On the Hartman-Grobman Theorem with Parameters

The Hartman-Grobman Theorem of linearization is extended to families of dynamical systems in a Banach space X, depending continuously on parameters. We prove that the conjugacy also changes continuously. The cases of nonlinear maps and flows are considered, and both in global and local versions, but global in the parameters. To use a special version of the Banach-Caccioppoli Theorem we introduce equivalent norms on X depending on the parameters. The functional setting is suitable for applications to some nonlinear evolution partial differential equations like the nonlinear beam equation.

The Genomic Ancestry of Individuals from Different Geographical Regions of Brazil Is More Uniform Than Expected

Based on pre-DNA racial/color methodology, clinical and pharmacological trials have traditionally considered the different geographical regions of Brazil as being very heterogeneous. We wished to ascertain how such diversity of regional color categories correlated with ancestry. Using a panel of 40 validated ancestry-informative insertion-deletion DNA polymorphisms we estimated individually the European, African and Amerindian ancestry components of 934 self-categorized White, Brown or Black Brazilians from the four most populous regions of the Country. We unraveled great ancestral diversity between and within the different regions. Especially, color categories in the northern part of Brazil diverged significantly in their ancestry proportions from their counterparts in the southern part of the Country, indicating that diverse regional semantics were being used in the self-classification as White, Brown or Black. To circumvent these regional subjective differences in color perception, we estimated the general ancestry proportions of each of the four regions in a form independent of color considerations. For that, we multiplied the proportions of a given ancestry in a given color category by the official census information about the proportion of that color category in the specific region, to arrive at a ""total ancestry"" estimate. Once such a calculation was performed, there emerged a much higher level of uniformity than previously expected. In all regions studied, the European ancestry was predominant, with proportions ranging from 60.6% in the Northeast to 77.7% in the South. We propose that the immigration of six million Europeans to Brazil in the 19(th) and 20(th) centuries - a phenomenon described and intended as the ""whitening of Brazil"" -is in large part responsible for dissipating previous ancestry dissimilarities that reflected region-specific population histories. These findings, of both clinical and sociological importance for Brazil, should also be relevant to other countries with ancestrally admixed populations.

Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice

We study trapping and propagation of a matter-wave soliton through the interface between uniform medium and a nonlinear optical lattice. Different regimes for transmission of a broad and a narrow solitons are investigated. Reflections and transmissions of solitons are predicted as a function of the lattice phase. The existence of a threshold in the amplitude of the nonlinear optical lattice, separating the transmission and reflection regimes, is verified. The localized nonlinear surface state, corresponding to the soliton trapped by the interface, is found. Variational approach predictions are confirmed by numerical simulations for the original Gross-Pitaevskii equation with nonlinear periodic potentials.

Free-fall in a uniform gravitational field in noncommutative quantum mechanics

We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM. (C) 2010 American Institute of Physics. [doi:10.1063/1.3466812]

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

UNIFORM APPROXIMATION ON IDEALS OF MULTILINEAR MAPPINGS

For each ideal of multilinear mappings M we explicitly construct a corresponding ideal (a)M such that multilinear forms in (a)M are exactly those which can be approximated, in the uniform norm, by multilinear forms in M. This construction is then applied to finite type, compact, weakly compact and absolutely summing multilinear mappings. It is also proved that the correspondence M bar right arrow (a)M. IS Aron-Berner stability preserving.

Polarização da cárie dentária em adolescentes, na região sudoeste do Estado de São Paulo, Brasil

A saúde bucal na maioria dos municípios brasileiros constitui ainda um grande desafio aos princípios doutrinários do SUS. Este estudo objetivou analisar a prevalência de cárie dentária (CPOD) e as diferenças quanto ao gênero e localização geográfica, Significant Caries Index (SiC) e a porcentagem de livres de cárie no município de Itaí, São Paulo, em 2006. Utilizou-se a metodologia da OMS (1997), em uma população constituída por 390; destes, 178 adolescentes aos 12 anos de idade e que correspondem a 46% dos adolescentes matriculados nas escolas do município. O exame foi realizado por um único examinador. O teste kappa foi calculado com valor de concordância de 0,95. O índice CPOD foi de 2, 45, o SiC de 5, 08, e 30% dos indivíduos se apresentaram livres de cárie. Observou-se que 34% dos adolescentes concentraram 70% da doença demonstrando a ocorrência da polarização da cárie dentária. Foram encontradas diferenças estatisticamente significantes na comparação do CPOD entre a localização geográfica e o mesmo não aconteceu com o gênero. Concluiu-se que está ocorrendo a polarização da cárie dentária em adolescentes, aos 12 anos, mas esta ocorrência não se apresenta de forma homogênea. Os problemas se intensificam em uma pequena parcela da população.

