CoordenaÃÃo de AperfeiÃoamento de NÃvel Superior / O cristal dipeptÃdeo L-Alanil-L-alanina (Ala-Ala) foi estudado atravÃs da tÃcnica de espalhamento Raman polarizado submetido a deformaÃÃes homogÃneas. Os cristais foram crescidos pela tÃcnica de evaporaÃÃo lenta a partir de uma soluÃÃo aquosa supersaturada do pà do cristal. Medidas de raios-x foram realizadas para confirmar a estrutura cristalina do cristal. Foram realizadas medidas de espalhamento Raman polarizado a temperatura ambiente, bem como anÃlise da teoria de grupos para o grupo fator C4 juntamente com uma classificaÃÃo exploratÃria dos modos normais de vibraÃÃo do cristal. As medidas de espalhamento Raman foram realizadas em baixas temperaturas, entre 300 K e 11 K e 11 K e 300 K, e altas temperaturas, entre 300 K e 520 K e 520 K e 300 K, na regiÃo espectral de 50 a 3300 cm-1. Da anÃlise dos resultados das medidas de baixas temperaturas foi possÃvel concluir que o cristal exibe uma transiÃÃo de fase de segunda ordem, entre 80 e 60 K, passando continuamente da estrutura tetragonal com grupo fator C4 para uma estrutura monoclÃnica com grupo fator C2 mantendo o mesmo nÃmero de molÃculas na cÃlula primitiva. O mecanismo proposto para explicar a transiÃÃo de fase à a ocupaÃÃo de sÃtios de simetria C1 nÃo equivalentes pelos Ãons moleculares CH3 numa estrutura monoclÃnica pertencente ao grupo fator C2. O cristal manteve-se estÃvel em todo o intervalo de alta temperatura estudado. Nestas experiÃncias foram observadas apenas mudanÃas quantitativas nas frequÃncias e larguras de linha dos modos Raman estudados, que à normal para qualquer material submetido a variaÃÃes de temperaturas da ordem de 220 K. Medidas de espalhamento polarizado no cristal de Ala â Ala no intervalo de pressÃo entre 0,1 GPa e 6,3 GPa, na compressÃo, e de 6,3 GPa e 0,1 GPa, na descompressÃo, na regiÃo espectral de 100 cm-1 a 3400 cm-1 mostraram dois intervalos de pressÃo em que ocorrem diversas mudanÃas qualitativas; o primeiro entre 1,7 GPa e 2,3 GPa e o segundo entre 4,5 GPa e 4,9 GPa. Entre 1,7 GPa e 2,3 GPa foram observadas mudanÃas qualitativas significantes na regiÃo dos modos externos, tais como, o desaparecimento de um modo da rede em torno de 130 cm-1 e o comportamento anÃmalo de outro modo da rede em torno de 110 cm-1 para pressÃo de 1,7 GPa. Estas mudanÃas qualitativas sugerem que o cristal exibe uma transiÃÃo de fase estrutural de segunda ordem. As outras regiÃes do espectro Raman do cristal apresentaram diversas mudanÃas qualitativas continuas no comportamento dos modos Raman das unidades que participam diretamente das pontes de hidrogÃnio, indicando que o cristal apresenta reorientaÃÃes espaciais dos grupos moleculares CO2, CH3 e NH3. Estas mudanÃas qualitativas caracterizam uma transiÃÃo de fase estrutural de segunda ordem. As principais mudanÃas qualitativas observadas entre 4,5 GPa e 5,2 GPa sÃo o desaparecimento dos modos externos e, quantitativamente, um grande aumento na largura de linha dos modos Raman indicando que o cristal exibe uma desordem na estrutura cristalina durante a transiÃÃo de fase de altas pressÃes, possivelmente uma amorfizaÃÃo. Na descompressÃo da amostra os espectros Raman sÃo quase que totalmente recuperados na sua forma inicial indicando que o cristal apresenta transiÃÃes de fase reversÃveis. / The dipeptide L-Alanyl â L-Alanine crystal was studied through polarized Raman scattering submitted to homogeneous deformations. The crystals were grown by slow evaporation technique from an aqueous supersaturated solution of the crystal powder. Rays-x diffractions measurements were realized to confirm a crystalline structure of the crystal. Polarized Raman scattering measurements were performed at room temperature, as well as the analysis of the group theory to the C4 factor group and a tentative assignment of the vibrational modes of crystal. Raman scattering measurements in the crystals as a function of temperature were realized between two intervals of temperature: first, at low temperature between 300 K and 11 K e 11 K and 300 K, and second, at high temperature between 300 K e 520 K and 520 K e 300 K, in the spectral range of 50 cm-1 to 3400 cm-1. From the results of low temperature measurements, it was possible to conclude that the crystal undergoes a second-order phase transition between 80 K and 60 K, from a tetragonal structure with C4 factor group to a monoclinic structure with C2 factor group, maintaining the same number of the molecules per primitive cell. The suggested mechanism to explain the phase transition is the occupation of non-equivalent sites by CH3 molecular groups present at Ala-Ala molecule. On the other hand, the crystal remained stable in the high temperature range studied, and the changes observed in the Raman spectra showed no evidence that the Ala-Ala crystal undergone phase transition or changes in molecule conformation. In those experiments were observed only quantitative changes in frequency and widths of the Raman modes, which are normal for any material subjected to variations in temperatures around 220 K. Raman scattering measurements in the crystals as a function of pressure in the pressure range between 0,1 GPa and 6,3 GPa, in compression and of 6,3 GPa and 0,1 GPa, in decompression, in the spectral region between 100 cm-1 and 3400 cm-1 showed two ranges where several qualitative changes occurred; the first, in low pressure interval between 1.7 GPa and 2.3 GPa and the second, at high pressure interval, between 4.5 GPa and 4.9 GPa. Between 1.7 GPa and 2.3 GPa, it was observed qualitative changes as well as the disappearance of an external mode around of 130 cm-1 and the anomalous behavior of other external mode around of 110 cm-1 for pressures of the order of 1,7 GPa. These qualitative changes suggest that the crystal exhibits a second order structural phase transition. Qualitative changes also were observed in others regions of the Raman spectrum through of special reorientation of the molecular groups CO2, CH3 and NH3. These qualitative changes characterize a structural second order phase transition. The mains qualitative changes observed between 4,5 GPa and 5,2 GPa were the disappearance of the external modes and the an large increasing of the width of the Raman modes, suggesting that the crystal exhibits a structural disorder in the crystalline structure when undergoes a phase transition for high pressures, possibly a amorphization. When performing decompression of the sample, the Raman spectrum returns to its initial form relative to pressure of 0,1 GPa indicating reversibility of phase transitions.

