The syntheses and catalytic properties of four new 1,2-acenaphthenyl N-heterocyclic carbene-supported palladium(II) catalysts are presented. The acenaphthenyl carbene can be prepared using either mesityl or 2,6-diisopropyl N-aryl substituents. In addition, two new heterogeneous analogs were synthesized with 2,6-diisopropyl N-aryl substituents that were anchored through the backbone to an insoluble silica-support. Comprehensive catalytic studies of the Suzuki coupling of aryl halides with aryl boronic acids were carried out. In general, the homogeneous diisopropyl-functionalized catalyst was found to exhibit superior selectivity and reactivity. A comparison of the performances of the aforementioned catalysts in toluene, dichloromethane and aqueous solutions are also presented. In organic solvents, the catalysts were found to be proficient for the homogeneous Suzuki coupling of aryl iodides, bromides and chlorides with boronic acids at low temperatures (35‒40 °C). Similar reactions that were carried out in aqueous media resulted in the formation of insoluble colloidal catalytic species. Nevertheless, these species still retained high activities in terms of in the Suzuki reaction with aryl chlorides. Moreover, the heterogeneous Pd precipitates can be easily recovered for subsequent use by means of filtration. The activation energies that were determined for the aryl bromide-based Suzuki reactions were found to fall in the range, 159.2‒171.2 kJ mol⁻¹ in organic solvents and 111.3‒115.9 kJ mol⁻¹ in water. The corresponding activation energy for the aryl chloride was found to be 321.8 kJ mol⁻¹ in aqueous media using the homogeneous diisopropyl-functionalized carbene catalyst. Conversely, the heterogeneous catalyst exhibited reactivity toward aryl iodides and bromides exclusively, and required significantly higher temperatures and catalyst loadings in both toluene and water. Additional experimental trials that were performed in tetrahydrofuran solution at lower temperatures resulted in substantially larger catalytic conversions. The heterogeneous catalyst allowed for easy separation and recovery. However, the catalyst exhibited a significant decrease in reactivity toward the aryl halides after two consecutive trials. / text

The rapid growth in Field Programmable Gate Array (FPGA) architecture design space has led to an explosion in architectural choices that exceed well over 1,000,000 configurations. This makes searching for pareto-optimal solutions using a CAD-based incremental design process near impossible for hardware architects and application engineers. Designers need fast and accurate analytical models in order to evaluate the impact of their design choices on performance. Despite the proliferation of FPGA models, todays state-of the art modeling tools suffer from two drawbacks. First, they rely on circuit characteristics extracted from various stages of the FPGA CAD flow making them CAD dependent. Second, they lack ability to take routing architecture parameters into account. These two factors pose as a barrier for converging to the desired implementation rapidly. In this research, we address these two challenges and propose the first static power and post-routing wirelength models in academia. Our models are unique as they are CAD-independent, and they take both logic and routing architecture parameters into account. Using the static power model we are able to estimate the active and idle leakage power dissipation in homogeneous FPGAs with average correlation factor of 95% and mean percentage error of 17% over experimental results based on MCNC benchmarks. Using our wirelength model, we are able to obtain a low mean percentage error of 4.2% and an average correlation factor of 84% using MCNC and VTR benchmarks. We also show that utilizing wirelength model for architecture optimization process reduces the design space exploration time by 53% compared to the CAD-based process. We finally propose an algorithmic approach to estimate the logic density (i.e., number of LUTs) of multiplexer-based circuits, and address the problem of discrete effects in FPGA analytical models. We show that a model that generates logic density of a fundamental circuit element, such as a multiplexer, can be used to estimate performance metrics, such as critical path delay and power.

No description available.