Effect of different ferrule designs on the fracture resistance and failure pattern of endodontically treated teeth restored with fiber posts and all-ceramic crowns

OBJECTIVE: This study investigated the effect of different ferrule heights on endodontically treated premolars. MATERIAL AND METHODS: Fifty sound mandibular first premolars were endodontically treated and then restored with 7-mm fiber post (FRC Postec Plus #1 Ivoclar-Vivadent) luted with self-polymerized resin cement (Multilink, Ivoclar Vivadent) while the coronal section was restored with hybrid composite core build-up material (Tetric Ceram, Ivoclar-Vivadent), which received all-ceramic crown. Different ferrule heights were investigated: 1-mm circumferential ferrule without post and core (group 1 used as control), a circumferential 1-mm ferrule (group 2), non-uniform ferrule 2-mm buccally and 1-mm lingually (group 3), non-uniform ferrule 3-mm buccally and 2-mm lingually (group 4), and finally no ferrule preparation (group 5). The fracture load and failure pattern of the tested groups were investigated by applying axial load to the ceramic crowns (n=10). Data were analyzed statistically by one-way ANOVA and Tukey's post-hoc test was used for pair-wise comparisons (α=0.05). RESULTS: There were no significant differences among the failure load of all tested groups (P<0.780). The control group had the lowest fracture resistance (891.43±202.22 N) and the highest catastrophic failure rate (P<0.05). Compared to the control group, the use of fiber post reduced the percentage of catastrophic failure while increasing the ferrule height did not influence the fracture resistance of the restored specimens. CONCLUSIONS: Within the limitations of this study, increasing the ferrule length did not influence the fracture resistance of endodontically treated teeth restored with glass ceramic crowns. Insertion of a fiber post could reduce the percentage of catastrophic failure of these restorations under function.

Use of chromosome microdissection in fish molecular cytogenetics

Chromosome microdissection is a technique in which whole chromosomes or chromosomal segments are dissected under an inverted microscope yielding chromosome-specific sequences. Several protocol modifications introduced during the past 15 years reduced the number of chromosomes required for most applications. This is of particular interest to fish molecular cytogenetics, since most species present highly uniform karyotypes which make impossible the collection of multiple copies of the same chromosome. Probes developed in this manner can be used to investigate chromosome homologies in closely related species. Here we describe a protocol recently used in the gymnotiform species group Eigenmannia and review the major steps involved in the generation of these markers focusing on protocol modifications aiming to reduce the number of required chromosomes.

Engagement of multifocal neural circuits during recall of autobiographical happy events

Happy emotional states have not been extensively explored in functional magnetic resonance imaging studies using autobiographic recall paradigms. We investigated the brain circuitry engaged during induction of happiness by standardized script-driven autobiographical recall in 11 healthy subjects (6 males), aged 32.4 ± 7.2 years, without physical or psychiatric disorders, selected according to their ability to vividly recall personal experiences. Blood oxygen level-dependent (BOLD) changes were recorded during auditory presentation of personal scripts of happiness, neutral content and negative emotional content (irritability). The same uniform structure was used for the cueing narratives of both emotionally salient and neutral conditions, in order to decrease the variability of findings. In the happiness relative to the neutral condition, there was an increased BOLD signal in the left dorsal prefrontal cortex and anterior insula, thalamus bilaterally, left hypothalamus, left anterior cingulate gyrus, and midportions of the left middle temporal gyrus (P < 0.05, corrected for multiple comparisons). Relative to the irritability condition, the happiness condition showed increased activity in the left insula, thalamus and hypothalamus, and in anterior and midportions of the inferior and middle temporal gyri bilaterally (P < 0.05, corrected), varying in size between 13 and 64 voxels. Findings of happiness-related increased activity in prefrontal and subcortical regions extend the results of previous functional imaging studies of autobiographical recall. The BOLD signal changes identified reflect general aspects of emotional processing, emotional control, and the processing of sensory and bodily signals associated with internally generated feelings of happiness. These results reinforce the notion that happiness induction engages a wide network of brain regions.