This present work to describe the code based on D5 as part of the application of Abstract Algebra, through Symmetry Groups, as well as its advantages over other codes in the case of detection of typos. To this end, we provide some definitions and theorems of the theory of groups useful for understanding this work. Study groups Permutation Groups and Symmetry, issues of great relevance to the study of dihedral groups, being these, particularly if those groups and the basis for the development of the code described herein. / Este trabalho tem como objetivo descrever o Código baseado em D5 como aplicação de parte da Álgebra Abstrata, através dos Grupos de Simetria, bem como suas vantagens em relação a outros códigos, em se tratando da detecção de erros de digitação. Para tanto, fornecemos algumas definições e teoremas da teoria dos Grupos úteis à compreensão deste trabalho. Estudamos os Grupos de Permutação e os Grupos de Simetria, assuntos de grande relevância para o estudo dos Grupos Diedrais, por serem, estes, caso particular dos grupos citados e base para o desenvolvimento do código aqui descrito.

Orientador: Dessislava Hristova Kochloukova / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T12:02:14Z (GMT). No. of bitstreams: 1 Martin_MariaEugenia_M.pdf: 974097 bytes, checksum: 862be4d1ac3b05cc1a28ba59cf6c0460 (MD5) Previous issue date: 2009 / Resumo: Nesta dissertação discutimos propriedades homológicas de grupos discretos e grupos pro-p. Em particular trabalhamos com grupos abstratos de dualidade de Poincaré orientáveis de dimensão três e seu completamento pro-p. Os primeiros capítulos da dissertação incluem uma exposição sobre as propriedades homológicas básicas de grupos abstratos e grupos pro-p. Finalmente, descrevemos um resultado recente de [KZ], publicado em Transactions MAS ( 2008), que clássica quando o completamento pro-p de um grupo de dualidade de Poincaré orientável de dimensão três de um grupo pro-p de dualidade de Poincaré orientável de dimensão três / Abstract: In this dissertation we discuss homological properties of discrete groups and pro-p groups. In particular we work with groups of abstract of Poincaré duality of dimension three steerable and its pro-p completion. The first chapters of the dissertation include a presentation on the basic homological properties of abstract groups and pro-p groups. Finally, we describe a recent result of [KZ], published in Transactions AMS (2008), which ranks as the pro-p completion of a group of Poincare-steerable dual dimension of three is a group of pro-p duality of Poincare -steerable in three dimensions / Mestrado / Mestre em Matemática

