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.

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.

Evaluation of dental pulp repair using low level laser therapy (688 nm and 785 nm) morphologic study in capuchin monkeys

The aim of this study was to evaluate the hypothesis that low-level laser therapy (LLLT) 688 nm and 785 nm accelerate dentin barrier formation and repair process after traumatic pulp exposure. The sample consisted of 45 premolars of capuchin monkeys (Cebus apella) with pulp exposure Class V cavities. All premolars were treated with calcium hydroxide (Ca(OH)(2)), divided in groups of 15 teeth each, and analyzed on 7(th), 25(th), and 60(th) day. Group GI - only Ca(OH)(2), GIF- laser 688 nm, and GIII - laser 785 nm. Laser beam was used in single and punctual dose with the parameters: continuous, 688 nm and 785 nm wavelength, tip`s area of 0.00785 cm(2), power 50 mW, application time 20 s, dose 255 J/cm(2), energy 2 J. Teeth were capped with Ca(OH)(2), Ca(OH)(2) cement and restored with amalgam. All groups presented pulp repair. On 25(th) day the thickness of the formed dentin barrier was different between the groups GI and GII (p < 0.05) and between groups GI and GIII (p < 0.01). On 60(th) day there was difference between GI and GIII (p < 0.01). It may be concluded that, LLLT 688 nm and 785 nm accelerated dentin barrier formation and consequently pulp repair process, with best results using infrared laser 785 nm. (c) 2009 by Astro Ltd. Published exclusively by WLLEY-VCH Verlag GmbH & Co. KGaA

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.

Platinum nanoparticle-modified electrodes, morphologic, and electrochemical studies concerning electroactive materials deposition

The present work describes the synthesis of platinum nanoparticles followed by their electrophoretic deposition onto transparent fluorine-doped tin oxide electrodes. The nano-Pt-modified electrodes were characterized by voltammetric studies in acidic solutions showing a great electrocatalytic behavior towards H(+) reduction being very interesting for fuel cell applications. Morphological characterization was performed by atomic force microscopy on different modified electrodes showing a very rough surface which can be tuned by means of time of deposition. Also, nickel hydroxide thin films were galvanostatically grown onto these electrodes showing an interesting electrochemical behavior as sharper peaks, indicating a faster ionic exchange from the electrolyte to the film.

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.

Classificação de sistemas meteorológicos e comparação da precipitação estimada pelo radar e medida pela rede telemétrica na bacia hidrográfica do alto Tietê

Foram analisadas características da precipitação estimada a partir de 145.194 campos de refletividade, de um total de 827 dias entre 1998 e 2003, obtidos do Radar Meteorológico de São Paulo (RSP). Os eventos foram classificados de acordo com intensidades de precipitação; em Convectivos (EC) e Estratiformes (EE). Quanto à morfologia, cinco tipos de sistemas foram identificados; Convecção Isolada (CI), Brisa Marítima (BM), Linhas de Instabilidade (LI), Bandas Dispersas (BD) e Frentes Frias (FF). Eventos convectivos dominam na primavera e verão e estratiformes no outono e inverno. A CI e a BM tiveram maiores picos de atuação entre outubro e março enquanto as FF de abril a setembro. BD atuam durante todo o ano e as LI só não foram observadas nos meses de junho e julho. Uma comparação pontual entre a precipitação medida pela telemetria e estimada com o radar foi realizada e, mostrou haver, na maioria dos casos, um viés positivo do RSP, para acumulações de 10, 30 e 60 minutos. Com o objetivo de integrar as estimativas de precipitação do radar com as medidas da rede telemétrica, por meio de uma análise objetiva estatística, foram obtidas dos campos de precipitação do radar as estruturas das correlações espaciais em função da distância para acumulações de chuva de 15, 30, 60 e 120 minutos para os cinco tipos de sistemas precipitantes que foram caracterizados. As curvas das correlações espaciais médias de todos os eventos de precipitação de cada sistema foram ajustadas por funções polinomiais de sexta ordem. Os resultados indicam diferenças significativas na estrutura espacial das correlações entre os sistemas precipitantes.

Effects of uterine cervix constriction on Wistar rats

PURPOSE: To verify if uterine cerclage can induce craniosynostosis or any cranial deformity in new born Wistar rats. METHODS: One pregnant female Wistar rat underwent laparotomy on day 18 of gestation and the uterus cervix was closed with a 3-0 nylon suture to avoid delivery, that occurs normally on the 21 day. The suture was released after 48 hours beyond the normal gestation period. The female rat delivered 11 pups. Six surviving rats from the delivery (group A - constrained group). Two rats were born from another mother and in the same age were used as control group (group B - 2 nonconstrained controls) were allowed to grow. They were sacrificed 1.2 years after their birth all the eight animals. Linear measurement, routine histology and computed tomography of the skull were performed at the time of their death to evaluate the cranial asymmetries by mesurements of the anatomical landmarks of the craniofacial skeleton of the rats on the two groups and compared then. RESULTS: We did not observe statistically significant differences in any of the compared measurements (p>0.05) obtained through the morphologic and radiologic methods. Histologic examinations did not reveal any sign of premature fusion or suture imbrications. Critical decrease in longitudinal body size was noticed as the limbs too in all the animals of group A. CONCLUSION: Constriction of uterine cervix leads to fetus suffering, even death for a few animals, associated to small body size, but not to craniosynostosis.