Els compostos organoborats són intermedis de reacció molt valuosos en síntesi orgànica, degut a que l'enllaç carboni-bor pot ser derivatitzat de múltiples maneres. La diboració catalitzada d'alquins i alquens ha estat ampliament estudiada en els darrers quinze anys, essent la diboració catalitzada d'alquins un procés en el que s'han obtingut elevats rendiments i activitats. No obstant això, en la diboració catalitzada d'alquens la presència de la reacció secundaria de b-eliminació de H sempre s'ha presentat com un seriós inconvenient, impedint un bon compromís entre activitat catalítica i quimioselectivitat. En el primer capítol de la present tesi es recull l'evolució a través de la bibliografia de les reaccions de diboració d'alquens i alquins, els diferents metalls i lligands utilitzats en la reacció catalítica de diboració i els estudis mecanístics que s'han realitzat fins a data d'avui. Tanmateix, s'han posat de manifest les diferents derivatitzacions que s'han dut a terme a partir d'intermitjos organoborats. També es descriu breument la tècnica de les microones. Com a punt final del capítol, s'introdueixen els objectius de la tesi, incloent-hi el desenvolupament de nous sistemes catalítics que millorin l'activitat, quimioselectivitat i enantioselectivitat dels catalitzadors reportats prèviament en la reacció de diboració catalítica, l'estudi del mecanisme de la reacció de diboració d'alquens catalitzada per rodi, i la busqueda de nous mètodes de fluorofuncionalització d'esters vinic(bisboronics). En el segon capítol es descriu l'activitat, quimioselectivitat i enantioselectivitat de diferents precursors catalítics en la diboració catalitzada d'alquens i alquins. En el primer apartat es porta a terme un estudi en profunditat de la diboració d'alquens catalitzada per compostos de Rh(I), observant-se que en aquest cas els efectes estèrics en el diborà tenen un efecte dramàtic en la quimioselectivitat de la reacció. També s'observa que el lligand que ofereix una major quimioselectivitat es el DPPM (bis(difenilfosfino)metà), mostrant una influència del bite angle del lligand, mentre que el lligand QUINAP (1-(2-difenilfosfino-1-naftil)isoquinolina) és el que ofereix una major enantioselectivitat. En els següents apartats es descriu la utilització de diferents complexos d’or, argent, coure i platí modificats amb lligands carbens, els quals augmenten la quimioselectivitat de la reacció, reduïnt la producció de subproductes de b-eliminació de H. Malgrat que s’han utilitzat diferents carbens quirals, només en un cas s’ha aconseguit induir asimetria, utilitzant un complex de Cu(I) modificat amb un lligand carbé quiral, però comprometent la quimioselectivitat. També es descriu l’aplicació de carbens de platí i coure a la diboració catalitzada d’alquins, obtenint-se bons resultats d’activitat i quimioselectivitat. La utilització d’unes noves condicions de reacció, en les que es requereix un excés de diborà (2 eq.) i l’addició d’una base (NaOAc), fa que precursors catalítics en principi inactius, com complexos d’Au(I) modificats amb lligands difosfina tipus BINAP (2,2'-bis(difenilfosfino)-1,1'-binaftil), donin bons resultats d’activitat i quimioselectivitat, encara que malauradament no indueixen asimetria. Per últim, es descriu l’aplicació de les tècniques de microones com a mitjà d’acceleració en la diboració d’alquins catalitzada per Pt(0), disminuint-se espectacularment els temps de reacció. En el tercer capítol de la tesi es porta a terme un estudi mecanístic de la reacció de diboració d’alquens catalitzada per Rh(I)-QUINAP. En primer lloc es porta a terme un estudi de RMN (Ressonància Magnètica Nuclear) per a detectar les possibles espècies metàl·liques implicades. A partir d’aquí, es realitza un estudi computacional DFT (Density Functional Theory) del mecanisme de reacció, observant-se que després de l’addició oxidant es produeix la inserció de l’alqué en un enllaç Rh-B, seguida d’un reordenament per a ocupar la posició vacant creada, finalitzant amb la eliminació reductora del producte, essent el camí més favorable aquell en el qual l’alquè queda coordinat trans al nitrogen del lligand QUINAP. L’estudi de la reacció secundària de b-eliminació de H demostra que la utilització de BINAP com a lligand l’afavoreix, en comparació amb la utilització del lligand QUINAP. En el quart capítol es descriu la flurofuncionalització d’ésters vinil (bisborònics), la qual dóna lloc a la formació de cetones a,a-difluorades a través d’un procés de fluoració electròfila. Primer de tot, es fa una petita introducció als processos de fluoració electròfila, amb especial interès en la fluoració electròfila de compostos organosilats, els quals estan força relacionats amb els compostos organoborats. La reacció es duu a terme a partir dels alquins, a través d’un procés tandem de diboració catalítica/fluoració electròfila. Només els esters vinil(bisborònics) derivats del bis(pinacolato)diborà són susceptibles d’ésser derivatitzats d’aquesta manera. Els alquins interns són més actius que els alquins terminals. També es descriu la síntesi d’a,a-difluoroimines directament a partir d’alquins mitjançant un procés tandem de diboració catalítica/fluoració electròfila/iminació, l’eficiència del qual depen de les propietats electròniques del sustrat. Per últim, en el capítol 5 es descriu la fluoració electròfila asimètrica d’a- nitroésters, la qual es porta