Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.

Folheações de dimensão 2 de R3 induzidas por 1-formas diferenciais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo de conjuntos minimais para sistemas descontínuos em dimensões 2 e 3

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Symptom dimensions are associated with age of onset and clinical course of obsessive-compulsive disorder

Meta-analysis of the heterogeneous symptoms of obsessive-compulsive disorder (OCD) has found a four-factor structure of symptom dimensions consisting of cleaning, forbidden thoughts, symmetry, and hoarding. Research into age of onset of symptom dimensions has yielded inconsistent results, and it is unknown whether symptoms along these dimensions differ in their clinical course. We assessed age of onset and clinical course of different OCD symptom dimensions in a large cohort of adult patients. Nine-hundred fifty-five subjects were assessed using the Dimensional Yale-Brown Obsessive-Compulsive Scale. For age of onset analysis, we tested across three methods of classification: (1) primary (more severe) symptom dimension (2) clinically significant symptoms within a dimension or (3) any symptoms within a dimension. Age of onset was defined as the earliest age of onset reported for any individual item within a symptom dimension. For analysis of different types of clinical course, we used chi-square tests to assess for differences between primary symptom dimensions. OCD symptoms in the symmetry dimension had an earlier age of onset than other OCD symptom dimensions. These findings remained significant across all three methods of classification and controlling for gender and comorbid tics. No significant differences were found between the other dimensions. Subjects with primary OCD symptoms in the forbidden thoughts dimension were more likely to report a waxing-and-waning course, whereas symmetry symptoms were less likely to be associated with a waxing-and-waning course. © 2013.

Fractal dimension and anisotropy of soil CO2 emission in a mechanically harvested sugarcane production area

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Self-energies for interacting fields with a compactified spatial dimension

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Oral rehabilitation of severely worn dentition using an overlay for immediate re-establishment of occlusal vertical dimension

The aim of this study was to describe the treatment used in an elderly patient presenting with bruxism and dental erosion, with good gingival health and bone support, but with decreased occlusal vertical dimension (OVD). The oral rehabilitation of elderly patients presenting with bruxism in association with tooth erosion has been a great challenge for dentists. The loss of OVD, the presence of occlusal instability and the absence of an effective anterior guide due excessive dental wear, can damage stomatognathic system (SS) biology, the function and the aesthetics. In the first treatment stage, an overlay removable partial denture (ORPD) was fabricated for the immediate re-establishment of function and aesthetics. After a 2-month follow up, with the patient presenting no symptoms, a second rehabilitation stage was accomplished, with fixed and removable prostheses. Oral rehabilitation with an ORPD was able to re-establish the SS biology, but a correct diagnosis and treatment plan are essential for success. The ORPD is a non-invasive and reversible restoring modality for general dentists that allow the re-establishment of the patient's immediate aesthetics and function at low cost.

Evaluation of the occlusion vertical dimension of complete dentures after microwave disinfection

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A new approach to integrable theories in any dimension

The zero curvature representation for two-dimensional integrable models is generalized to spacetimes of dimension d + 1 by the introduction of a d-form connection. The new generalized zero curvature conditions can be used to represent the equations of motion of some relativistic invariant field theories of physical interest in 2 + 1 dimensions (BF theories, Chern-Simons, 2 + 1 gravity and the CP1 model) and 3 + 1 dimensions (self-dual Yang-Mills theory and the Bogomolny equations). Our approach leads to new methods of constructing conserved currents and solutions. In a submodel of the 2 + 1-dimensional CP1 model, we explicitly construct an infinite number of previously unknown non-trivial conserved currents. For each positive integer spin representation of sl(2) we construct 2j + 1 conserved currents leading to 2j + 1 Lorentz scalar charges. (C) 1998 Elsevier B.V. B.V.

Immersions in the metastable dimension range via the normal bordism approach

Let f : M --> N be a continuous map between two closed n-manifolds such that f(*): H-*(M, Z(2)) --> H-* (N, Z(2)) is an isomorphism. Suppose that M immerses in Rn+k for 5 less than or equal to n < 2k. Then N also immerses in Rn+k. We use techniques of normal bordism theory to prove this result and we show that for a large family of spaces we can replace the homolog condition by the corresponding one in homotopy. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Uranium distribution and radon exhalation from Brazilian dimension stones

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.

Remarks on immersions in the metastable dimension range

In this work we present a generalization of an exact sequence of normal bordism groups given in a paper by H. A. Salomonsen (Math. Scand. 32 (1973), 87-111). This is applied to prove that if h : M-n --> Xn+k, 5 less than or equal to n < 2k, is a continuous map between two manifolds and g : M-n --> BO is the classifying map of the stable normal bundle of h such that (h, g)(*) : H-i (M, Z(2)) --> H-i (X x BO, Z(2)) is an isomorphism for i < n - k and an epimorphism for i = n - k, then h bordant to an immersion implies that h is homotopic to an immersion. The second remark complements the result of C. Biasi, D. L. Goncalves and A. K. M. Libardi (Topology Applic. 116 (2001), 293-303) and it concerns conditions for which there exist immersions in the metastable dimension range. Some applications and examples for the main results are also given.