115 resultados para Trigonometry Formulas


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Hughston has shown that projective pure spinors can be used to construct massless solutions in higher dimensions, generalizing the four-dimensional twistor transform of Penrose. In any even (euclidean) dimension d = 2n, projective pure spinors parameterize the coset space SO(2n)/U(n), which is the space of all complex structures on ℝ2n. For d = 4 and d = 6, these spaces are ℂℙ1 and ℂℙ3 and the appropriate twistor transforms can easily be constructed. In this paper, we show how to construct the twistor transform for d > 6 when the pure spinor satisfies nonlinear constraints, and present explicit formulas for solutions of the massless field equations. © SISSA/ISAS 2005.

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With the considerable increase of the losses in electric utilities of developing countries, such as Brazil, there is an investigation for loss calculation methodologies, considering both technical (inherent of the system) and non-technical (usually associated to the electricity theft) losses. In general, all distribution networks know the load factor, obtained by measuring parameters directly from the network. However, the loss factor, important for the energy loss cost calculation, can only be obtained in a laborious way. Consequently, several formulas have been developed for obtaining the loss factor. Generally, it is used the expression that relates both factors, through the use of a coefficient k. Last reviews introduce a range of factor k within 0.04 - 0.30. In this work, an analysis with real life load curves is presented, determining new values for the coefficient k in a Brazilian electric utility. © 2006 IEEE.

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We present general explicit expressions for a shell-model calculation of the vector hypernuclear parameter in nonmesonic weak decay. We use a widely accepted effective coupling Hamiltonian involving the exchange of the complete pseudoscalar and vector meson octets (π, η, K, ρ, ω, K*). In contrast to the approximated formula widely used in the literature, we correctly treat the contribution of transitions originated from single-proton states beyond the s-shell. Exact and simple analytical expressions are obtained for the particular cases of Λ 5He and Λ 12C, within the one-pion-exchange model. Numerical computations of the asymmetry parameter, aΛ, are presented. Our results show a qualitative agreement with other theoretical estimates but also a contradiction with recent experimental determinations. Our simple analytical formulas provide a guide in searching the origin of such discrepancies, and they will be useful for helping to solve the hypernuclear weak decay puzzle.

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The pCT deals with relatively thick targets like the human head or trunk. Thus, the fidelity of pCT as a tool for proton therapy planning depends on the accuracy of physical formulas used for proton interaction with thick absorbers. Although the actual overall accuracy of the proton stopping power in the Bethe-Bloch domain is about 1%, the analytical calculations and the Monte Carlo simulations with codes like TRIM/SRIM, MCNPX and GEANT4 do not agreed with each other. A tentative to validate the codes against experimental data for thick absorbers bring some difficulties: only a few data is available and the existing data sets have been acquired at different initial proton energies, and for different absorber materials. In this work we compare the results of our Monte Carlo simulations with existing experimental data in terms of reduced calibration curve, i.e. the range - energy dependence normalized on the range scale by the full projected CSDA range for given initial proton energy in a given material, taken from the NIST PSTAR database, and on the final proton energy scale - by the given initial energy of protons. This approach is almost energy and material independent. The results of our analysis are important for pCT development because the contradictions observed at arbitrary low initial proton energies could be easily scaled now to typical pCT energies. © 2010 American Institute of Physics.

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Cytogenetic analyses were performed in four species of the Hypostominae subfamily, three from Hypostomus (Hypostomini) genus and Rhinelepis aspera (Rhinelepini). Three populations of Hypostomus ancistroides were analyzed, which had 2n=68 chromosomes, but presented different karyotype formulas. Hypostomus regani and H. strigaticeps, both from Ivaí river, showed 2n=72 chromosomes with two distinct cytotypes. In turn, R. aspera of the upper Paraná river basin presented 2n=54 chromosome. Multiple Nucleolar Organizer Regions (NORs) have been evidenced by silver nitrate staining in species of Hypostomus and single NOR in R. aspera. The observed variation in the chromosome number and the marked variability in karyotype formulas and NORs reveal a certain amount of karyotype variation in the genus Hypostomus suggesting the probable existence of cryptic species with independent chromosome traits. Therefore, our data can be of great value in discriminating species and understanding their chromosomal evolution.

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We solve the three-body bound-state problem in three dimensions for mass imbalanced systems of two identical bosons and a third particle in the universal limit where the interactions are assumed to be of zero range. The system displays the Efimov effect and we use the momentum-space wave equation to derive formulas for the scaling factor of the Efimov spectrum for any mass ratio assuming either that two or three of the two-body subsystems have a bound state at zero energy. We consider the single-particle momentum distribution analytically and numerically and analyze the tail of the momentum distribution to obtain the three-body contact parameter. Our findings demonstrate that the functional form of the three-body contact term depends on the mass ratio, and we obtain an analytic expression for this behavior. To exemplify our results, we consider mixtures of lithium with either two caesium or rubidium atoms which are systems of current experimental interest. © 2013 American Physical Society.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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

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Pós-graduação em Agronomia (Energia na Agricultura) - FCA