a terme mitjançant la utilització d’auxiliars quirals derivats d’alcaloids de cincona, obtenint-se excessos enantiomèrics de fins a un 40%. / Organoboron compounds are very useful intermediates in organicsynthesis, because the carbon-boron bond can be cleaved in a variety of ways leading to the formation of useful functional groups. The catalyzed diboration ofalkenes and alkynes has been widely studied in the last 15 years, obtaining high yields and activities in the alkyne catalyzed diboration reaction. However, when alkenes are used as substrates in the catalyzed diboration reaction, the problem of b-hydride elimination could arise, preventing a good agreement between catalytic activity and chemoselectivity. In the first chapter of this thesys an overview of the precedents of the diboration reactions of alkenes and alkynes is presented, including the different metals and ligands used in this reactions and the mechanistic studies published to date. Moreover, there has been collected the different derivatizations of organoboron intermediates carried out. The microwave technique is also described briefly. Finally, the scope of this thesys is explained, including the development of new catalytic systems which improve the activity, chemoselectivity and enantioselectivity of the catalytic systems previously reported, the study of the mechanism of the rhodium catalyzed alkene diboration reaction, and the search of new routes for the fluorofunctionalization of organoboron compounds. In the second chapter, the activity, chemoselectivity and enantioselectivity of different catalytic precursors in the alkene and alkyne catalytic diboration reaction is described. In the first part, a deep study on the rhodium catalyzed alkene diboration reaction is carried out, finding in this case that the steric effects on the diborating reagent have a dramatic effect on the chemoselectivity of the reaction. It is also observed that the DPPM (bis(diphenylphosphino)methane) is the ligand which provide a better chemoselectivity, showing an important bite angle influence on the ligand, while QUINAP (1-(2-diphenilphosphino-1-naphthyl)isoquinoline) is the ligand which offers a higher enantioselectivity. In the next parts it is described the utilization of different gold, silver, copper and platinum complexes as catalyst precursors, which improve the chemoselectivity of the reaction, reducing the b-hydride elimination side reaction. Despite several chiral carbene modified complexes have been used, only in one case some enantioselectivity was induced, using a carbene modified copper complex, but reducing chemoselectivity. It is also described the application of arbene modified copper and platinum complexes as catalyst precursors in the alkyne diboration reaction, obtaining good results in activity and chemoselectivity. The utilization of new reaction conditions, in which an excess of the diborating reagent (2 eq.) and the addition of a base (NaOAc) is required, improve the activity of catalytic systems like BINAP 2,2’-bis(difenilfosfino)-1,1’-binaphthyl) modified gold complexes, whose activity was very low under the typical conditions; unfortunately, no enantioselectivity was obtained in this case. Finally, it is described the application of microwave techniques to the platinum catalyzed alkyne diboration reaction, in order to reduce the reaction times.In the third chapter, an in-depth study of the mechanism of the Rh(I)-catalyzed alkene diboration reaction is described. First of all, an NMR (Nuclear Magnetic Ressonance) study was carried out in order to identify plausible intermediates. Next, a DFT (Density Functional Theory) study of the reaction mechanism was carried out, finding that after the oxidative addition of the diborane, an insertion of the alkene into a Rh-B bond is produced, followed by an internal rearrangement in order to ocupy the vacant position created, and,finally, reductive elimination of the product is produced, being the most favourable path that in which the alkene is placed trans to the nitrogen of the QUINAP ligand. The study of the b-hydride elimination side reaction shows that the utilization of BINAP as ligand favours it, with respect to the utilization of QUINAP. In the fourth chapter, the fluorofunctionalization of cis-1,2-bis(boryl)alkenes is described, leading to the formation of a,a-difluorinated ketones through an eletrophilic fluorination process. First of all, a little introduction to the electrophilic fluorination processes is made, with special interest to the electrophilic fluorination of organosilanes, which are quite similar to the organoboron compounds. The reaction is carried out starting from alkynes, through a tandem catalytic diboration/electrophilic fluorination process process. Only the cis-1,2-bis(boryl)alkenes derived from bis(pinacolato)diboron are susceptible to the fluorination process. Internal alkynes are more reactive than terminal ones. It is also described the synthesis of a,a-difluoroimines directly from alkynes through a tandem catalytic diboration/electrophilic fluorination/imination process, the efficiency of which depends on the electronic properties of the substrate.Finally, in the fifth chapter, the asymmetric electrophilic fluorination of a-nitro esters is described. This process was carried out using cinchona derivatives chiral auxiliaries, obtaining enantiomeric excesses up to 40%.