Numerical investigation of the three-dimensional secondary instabilities in the time-developing compressible mixing layer

Mixing layers are present in very different types of physical situations such as atmospheric flows, aerodynamics and combustion. It is, therefore, a well researched subject, but there are aspects that require further studies. Here the instability of two-and three-dimensional perturbations in the compressible mixing layer was investigated by numerical simulations. In the numerical code, the derivatives were discretized using high-order compact finite-difference schemes. A stretching in the normal direction was implemented with both the objective of reducing the sound waves generated by the shear region and improving the resolution near the center. The compact schemes were modified to work with non-uniform grids. Numerical tests started with an analysis of the growth rate in the linear regime to verify the code implementation. Tests were also performed in the non-linear regime and it was possible to reproduce the vortex roll-up and pairing, both in two-and three-dimensional situations. Amplification rate analysis was also performed for the secondary instability of this flow. It was found that, for essentially incompressible flow, maximum growth rates occurred for a spanwise wavelength of approximately 2/3 of the streamwise spacing of the vortices. The result demonstrated the applicability of the theory developed by Pierrehumbet and Widnall. Compressibility effects were then considered and the maximum growth rates obtained for relatively high Mach numbers (typically under 0.8) were also presented.

Supressão das anomalias de fase e batimentos laterais em espectros de RMN 13c obtidos com a sequência de precessão livre no estado estacionário

The Steady-State Free Precession (SSFP) sequence has been widely used in low-field and low-resolution imaging NMR experiments to increase the signal-to-noise ratio (s/n) of the signals. Here, we analyzed the Scrambled Steady State - SSS and Unscrambled Steady State - USS sequences to suppress phase anomalies and sidebands of the 13C NMR spectrum acquired in the SSFP regime. The results showed that the application of the USS sequence allowed a uniform distribution of the time interval between pulses (Tp), in the established time range, allowing a greater suppression of phase anomalies and sidebands, when compared with the SSS sequence.

Ressonância não linear de uma bússola em campos magnéticos

Fenômenos oscilatórios e ressonantes são explorados em vários cursos experimentais de física. Em geral os experimentos são interpretados no limite de pequenas oscilações e campos uniformes. Neste artigo descrevemos um experimento de baixo custo para o estudo da ressonância em campo magnético da agulha de uma bússola fora dos limites acima. Nesse caso, termos não lineares na equação diferencial são responsáveis por fenômenos interessantes de serem explorados em laboratórios didáticos.

Spatial analysis of urban violence based on emergency room data

OBJECTIVE: To estimate the spatial intensity of urban violence events using wavelet-based methods and emergency room data. METHODS: Information on victims attended at the emergency room of a public hospital in the city of São Paulo, Southeastern Brazil, from January 1, 2002 to January 11, 2003 were obtained from hospital records. The spatial distribution of 3,540 events was recorded and a uniform random procedure was used to allocate records with incomplete addresses. Point processes and wavelet analysis technique were used to estimate the spatial intensity, defined as the expected number of events by unit area. RESULTS: Of all georeferenced points, 59% were accidents and 40% were assaults. There is a non-homogeneous spatial distribution of the events with high concentration in two districts and three large avenues in the southern area of the city of São Paulo. CONCLUSIONS: Hospital records combined with methodological tools to estimate intensity of events are useful to study urban violence. The wavelet analysis is useful in the computation of the expected number of events and their respective confidence bands for any sub-region and, consequently, in the specification of risk estimates that could be used in decision-making processes for public policies.

Redescription of Hanleya brachyplax (Polyplacophora, Hanleyidae) from the south-southeastern Brazilian coast

Hanleya brachyplax Simone & Jardim in Rios, 2009 is described in detail. The species occurs off the southeastern and south coast of Brazil (São Paulo and Santa Catarina states) in depths from 250 to 408 m. It differs from its congeners in having uniform white valves; wide intermediate valves; the tail valve with straight profile in the antemucronal area, and a concave postmucronal surface; and a cream-colored girdle, covered by non-articulated spines. An anatomical investigation was also performed, showing the main muscle groups; the presence of gills in the posterior third of the pallial groove; auricle with six orifices; a very flat kidney, restricted to the posterior half of the animal; and a simple esophageal region. The odontophore has a single pair of long cartilages. The buccal musculature is also described.