Durante o desenvolvimento de holometálobos alguns tecidos são eliminados/remodelados durante a metamorfose. A autofagia age nesse processo degradando componentes citoplasmáticos, inicialmente isolando-os em dupla membrana, estrutura chamada autofagossomo e esses conteúdos são degradados por hidrolases lisossomais. Porém, aspectos apoptóticos podem estar presentes nesse processo, como o envolvimento de caspases e a fragmentação nuclear. Alterações morfológicas na glândula salivar e no corpo gorduroso, que são bons exemplos de órgãos que sofrem morte celular programada (MCP) no desenvolvimento de R. americana, foram analisados por microscopia de luz e eletrônica. Durante a remoção desses órgãos, núcleos apresentam morfologia condensada e com fragmentação confirmada por TUNEL. Ambos tecidos mostraram formação de autofagossomos, mas a glândula salivar completa o processo de MCP durante a metamorfose. Genes antiapoptóticos e autofágicos que têm importante papel na MCP foram caracterizados. MCP em R. americana apresenta cooperação de aspetos da autofagia e da apoptose. / In the development of holometabolous insects, some tissues are eliminated/remodelated during metamorphosis. Autophagy acts in this process by degrading cytoplasm contents, initially by surrounding them within a double membrane, a structure called autophagosome and its contents are degraded by lysosomal hydrolases. However, some features of apoptotic cell death may be present in this process, such as the involvement of caspases and nuclear fragmentation. Morphological changes of salivary gland and fat body, good examples of organs that suffer programmed cell death (PCD) during R. americana development, were analyzed by light and electron microscopy. During the removal of these organs, nuclei present fragmented and condensed morphology, confirmed by TUNEL assay. Both tissues show the formation of autophagosomes, but the salivary gland completes the process of PCD during metamorphosis. Antiapoptotic and autophagic genes that play important function in the PCD, were characterized. R. americana PCD occurs with the cooperation of autophagy and apoptosis features.

A existência de seções globais para uxos é de central importância na teoria de sistemas dinâmicos, pois uma seção global simplica o estudo da dinâmica de um uxo reduzindo-o ao estudo da dinâmica de um difeomorsmo. Apresentamos detalhadamente a construção feita Hofer, Zehnder e Wysocki (em \'\'The dynamics on a strictly convex energy surface in R4\'\') de uma seção global para o uxo Hamiltoniano restrito a um nível de energia convexo em R4 . Uma importante consequência da existência dessa seção global é que o uxo Hamiltoniano restrito a um nível de energia convexo em R4 tem 2 ou innitas órbitas periódicas. Essa construção utiliza-se da teoria de curvas pseudo-holomorfas em simplectizações de variedades de contato desenvolvida pelos mesmos autores. Os argumentos apresentados também dão uma nova prova da Conjectura de Weinstein para formas de contato tight em S3 . / The existence of global surfaces of section to ows is of central importance in the theory of dynamical systems, as a global surface of section simplies the study of the dynamics of a ow reducing it to the study of the dynamics of a dieomorphism. We present in detail the construction due to Hofer, Wysocki and Zehnder (in \'\'The dynamics on a strictly convex energy surface in R4\'\') of a global surface of section for the Hamiltonian ow restricted to a convex energy level in R4 . An important consequence of the existence of the global surface of section is that the Hamiltonian ow restricted to a convex energy level in R4 has either 2 or innitely many periodic orbits. This construction makes use of the theory of pseudo-holomorphic curves in symplectizations of contact manifolds developed by the same authors. The arguments also give a new proof of Weinstein conjecture for tight contact forms in S3 .

