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.

A novel voltage step-down/up ZCS-PWM Zeta converter

This paper presents an analysis of a novel pulse-width-modulated (PWM) voltage step-down/up Zeta converter, featuring zero-current-switching (ZCS) at the active switches. The applications in de to de and ac to de (rectifier) operation modes are used as examples to illustrate the performance of this new ZCS-PWM Zeta converter. Regarding to the new ZCS-PWM Zeta rectifier proposed, it should be noticed that the average-current mode control is used in order to obtain a structure with high power-factor (HPF) and low total harmonic distortion (THD) at the input current.Two active switches (main and auxiliary transistors), two diodes, two small resonant inductors and one small resonant capacitor compose the novel ZCS-PWM soft-commutation cell, used in these new ZCS-PWM Zeta converters. In this cell, the turn-on of the active switches occurs in zero-current (ZC) and their turn-off in zero-current and zero-voltage (ZCZV). For the diodes, their turn-on process occurs in zero-voltage (ZV) and their reverse-recovery effects over the active switches are negligible. These characteristics make this cell suitable for Insulated-Gate Bipolar Transistors (IGBTs) applications.The main advantages of these new Zeta converters, generated from the new soft-commutation cell proposed, are possibility of obtaining isolation (through their accumulation inductors), and high efficiency, at wide load range. In addition, for the rectifier application, a high power factor and low THD in the input current ran be obtained, in agreement with LEC 1000-3-2 standards.The principle of operation, the theoretical analysis and a design example for the new de to de Zeta converter operating in voltage step-down mode are presented. Experimental results are obtained from a test unit with 500W output power, 110V(dc) output voltage, 220V(dc) input voltage, operating at 50kHz switching frequency. The efficiency measured at rated toad is equal to 97.3%for this new Zeta converter.Finally, the new Zeta rectifier is analyzed, and experimental results from a test unit rated at 500W output power, 110V(dc) output voltage, 220V(rms) input voltage, and operating at 50kHz switching frequency, are presented. The measured efficiency is equal to 96.95%, the power-factor is equal to 0.98, and the input current THD is equal to 19.07%, for this new rectifier operating at rated load.

A possible stellar metallic enhancement in post-T Tauri stars by a planetesimal bombardment

The photospheres of stars hosting planets have larger metallicity than stars lacking planets. This could be the result of a metallic star contamination produced by the bombarding of hydrogen-deficient solid bodies. In the present work we study the possibility of an earlier metal enrichment of the photospheres by means of impacting planetesimals during the first 20-30 Myr. Here we explore this contamination process by simulating the interactions of an inward migrating planet with a disc of planetesimal interior to its orbit. The results show the percentage of planetesimals that fall on the star. We identified the dependence of the planet's eccentricity (e(p)) and time-scale of migration (tau) on the rate of infalling planetesimals. For very fast migrations (tau= 10(2) and 10(3) yr) there is no capture in mean motion resonances, independently of the value of e(p). Then, due to the planet's migration the planetesimals suffer close approaches with the planet and more than 80 per cent of them are ejected from the system. For slow migrations (tau= 10(5)and 10(6) yr) the percentage of collisions with the planet decreases with the increase of the planet's eccentricity. For e(p) = 0 and 0.1 most of the planetesimals were captured in the 2:1 resonance and more than 65 per cent of them collided with the star. Whereas migration of a Jupiter mass planet to very short pericentric distances requires unrealistic high disc masses, these requirements are much smaller for smaller migrating planets. Our simulations for a slowly migrating 0.1 M-Jupiter planet, even demanding a possible primitive disc three times more massive than a primitive solar nebula, produces maximum [Fe/H] enrichments of the order of 0.18 dex. These calculations open possibilities to explain hot Jupiter exoplanet metallicities.

On computing discriminants of subfields of Q(zeta(pr))

The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(Q(zeta(n))/Q), the discriminant of K can be obtained from H by computing the product of the conductors of all characters defined modulo n which are associated to K. By calculating these conductors explicitly, we derive a formula to compute the discriminant of any subfield of Q(zeta(p)r), where p is an odd prime and r is a positive integer. (C) 2002 Elsevier B.V. (USA).