Orientador: Dessislava Hristova Kochloukova / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T17:04:33Z (GMT). No. of bitstreams: 1 Lima_IgordosSantos_D.pdf: 1446540 bytes, checksum: 1e68bfb627d234fa97739cd2e813b4a9 (MD5) Previous issue date: 2012 / Resumo: Neste trabalho, nos Teoremas Principais, damos condições suficientes para que o completamento pro-p de um grupo abstrato PDn seja virtualmente um grupo pro-p PDs para algum s ? n - 2 com n ? 4. Esse resultado é uma generalização do Teorema 3 em [K-2009]. Nossa prova é baseada em [K-2009] e nos resultados de A. A. Korenev [Ko-2004] e [Ko-2005]. Além disso, damos alguns exemplos de grupos que satisfazem as condições dos Teoremas Principais / Abstract: In this work we give in the Main Theorems suffiient conditions for that the pro- p completion of an abstract orientable PDn group to be virtually a pro-p PDs group for some s ? n - 2 with n ? 4. This result is a generalization of the Theorem 3 in [K-2009]. Our proof is based on [K-2009] and on the results of A. A. Korenev [Ko-2004] and [Ko-2005]. Furthermore we give some examples of groups that satisfy the conditions of the Main Theorems / Doutorado / Matematica / Doutor em Matemática

Le groupe de Cremona en n variables Cr_n(C) est le groupe des transformations birationnelles de l'espace projectif complexe de dimension n. Dans cette thèse, on étudie les groupes de Cremona en considérant certaines classes de „grands'' sous-groupes. Dans la première partie on considère des plongements algébriques de Cr_2(C) vers Cr_n(C). On décrit notamment quelques propriétés géométriques d'un plongement de Cr_2(C) dans Cr_5(C) dû à Gizatullin. En outre, on classifie tous les plongements algébriques de Cr_2(C) dans Cr_3(C) et on généralise ce résultat partiellement pour les plongements de Cr_n(C) dans Cr_{n+1}(C). Dans la deuxième partie, on regarde les suites des degrés des transformations birationnelles des variétés définies sur un corps quelconque. On montre qu'il n'existe qu'un nombre dénombrable de telles suites et on donne de nouvelles contraintes sur la croissance des degrés des automorphismes de l'espace affine de dimension n. Dans la troisième partie, on classifie les sous-groupes de Cr_2(C) qui ne contiennent que des éléments elliptiques, c'est-`a-dire des éléments dont les degrés des itérés sont bornés. On en déduit notamment l'alternative de Tits pour les sous-groupes quelconques de Cr_2(C). Dans la dernière partie on montre que tous les sous-groupes simples de type fini de Cr_2(C) sont finis et, sous l'hypothèse d'un lemme conjectural, qu'un groupe simple se plonge dans Cr_2(C) si et seulement s'il se plonge dans PGL_3(C). / The Cremona group in n-variables Cr_n(C) is the group of birational transformations of the complex projective n-space. This thesis contributes to the research on Cremona groups through the study of certain classes of „large'' subgroups. In the first part we consider algebraic embeddings of Cr_2(C) into Cr_n(C). In particular, we describe geometrical properties of an embedding of Cr_2(C) into Cr_5(C) that was discovered by Gizatullin. We also classify all algebraic embeddings from Cr_2(C) into Cr_3(C), and we partially generalize this result to embeddings of Cr_n(C) into Cr_{n+1}(C). In a second part, we look at degree sequences of birational transformations of varieties over arbitrary fields. We show that there exist only countably many such sequences and we give new obstructions on the degree growth of automorphisms of affine n-space. In the third part, we classify subgroups of Cr_2(C) containing only elliptic elements, i.e. elements whose iterates are of bounded degree. From this we deduce in particular the Tits alternative for arbitrary subgroups of Cr_2(C). In the last part, we show that every finitely generated simple subgroup of Cr_2(C) is finite and, under the hypothesis of an unproven conjectural lemma, that a simple group can be embedded into Cr_2(C) if and only if it can be embedded into PGL_3(C).

