A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

Role of Surfactants in Carbon Nanotubes Density Gradient Separation

Several strategies aimed at sorting single-walled carbon nanotubes (SWNT) by diameter and/or electronic structure have been developed in recent years. A nondestructive sorting method was recently proposed in which nanotube bundles are dispersed in water-surfactant solutions and submitted to ultracentrifugation in a density gradient. By this method, SWNTs of different diameters are distributed according to their densities along the centrifuge tube. A mixture of two anionic amphiphiles, namely sodium dodecylsulfate (SIDS) and sodium cholate (SC), presented the best performance in discriminating nanotubes by diameter. We present molecular dynamics studies of the water-surfactant-SWNT system. The simulations revealed one aspect of the discriminating power of surfactants: they can actually be attracted toward the interior of the nanotube cage. The binding energies of SDS and SC on the outer nanotube surface are very similar and depend weakly on diameter. The binding inside the tubes, on the contrary, is strongly diameter dependent: SDS fits best inside tubes with diameters ranging from 8 to 9 angstrom, while SC is best accommodated in larger tubes, with diameters in the range 10.5-12 angstrom. The dynamics at room temperature showed that, as the amphiphile moves to the hollow cage, water molecules are dragged together, thereby promoting the nanotube filling. The resulting densities of filled SWNT are in agreement with measured densities.

CONSTRUCTING QUANTUM OBSERVABLES AND SELF-ADJOINT EXTENSIONS OF SYMMETRIC OPERATORS. III. SELF-ADJOINT BOUNDARY CONDITIONS

This paper completes the review of the theory of self-adjoint extensions of symmetric operators for physicists as a basis for constructing quantum-mechanical observables. It contains a comparative presentation of the well-known methods and a newly proposed method for constructing ordinary self-adjoint differential operators associated with self-adjoint differential expressions in terms of self-adjoint boundary conditions. The new method has the advantage that it does not require explicitly evaluating deficient subspaces and deficiency indices (these latter are determined in passing) and that boundary conditions are of explicit character irrespective of the singularity of a differential expression. General assertions and constructions are illustrated by examples of well-known quantum-mechanical operators like momentum and Hamiltonian.

A new proposal for the picture changing operators in the minimal pure spinor formalism

Using a new proposal for the ""picture lowering"" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the. Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the. Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green`s function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.

Multilevel Training of Binary Morphological Operators

The design of binary morphological operators that are translation-invariant and locally defined by a finite neighborhood window corresponds to the problem of designing Boolean functions. As in any supervised classification problem, morphological operators designed from a training sample also suffer from overfitting. Large neighborhood tends to lead to performance degradation of the designed operator. This work proposes a multilevel design approach to deal with the issue of designing large neighborhood-based operators. The main idea is inspired by stacked generalization (a multilevel classifier design approach) and consists of, at each training level, combining the outcomes of the previous level operators. The final operator is a multilevel operator that ultimately depends on a larger neighborhood than of the individual operators that have been combined. Experimental results show that two-level operators obtained by combining operators designed on subwindows of a large window consistently outperform the single-level operators designed on the full window. They also show that iterating two-level operators is an effective multilevel approach to obtain better results.

Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.

Comparasion of two minimally invasive methods on the longevity of glass ionomer cement restorations: short-term results of a pilot study

