Zeros da função zeta de Riemann e o teorema dos números primos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Teorema de Riemann-Roch, morfismos de Frobenius e a hipótese de Riemann

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

Três métodos para o cálculo da série zeta(2n) de Riemann

Neste trabalho apresentamos três métodos distintos provando que S(n) = +1 X k=−1 (4k + 1)−n é um múltiplo racional de n para todos os inteiros n = 1, 2, 3, . . . O primeiro utiliza a teoria das função analíticas e funções geradoras. No segundo reduzimos o problema, via mudança de variável devida a E. Calabi, ao cálculo do volume de certos politopos em Rn enquanto que no terceiro usamos a teoria dos operadores integrais compactos. Cada um dos métodos tem um interesse intrínsico e está sujeito a generalizações para aplicações em novas situações.

Cyclic variability of the circumstellar disk of the Be star zeta Tauri II. Testing the 2D global disk oscillation model

Context. About 2/3 of the Be stars present the so-called V/R variations, a phenomenon characterized by the quasi-cyclic variation in the ratio between the violet and red emission peaks of the HI emission lines. These variations are generally explained by global oscillations in the circumstellar disk forming a one-armed spiral density pattern that precesses around the star with a period of a few years. Aims. This paper presents self-consistent models of polarimetric, photometric, spectrophotometric, and interferometric observations of the classical Be star zeta Tauri. The primary goal is to conduct a critical quantitative test of the global oscillation scenario. Methods. Detailed three-dimensional, NLTE radiative transfer calculations were carried out using the radiative transfer code HDUST. The most up-to-date research on Be stars was used as input for the code in order to include a physically realistic description for the central star and the circumstellar disk. The model adopts a rotationally deformed, gravity darkened central star, surrounded by a disk whose unperturbed state is given by a steady-state viscous decretion disk model. It is further assumed that this disk is in vertical hydrostatic equilibrium. Results. By adopting a viscous decretion disk model for zeta Tauri and a rigorous solution of the radiative transfer, a very good fit of the time-average properties of the disk was obtained. This provides strong theoretical evidence that the viscous decretion disk model is the mechanism responsible for disk formation. The global oscillation model successfully fitted spatially resolved VLTI/AMBER observations and the temporal V/R variations in the H alpha and Br gamma lines. This result convincingly demonstrates that the oscillation pattern in the disk is a one-armed spiral. Possible model shortcomings, as well as suggestions for future improvements, are also discussed.

Cyclic variability of the circumstellar disk of the Be star zeta Tauri I. Long-term monitoring observations

Context. Emission lines formed in decretion disks of Be stars often undergo long-term cyclic variations, especially in the violet-to-red (V/R) ratio of their primary components. The underlying structural and dynamical variations of the disks are only partly understood. From observations of the bright Be-shell star. Tau, the possibly broadest and longest data set illustrating the prototype of this behaviour was compiled from our own and archival observations. It comprises optical and infrared spectra, broad-band polarimetry, and interferometric observations. Aims. The dense, long-time monitoring permits a better separation of repetitive and ephemeral variations. The broad wavelength coverage includes lines formed under different physical conditions, i.e. different locations in the disk, so that the dynamics can be probed throughout much of the disk. Polarimetry and interferometry constrain the spatial structure. All together, the objective is a better understand the dynamics and life cycle of decretion disks. Methods. Standard methods of data acquisition, reduction, and analysis were applied. Results. From 3 V/R cycles between 1997 and 2008, a mean cycle length in Ha of 1400-1430 days was derived. After each minimum in V/R, the shell absorption weakens and splits into two components, leading to 3 emission peaks. This phase may make the strongest contribution to the variability in cycle length. There is no obvious connection between the V/R cycle and the 133-day orbital period of the not otherwise detected companion. V/R curves of different lines are shifted in phase. Lines formed on average closer to the central star are ahead of the others. The shell absorption lines fall into 2 categories differing in line width, ionization/excitation potential, and variability of the equivalent width. They seem to form in separate regions of the disk, probably crossing the line of sight at different times. The interferometry has resolved the continuum and the line emission in Br gamma and HeI 2.06. The phasing of the Br gamma emission shows that the photocenter of the line-emitting region lies within the plane of the disk but is offset from the continuum source. The plane of the disk is constant throughout the observed V/R cycles. The observations lay the foundation for the fully self-consistent, one-armed, disk-oscillation model developed in Paper II.