This study investigated the perceived strategies used to deal with mixed ability classes of four English teachers, two working at a year 4-9 compulsory school, and two at an upper secondary school in Sweden. The same teachers were asked about their attitudes towards and experience of ability grouping. The findings of the latter part of this investigation were discussed in reference to research concerning the field of ability grouping.Semi structured interviews were used. Strategies used by teachers included grouping devices, issues of communication, giving individual attention inside and outside the classroom and encouraging self- and peer reviewing. Two teachers in the 4-9 school used ability grouping sparingly but clearly and had experienced an ability grouping of a year nine class which was perceived to have predominantly positive results in academic terms and both positive and negative results in social areas. The teachers of upper secondary school did not use ability grouping – either on democratic grounds or because it was perceived to be unacceptable in the particular school climate. Because the research in ability grouping is diverse, many of the teachers’ attitudes could be supported, and refuted in the research. The teachers using ability grouping felt themselves to be going against research made, but were confident in the decisions they made. Further investigations about maximum numbers of students in heterogeneous classes and time spent with an extra teacher contra own teacher were encouraged.

Bakalauro darbe nagrinėjama nehomogeninė šilumos laidumo lygtis. Darbo tikslas rasti lygties bendruosius sprendinius, kurie tenkintų duotąją pradinę ir kraštines sąlygas. Ieškant sprendinių mišrusis uždavinys nehomogeninei lygčiai su nehomogenine pradine sąlyga suvestas į du mišriuosius uždavinius - homogeninei lygčiai su nehomogenine pradine sąlyga ir nehomogeninei lygčiai su homogenine pradine sąlyga. Remdamiesi gautais šių uždavinių sprendiniais, gavome mišriojo uždavinio nehomogeninei šilumos laidumo lygčiai sprendinius. / There was analyzed non-homogeneous heat conduction equation in the bachelor work. This work objective is to find equation general solutions, which have to fulfill of the given initial and boundaries conditions. The mixed problem to non-homogeneous equation with non-homogeneous initial was piece together in two mixed problems – to homogeneous equation with non-homogeneous initial and to non-homogeneous equation with homogeneous initial when we were searching solutions. Based on the obtained these solutions, we got solutions of the mixed problem to non-homogeneous heat conduction equation.

Thesis (Ph. D.)--University of Chicago, Dept. Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.

