Equifocality of a singular Riemannian foliation

A singular foliation on a complete Riemannian manifold M is said to be Riemannian if each geodesic that is perpendicular to a leaf at one point remains perpendicular to every leaf it meets. We prove that the regular leaves are equifocal, i.e., the end point map of a normal foliated vector field has constant rank. This implies that we can reconstruct the singular foliation by taking all parallel submanifolds of a regular leaf with trivial holonomy. In addition, the end point map of a normal foliated vector field on a leaf with trivial holonomy is a covering map. These results generalize previous results of the authors on singular Riemannian foliations with sections.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

A collocation method for solving singular integro-differential equations

This paper describes a collocation method for numerically solving Cauchy-type linear singular integro-differential equations. The numerical method is based on the transformation of the integro-differential equation into an integral equation, and then applying a collocation method to solve the latter. The collocation points are chosen as the Chebyshev nodes. Uniform convergence of the resulting method is then discussed. Numerical examples are presented and solved by the numerical techniques.

A singular integro-differential equation model for dryout in LMFBR boiler tubes

A 2D steady model for the annular two-phase flow of water and steam in the steam-generating boiler pipes of a liquid metal fast breeder reactor is proposed The model is based on thin-layer lubrication theory and thin aerofoil theory. The exchange of mass between the vapour core and the liquid film due to evaporation of the liquid film is accounted for using some simple thermodynamics models, and the resultant change of phase is modelled by proposing a suitable Stefan problem Appropriate boundary conditions for the now are discussed The resulting non-lineal singular integro-differential equation for the shape of the liquid film free surface is solved both asymptotically and numerically (using some regularization techniques) Predictions for the length to the dryout point from the entry of the annular regime are made The influence of both the traction tau provided by the fast-flowing vapour core on the liquid layer and the mass transfer parameter eta on the dryout length is investigated

Beyond the average: Detecting global singular nodes from local features in complex networks

Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks. Six measurements quantifying different and complementary features of the connectivity around each node of a network were calculated, and multivariate statistical methods applied to identify singular nodes. The potential of the presented concepts and methodology was illustrated with respect to different types of complex real-world networks, namely the US air transportation network, the protein-protein interactions of the yeast Saccharomyces cerevisiae and the Roget thesaurus networks. The obtained singular motifs possessed unique functional roles in the networks. Three classic theoretical network models were also investigated, with the Barabasi-Albert model resulting in singular motifs corresponding to hubs, confirming the potential of the approach. Interestingly, the number of different types of singular node motifs as well as the number of their instances were found to be considerably higher in the real-world networks than in any of the benchmark networks. Copyright (C) EPLA, 2009

ON CLOSED GEODESICS IN THE LEAF SPACE OF SINGULAR RIEMANNIAN FOLIATIONS

In this paper we prove the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations (s.r.f.), namely s.r.fs. that admit sections or have no horizontal conjugate points. We also investigate the shortening process with respect to Riemannian foliations.

Desingularization of singular Riemannian foliation

Let F be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F we construct a regular Riemannian foliation (F) over cap on a compact Riemannian manifold (M) over cap and a desingularization map (rho) over cap : (M) over cap -> M that projects leaves of (F) over cap into leaves of F. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F are compact, then, for each small epsilon > 0, we can find (M) over cap and (F) over cap so that the desingularization map induces an epsilon-isometry between M/F and (M) over cap/(F) over cap. This implies in particular that the space of leaves M/F is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {((M) over cap (n)/(F) over cap (n))}.

Ontogenesis of stomata in Velloziaceae: paracytic versus tetracytic?

In Velloziaceae, the number of subsidiary cells has been used to characterize species and support groups. Nevertheless, the homology of the stomatal types have not been scrutinized. Stomatal ontogenesis of Vellozia epidendroides and V. plicata, assigned to have tetracytic stomata, and of V. glauca and Barbacenia riparia, assigned to have paracytic stomata, were investigated. In the four species studied, stomata followed perigenic development. Subsidiary cells arise from oblique divisions of neighbouring cells of the guard mother cell (GMC). These cells are elongated and parallel to the longer axis of the stoma. Polar cells show wide variation, following the shape and size of the epidermal cells in the vicinity. Hence, these cells cannot be called subsidiary cells. This wide variation is due to a much higher density of stomata in some regions of the leaf blade. This distribution of stomata forces the development of short polar cells, leading to an apparently tetracytic stomata. In regions of low concentration of stomata, higher spatial availability between the GMCs allows the elongation of polar cells, leading to evident paracytic stomata. Therefore, the four studied species are considered braquiparacytic, questioning the classification of stomata into tetracytic and paracytic in Velloziaceae.