The purpose of this study was to evaluate the clinical performance of glass ionomer cement (GIC) restorations comparing two minimally invasive methods in permanent teeth after 12 months. Fifty pregnant women (second trimester of pregnancy), mean age 22 ± 5.30 years, were treated by two previously trained operators. The treatment approaches tested were: chemomechanical method (CarisolvTM; MediTeam) and atraumatic restorative treatment (ART). A split-mouth study design was used in which the two treatments were randomly placed in 50 matched pairs of permanent teeth. The chemomechanical method (CM) was the test group and the ART was the control group. The treatments were performed in Public Health Centers. The tested restorative material was a high-strength GIC (Ketac Molar; 3M/ESPE). The restorations were placed according to the ART guidelines. Two calibrated independent examiners evaluated the restorations in accordance with ART criteria. The inter-examiner kappa was 0.97. Data were analyzed using 95% confidence interval on the binomial distribution and Fisher's exact test at 5% significance level. In a 12-month follow-up, 86% of the restorations were evaluated. In the test group (CM), 100% (CI=93.3-100%) of the restorations were considered successful. In the control group (ART) 97.6% (CI=87.4-99.9%) of the restorations were considered successful and 2.4% unsuccessful (marginal defect >0.5 mm). There was no statistically significant difference between the 12-mounth success rate for both groups (Fisher's exact test: P=0.49) and between the two operators (Fisher's exact test: P=1.00). Both minimally invasive methods, chemomechanical method and ART, showed a similar clinical performance after 12 months of follow up.

Use of flowable composite as intermediary layer in non-carious cervical lesions restored with composite resin: 48-month follow-up

PURPOSE: In this case report, the clinical performance of a microhybrid resin composite placed with or without a flowable resin composite was compared, over a 48-month period. CASE DESCRIPTION: The patient of this case report presented 2 pairs of equivalent cervical abfraction lesions, under occlusion. Four restorations were placed in teeth 34, 35, 44 and 45. The restorations were divided into groups (Single Bond + Filtek-Flow + Filtek Z250 or Single Bond + Filtek Z250) and the materials were applied according to the manufactures instructions. Two previously calibrated operators placed the restorations and two other independent examiners evaluated the restorations at baseline and after 48 months, according to the USPHS criteria and modified criteria for color match. CONCLUSION: After 48 months of evaluation the lesions restored with Filtek-Flow as a liner under Filtek Z250 did not show better clinical performance than the restorations without Filtek-Flow. All restorations showed a trend toward dark yellowing after 48 months.

Estudo de caso de uma situação atmosférica entre 12 e 19 de setembro de 2008, com algumas características semelhantes ao evento Catarina

Este trabalho apresenta uma análise das condições sinótica e dinâmica associadas ao desenvolvimento do ciclone ocorrido entre 12 e 19 de setembro de 2008, com o objetivo de destacar diferenças e semelhanças com o ambiente em que se inseriu o evento Catarina em março de 2004. As principais semelhanças foram encontradas no padrão sinótico geral: a ocorrência de um padrão típico de bloqueio do tipo dipolo associado à anomalia de vorticidade potencial em altos níveis; cavado em níveis médios com inclinação para oeste; a presença de uma coluna de vorticidade ciclônica desde a superfície até a baixa estratosfera; e, em superfície, o padrão de uma alta ao sul de uma baixa pressão. Apesar das semelhanças no padrão geral, diferenças ocorreram entre os dois eventos que influenciaram na intensidade dos sistemas: o Catarina ocorreu em latitudes mais baixas em relação ao caso de setembro de 2008; o padrão típico de bloqueio associado ao caso de setembro de 2008 durou um dia e meio, enquanto no evento Catarina foi de três dias; a configuração da advecção de temperatura na camada entre 1000-500 hPa favoreceu o deslocamento do evento de setembro de 2008 para leste/sudeste, ao contrário do Catarina, a advecção de ar quente a leste do ciclone foi praticamente suprimida e a tendência de altura geopotencial passou a ser positiva, padrões que impedem o deslocamento do sistema para leste; no caso de setembro de 2008 o padrão da inversão do gradiente meridional de temperatura potencial na superfície de -2,0 unidade de vorticidade potencial (UVP) foi caracterizado pela incursão de uma região alongada de ar quente vinda do equador em direção ao sul e ar frio vinda do sul em direção ao equador, enquanto no caso Catarina a inversão ocorre pelo isolamento de uma bolha de ar frio ao norte e uma bolha de ar quente ao sul, o que pode ter contribuído para maior duração do padrão de bloqueio, pois a dissipação neste caso é dificultada. Sistemas como o Catarina podem ser raros no Atlântico Sul, mas isso não ocorre em relação ao ambiente sinótico em que se formou o Catarina. Para melhor entender o processo atmosférico que levou à formação do Catarina, é necessário realizar experimentos numéricos de sensibilidade para o caso de setembro de 2008 com o objetivo de verificar a possibilidade do ciclone extratropical se tornar um ciclone tropical.