Avaliação de modelos geoidais gravimétricos determinados com funções covariâncias planas e esféricas (Estudo de Caso: Estado de São Paulo e adjacências)

The least squares collocation is a mathematical technique which is used in Geodesy for representation of the Earth's anomalous gravity field from heterogeneous data in type and precision. The use of this technique in the representation of the gravity field requires the statistical characteristics of data through covariance function. The covariances reflect the behavior of the gravity field, in magnitude and roughness. From the statistical point of view, the covariance function represents the statistical dependence among quantities of the gravity field at distinct points or, in other words, shows the tendency to have the same magnitude and the same sign. The determination of the covariance functions is necessary either to describe the behavior of the gravity field or to evaluate its functionals. This paper aims at presenting the results of a study on the plane and spherical covariance functions in determining gravimetric geoid models.

ZETA DETERMINANT AND OPERATOR DETERMINANTS

We apply techniques of zeta functions and regularized products theory to study the zeta determinant of a class of abstract operators with compact resolvent, and in particular the relation with other spectral functions.

Rheological behavior, zeta potential, and accelerated stability tests of Buriti oil (Mauritia flexuosa) emulsions containing lyotropic liquid crystals

Background: It is well known that the Amazon region presents a huge biodiversity; therefore, countless natural resources are being employed in the production of phytocosmetics and phytomedicines. Objective: The purpose of this work was to obtain emulsions produced with Buriti oil and nonionic surfactants. Methods: Two surfactant systems were employed (Steareth-2 associated to Ceteareth-5 and to Ceteareth-20) to produce the emulsions using phase diagram method. Emulsions were obtained by echo-planar imaging method at 75 degrees C. Rheological behavior and zeta potential were evaluated, and accelerated stability tests were performed. Results: All emulsions analyzed presented pseudoplastic behavior. Zeta potential values were obtained between -14.2 and -53.3 mV. The formulations did not show changes in either physical stability, pH, or rheological behavior after accelerated stability tests. Significant differences were observed only after temperature cycling test. Conclusion: Based on these results, the emulsions obtained could be considered as promising delivery systems.

Efficacy of zeta-cypermethrin as pour-on or spray formulations for the control of buffalo fly (Haematobia irritans exigua) in cattle

Objective To determine the efficacy of zeta-cypermethrin in controlling buffalo fly (Haematobia irritans exigua). Design Five field trials in northern and central Queensland. Procedure Zeta-cypermethrin pour-on at 2.5 mg/kg, spray at 62.5 ppm, deltamethrin pour-on and pour-on vehicle were applied to groups of 20 cattle. Buffalo fly counts were conducted three times before treatment and 3, 7, 14, 21, 28 and 35 days after treatment. Results In central Queensland where synthetic pyrethroid resistance in buffalo fly populations was rare, 2.5 mg/kg of zeta-cypermethrin pour-on gave good control of buffalo fly for 4 weeks and was better than a deltamethrin product. A zeta-cypermethrin spray used at 62.5 ppm gave 14 days control. In far-north Queensland where resistance to synthetic pyrethroids and heavy rain was common, the maximum period of efficacy of zeta-cypermethrin pour-on was reduced to 2 weeks. Conclusion In areas where there is low resistance to synthetic pyrethroids among buffalo flies, zeta-cypermethrin pour-on can be expected to give good control for 4 weeks.

Therapeutic efficacy of zeta-cypermethrin pour-on for the treatment of biting and sucking lice in cattle under field conditions

Objective To assess the efficacy of zeta-cypermethrin pour-on to control cattle lice. Design Five field trials in south-eastern Australia. Procedure Zeta-cypermethrin pour-on, deltamethrin pour-on and pour-on vehicle were applied to groups of 10 cattle. Lice were counted before treatment and 14, 28, 42 and 56 days after treatment. Results Zeta-cypermethrin pour-on given at 2.5 mg/kg was equivalent to, or marginally more effective than a deltamethrin pour-on at 0.75 mg/kg. It eliminated B bovis and H eurysternus and gave good control of L vituli and S capillatus. Zeta-cypermethrin at 1 mg/kg gave good control of B bovis and H eurysternus but was not satisfactory against L vituli and S capillatus. Conclusion Zeta-cypermethrin pour-on, given at 2.5 mg/kg, is an effective treatment for cattle lice control. Zeta-cypermethrin, and other synthetic pyrethroid pour-ons, are the treatment of choice to control B bovis.