Resumo: Neste trabalho avaliou-se o efeito da microestrutura na cintilação de nanopartículas de Y2O3:Eu3+. Neste contexto utilizam-se dois métodos de síntese, o método Pechini, que apresenta matéria orgânica remanescente de síntese, assim como, aglomerados micrométricos constituídos de partículas nanométricas com variação da forma e tamanho. Utilizando o método de precipitação homogênea modificado, estudou-se a influência de partículas com estreita distribuição de tamanho e morfologia esférica. A estrutura apresenta simetria cubica (grupo espacial Ia3) e com os estudos espectroscópicos caracterizou-se a presença de pelo menos dois sítios de simetria sendo eles C2 e S6. Avaliou-se o efeito da temperatura de tratamento térmico de 700 a 1100 ºC na cristalinidade do material através de difratometria de raios x do pó. Por meio da espectroscopia de luminescência com excitação de raios X, avaliou-se o efeito da microestrutura do material na cintilação. Por meio da área integrada da transição 5D0→7F2 observou-se a relação da intensidade de emissão com as temperaturas de tratamento térmico e com o tamanho de cristalito, calculados pela equação de Scherrer. Observou-se o efeito de defeitos na cintilação das partículas, pois, em menores temperaturas de tratamento térmico e/ou menores tamanhos de cristalitos os defeitos presentes no material se apresentam em maiores proporções, deste modo proporcionando mecanismos não radiativos de recombinação. Utilizando as curvas de danos de radiação pode-se caracterizar algumas etapas envolvidas na cintilação, como a criação de defeitos, que apresentaram dependência com o tamanho de cristalito obtido para o método Pechini. Após longos períodos sob radiação X os materiais apresentam intensidade de emissão inalterada ou até mesmo um aumento significativo, comportamento que depende dos mecanismos de... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In this work one consider the effects of microstructure in the scintillations properties of Y2O3:Eu3+. Two preparation methods were used; the Pechini method, which exhibits remaining organic matter derived from the synthesis, and tends to form agglomerates of nanoparticles with variable shape and size. By using a modified method of homogeneous precipitation one studied the effects of spherical particles with narrow distribution of particle size in its scintillation properties. The Y2O3 presents cubic symmetry (Ia3 space group) and with spectroscopy results at least two Y3+ symmetry sites were identified, a C2 and a S6 site. The firing temperature of the samples (700- 1100oC) was correlated with its crystallinity by X-ray diffractometry data. The relation between the integrated emission intensity of 5D0 ® 7F2 transition and the firing temperature or the Scherrer crystallite size were analyzed, and from these results were observed the influence of defects in the scintillation of particles, since in lower firing temperatures and/or lower crystallite sizes defects are presented in higher concentrations, leading to non-radiactive paths of pairs recombination. By using radiation damage measurements it was possible to identify the steps involved in the scintillation process, as the creation of defects, which presents a direct relation with the particles characteristics. After a long exposition time to the incoming ionizing radiation, the materials present constant scintillation intensity or a linear growth by means of recovery processes. Samples prepared by the homogeneous precipitation presented higher scintillation intensity and a higher recovery ability when fired at high temperatures. A comparison between the two methods in relation to crystallinity (firing temperature of 1100oC) revels similar results, however spherical particles presented higher scintillation intensity and... (Complete abstract click eletronic access below) / Orientador: Marian Rosaly Davolos / Coorientador: Marco Aurélio Cebim / Banca: Flávio Maron Vichi / Banca: Vera Regina Leopoldo Constantino / Mestre

Made available in DSpace on 2014-06-11T19:29:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-25Bitstream added on 2014-06-13T19:38:16Z : No. of bitstreams: 1 krauser_mo_me_araiq.pdf: 1145204 bytes, checksum: 683766857936c0e93d62901593ab5343 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho avaliou-se o efeito da microestrutura na cintilação de nanopartículas de Y2O3:Eu3+. Neste contexto utilizam-se dois métodos de síntese, o método Pechini, que apresenta matéria orgânica remanescente de síntese, assim como, aglomerados micrométricos constituídos de partículas nanométricas com variação da forma e tamanho. Utilizando o método de precipitação homogênea modificado, estudou-se a influência de partículas com estreita distribuição de tamanho e morfologia esférica. A estrutura apresenta simetria cubica (grupo espacial Ia3) e com os estudos espectroscópicos caracterizou-se a presença de pelo menos dois sítios de simetria sendo eles C2 e S6. Avaliou-se o efeito da temperatura de tratamento térmico de 700 a 1100 ºC na cristalinidade do material através de difratometria de raios x do pó. Por meio da espectroscopia de luminescência com excitação de raios X, avaliou-se o efeito da microestrutura do material na cintilação. Por meio da área integrada da transição 5D0→7F2 observou-se a relação da intensidade de emissão com as temperaturas de tratamento térmico e com o tamanho de cristalito, calculados pela equação de