A contribution to the phytogeography of Brazilian campos: an analysis based on Poaceae

Twenty areas from eight Brazilian states were compared according to a list of 224 species of Poaceae. In order to determinate affinity patterns between the areas, a binary matrix was submitted to cluster and ordination analysis. The patterns found were then faced to climate and geographic position. The scores corresponding to the areas obtained from the cluster analysis showed a strong correlation to temperature. The scores corresponding to the species suggest a gradient that associates distribution patterns to the photosynthetic pathway (C3 or C4). The current results suggest that the traditional classification of the Southern American grasslands might require some modification in order to be broadly applicable in the Brazilian context.

Influence of light and temperature on seed germination of Cereus pernambucensis Lemaire (Cactaceae)

The objective of the present study was to evaluate the effects of light and temperature on germination of Cereus pernambucensis seeds, a species of columnar cactus native to Brazil and naturally incident in the restinga. Cereus pernambucensis seeds were incubated under different temperatures, from 5 to 45 °C, with 5 °C intervals, and under alternating temperatures of 15-20 °C, 15-30 °C, 20-25 °C, 20-30 °C, 20-35 °C, 25-30 °C, 25-35 °C, and 30-35 °C, both under continuous white light and dark. The seeds were also incubated in a gradient of phytochrome photoequilibrium at 25 °C. The highest percentage germination in this species was between 25 and 30 °C. The minimum temperature was between 15 and 20 °C and the maximum between 35 and 40 °C. Alternating temperatures did not affect the percentage of seed germination, but it did alter the rate and synchronization indexes. Seeds incubated in the dark did not germinate under any of the conditions tested, indicating that this species when cultivated present light sensitive seeds controlled by phytochrome. The seeds can tolerate a lot of shade conditions, germinating under very low fluence response of phytochrome.

Diversidade de abelhas (Hymenoptera, Apidae) ao longo de um gradiente latitudinal na Mata Atlântica

A Mata Atlântica é um dos ambientes mais ricos e ameaçados do mundo, o que deveria ter estimulado em muito o estudo e a conservação do Bioma, mas a fauna de Hymenoptera permanece ainda relativamente pouco conhecida. Em especial, a fauna de abelhas da floresta ombrófila densa é pouco estudada em comparação à fauna das áreas abertas brasileiras. O projeto temático "Biodiversidade de Hymenoptera e Isoptera: riqueza e diversidade ao longo de um gradiente latitudinal na Mata Atlântica - a floresta úmida do leste do Brasil", integrante do Programa Biota-Fapesp, foi idealizado com o objetivo de catalogar térmitas, formigas e famílias selecionadas de vespas ao longo da Mata Atlântica, disponibilizando dados que permitam melhor embasar a conservação deste bioma. O protocolo de amostragem aplicada para a coleta de himenópteros (excluindo as formigas) empregou armadilhas Malaise, pratos-armadilha de cor amarela e esforço similar na varredura de vegetação ao longo de 17 localidades selecionadas, representando um gradiente de quase 20° de latitude na Mata Atlântica, dos Estados da Paraíba até Santa Catarina. Este protocolo foi definido para otimizar a coleta de vespas, sendo as abelhas um produto secundário da amostragem (levantamentos de abelhas em geral utilizam captura em flores ao longo das estações do ano). No entanto, devido à escala regional do projeto e ao grande esforço de amostragem, uma expressiva quantidade de abelhas foi coletada durante o projeto, incluindo novos registros de abelhas para a Mata Atlântica. Foi amostrado um total de 797 espécimes distribuídos em 105 espécies de abelhas; o grupo de abelhas mais rico e abundante foi Meliponina. Uma análise de correspondência "destendenciada" ('detrended correspondence analysis') aplicada à uma matriz de presença ou ausência de Meliponina revela a relativamente fraca influência do gradiente latitudinal na composição das assembléias de abelhas de Mata Atlântica. Uma listagem das espécies amostradas por localidade, com suas freqüências relativas, é apresentada e discutida.