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

As técnicas NASVD e MNF e sua aplicação na redução de ruídos em dados gamaespectrométricos

A desintegração radioativa é um processo aleatório e a estimativa de todas as medidas associadas é governada por leis estatísticas. Os perfis de taxas de contagem são sempre "ruidosos" quando utilizados períodos curtos como um segundo para cada medida. Os filtros utilizados e posteriormente as correções feitas no processamento atual de dados gamaespectrométricos não são suficientes para remover ou diminuir, consideravelmente, o ruído oriundo do espectro. Dois métodos estatísticos que atuam diretamente nos dados coletados, isto é, nos espectros, vêm sendo sugeridos na literatura para remover e minimizar estes ruídos remanescentes o Noise-Adjusted Singular Value Decomposition - NASVD e Maximum Noise Fraction - MNF. Estes métodos produzem uma redução no ruído de forma significativa. Neste trabalho eles foram implementados dentro do ambiente de processamento do software Oasis Montaj e aplicados na área compreendida pelos blocos I e II do levantamento aerogeofísico que recobre a porção oeste da Província Mineral do Tapajós, entre os Estados do Pará e Amazonas. Os dados filtrados e não-filtrados com as técnicas de NASVD e MNF foram processados com os parâmetros e constantes fornecidos pela empresa Lasa Engenharia e Prospecções S.A., sendo estes comparados. Os resultados da comparação entre perfis e mapas apresentaram-se de forma promissora, pois houve um ganho na resolução dos produtos.

“Memória e sociedade”: ciência poética e referência de humanismo

O artigo apresenta um conjunto articulado de reflexões a respeito do livro Memória e Sociedade: Lembranças de Velhos, de Ecléa Bosi, aqui considerado como obra-prima da psicologia social e das ciências humanas. Procura destacar as originalidades de natureza teórico-metodológica do texto, a começar por uma composição singular que incorpora poesia na construção científica, passando por uma redefinição das relações entre sujeito e objeto do conhecimento, ao desenvolver a perspectiva de alternância da condição entre ambos, no desdobramento da pesquisa. Mostra, também, como o estudo de Ecléa Bosi se fundamenta em estreitos vínculos entre a pesquisadora e os velhos pesquisados, de modo a se formar entre eles uma comunidade de destino.

Scripts em cena: HIV e mercado sexual no contexto turístico

A atividade turística tem impacto também na saúde das populações de comunidades anfitriãs. Com base em estudo etnográfico e em 14 entrevistas com monitores(as) de turismo ambiental, o objetivo deste artigo é analisar como o cenário sexual no contexto do turismo e seus scripts sexuais constroem a vulnerabilidade de caiçaras às DSTs/HIV e ao mercado sexual. Scripts sexuais tradicionais operacionalizados num cenário de "curtição", "prazer", "desinibição sexual", evidenciaram desigualdades sociais entre caiçaras e turistas que ampliam a vulnerabilidade dos jovens às DSTs/HIV e à mercantilização de sua sexualidade. Os scripts sexuais femininos (passividade/ingenuidade) dificultavam a negociação do preservativo nas cenas sexuais coletadas; os "mais pró-ativos" eram interpretados como disponibilidade para "programas". Os scripts "não negar fogo", "catar as turistas" também ampliavam a vulnerabilidade dos rapazes. O contexto turístico constrói um cenário sexual singular e atravessa as trajetórias socioafetivas dos moradores. Seu impacto deve ser considerado por políticas e programas de saúde locais.

E o Iphan retirou o véu da noiva e disse sim: ecletismo e modernismo no edifício Luciano Costa

São raros os momentos, na história das políticas de preservação do patrimônio no Brasil, em que se vê a dimensão de um conflito - gerado pela atribuição de valores a um bem cultural - alcançar repercussão significativa, mobilizando diversos agentes. O caso do edifício Luciano Costa, no Recife, é um exemplo dessa natureza. Neste artigo, procuramos apresentar -a partir da interpretação de uma trama complexa de discursos e ações - a polêmica preservacionista em torno desse edifício, um exemplar arquitetônico singular, por ter simultaneamente duas fachadas, uma eclética e uma modernista. Em grande parte inéditos, os documentos técnico-administrativos da 5ª Superintendência Regional e do Departamento de Documentação do Iphan, assim como aqueles da fundação do Patrimônio Histórico e Artístico de Pernambuco (fundarpe), da Diretoria de Projetos Especiais da Empresa de Urbanização do Recife (URb-Recife) e do Ministério Público de Pernambuco foram as fontes primárias privilegiadas.

Chaotic Patterns in Aeroelastic Signals

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincare sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincare mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents. Copyright (C) 2009 F. D. Marques and R. M. G. Vasconcellos.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.