Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.On hyvin tunnettua, että (Arnoldin ja Jostin mielessä) integroituva Hamiltonin systeemi synnyttää kvasiperiodisia ratoja invarianteilla toruksilla. Nämä torukset folioivat koko vaiheavaruuden. Jos systeemiä häiritään, kertoo Kolmogorovin, Arnoldin ja Moserin (KAM-) lause, että erään ei-degeneroituvuus-ehdon vallitessa ja häiriön ollessa riittävän pieni suurin osa toruksista säilyy hieman muotoaan muuttaneena. Väitöskirjan ensimmäisessä osassa todistetaan klassinen KAM-lause renormalisaatioryhmän avulla siinä tapauksessa, että häiriö on riittävän useasti derivoituva. Tämö tapahtuu ratkaisemalla jono ongelmia, jossa häiriöt ovat alkuperäisen analyyttisiä approksimaatioita. Näiden ratkaisuiden osoitetaan suppenevan alkuperäisen ongelman ratkaisuun. Toisessa osassa ongelmaa lähestytään jatkuvan renormalisaatioryhmän avulla. Klassisessa KAM-lauseen renormalisaatiotodistuksessa esiintyvän iteratiivisen yhtälön sijaan päädytään nyt osittaisdifferentiaaliyhtälöön. Tätä hyödyntäen pelkistyy ongelma lopulta Banachin kiintopistelauseeseen sopivassa avaruudessa

A Renormalization Proof of the KAM Theorem for Non-Analytic Perturbations

We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which the perturbations are analytic approximations of the original one. We shall finally show that the sequence of the approximate solutions will converge to a differentiable solution of the original problem.Comment: 33 pages, no figure

Diálogos sobre o trabalho do professor de espanhol para crianças numa perspectiva discursiva

IX Congresso Brasileiro de Hispanistas realizado nos dias 22 a 25 agosto 2016Nossa comunicação tem por objetivo analisar discursos sobre o trabalho do professor de espanhol para crianças em formação, a partir dos resultados obtidos com a aplicação de um questionário aos graduandos em Letras: PortuguêsEspanhol, participantes do projeto de Iniciação à Docência O espanhol como língua estrangeira (E/LE) nas séries iniciais do ensino fundamental: uma nova perspectiva na formação docente, da Universidade do Estado do Rio de Janeiro (UERJ). Acreditamos que, com esses discursos, é possível verificar que concepção de ensino fundamentaria seu trabalho com esse públicoalvo, observando que imagens de professor e de aluno se constroem a partir da análise de suas falas. Entendemos que, embora o corpus da pesquisa seja reduzido, uma vez que constituem a comunidade dialógica da pesquisa poucos voluntários, os dados obtidos nos permitem levantar reflexões importantes, visto que, baseandonos na teoria bakhtiniana (BAKHTIN, 2003) sobre o enunciado concreto ser um elo na cadeia discursiva, podemos afirmar que o discurso dos graduandos traz a ressonância de outras vozes circulantes nesse ambiente de formação de professores de E/LE. Nossa proposta busca articular a linguagem com o universo laboral, numa aproximação entre os Estudos Discursivos (MAINGUENEAU, 2004) e a Ergologia (SCHWARTZ, 1997), de forma a promover a reflexão e a análise desse entorno e preparar professores de espanhol para crianças que possam vir a atuar de forma criativa e transformadora no âmbito da Educação BásicaUNILA­-UNIOEST

Um material didático sobre desengajamento moral e violência de gênero

A violência de gênero contra a mulher é uma das manifestações mais vigorosas da assimetria de gênero nas relações sociais. Estudos comprovam que mulheres sofrem diversas formas de violência, que vão desde o assédio sexual disfarçado de cantada a casos de feminicídio em que o agressor justifica sua ação em nome da honra. Para ocultar a gravidade das ações, é comum a alusão a mecanismos de desengajamento moral. Considerando a importância da escola para fomentar a reflexão crítica sobre o tema, foi desenvolvido, em uma pesquisa de Mestrado Profissional, um produto educacional para abordar essa temática no contexto das aulas de Espanhol/Língua Adicional. O presente artigo tem como objetivo descrever a estrutura, a fundamentação e o processo de avaliação por pares desse material didático

Personalised, image-guided, noninvasive brain stimulation in gliomas : Rationale, challenges and opportunities

Malignant brain tumours are among the most aggressive human cancers, and despite intensive efforts made over the last decades, patients' survival has scarcely improved. Recently, high-grade gliomas (HGG) have been found to be electrically integrated with healthy brain tissue, a communication that facilitates tumour mitosis and invasion. This link to neuronal activity has provided new insights into HGG pathophysiology and opened prospects for therapeutic interventions based on electrical modulation of neural and synaptic activity in the proximity of tumour cells, which could potentially slow tumour growth. Noninvasive brain stimulation (NiBS), a group of techniques used in research and clinical settings to safely modulate brain activity and plasticity via electromagnetic or electrical stimulation, represents an appealing class of interventions to characterise and target the electrical properties of tumour-neuron interactions. Beyond neuronal activity, NiBS may also modulate function of a range of substrates and dynamics that locally interacts with HGG (e.g., vascular architecture, perfusion and blood-brain barrier permeability). Here we discuss emerging applications of NiBS in patients with brain tumours, covering potential mechanisms of action at both cellular, regional, network and whole-brain levels, also offering a conceptual roadmap for future research to prolong survival or promote wellbeing via personalised NiBS interventions

Pregnancy after sexuality preserving cystectomy with urinary diversion for bladder cancer. case report and review of the literature

Background: Radical cystectomy for bladder cancer represents a high demolitive surgical procedure with a significative impact on quality of life. Sexuality preserving techniques have been proposed in order to improve functional outcomes. Although sex-sparing techniques would provide women with the chance of having pregnancy, experience is still limited when malignant conditions are considered. We report the outcomes of pregnancy and delivery in a 43-year-old woman with a Padua ileal orthotopic neobladder after robot-assisted sexuality preserving cystectomy for muscle-invasive urothelial bladder cancer performed four years earlier, at age 39. Case presentation: Since pregnancy was confirmed, the patient had been under close urological and gynecological observation. Hydronephrosis and voiding-relating complications were reported and treated by inserting a nephrostomy tubes and indwelling bladder catheter. At the time of delivery, elective caesarian section was performed without complications. Conclusions: Sexuality preserving cystectomy could be an option in selected and highly motivated young patients with diagnosis of bladder cancer. A multidisciplinary team of experts included gynecologists, urologists, radiologists, anesthesiologists and neonatologists is required for the optimal management of pregnancy and peripartum care in women with urinary diversion