Zeta potential and doping in polyaniline dispersions

Polyaniline (PAni) has been classified as an intractable polymer, particularly in its conducting form, the emeraldine salt (ES). Therefore one can consider the mixture of water and PAni as a suspension. The conducting form of PAni can be obtained by a doping process known as acid doping, in which a strong acid turns PAni from its insulating form, the emeraldine base (EB), into the conducting form, the emeraldine salt. With the objective of establishing a correlation between the doping level and the zeta potential of polyaniline dispersions, polyaniline + HCl aqueous suspensions were prepared. Positive zeta potential values for the various suspensions of PAni showed that it acquired positive charges after the doping process. It was also observed an increase in zeta potential values as HCl concentration increased, which could be correlated to UV-visible spectra of PAni suspensions.

New integrated Zeta and Cuk inverters intended for standalone and grid-connected applications

This paper presents new inverter topologies based on the integration of a DC to DC Zeta or Cuk converter with a voltage source inverter (VSI). The proposed integration procedure aims to reduce the amount of components, meaning lower volume, weight and costs. In this context, new families of single-phase and three-phase integrated inverters are also presented. Therefore, considering the novelty for Zeta and Cuk integrated inverters structures, the proposed single-phase and three-phase inverters versions are analyzed for grid-tied and stand-alone applications. Furthermore, in order to demonstrate the feasibility of the proposal, the main simulation and experimental results are presented. © 2011 IEEE.

Identification of phospholipase C zeta in normospermic and teratospermic domestic cat sperm

In mammalian species, oocyte activation is initiated by oscillations in the intracellular concentration of free calcium ([Ca2+]i), which are also essential to allow embryonic development. To date, evidence supporting the hypothesis that a sperm factor is responsible for initiating oocyte activation has been presented in various mammalian species. Among the possible candidates to be the active sperm factor is the novel sperm-specific phospholipase C ζ (PLCζ), which besides its testis-specific expression is capable of initiating [Ca2+]i oscillations. In this study, we investigated the presence of PLCζ in the sperm of the domestic cat and whether normospermic and teratospermic cats differ in their PLCζ expression. Immunoblotting with anti-PLCζ antibodies confirmed the presence of an immunoreactive band of ~70 kDa in whole sperm lysates of domestic cat as well as in both soluble and insoluble fractions from this sperm. Additional immunoreactive bands, probably C- and N-terminal truncated versions of PLCζ, were also visualized in the soluble sperm fractions. Interestingly, immunoreactivity of PLCζ was detectable in teratospermic sperm, although with slightly less intensity than in normospermic sperm. In conclusion, domestic cat sperm express PLCζ in both cytosolic and high-pH fractions, which is consistent with data in other mammals. Sperm from teratospermic cats also express PLCζ, albeit at reduced concentrations, which may affect the fertility of these males. © 2013 Elsevier Inc..

Localização da proteína fosfolipase C zeta em extratos esppermáticos de gatos domésticos normospérmicos

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

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

RIEMANN ZETA ZEROS AND PRIME NUMBER SPECTRA IN QUANTUM FIELD THEORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

ZETA DETERMINANT FOR DOUBLE SEQUENCES OF SPECTRAL TYPE

We study the spectral functions, and in particular the zeta function, associated to a class of sequences of complex numbers, called of spectral type. We investigate the decomposability of the zeta function associated to a double sequence with respect to some simple sequence, and we provide a technique for obtaining the first terms in the Laurent expansion at zero of the zeta function associated to a double sequence.

Funzioni zeta e fattorizzazione unica in anelli quadratici di curve su campi finiti

In questa tesi si esaminano alcune questioni riguardanti le curve definite su campi finiti. Nella prima parte si affronta il problema della determinazione del numero di punti per curve regolari. Nella seconda parte si studia il numero di classi di ideali dell’anello delle coordinate di curve piane definite da polinomi assolutamente irriducibili, per ottenere, nel caso delle curve ellittiche, risultati analoghi alla classica formula di Dirichlet per il numero di classi dei campi quadratici e delle congetture di Gauss.