Transcendental Brauer groups of products of CM elliptic curves

Let L be a number field and let E/L be an elliptic curve with complex multiplication by the ring of integers O_K of an imaginary quadratic field K. We use class field theory and results of Skorobogatov and Zarhin to compute the transcendental part of the Brauer group of the abelian surface ExE. The results for the odd order torsion also apply to the Brauer group of the K3 surface Kum(ExE). We describe explicitly the elliptic curves E/Q with complex multiplication by O_K such that the Brauer group of ExE contains a transcendental element of odd order. We show that such an element gives rise to a Brauer-Manin obstruction to weak approximation on Kum(ExE), while there is no obstruction coming from the algebraic part of the Brauer group.

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.

BIRD FORAGING IN ANACARDIUM PATCHES IN CENTRAL BRAZILIAN FIRE BREAKS: RELATIONSHIP BETWEEN FLOCK SIZE AND PATCH SIZE

Fire management ran increase the biomass of some plant species at fire breaks in reserves of the Cerrado. For example, numerous and large patches of monkey-nuts (Anacardium humile, Anacardiaceae) provide abundant food resources for wildlife in the lower strata of savanna woodlands managed by fire. The objective of this study was to examine the exploitation of A. humile patches by birds in managed savanna woodlands (fire breaks) at Emas National Park, southwest Brazil. The relationship between flock size and the size of Anacardium patches were also investigated. Fire breaks were sampled in September and October 2006, when fruits and flowers were abundant. Ara ararauna was often recorded exploiting resources of Anacardium patches. This species and other psittacids (Amazona aestiva, Alipiopsittaca xanthops, and Diopsittaca nobilis) consumed seeds usually on the ground around fruiting patches. Members of Aratinga aurea flocks and Ramphastos toco consumed pseudo-fruits. Larger flocks detected were those of A. aurea and A. ararauna. Groups of A. ararauna that exploited larger patches tended to be larger than flocks that exploited smaller patches. This study suggests that intra- and interspecific interactions and characteristics of Anacardium patches and of the surrounding vegetation are involved in the feeding ecology of birds in the lower stratum of managed woodlands. Fruiting Anacardium patches attract numerous frugivorous birds to fire breaks at Emas National Park. Further research is needed to a better understanding of the influence of fire management on birds in the Cerrado. Accepted 31 July 2009.

INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

Semilinear elliptic problems near resonance with a nonprincipal eigenvalue

We consider the Dirichlet problem for the equation -Delta u = lambda u +/- (x, u) + h(x) in a bounded domain, where f has a sublinear growth and h is an element of L-2. We find suitable conditions on f and It in order to have at least two solutions for X near to an eigenvalue of -Delta. A typical example to which our results apply is when f (x, u) behaves at infinity like a(x)vertical bar u vertical bar(q-2)u, with M > a(x) > delta > 0, and I < q < 2. (C) 2007 Elsevier Inc. All rights reserved.

NeXSPheRIO results on elliptic flow and directed flow for Au plus Au and Cu plus Cu collisions at RHIC

Hydrodynamics has been rather successful at describing results obtained in relativistic nuclear collisions at RHIC. Here we show results obtained with NeXSPheRIO on Au+Au collisions and the less studied Cu+Cu collisions. We study elliptic flow and its connection with eccentricity suggested by PHOBOS, as well as present elliptic flow fluctuations. We also show results for directed flow and compare with PHOBOS and STAR data.

NeXSPheRIO results on elliptic-flow fluctuations at RHIC

By using the NeXSPheRIO code, we study the elliptic-flow fluctuations in Au + Au collisions at 200 A GeV. It is shown that, by fixing the parameters of the model to correctly reproduce the charged pseudorapidity and the transverse-momentum distributions, reasonable agreement of < v(2)> with data is obtained, both as function of pseudorapidity as well as of transverse momentum, for charged particles. Our results on elliptic-flow fluctuations are in good agreement with the recently measured data on experiments.

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

Desenvolvimento de antenas de microfita com Patch em anel utilizando materiais ferrimagnéticos e metamateriais

In general, the materials used as substrates in the project of microstrip antennas are: isotropic, anisotropic dielectrics and ferrimagnetic materials (magnetic anisotropy). The use of ferrimagnetic materials as substrates in microstrip patch antennas has been concentrated on the analysis of antennas with circular and rectangular patches. However, a new class of materials, called metamaterials, has been currently the focus of a great deal of interest. These materials exhibit bianisotropic characteristics, with permittivity and permeability tensors. The main objective of this work is to develop a theoretical and numerical analysis for the radiation characteristics of annular ring microstrip antennas, using ferrites and metamaterials as substrates. The full wave analysis is performed in the Hankel transform domain through the application of the Hertz vector potentials. Considering the definition of the Hertz potentials and imposing the boundary conditions, the dyadic Green s function components are obtained relating the surface current density components at the plane of the patch to the electric field tangential components. Then, Galerkin s method is used to obtain a system of matrix equations, whose solution gives the antenna resonant frequency. From this modeling, it is possible to obtain numerical results for the resonant frequency, radiation pattern, return loss, and antenna bandwidth as a function of the annular ring physical parameters, for different configurations and substrates. The theoretical analysis was developed for annular ring microstrip antennas on a double ferrimagnetic/isotropic dielectric substrate or metamaterial/isotropic dielectric substrate. Also, the analysis for annular ring microstrip antennas on a single ferrimagnetic or metamaterial layer and for suspended antennas can be performed as particular cases

