2006 led to the following findings: (1) there was overrepresentation of Black students in secondary schools in the state of Florida and that 42 school districts were not in compliance with unitary status guidelines; (2) Black students were overrepresented in school discipline when compared to Hispanic and Multiracial students; (3) the effect of grade (6, 7, 8, and 9) was not significant in the representation of Black students in school discipline; (4) 18 Florida public school districts have attained unitary status, 16 public school districts remained under court jurisdiction, and 33 public school districts were never subject to desegregation litigation; and, (5) Black students were overrepresented in the administration of school discipline in school districts that have attained unitary status.

<p> A multiple-input multiple-output (MIMO) communication system has the potential to provide reliable transmissions at high data rates. However, the computational cost of achieving this promising performance can be quite substantial. With an emphasis on practical implementations, the MIMO systems employing the low cost linear receivers are studied in this thesis. The optimum space-time block codes (STBC) that enable a linear receiver to achieve its best possible performance are proposed for various MIMO systems. These codes satisfy an intra and inter orthogonality property, and are called unitary trace-orthogonal codes. In addition, several novel transmission schemes are specially designed for linear receivers with the use of the proposed code structure. The applications of the unitary trace-orthogonal code are not restricted to systems employing linear receivers. The proposed code structure can be also applied to the systems employing other types of receivers where several originally intractable code design problems are successfully solved.</p> <p>The communication schemes presented in this thesis are outlined as follows: •For a MIMO system with N ≥ M, where M and N are the number of transmitter and receiver antennas, respectively, the optimal full rate linear STBC for linear receivers is proposed and named unitary trace-orthogonal code. The proposed code structure is proved to be necessary and sufficient to achieve the minimum detection error probability for the system. • When applied to a multiple input single output (MISO) communication system, a special linear unitary trace-orthogonal code, named the Toeplitz STBC, is proposed. The code enables a linear receiver to provide full diversity and to achieve the optimal tradeoff between the detection error and the data transmission rate. This is, thus far, the first code that possesses such properties for an arbitrary MISO system that employs a linear receiver. • In MIMO systems in which N ≥ M and the signals are transmitted at full symbol rate, the highest diversity gain achievable by linear receivers is analyzed and shown to be N - M + 1. To improve the performance of a linear receiver, a multi-block transmission scheme is proposed, in which signals are coded so that they span multiple independent channel realizations. An optimal full rate linear STBC for this system that minimizes the detection error probability is presented. The code is named multi-block unitary trace-orthogonal code. The resulting system has an improved diversity gain. Furthermore, by relaxing the code from the full symbol rate constraint, a special multi-block transmission scheme is proposed. This scheme achieves a much improved diversity gain than those with full symbol rate. • The unitary trace-orthogonal code can also be applied to a system that employs a maximum-likelihood (ML) receiver rather than the simple linear receiver. For such a system, a systematic design of full diversity unitary trace-orthogonal code is presented for an arbitrary data transmission rate. </p> <p>In summary, when a simple linear receiver is employed, unitary trace-orthogonal codes and their optimality properties are exploited for various multiple antenna communication systems. Some members from this code family can also enable an optimal performance of ML detection. </P> / Thesis / Doctor of Philosophy (PhD)

This thesis is split up into two parts: the first concerns certain applications of the de la Harpe-Skandalis determinant to K-theory of appropriately regular C*-algebras. The second is concerned with (unital) inclusions of C*-algebras which satisfy a strong tensorial absorption condition. The first chapter following the preliminary section is joint work with Aaron Tikuisis [ST23], while the following chapters are independent. The penultimate chapter is [Sar23b] and the last chapter is essentially [Sar23a]. In the first chapter following the preliminaries, we examine the interplay between the algebraic K₁-group and the unitary algebraic K₁-group of a unital C*-algebra. We prove that for an abundance of unital C*-algebras, the algebraic K₁-group splits naturally as a direct sum of the unitary algebraic K₁-group and the space of continuous real-valued affine functions on the trace simplex. We further prove that if one considers Hausdorffized variants, then for any unital C*-algebra, there is a natural splitting of the Hausdorffized algebraic K₁-group in terms of the Hausdorffized unitary algebraic K₁-group and the space of continuous real-valued affine functions on the trace simplex. Moreover, this a splitting of topological groups. The following chapter studies how certain group homomorphisms between unitary groups of C*-algebras induce maps on the trace simplex. In particular, we show that a contractive group homomorphism between unital C*-algebras which sends the circle to the circle, induces a map between their trace simplices. Under mild regularity conditions these further induce maps between Elliott invariants. As a consequence we show that certain inclusions of C*-algebras are in a correspondence with certain inclusions of unitary groups. Finally we investigate what we call "D-stable inclusions" of C*-algebras, where D is strongly self-absorbing. We give a systematic study and prove that such inclusions between unital, separable, D-stable C*-algebras exist, are abundant, and are non-trivial.

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Many quantum computation algorithms, and processes like measurement based quantum computing, require the initial state of the quantum computer to be an eigenstate of a specific unitary operator. Here we study how quantum states that are eigenstates of finite dimensional irreducible representations of the special unitary (SU(d)) and the permutation (S_n) groups can be efficiently constructed in the computational basis formed by tensor products of the qudit states. The procedure is a unitary transform, which first uses Schur-Weyl duality to map every eigenstate to a unique Schur basis state, and then recursively uses the Clebsch - Gordan transform to rotate the Schur basis state to the computational basis. We explicitly provide an efficient quantum algorithm, and the corresponding quantum logic circuit, to generate any desired eigenstate of SU(2) and SU(3) irreducible representations in the computational basis.