We generalize the notions of structural stability and hyperbolicity for the family of (multivalued) complex maps Hc(z) = zr + c; where r > 1 is rational and zr = exp r log z: We discovered that Hc is structurally stable at every hyperbolic parameter satisfying the escaping condition. Surprisingly, there may be infinitely many attracting periodic points for Hc. The set of such points gives rise to the dual Julia set, which is a Cantor set coming from a Conformal Iterated Funcion System. Both the Julia set and its dual are projections of holomorphic motions of dynamical systems (single valued maps) defined on compact subsets of Banach spaces, denoted by Xc and Wc, respectively. For c close to zero: (1) we show that Jc is a union of quasiconformal arcs around the unit circle; (2) the set Xc is an holomorphic motion of the solenoid X0; (3) using the formalism of Gibbs states we exhibit an upper bound for the Hausdorff dimension of Jc; which implies that Jc has zero Lebesgue measure. / Generalizamos as noções de estabilidade estrutural e hiperbolicidade para a família de correspondências holomorfas Hc(z) = zr + c; onde r > 1 é racional e zr = exp r log z: Descobrimos que Hc é estruturalmente estável em todos os parâmetros hiperbólicos satisfazendo a condição de fuga. Tipicamente Hc possui infinitos pontos periódicos atratores, fato totalmente inesperado, uma vez que este número é sempre finito para aplicações racionais. O conjunto de tais pontos dá origem ao chamado conjunto de Julia dual, que é um conjunto de Cantor proveniente de um Conformal Iterated Function System. Tanto o conjunto de Julia e quanto seu dual são projeções de movimentos holomorfos de sistemas definidos em subconjuntos compactos denotados por Xc e Wc; respectivamente de um espaço de Banach. Para todo c próximo de zero: (1) mostramos que Jc é reunião de arcos quase-conformes próximos do círculo unitário; (2) o conjunto Xc é um movimento holomorfo do solenóide X0; (3) utilizando o formalismo dos estados de Gibbs, exibimos um limitante superior para a dimensão de Hausdorff de Jc. Consequentemente, Jc possui medida de Lebesgue nula.

Nous étudions les relations entre des propriétés géométriques et des propriétés métriques dans les domaines de C^n.Plus précisément, nous nous intéressons au comportement des courbures bisectionnelles holomorphes de métriques de Kähler invariantes, la métrique de Bergman et la métrique de Kähler-Einstein, au voisinage du bord des domaines pseudoconvexe bornés à bord lisse.Nous prouvons qu'aux points de stricte pseudoconvexité ou tels que la fonction squeezing du domaine tend vers 1 les courbures bisectionnelles holomorphes de la métrique de Kähler-Einstein du domaine tendent vers les courbures bisectionnelles holomorphes de la métrique de Kähler-Einstein de la boule.Nous étudions également les courbures de la métrique de Kähler-Einstein et de la métrique de Bergman dans certains domaines polynomiaux (notamment les domaines tubes et les domaines de Thullen de C^2) qui servent de modèles locaux aux points du bord qui sont de type fini. A partir de ces études nous prouvons qu'en certains points du bord de domaines convexes bornés lisse de type fini dans C^2 il existe un voisinage non tangentiel tel que les courbures bisectionnelles holomorphes de la métrique de Kâhler-Einstein sont pincées négativement. Nous prouvons également que pour tout domaine pseudoconvexe borné de type fini qui est Reinhardt complet il existe un voisinage du bord relatif au domaine tel que les courbures bisectionnelles holomorphes de la métrique de Bergman sont comprises entre deux constantes strictement négatives. / We study the relationships between geometric properties and metric properties of domains in C^n.More precisely, we are interested in the behavior of holomorphic bisectional curvatures of invariant Kähler metrics, namely the Bergman metric and the Kähler-Einstein metric, near the boundary of bounded pseudoconvex domains with smooth boundary.We prove that at boundary points that are either strictly pseudoconvex or such that the squeezing function of the domain tends to one the holomorphic bisectional curvatures of the Kähler-Einstein metric of the domain tends to the holomorphic bisectional curvatures of the Kähler-Einstein metric of the ball.We also study the holomorphic bisectional curvatures of the Kähler-Einstein metric and of the Bergman metric in some polynomial domains (namely tube and Thullen domains in C^2) which serve as local models at boundary point of finite type. Using these studies we prove that at certain boundary points of smoothly bounded convex domains of finite type there exists a non tangential neighbourhood such the holomorphic bisectional curvatures of the Kähler-Einstein metric are pinched between two negative constants. We also prove that for every smoothly bounded pseudoconvex complete Reinhardt domain of finite type inf C^2 there exists a neighbourhood of the boundary relative to the domain in which the holomorphic bisectional curvatures of the Bergman metric are pinched between two negative constants.

<p>We investigate the spectrum of certain Banach algebras. Properties</p><p>like generators of maximal ideals and generalized Shilov boundaries are studied. In particular we show that if the ∂-equation has solutions in the algebra of bounded functions or continuous functions up to the boundary of a domain D ⊂⊂ Cⁿ then every maximal ideal over D is generated by the coordinate functions. This implies that the fibres over D in the spectrum are trivial and that the projection on Cn of the n − 1 order generalized Shilov boundary is contained in the boundary of D.</p><p>For a domain D ⊂⊂ Cⁿ where the boundary of the Nebenhülle coincide</p><p>with the smooth strictly pseudoconvex boundary points of D we show that there always exist points p ∈ D such that D has the Gleason property at p.</p><p>If the boundary of an open set U is smooth we show that there exist points in</p><p>U such that the maximal ideals over those points are generated by the coordinate functions.</p><p>An example is given of a Riemann domain, Ω, spread over Cⁿ where the fibers over a point p ∈ Ω consist of m > n elements but the maximal ideal over p is generated by n functions.</p>

