On the geometry of non-classical curves

In this paper we relate the numerical invariants attached to a projective curve, called the order sequence of the curve, to the geometry of the varieties of tangent linear spaces to the curve and to the Gauss maps of the curve. © 1992 Sociedade Brasileira de Matemática.

Combining genetic algorithm and simulated annealing: A molecular geometry optimization study

We introduce a new hybrid approach to determine the ground state geometry of molecular systems. Firstly, we compared the ability of genetic algorithm (GA) and simulated annealing (SA) to find the lowest energy geometry of silicon clusters with six and 10 atoms. This comparison showed that GA exhibits fast initial convergence, but its performance deteriorates as it approaches the desired global extreme. Interestingly, SA showed a complementary convergence pattern, in addition to high accuracy. Our new procedure combines selected features from GA and SA to achieve weak dependence on initial parameters, parallel search strategy, fast convergence and high accuracy. This hybrid algorithm outperforms GA and SA by one order of magnitude for small silicon clusters (Si6 and Si10). Next, we applied the hybrid method to study the geometry of a 20-atom silicon cluster. It was able to find an original geometry, apparently lower in energy than those previously described in literature. In principle, our procedure can be applied successfully to any molecular system. © 1998 Elsevier Science B.V.

Energy and angular momentum of the gravitational field in the teleparallel geometry

The Hamiltonian formulation of the teleparallel equivalent of general relativity is considered. Definitions of energy, momentum and angular momentum of the gravitational field arise from the integral form of the constraint equations of the theory. In particular, the gravitational energy-momentum is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. The definition for the gravitational energy is investigated in the context of the Kerr black hole. In the evaluation of the energy contained within the external event horizon of the Kerr black hole, we obtain a value strikingly close to the irreducible mass of the latter. The gravitational angular momentum is evaluated for the gravitational field of a thin, slowly rotating mass shell. © 2002 The American Physical Society.

Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

In the context of the hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes. © SISSA/ISAS 2003.

Mapping deformed hyperbolic potentials into nondeformed ones

In this work we introduce a mapping between the so-called deformed hyperbolic potentials, which are presenting a continuous interest in the last few years, and the corresponding nondeformed ones. As a consequence, we conclude that these deformed potentials do not pertain to a new class of exactly solvable potentials, but to the same one of the corresponding nondeformed ones. Notwithstanding, we can reinterpret this type of deformation as a kind of symmetry of the nondeformed potentials. © 2005 Elsevier B.V. All rights reserved.

Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.

The surface geometry of exotic nuclei

We analyze the surface geometry of the spherical even-even Ca, Ni, Sn and Pb nuclei using two approaches: The relativistic Dirac-Hartree-Bogoliubov one with several parameter sets and the non-relativistic Hartree-Fock-Bogoliubov one with the Gogny force. The proton and neutron density distributions are fitted to two-parameter Fermi density distributions to obtain the half-density radii and diffuseness parameters. Those parameters allow us to determine the nature of the neutron skins predicted by the models. The calculations are compared with existing experimental data. © 2007 American Institute of Physics.

Influence of the tool edge geometry on specific cutting energy at high-speed cutting

This paper presents specific cutting energy measurements as a function of the cutting speed and tool cutting edge geometry. The experimental work was carried out on a vertical CNC machining center with 7,500 rpm spindle rotation and 7.5 kW power. Hardened steels ASTM H13 (50 HRC) were machined at conventional cutting speed and high-speed cutting (HSC). TiN coated carbides with seven different geometries of chip breaker were applied on dry tests. A special milling tool holder with only one cutting edge was developed and the machining forces needed to calculate the specific cutting energy were recorded using a piezoelectric 4-component dynamometer. Workpiece roughness and chip formation process were also evaluated. The results showed that the specific cutting energy decreased 15.5% when cutting speed was increased up to 700%. An increase of 1 °in tool chip breaker chamfer angle lead to a reduction in the specific cutting energy about 13.7% and 28.6% when machining at HSC and conventional cutting speed respectively. Furthermore the workpiece roughness values evaluated in all test conditions were very low, closer to those of typical grinding operations (∼0.20 μm). Probable adiabatic shear occurred on chip segmentation at HSC Copyright © 2007 by ABCM.

Sharp Turán inequalities via very hyperbolic polynomials

We present new sharp inequalities for the Maclaurin coefficients of an entire function from the Laguerre-Pólya class. They are obtained by a new technique involving the so-called very hyperbolic polynomials. The results may be considered as extensions of the classical Turán inequalities. © 2010 Elsevier Inc.

Simultaneous linearization of a class of pairs of involutions with normally hyperbolic composition

In this paper we obtain a result on simultaneous linearization for a class of pairs of involutions whose composition is normally hyperbolic. This extends the corresponding result when the composition of the involutions is a hyperbolic germ of diffeomorphism. Inside the class of pairs with normally hyperbolic composition, we obtain a characterization theorem for the composition to be hyperbolic. In addition, related to the class of interest, we present the classification of pairs of linear involutions via linear conjugacy. © 2012 Elsevier Masson SAS.