Antenas de microfita com patch quase-fractal para aplicações em Redes WPAN/WLAN

The microstrip antennas are in constant evidence in current researches due to several advantages that it presents. Fractal geometry coupled with good performance and convenience of the planar structures are an excellent combination for design and analysis of structures with ever smaller features and multi-resonant and broadband. This geometry has been applied in such patch microstrip antennas to reduce its size and highlight its multi-band behavior. Compared with the conventional microstrip antennas, the quasifractal patch antennas have lower frequencies of resonance, enabling the manufacture of more compact antennas. The aim of this work is the design of quasi-fractal patch antennas through the use of Koch and Minkowski fractal curves applied to radiating and nonradiating antenna s edges of conventional rectangular patch fed by microstrip inset-fed line, initially designed for the frequency of 2.45 GHz. The inset-fed technique is investigated for the impedance matching of fractal antennas, which are fed through lines of microstrip. The efficiency of this technique is investigated experimentally and compared with simulations carried out by commercial software Ansoft Designer used for precise analysis of the electromagnetic behavior of antennas by the method of moments and the neural model proposed. In this dissertation a study of literature on theory of microstrip antennas is done, the same study is performed on the fractal geometry, giving more emphasis to its various forms, techniques for generation of fractals and its applicability. This work also presents a study on artificial neural networks, showing the types/architecture of networks used and their characteristics as well as the training algorithms that were used for their implementation. The equations of settings of the parameters for networks used in this study were derived from the gradient method. It will also be carried out research with emphasis on miniaturization of the proposed new structures, showing how an antenna designed with contours fractals is capable of a miniaturized antenna conventional rectangular patch. The study also consists of a modeling through artificial neural networks of the various parameters of the electromagnetic near-fractal antennas. The presented results demonstrate the excellent capacity of modeling techniques for neural microstrip antennas and all algorithms used in this work in achieving the proposed models were implemented in commercial software simulation of Matlab 7. In order to validate the results, several prototypes of antennas were built, measured on a vector network analyzer and simulated in software for comparison

Arranjo de antenas de microfita com substrato anisotrópico com patch supercondutor e aplicações em nanotecnologia

The main objective in this work is the analysis of resonance frequency microstrip structures with glass fiber and electromagnetic band gap (EBG/PBG) substrate and analysis of microstrip antennas with rectangular patch of superconductor of high critical temperature (HTS). In this work was used the superconductors YBCO (critical temperature of 90K), SnBaCaCuOy (critical temperature of 160K), and Sn5InCa2Ba4Cu10Oy (critical temperature of 212K) with results in Gigahertz and Terahertz. Was used microstrip antennas arrays planar and linear phase and linear phase planar with patch with superconductor. It presents a study of the major theories that explain superconductivity. In phase arrays were obtained the factors arrays for such configurations, and the criteria of phase and spacing between the elements compound in the array, which were examined in order to get a main lobe with high directivity and high gain. In the analysis we used the method of Transverse Transmission Line (TTL) used in domain of the Fourier Transform (FTD). The LTT is a full wave method, which obtains the electromagnetic field in terms of the components transverse of the structure. The addition of superconductive patch is made using the boundary condition resistive complex. Results are obtained resonance frequency as a function of the parameters of the antenna, radiation patterns of the E and H Planes, for the phase antenna arrays in linear and planar configurations, for different values of the phase and the spacing between elements

Aplicações de arranjos de antenas de microfita com patch supercondutor

This work has as main objective the study of arrays of microstrip antennas with superconductor rectangular patch. The phases and the radiation patterns are analyzed. A study of the main theories is presented that explain the microscopic and macroscopic phenomena of superconductivity. The BCS, London equations and the Two Fluid Model, are theories used in the applications of superconductors, at the microstrip antennas and antennas arrays. Phase Arrangements will be analyzed in linear and planar configurations. The arrangement factors of these configurations are obtained, and the phase criteria and the spacing between the elements, are examined in order to minimize losses in the superconductor, compared with normal conductors. The new rectangular patch antenna, consist of a superconducting material, with the critical temperature of 233 K, whose formula is Tl5Ba4Ca2Cu9Oy, is analyzed by the method of the Transverse nTransmission Line (TTL), developed by H. C. C. Fernandes, applied in the Fourier Transform Domain (FTD). The TTL is a full-wave method, which has committed to obtaining the electromagnetic fields in terms of the transverse components of the structure. The inclusion of superconducting patch is made using the complex resistive boundary condition, using the impedance of the superconductor in the Dyadic Green function, in the structure. Results are obtained from the resonance frequency depending on the parameters of the antenna using superconducting material, radiation patterns in E-Plane and H -Plane, the phased antennas array in linear and planar configurations, for different values of phase angles and different spacing between the elements