We investigate the spectrum of certain Banach algebras. Properties like generators of maximal ideals and generalized Shilov boundaries are studied. In particular we show that if the ∂-equation has solutions in the algebra of bounded functions or continuous functions up to the boundary of a domain D ⊂⊂ Cn then every maximal ideal over D is generated by the coordinate functions. This implies that the fibres over D in the spectrum are trivial and that the projection on Cn of the n − 1 order generalized Shilov boundary is contained in the boundary of D. For a domain D ⊂⊂ Cn where the boundary of the Nebenhülle coincide with the smooth strictly pseudoconvex boundary points of D we show that there always exist points p ∈ D such that D has the Gleason property at p. If the boundary of an open set U is smooth we show that there exist points in U such that the maximal ideals over those points are generated by the coordinate functions. An example is given of a Riemann domain, Ω, spread over Cn where the fibers over a point p ∈ Ω consist of m &gt; n elements but the maximal ideal over p is generated by n functions.

We look at three distinct topics in analysis. In the first we give a direct and easy proof that the usual Newton-Leibniz rule implies the fundamental theorem of algebra that any nonconstant complex polynomial of one complex variable has a complex root. Next, we look at the Riesz representation theorem and show that the Riesz representing measure often can be given in the form of mini sums just like in the case of the usual Lebesgue measure on a cube. Lastly, we look at the idea of holomorphic domination and use it to define a class of complex Banach manifolds that is similar in nature and definition to the class of Stein manifolds.

abstract: The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle. / Dissertation/Thesis / Ph.D. Mathematics 2011

The main aim of this paper is proof that the reduction of the singularities of a generalized hypersurfaces agrees with a reduction of singularities of its separatrix; which is a generalization of the result presented in [8] by the first two authors. / El objetivo principal de este artículo es demostrar que la reduccióon de singularidades de una hipersupercie generalizada coincide con una reducción de singularidades de su separatriz; el cual es una generalización del resultado presentado en [8] por los dos primeros autores.

Dans cette thèse, on s'intéresse aux systèmes dynamiques holomorphes dépendants de paramètres. Notre objectif est de contribuer à une théorie de la stabilité et des bifurcations en plusieurs variables complexes, généralisant celle des applications rationnelles fondées sur les travaux de Mané, Sad, Sullivan et Lyubich. Pour une famille d'applications d'allure polynomiale, on prouve l'équivalence de plusieurs notions de stabilité, entre autres une version asymptotique du mouvement holomorphe des cycles répulsifs et d'un sous-ensemble de l'ensemble de Julia de mesure pleine. Cela peut etre considéré comme une généralisation mesurable à plusieurs variables du célèbre lambda-lemme et nous permet de dégager un concept cohérent de stabilité dans ce cadre. Après avoir compris les bifurcations holomorphes, on s'intéresse à la continuité Hausdorff des ensembles de Julia. Nous relions cette propriété à l'existence de disques de Siegel dans l'ensemble de Julia, et donnons un exemple de ce phénomène. Finalement, on étudie la continuité du point de vue de l'implosion parabolique. Nous établissons un théorème de Lavaurs deux-dimensionel, ce qui nous permet d'étudier des phénomènes de discontinuité pour des perturbations d'applications tangentes à l'identité. / In this thesis we study holomorphic dynamical systems depending on parameters. Our main goal is to contribute to the establishment of a theory of stability and bifurcation in several complex variables, generalizing the one for rational maps based on the seminal works of Mané, Sad, Sullivan and Lyubich. For a family of polynomial like maps, we prove the equivalence of several notions of stability, among the others an asymptotic version of the holomorphic motion of the repelling cycles and of a full-measure subset of the Julia set. This can be seen as a measurable several variables generalization of the celebrated lambda-lemma and allows us to give a coherent definition of stability in this setting. Once holomorphic bifurcations are understood, we turn our attention to the Hausdorff continuity of Julia sets. We relate this property to the existence of Siegel discs in the Julia set, and give an example of such phenomenon. Finally, we approach the continuity from the point of view of parabolic implosion and we prove a two-dimensional Lavaurs Theorem, which allows us to study discontinuities for perturbations of maps tangent to the identity.