Estádio sucessional e fatores geográficos como determinantes da similaridade florística entre comunidades florestais no Planalto Atlântico, Estado de São Paulo, Brasil

A análise das relações de similaridade florística entre comunidades geralmente conduz ao estabelecimento de padrões, condicionados por fatores diversos que determinam a ocorrência ou não das espécies em diferentes locais. Em busca de tais padrões, foram analisadas as relações de similaridade florística entre comunidades florestais localizadas na região do Planalto de Ibiúna, estado de São Paulo, Brasil. Incluíram-se na análise 21 fragmentos florestais e seis sítios em uma Reserva Florestal contínua, sendo que a composição florística e a estrutura da comunidade arbórea (DAP mínimo 5 cm) em cada local foram amostradas pelo método de quadrantes. Aplicaram-se dois métodos de análises multivariadas: 1) Análise de Correspondência Destendenciada (DCA), com base no índice de similaridade de Sørensen; e 2) Divisão Hierárquica Dicotômica (TWINSPAN). A similaridade florística foi mais elevada entre comunidades em estádios sucessionais semelhantes, especialmente se estivessem geograficamente próximas. Há um gradiente florístico associado à latitude, indicando tratar-se de uma região de transição entre biomas. Nos sítios situados na face norte da região de estudo estão presentes espécies que também ocorrem no cerradão e em floresta estacional semidecidual, enquanto nos sítios situados na face sul prevalecem espécies características da floresta ombrófila densa.

Physiological implications of the regulation of vacuolar H+-ATPase by chloride ions

Vacuolar H+-ATPase is a large multi-subunit protein that mediates ATP-driven vectorial H+ transport across the membranes. It is widely distributed and present in virtually all eukaryotic cells in intracellular membranes or in the plasma membrane of specialized cells. In subcellular organelles, ATPase is responsible for the acidification of the vesicular interior, which requires an intraorganellar acidic pH to maintain optimal enzyme activity. Control of vacuolar H+-ATPase depends on the potential difference across the membrane in which the proton ATPase is inserted. Since the transport performed by H+-ATPase is electrogenic, translocation of H+-ions across the membranes by the pump creates a lumen-positive voltage in the absence of a neutralizing current, generating an electrochemical potential gradient that limits the activity of H+-ATPase. In many intracellular organelles and cell plasma membranes, this potential difference established by the ATPase gradient is normally dissipated by a parallel and passive Cl- movement, which provides an electric shunt compensating for the positive charge transferred by the pump. The underlying mechanisms for the differences in the requirement for chloride by different tissues have not yet been adequately identified, and there is still some controversy as to the molecular identity of the associated Cl--conducting proteins. Several candidates have been identified: the ClC family members, which may or may not mediate nCl-/H+ exchange, and the cystic fibrosis transmembrane conductance regulator. In this review, we discuss some tissues where the association between H+-ATPase and chloride channels has been demonstrated and plays a relevant physiologic role.

Novos paradigmas e velhos discursos: analisando processos de adolescentes em conflito com a lei

Este artigo evidencia análises contidas na dissertação cujo objetivo foi analisar os discursos dos operadores jurídico-sociais em processos judiciais de Varas da Infância e Juventude de duas cidades brasileiras. Os direitos das crianças e adolescentes, a questão social e a análise do discurso configuraram-se como referenciais teóricos e de análise. Resultados evidenciaram discursos de proteção e revelaram também a intenção de punição. A questão social foi ignorada pelos operadores a despeito dos contextos em que ocorreram as infrações.