Etant donné trois entiers k, s et a, nous prouvons dans le premier chapitre qu'il existe un graphe k-régulier fini (resp. un graphe k-régulier connexe fini) dont le groupe d'automorphismes a exactement s orbites sur l'ensemble des sommets et a orbites sur l'ensemble des arêtes si et seulement si<p><p>(s,a)=(1,0) si k=0,<p>(s,a)=(1,1) si k=1,<p>s=a>0 si k=2,<p>0< s <= 2a <= 2ks si k>2.<p><p>(resp.<p>(s,a)=(1,0) si k=0,<p>(s,a)=(1,1) si k=1 ou 2,<p>s-1<=a<=(k-1)s+1 et s,a>0 si k>2.)<p><p>Nous étudions les polyèdres convexes de R³ dans le second chapitre. Pour tout polyèdre convexe P, nous notons Isom(P) l'ensemble des isométries de R³ laissant P invariant. Si G est un sous-groupe de Isom(P), le f_G-vecteur de P est le triple d'entiers (s,a,f) tel que G ait exactement s orbites sur l'ensemble sommets de P, a orbites sur l'ensemble des arêtes de P et f orbites sur l'ensemble des faces de P. Remarquons que (s,a,f) est le f_{id}-vecteur (appelé f-vecteur dans la littérature) d'un polyèdre si ce dernier possède exactement s sommets, a arêtes et f faces. Nous généralisons un théorème de Steinitz décrivant tous les f-vecteurs possibles. Pour tout groupe fini G d'isométries de R³, nous déterminons l'ensemble des triples (s,a,f) pour lesquels il existe un polyèdre convexe ayant (s,a,f) comme f_G-vecteur. Ces résultats nous permettent de caractériser les triples (s,a,f) pour lesquels il existe un polyèdre convexe tel que Isom(P) a s orbites sur l'ensemble des sommets, a orbites sur l'ensemble des arêtes et f orbites sur l'ensemble des faces.<p><p>La structure d'incidence I(P) associée à un polyèdre P consiste en la donnée de l'ensemble des sommets de P, l'ensemble des arêtes de P, l'ensemble des faces de P et de l'inclusion entre ces différents éléments (la notion de distance ne se trouve pas dans I(P)). Nous déterminons également l'ensemble des triples d'entiers (s,a,f) pour lesquels il existe une structure d'incidence I(P) associée à un polyèdre P dont le groupe d'automorphismes a exactement s orbites de sommets, a orbites d'arêtes et f orbites de sommets. / Doctorat en sciences, Spécialisation mathématiques / info:eu-repo/semantics/nonPublished

Étant donné un complexe de groupes, quand peut-on déduire une propriété de son groupe fondamental à partir des propriétés analogues de ses groupes locaux ? Ce problème naturel de géométrie des groupes a fait l'objet de nombreux travaux dans le cas des graphes de groupes et des complexes de groupes finis. Cette thèse se propose de développer des outils géométriques pour étudier le cas des complexes de groupes à courbure négative ou nulle. Nous nous intéressons à des propriétés de nature asymptotique : EZ-structures, hyperbolicité. Ce faisant, nous démontrons un théorème de combinaison pour les groupes hyperboliques qui généralise au complexe de groupes de dimension arbitraire un théorème de Bestvina-Feighn. / Given a complex of groups, when is it possible to deduce a property for its fundamental group out of the analogous properties of its local groups? This natural problem of geometric group theory has been adressed mainly for graphs of groups and complexes of finite groups. In this thesis, we develop geometric tools to study non-positively curved complexes of groups. We focus on properties of an asymptotic nature: EZ-structures, hyperbolicity. This allows us to prove a combination theorem for hyperbolic groups, which generalises a theorem of Bestvina-Feighn to complexes of groups of arbitrary dimension.