Further investigation of the initial fission-track length and geometry factor in apatite fission-track thermochronology

The external detector method (EDM) is a widely used technique in fission track thermochronology (FTT) in which two different minerals are concomitantly employed: spontaneous tracks are observed in apatite and induced ones in the muscovite external detector. They show intrinsic differences in detection and etching properties that should be taken into account. In this work, new geometry factor values, g, in apatite, were obtained by directly measuring the ρed/ρis ratios and independently determined [GQR]ed/is values through the measurement of projected lengths. Five mounts, two of which were large area prismatic sections and three samples composed of random-orientation pieces have been used to determine the g-values. A side effect of applying EDM is that the value of the initial confined induced fission track, L0, is not measured in routine analyses. The L 0-value is an important parameter to quantify with good confidence the degree of annealing of the spontaneous fission tracks in unknown-age samples, and is essential for accurate thermal history modeling. The impact of using arbitrary L0-values on the inference of sample thermal history is investigated and discussed. The measurement of the L0-value for each sample to be dated using an extra irradiated apatite mount is proposed. This extra mount can be also used for determining the g value as an extension of the ρed/ρis ratio method. Eight apatite samples from crystalline basement, with grains at random orientation, were used to determine the g-values. The results found are statistically in agreement with the values found for apatite samples (from Durango, Mexico) measured in prismatic section and also measured at random orientation. There was no observable variation in efficiency regarding crystal orientation, showing that it is relatively safe using non-prismatic grains, especially in samples with paucity of grains, as it is the case of most basin samples. Implications for the ζ-calibration and for the calibration of the direct (spectrometer-based) fission-track dating are also discussed.

Approximation of hyperbolic tangent activation function using hybrid methods

Artificial Neural Networks are widely used in various applications in engineering, as such solutions of nonlinear problems. The implementation of this technique in reconfigurable devices is a great challenge to researchers by several factors, such as floating point precision, nonlinear activation function, performance and area used in FPGA. The contribution of this work is the approximation of a nonlinear function used in ANN, the popular hyperbolic tangent activation function. The system architecture is composed of several scenarios that provide a tradeoff of performance, precision and area used in FPGA. The results are compared in different scenarios and with current literature on error analysis, area and system performance. © 2013 IEEE.

Transformações de Möbius e inversões

Pós-graduação em Matemática Universitária - IGCE

Determinação das velocidades intervalares usando a teoria paraxial do raio: aproximação de segunda ordem dos tempos de trânsito

Neste trabalho foi desenvolvido um método de solução ao problema inverso para modelos sísmicos compostos por camadas homogêneas e isotrópicas separadas por superfícies suaves, que determina as velocidades intervalares em profundidade e calcula a geometria das interfaces. O tempo de trânsito é expresso como uma função de parâmetros referidos a um sistema de coordenadas fixo no raio central, que é determinada numericamente na superfície superior do modelo. Essa função é posteriormente calculada na interface anterior que limita a camada não conhecida, através de um processo que determina a função característica em profundidade. A partir da função avaliada na interface anterior se calculam sua velocidade intervalar e a geometria da superfície posterior onde tem lugar a reflexão do raio. O procedimento se repete de uma forma recursiva nas camadas mais profundas obtendo assim a solução completa do modelo, não precisando em nenhum passo informação diferente à das camadas superiores. O método foi expresso num algoritmo e se desenvolveram programas de computador, os quais foram testados com dados sintéticos de modelos que representam feições estruturais comuns nas seções geológicas, fornecendo as velocidades em profundidade e permitindo a reconstrução das interfaces. Uma análise de sensibilidade sobre os programas mostrou que a determinação da função característica e a estimação das velocidades intervalares e geometria das interfaces são feitos por métodos considerados estáveis. O intervalo empírico de aplicabilidade das correções dinâmicas hiperbólicas foi tomado como uma estimativa da ordem de magnitude do intervalo válido para a aplicação do método.

Influence of distance, geometry and number of control stations on quality of local geodetic networks for the purpose of georeferencing of rural properties

The implementation of local geodetic networks for georeferencing of rural properties has become a requirement after publication of the Georeferencing Technical Standard by INCRA. According to this standard, the maximum distance of baselines to GNSS L1 receivers is of 20 km. Besides the length of the baseline, the geometry and the number of geodetic control stations are other factors to be considered in the implementation of geodetic networks. Thus, this research aimed to examine the influence of baseline lengths higher than the regulated limit of 20 km, the geometry and the number of control stations on quality of local geodetic networks for georeferencing, and also to demonstrate the importance of using specific tests to evaluate the solution of ambiguities and on the quality of the adjustment. The results indicated that the increasing number of control stations has improved the quality of the network, the geometry has not influenced on the quality and the baseline length has influenced on the quality; however, lengths higher than 20 km has not interrupted the implementation, with GPS L1 receiver, of the local geodetic network for the purpose of georeferencing. Also, the use of different statistical tests, both for the evaluation of the resolution of ambiguities and for the adjustment, have enabled greater clearness in analyzing the results, which allow that unsuitable observations may be eliminated.