Made available in DSpace on 2016-07-27T13:53:58Z (GMT). No. of bitstreams: 1 Hugo Eduardo Peres.pdf: 403936 bytes, checksum: 7833e62290c72d4b7278aa5a98ea6b3d (MD5) Previous issue date: 2007-08-25 / This research work, accomplished through a qualitative research, aims at understanding the existent relations between the physical education practices at the Federal Center of Technological Education of Goiás (Cefet-GO), an educational institution that prepares professionals for the job market, and the professional formation required by the job market. The subjects of this research: teachers of physical education at the secondary school level, in Cefet-GO, were initially surveyed by means of a semi-structured interview, through which we tried to obtain answers to the major questions posed in this research. The admission to the Cefet-GO allowed us to understand the existence of clear relation between the physical education classes given and the job market and the lack of a politicalpedagogic project to support the teachers practices. Among the main categories of analysis selected to aid us throughout this research, there are those that try to show a clear picture of the relations established between work and education, especially discussed by Frigotto and Gentili; those that try to clarify the divergence between intellectual and manual work, developed by Kuenzer; and those that discuss the idea of a unified school thought of by Gramsci. From this investigation, the conceptions upon which the physical education practices developed at Cefet-GO are based and their purposes with these practices could then be understood, having as a parameter the main approaches that have influenced the physical education since the 1980 s. It was concluded that it is necessary to overcome the existing contradiction between the physical education and the preparation for the job market for the formation of a conscious and free individual, having in mind a critical perspective as a support for the physical education practices. / Este trabalho investigativo, realizado por meio de uma pesquisa qualitativa, tem como objetivo compreender as relações existentes entre as práticas de educação física que ocorrem no Centro Federal de Educação Tecnológica de Goiás (Cefet-GO), instituição educativa que prepara profissionais para o mercado de trabalho, e a formação profissional exigida pelo mundo do trabalho. Os sujeitos desta pesquisa: professores de Educação Física do ensino médio, buscados no Cefet-GO, foram investigados a partir de um roteiro de entrevista semi-estruturado, por meio do qual, procurou-se obter respostas para as principais questões levantadas nesta pesquisa. O ingresso na escola permitiu o entendimento da existência de relações claras entre as aulas de educação física ministradas e o mundo do trabalho e a ausência de um projeto político-pedagógico que subsidiasse as práticas dos professores. Dentre as principais categorias de análise selecionadas, para auxiliar nos caminhos desta pesquisa, constam as que buscam deixar claras as relações estabelecidas entre trabalho e educação, discutidas especialmente por Frigotto e Gentili; as que visam esclarecer, a cisão entre trabalho intelectual e manual, desenvolvidas por Kuenzer; e as que discutem e a idéia de escola unitária pensadas por Gramsci. A partir da investigação realizada, as concepções que fundamentam as práticas de educação física desenvolvidas no Cefet-GO e as suas finalidades destas práticas puderam ser compreendidas, tendo como parâmetro as principais abordagens que influenciaram a educação física a partir dos anos 1980. Apreendeu-se que, a superação da contradição existente entre a educação física e a preparação para o mundo do trabalho, para a formação de um sujeito crítico e emancipado se faz necessário tendo como pilar para a sustentação das práticas de educação física, uma perspectiva crítica.

Esta tese investiga proximidades entre as proposições de Hélio Oiticica e conceitos como \'construção de situação\', \'deriva\' e \'urbanismo unitário\' desenvolvidos pela Internacional Situacionista - IS (1957-1972). Além da literatura da área, foram explorados dois corpus documental, os Boletins da Internacional Situacionista e o Catalogue Raisonné de Hélio Oiticica. A partir dos Boletins foi possível compreender a formulação dos principais conceitos situacionistas, enquanto o Catalogue Raisonné de Hélio Oiticica possibilitou reconstituir suas deambulações urbanas. Suas caminhadas pela cidade refletem sua crítica à cidade e aos modos de vida urbano. Este caráter crítico está presente no desenvolvimento de seu Programa Ambiental, onde suas proposições estéticas buscam reestabelecer, justamente, as relações entre o indivíduo e a cidade. Os arquivos consultados, manuscritos, cartas, entrevistas, e um grande número de documentos inéditos foram fundamentais para a reconstrução de seus \'passos\' e o entendimento, a partir de seu próprio discurso, de suas relações com a crítica social e urbana desenvolvida pelos situacionistas. / This thesis investigates proximities between propositions of Hélio Oiticica and concepts such as \'situation\', \'dérive\' and \'unitary urbanism\' developed by the Situationist International - IS (1957-1972). Besides the literature of the field, two documentary corpus were explored, the Bulletins of the Situationist International and Catalogue Raisonné of Hélio Oiticica. From the Bulletins it was possible to understand fundamental Situationist concepts, while the Catalogue Raisonné of Hélio Oiticica allowed to reconstitute its urban wanderings. His strolls reflect his criticism to the city and urban lifestyles. This criticality is present in the developing of his Environmental Program, where his aesthetic propositions seek to reestablish precisely the relationship between the individual and the city. The archives consulted, manuscripts, letters, interviews, and a large number of unpublished documents were key elements to rebuilding his \'steps\' and the understanding, based on his own speech, of the relationship between Oiticica and social and urban critics developed by the Situationists.