Un groupe de Baumslag-Solitar est un groupe dont la présentation est, pour p et q entiers non nuls. A chaque groupe de Baumslag-Solitar est associé un espace de déformation D p, q d'actions sur des arbres analogue à l'outre espace. Aut(BS(p, q)) agit sur cet espace ce qui induit une action du groupe des automorphismes extérieurs Out(BS(p,q)). Nous nous intéresserons au cas plus complexe où q est un multiple de p et dans un premier temps, nous démontrerons que tout automorphisme de BS(p, pn) est réductible ce qui signifie qu'il existe un BS(p,pn)-arbre T et une application laissant invariante un certain type de forêt. Ce résultat nous amènera à introduire un nouvel espace de déformation et une classification des automorphismes de BS(p, pn) en trois catégories : elliptique, parabolique ou hyperbolique. A l'aide de cette classification, nous démontrerons que tout automorphisme est à croissance soit polynomiale soit exponentielle. / A Baumslag-Solitar group is a group given by the group presentation, for p and q non-zero integers. For each Baumslag-Solitar group we consider a deformation space D p, q which is analogue of Culler-Vogtmann's Outer Space. The action of Aut(BS(p, q)) on D p, q induces an action of the outer automorphism group Out(BS(pq)). We will focus on the case where p divides q. Firstly, we will show that every automorphism of BS(p,pn) is reducible which means that we can find a BS(p,pn)-tree T and a map that leaves a certain type of subforest invariant. This result leads us to introduce a new deformation space and a classification of the automorphisms of BS(p,pn) in three types : elliptic, parabolic or hyperbolic. Using this classification, we will show that the growth of every automorphism of BS(p,pn) is exponential or polynomial.

No description available.

Soit G un groupe dénombrable, qui se scinde en un produit libre de la forme G=G_1*...*G_k*F, où F est un groupe libre de type fini, et les G_i sont librement indécomposables et non isomorphes à Z. Nous montrons que le groupe Out(G) des automorphismes extérieurs de G satisfait l'alternative de Tits, dès lors que chacun des groupes G_i et Out(G_i) la satisfait. Par des méthodes similaires, nous montrons aussi l'alternative suivante pour tout sous-groupe H de Out(F_N), due à Handel et Mosher lorsque H est de type fini : soit H fixe virtuellement la classe de conjugaison d'un facteur libre propre de F_N, soit H contient un automorphisme complètement irréductible. Nos méthodes, géométriques, utilisent l'étude de la dynamique de l'action de certains sous-groupes de Out(G) sur des espaces hyperboliques. Nous décrivons notamment l'adhérence de l'outre-espace de G relatif aux G_i, et le bord de Gromov du complexe (hyperbolique) des scindements cycliques relatifs associé. Nous étudions par ailleurs les marches aléatoires sur Out(F_N). Sous un certain nombre de conditions sur la mesure de probabilité mu, nous montrons que presque toute trajectoire de la marche aléatoire sur (Out(F_N),mu) converge vers un point du bord de Gromov du complexe des facteurs libres de F_N, que nous identifions au bord de Poisson de (Out(F_N),mu). Par ailleurs, nous décrivons l'horofrontière de l'outre-espace. Ceci a des applications à l'étude de la croissance des classes de conjugaison de F_N sous l'effet de produits aléatoires d'automorphismes extérieurs. / Let G be a countable group that splits as a free product of the form G=G_1*...*G_k*F, where F is a finitely generated free group, and the groups G_i are freely indecomposable and not isomorphic to Z. We show that Out(G) satisfies the Tits alternative, as soon as all the groups G_i and Out(G_i) do. Similar techniques also yield another alternative for subgroups H of Out(F_N), due to Handel and Mosher when H is finitely generated, namely: either H virtually fixes the conjugacy class of some proper free factor of F_N, or H contains a fully irreducible automorphism. Our methods are geometric, and require understanding the dynamics of the action of some subgroups of Out(G) on Gromov hyperbolic spaces. In particular, we determine the closure of the outer space of G relative to the G_i's, as well as the Gromov boundary of the (hyperbolic) complex of relative cyclic splittings of G. We also study random walks on Out(F_N). Given a probability measure mu on Out(F_N) (satisfying some conditions), we prove that almost every sample path of the random walk on (Out(F_N),mu) converges to a point of the Gromov boundary of the free factor complex of F_N, which we identify with the Poisson boundary of (Out(F_N),mu). We also describe the horoboundary of outer space, and give applications to growth of conjugacy classes of F_N under random products of outer automorphisms.