Scherrer. Observou-se o efeito de defeitos na cintilação das partículas, pois, em menores temperaturas de tratamento térmico e/ou menores tamanhos de cristalitos os defeitos presentes no material se apresentam em maiores proporções, deste modo proporcionando mecanismos não radiativos de recombinação. Utilizando as curvas de danos de radiação pode-se caracterizar algumas etapas envolvidas na cintilação, como a criação de defeitos, que apresentaram dependência com o tamanho de cristalito obtido para o método Pechini. Após longos períodos sob radiação X os materiais apresentam intensidade de emissão inalterada ou até mesmo um aumento significativo, comportamento que depende dos mecanismos de... / In this work one consider the effects of microstructure in the scintillations properties of Y2O3:Eu3+. Two preparation methods were used; the Pechini method, which exhibits remaining organic matter derived from the synthesis, and tends to form agglomerates of nanoparticles with variable shape and size. By using a modified method of homogeneous precipitation one studied the effects of spherical particles with narrow distribution of particle size in its scintillation properties. The Y2O3 presents cubic symmetry (Ia3 space group) and with spectroscopy results at least two Y3+ symmetry sites were identified, a C2 and a S6 site. The firing temperature of the samples (700- 1100oC) was correlated with its crystallinity by X-ray diffractometry data. The relation between the integrated emission intensity of 5D0 ® 7F2 transition and the firing temperature or the Scherrer crystallite size were analyzed, and from these results were observed the influence of defects in the scintillation of particles, since in lower firing temperatures and/or lower crystallite sizes defects are presented in higher concentrations, leading to non-radiactive paths of pairs recombination. By using radiation damage measurements it was possible to identify the steps involved in the scintillation process, as the creation of defects, which presents a direct relation with the particles characteristics. After a long exposition time to the incoming ionizing radiation, the materials present constant scintillation intensity or a linear growth by means of recovery processes. Samples prepared by the homogeneous precipitation presented higher scintillation intensity and a higher recovery ability when fired at high temperatures. A comparison between the two methods in relation to crystallinity (firing temperature of 1100oC) revels similar results, however spherical particles presented higher scintillation intensity and... (Complete abstract click eletronic access below)

Orientadores: Luiz Antonio Barrera San Martin, Osvaldo Germano do Rocio / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-08T09:10:31Z (GMT). No. of bitstreams: 1 Verdi_MarcosAndre_D.pdf: 586732 bytes, checksum: c0182ba0a69107acd3d5548e682641df (MD5) Previous issue date: 2007 / Resumo:Neste trabalho estudamos dois problemas distintos: ações de semigrupos em órbitas adjuntas e compactificações de semigrupos. Quanto ao estudo das ações de semigrupos, consideramos um grupo de Lie semi-simples, não compacto, conexo e com centro finito G e a órbita adjunta de G através de elementos H pertencentes a uma subalgebra abeliana maximal contida na parte não-compacta de uma decomposição de Cartan de G. Tomamos então um semigrupo S Ì G com pontos interiores e descrevemos os conjuntos de controle para a ação de S nestas órbitas. Mostramos também que esses conjuntos não são comparáveis utilizando a relação de ordem usual para conjuntos de controle e descrevemos seus domínios de atração. Consideramos também o caso em que S é um semigrupo maximal, obtendo uma descrição melhor dos conjuntos de controle. Para compactificações de semigrupos, adotamos as mesmas hipóteses sobre G e tomamos S como o semigrupo de compressão de um subconjunto fechado da variedade ??ag?maximal de G. Obtemos uma compactificação do espaço homogêneo G/H, onde H denota o grupo das unidades de S, como um subconjunto dos conjuntos fechados de G e mostramos que quando G tem posto 1 é possível realizar a imagem de S/H por essa compactificações no conjunto dos subconjuntos fechados da variedade flag maximal de G / Abstract: In this work we study two distinct problems: semigroup actions on adjoint orbits and compactication of semigroups. For the study of the semigroup actions, we consider a semi-simple connected noncompact Lie group G and the adjoint orbit through elements in a maximal abelian subalgebra contained in the complement of a maximal compactly embedded subalgebra of the Lie algebra of G. We take then a semigroup S Ì G with interior points and describe the control sets for the S-action on these orbits. It is proved here that these control sets are no comparable and we describe its domains of attraction. We also consider the case in that S is a maximal semigroup and obtain a better description of the control sets. For the compactication of semigroups, we use the same hypothesis about G and consider S as the compression semigroup of a closed subset in the maximal ag manifold of G. We obtain a compactication of the homogeneous space G/H, where H=S ÇS-1, as a subset of the set of closed sets of G and we show that when G has rank one is possible to realize the image of S/H under this compacti?cation in the set of the closed subsets of the maximal ag manifold / Doutorado / Doutor em Matemática