Anosov Diffeomorphisms and γ -Tilings

We consider a toral Anosov automorphism G γ : T γ → T γ given by G γ (x, y) = (ax+ y, x) in the base, where a∈ N\ { 1 } , γ= 1 / (a+ 1 / (a+ 1 / …)) , v= (γ, 1) and w= (- 1 , γ) in the canonical base of R 2 and T γ = R 2 / (vZ× wZ). We introduce the notion of γ-tilings to prove the existence of a one-to-one correspondence between (i) marked smooth conjugacy classes of Anosov diffeomorphisms, with invariant measures absolutely continuous with respect to the Lebesgue measure, that are in the isotopy class of G γ ; (ii) affine classes of γ-tilings; and (iii) γ-solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences.info:eu-repo/semantics/publishedVersio

Tilings and Anosov diffeomorphisms

A. Pinto and D. Sullivan [4] proved a one-to-one correspondence between: (i) C1+ conjugacy classes of expanding circle maps; (ii) solenoid functions and (iii) Pinto-Sullivan’s dyadic tilings on the real line. A. Pinto [1,3] introduced the notion of golden tilings and proved a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, that are topologically conjugate to the linear automorphism G(x; y) = (x + y; x), (ii) affine classes of golden tilings and (iii) solenoid functions. Here we extend this last result and we exhibit a natural one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, that are topologically conjugate to the linear automorphism G(x; y) = (ax+y; ax), where a 2 N, (ii) affine classes of tilings in the real line and (iii) solenoid functions. The solenoid functions give a parametrization of the infinite dimensional space consisting of the mathematical objects described in the above equivalences

Golden tilings

In this talk we present the definition of a golden sequence {ri}i2N. These golden sequences have the property of being Fibonacci quasi-periodic and determine a tiling in the real line. We prove a one-to-one correspondence between: (i) affine classes of golden tilings; (ii) smooth conjugacy classes of Anosov difeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, that are topologically conjugate to the Anosov automorphis

Golden tilings

A. Pinto and D. Sullivan [3] proved a one-to-one correspondence between: (i) Cl+ conjugacy classes of expanding circle maps; (ii) solenoid functions and (iii) Pinto-Sullivan's dyadic tilings on the real line. Here, we prove a one-to-one correspondence between: (i) golden tilings; (ii) smooth conjugacy classes of golden diffeomorphism of the circle that are fixed points of renormalization; (iii) smooth conjugacy classes of Anosov difeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, that are topologically conjugated to the Anosov automorphism G(x, y) = (x + y, x) and (iv) solenoid functions

Trace Elements in the Human Milk

Human breast milk is considered to be the perfect food for infants, specifically adapted to their needs. Before birth, the mother transfers all the nutrients and bioactive components to the fetus through the placenta. After birth, these substances have to be transferred through colostrum and milk. In particular, human breast milk is supposed to provide all the essential trace elements that are required by the normal term newborn infant. Therefore, the composition of human breast milk and its changes during lactation is a topic of major importance and has been the subject for intensive research. Conversely, human milk can also be a transfer medium of undesirable (toxic) elements from the mother to the infant. An extensive review of the most recent literature was carried out focusing on the current trace elements levels and their changes during lactation. For several elements, there is a consistent knowledge of their characteristic concentrations throughout the various stages of lactation, their dependence on maternal nutritional status, inter-individual and geographical variability, metabolic pathways, inter-elemental relationships, and effects on child development. For many other elements, this knowledge does not exist or is quite limited

Épidémiologie de l’Asthme et des Allergies dans les Pays de Langue Portugaise

The application of the same epidemiological methods in different countries allows important comparisons between different races and cultures. During the last decade, two large multi-centres epidemiological studies, the Portuguese Study of Allergic Diseases in Childhood (PAC study) and the International Study of Asthma and Allergies in Childhood (ISAAC study), were implemented in Portuguese speaking regions. The main objectives were to assess and compare allergic diseases prevalence. The authors stress out the significant differences observed in schoolchildren from the three continents, with different genetic and environmental background. It was found an increase trend in the prevalence of all allergic diseases, mainly rhinitis, in last decade. Rhinitis has been identified as an independent risk factor for asthma in Caucasian population

Renormalization of circle diffeomorphism sequences and markov sequences

We show a one-to-one correspondence between circle diffeomorphism sequences that are C^{ 1+n}-periodic points of renormalization and smooth Markov sequences.We thank the financial support of LIAAD–INESC TEC through program PEst, USP-UP project, Faculty of Sciences, University of Porto, Calouste Gulbenkian Foundation, FEDER and COMPETE Programmes, PTDC/MAT/121107/2010 and Fundação para a Ciência e a Tecnologia (FCT). J. P.Almeida acknowledges the FCT support given through Grant SFRH/PROTEC/49754/2009

Ladrilhamentos dourados da recta real

Apresentaremos a definição de sucessão dourada {r_i}. Estas sucessões possuem a propriedade de serem Fibonacci quasi-periodicas e determinam um ladrilhamento na recta real. Provaremos uma correspondência bijectiva entre: (i) sucessões douradas; (ii) Classes de conjugação diferenciáveis de difeomorfismos de Anosov na classe de conjugação topológica do automorfismo hiperbólico do toro G(x,y) =(x+y,x); (iii) Classes de conjugação diferenciáveis de difeomorfismos da circunferência com número de rotação igual ao inverso do número de ouro e que são pontos fixos do operador renormalização

Exercise-Induced Asthma in Children a Contribution for the Standardization of Challenge Tests

A asma induzida pelo exercício (AIE), apesar de entidade muito prevalente na criança asmática,apresenta aspectos etiopatogénicos não totalmente esclarecidos. De igual modo, os aspectos metodológicos das provas de provocação utilizadas para o diagnóstico da AIE não estão normalizados. Objectivos: Foram objectivos deste trabalho estudar sensibilidade e especificidade de diferentes parâmetros funcionais (DEMI vs VEMS) e equipamentos(bicicleta ergométrica vs tapete rolante) utilizados nas provas de esforço, monitorizar a ocorrência de respostas tardias ao esforço e correlacionar os resultados com os de uma prova de provocação brônquica inespecífica normalizada (metacolina). Métodos: Foram incluídas 22 crianças com asma e 10 com rinite (grupo controle), com 7-15 anos. Todas as crianças foram submetidas a três provas de provocação efectuadas no intervalo de 1 mês, provas de esforço em tapete rolante (T) e com bicicleta ergométrica (B) e prova de metacolina, efectuadas sob condições ambientais controladas e com interrupção da medicação relevante. Resultados: Sensibilidade: T - redução VEMS >=10%=82%; B - redução VEMS>=10%=57%; T - redução DEMI>=10%=86%; B - redução DEMI >=10%=81%. Especificidade: T & B - redução VEMS >=10%=100%; T - redução DEMI>=10%=40%; B - redução DEMI>=10%=33%. Não se identificaram respostas broncoconstritoras tardias ao exercício. As crianças asmáticas com prova de esforço positiva apresentaram uma reactividade à metacolina significativamente superior à dos asmáticos com prova negativa.Conclusões: A prova de esforço em tapete rolante representa o melhor teste para diagnóstico da AIE na criança. O parâmetro funcional normalizado a ser utilizado deverá ser o VEMS, aceitando-se uma redução de 10% como critério de positividade. Os doentes com resposta positiva ao esforço foram igualmente mais reactivos à prova de metacolina, isto é apresentam hiperreactividade brônquica inespecífica mais grave, o que substancia o interesse da terapêutica preventiva anti-inflamatória com corticóides tópicos e/ou antileucotrienos no controle da AIE