Residues of zeta-cypermethrin in bovine tissues and milk following pour-on and spray application

The depletion of zeta-cypermethrin residues in bovine tissues and milk was studied. Beef cattle were treated three times at 3-week intervals with 1 ml 10 kg(-1) body weight of a 25 g litre(-1) or 50 g litre(-1) pour-on formulation (2.5 and 5.0 mg zeta-cypermethrin kg(-1) body weight) or 100 mg kg(-1) spray to simulate a likely worst-case treatment regime. Friesian and Jersey dairy cows were treated once with 2.5 mg zeta-cypermethrin kg(-1) in a pour-on formulation. Muscle, liver and kidney residue concentrations were generally less than the limit of detection (LOD = 0.01 mg kg(-1)). Residues in renal-fat and back-fat samples from animals treated with 2.5 mg kg(-1) all exceeded the limit of quantitation (LOQ = 0.05 mg kg(-1)), peaking at 10 days after treatment. Only two of five kidney fat samples were above the LOQ after 34 days, but none of the back-fat samples exceeded the LOQ at 28 days after treatment. Following spray treatments, fat residues were detectable in some animals but were below the LOQ at all sampling intervals. Zeta-cypermethrin was quantifiable (LOQ = 0.01 mg kg(-1)) in only one whole-milk sample from the Friesian cows (0.015 mg kg(-1), 2 days after treatment). In whole milk from Jersey cows, the mean concentration of zeta-cypermethrin peaked 1 day after treatment, at 0.015 mg kg(-1), and the highest individual sample concentration was 0.025 mg kg(-1) at 3 days after treatment. Residues in milk were not quantifiable beginning 4 days after treatment. The mean concentrations of zeta-cypermethrin in milk fat from Friesian and Jersey cows peaked two days after treatment at 0.197 mg kg(-1) and 0.377 mg kg(-1), respectively, and the highest individual sample concentrations were 2 days after treatment at 0.47 mg kg(-1) and 0.98 mg kg(-1), respectively. (C) 2001 Society of Chemical Industry.

Kainic acid induces 14-3-3 zeta expression in distinct regions of rat brain

Areas of the limbic system of adult male Wistar rats were screened for kainic-acid-induced gene expression. Polymerase-chain-reactionbased differential display identified a 147-bp cDNA fragment, which represented an mRNA that was upregulated in the entorhinal cortex and hippocampus in the kainic-acid-treated animals. The sequence was 97.8% homologous to rat 14-3-3 zeta isoform mRNA. Detailed Northern analysis revealed increased mRNA levels in the entorhinal cortex I h after kainic acid exposure and continued elevation 24 h post-injection in both the entorhinal cortex and hippocampus. Western blot analyses confirmed that the protein product of this gene was also present in increased amounts over the same time period. Immunohistochemistry and terminal transferase-mediated dUTP nick end labelling (TUNEL) detected expression of 14-3-3 protein exclusively in the entorhinal cortex and hippocampus, and only in TUNEL-positive neuronal cells. Expression of the tumor suppressor protein, p53 was also induced by kainate injection, and was co-localized with 14-3-3 zeta protein in selected cells only in the affected brain regions. The increase gene expression of 14-3-3 represents a transcription-mediated response associated with region selective neuronal damage induced by kainic acid. (C) 2002 Elsevier Science B.V. All rights reserved.

Funções gerenciais na gestão educacional : caracterização do trabalho gerencial dos gestores da Secretaria Municipal de Educação de Santa Maria de Jetibá-ES

Esta pesquisa tem a intenção de descrever as características do trabalho gerencial de gestores educacionais, iniciando-se de estudo realizado com gestores escolares, coordenadores pedagógicos que atendem às escolas multisseriadas da secretaria de educação do município de Santa Maria de Jetibá (ES). Buscou-se caracterizar a ação gerencial desses gestores partindo das percepções deles sobre os trabalhos realizados junto aos demais membros da comunidade escolar, equipes de gestão e gestão da secretaria municipal, não deixando de lado as particularidades da área educacional, principalmente sobre gestão democrática e autonomia. Para se entender a diversidade, a complexidade e as dinâmicas relações dos gestores, foram realizadas entrevistas semiestruturadas que contribuíram para aprofundamento nessas dinâmicas. Documentos foram analisados para conhecimento e caracterização da formatação da estrutura organizacional da secretaria de educação. Os relatos das entrevistas apresentaram fragmentos que puderam nortear ideias para um melhor tratamento dos dados, que foram realizados analisando os conteúdos apresentados pelos gestores entrevistados. As conversas realizadas com esses entrevistados mostraram ambiguidade, dinamismo e pluralidade no desenvolvimento das “funções gerenciais” dos gestores educacionais, que são líderes, companheiros e executores de trabalhos junto aos demais componentes das relações do ambiente educacional. Assim, as expectativas são de que esta pesquisa possa fazer com que novos diálogos surjam para discutir as relações dos gestores educacionais, principalmente sobre as ações dos coordenadores que atuam junto às escolas multisseriadas.