Características morfológicas da pars de C2 de humanos

OBJETIVO: avaliar a morfometria da pars da segunda vértebra cervical, verificar as variações existentes e predizer sua segurança para a colocação de parafusos por meio de uma abordagem cervical posterior. MÉTODOS: 58 vértebras foram obtidas para estudo anatômico (116 pars de C2) e foram medidas a altura e largura da pars, além do comprimento eixo-pedículo, largura e comprimento do pedículo, angulação sagital e medial. Todas as medidas foram separadas quanto aos seus lados direito e esquerdo; foi realizado o cálculo da média, variação, desvio padrão e a médica foi comparada com os estudos prévios. RESULTADOS: a largura média da pars de C2 foi de 9,5 mm; a altura, 9,5 mm; não houve diferença significativa entre os lados esquerdo e direito. O comprimento médio do pedículo foi de 10,5 mm; a medida média encontrada para o comprimento eixo-pedículo foi de 24,9 mm; a largura do pedículo foi de 2,8 mm. A angulação sagital encontrada foi de 19,6º e a horizontal foi de 28,5º. CONCLUSÕES: este estudo demonstra a viabilidade para a colocação de parafuso na pars de C2 em uma população caucasiana, destacando-se, porém, a grande variabilidade anatômica encontrada nas referidas medidas.

Early morphological and histochemical alterations in rats subjected to ileocystoplasty

PURPOSE: To study morphologic and histochemical alterations arising at the ileocystoplasty site. METHODS: Sixteen Wistar female rats were subjected to ileocystoplasty and sacrificed after eight weeks. Material collected was divided into four groups for histological and histochemical studies: Group I (control) - isolated ileum segment removed during ileocystoplasty; Group II - ileoileal anastomosis; Group III - ileovesical anastomosis and Group IV - ileal segment from the neobladder. Histological and histochemical study assessed dysplasia, metaplasia, acute and chronic inflammation, fibrosis, atrophy, hypertrophy, total mucins, sialomucins and sulfomucins. The non-parametric Wilcoxon and Mann-Whitney tests were employed in statistical analysis. RESULTS: None of the groups presented dysplasia. Acute inflammation and atrophy occurred in Groups II, III and IV, not reaching statistical significance. Metaplasia was significant only in Group III (p=0.012). Chronic inflammation, fibrosis and hypertrophy were significant in Groups II, III and IV. There was a significant increase in total mucin content in Group IV (p=0.014) and a reduction in Group III (p=0.016). Increases in sialomucins were observed in samples for Groups III (p=0.003) and IV (p=0.002) along with reduced sulfomucins in samples from Groups III (p=0.013) and IV (p=0.008). CONCLUSION: Ileocystoplasty in female rats caused squamous metaplasia, chronic inflammatory infiltration, fibrosis, hypertrophy, increase in sialomucin content, reduction in sulfomucins, and alterations in total mucin content with statistical significance, as well acute inflammatory infiltration and muscular atrophy with less intensity.

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.

Utilização de métodos acústicos em estudos de dinâmica costeira: exemplo na desembocadura lagunar de cananéia

Em função de suas condições de interface entre águas doces e salinas, desembocaduras estuarinas e lagunares constituem sistemas geomorfológicos altamente complexos e dinâmicos. Como conseqüência da variabilidade espacial e temporal dos fluxos de maré, o leito responde com uma grande variabilidade nas características morfológicas e sedimentares. Neste sentido, é possível relacionar diretamente a circulação de fundo e o transporte sedimentar com as feições submersas geradas. Perfis de ecossondagem, sonar de varredura lateral e sísmica de alta resolução, executados na desembocadura lagunar de Cananéia, revelaram a existência de uma dinâmica de fundo extremamente complexa, caracterizada por marcas onduladas e ondas de areia de alturas métricas. As maiores ondas de areia, localizadas em uma depressão na desembocadura lagunar, apresentam inversão de polaridade em sua assimetria, com a presença de ondas simétricas de grande tamanho no ponto de inversão. Este padrão morfológico não apresenta variação temporal em escala anual, sugerindo a persistência de um padrão de fluxos sobre o leito. Esta dinâmica revela, também, a constância de fluxos convergentes que aparentemente independem das condições de maré enchente ou vazante. Os resultados permitiram o estabelecimento de um primeiro modelo qualitativo de circulação de fundo na área, com aplicações potenciais na navegação e estudos de proteção da costa.