Massless and massive one-loop three-point functions in negative dimensional approach

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of the external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time is D. Our approach reproduces the known results; it produces other solutions as yet unknown in the literature as well. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories.

One-loop n-point equivalence among negative-dimensional, Mellin-Barnes and Feynman parametrization approaches to Feynman integrals

We show that at one-loop order, negative-dimensional, Mellin-Barnes (MB) and Feynman parametrization (FP) approaches to Feynman loop integral calculations are equivalent. Starting with a generating functional, for two and then for n-point scalar integrals, we show how to reobtain MB results, using negative-dimensional and FP techniques. The n-point result is valid for different masses, arbitrary exponents of propagators and dimension.

On Clifford subalgebras, spacetime splittings and applications

Z(2)-gradings of Clifford algebras are reviewed and we shall be concerned with an alpha-grading based on the structure of inner automorphisms, which is closely related to the spacetime splitting, if we consider the standard conjugation map automorphism by an arbitrary, but fixed, splitting vector. After briefly sketching the orthogonal and parallel components of products of differential forms, where we introduce the parallel [orthogonal] part as the space [time] component, we provide a detailed exposition of the Dirac operator splitting and we show how the differential operator parallel and orthogonal components are related to the Lie derivative along the splitting vector and the angular momentum splitting bivector. We also introduce multivectorial-induced alpha-gradings and present the Dirac equation in terms of the spacetime splitting, where the Dirac spinor field is shown to be a direct sum of two quaternions. We point out some possible physical applications of the formalism developed.

Bose-Einstein condensates with inhomogeneous scattering length in one and two dimensions

We report on investigations of the properties of bright solitons in Bose-Einstein condensates in the presence of point-like spatial inhomogeneities, in one and two dimensions. By considering an analytical variational approach and full numerical simulations, we describe such processes due to interactions between the soliton and the inhomogeneity as the trapping, reflection, and transmission of bright matter solitons. We also study the critical number of particles as a function of the magnitude of the impurity.

The two-loop massless (lambda/4!)phi(4) model in nontranslational invariant domain

We study the (lambda/4!)phi(4) massless scalar field theory in a four-dimensional Euclidean space, where all but one of the coordinates are unbounded. We are considering Dirichlet boundary conditions in two hyperplanes, breaking the translation invariance of the system. We show how to implement the perturbative renormalization up to two-loop level of the theory. First, analyzing the full two and four-point functions at the one-loop level, we show that the bulk counterterms are sufficient to render the theory finite. Meanwhile, at the two-loop level, we must also introduce surface counterterms in the bare Lagrangian in order to make finite the full two and also four-point Schwinger functions. (c) 2006 American Institute of Physics.

Pure spinor superspace identities for massless four-point kinematic factors

Using the pure spinor formalism we prove identities which relate the tree-level, one-loop and two-loop kinematic factors for massless four-point amplitudes. From these identities it follows that the complete supersymmetric one- and two-loop amplitudes are immediately known once the tree-level kinematic factor is evaluated. In particular, the two-loop equivalence with the RNS formalism (up to an overall coefficient) is obtained as a corollary.

Notes on the overall coefficient of the two-loop superstring amplitude using pure spinor

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

Short comments on self-synchronization of two non-ideal sources supported by a flexible portal frame structure

A practical problem of synchronization of a non-ideal (i.e. when the excitation is influenced by the response of the system) and non-linear vibrating system was posed and investigated by means of numerical simulations. Two rotating unbalanced motors compose the mathematical model considered here with limited power supply mounted on the horizontal beam of a simple portal frame. As a starting point, the problem is reduced to a four-degrees-of-freedom model and its equations of motion, derived elsewhere via a Lagrangian approach, are presented. The numerical results show the expected phenomena associated with the passage through resonance with limited power. Further, for a two-to-one relationship between the frequencies associated with the first symmetric mode and the sway mode, by using the variation of torque constants, the control of the self-synchronization and synchronization (in the system) are observed at certain levels of excitations.

THE EFFECT of WEAK DISSIPATION IN TWO-DIMENSIONAL MAPPING

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the Betti number of the union of two generic map images

Let f: M --> N and g: K --> N be generic differentiable maps of compact manifolds without boundary into a manifold such that their intersection satisfies a certain transversality condition. We show, under a certain cohomological condition, that if the images f(M) and g(K) intersect, then the (upsilon + 1)th Betti number of their union is strictly greater than the sum of their (upsilon + 1)th Betti numbers, where upsilon = dim M + dim K - dim N. This result is applied to the study of coincidence sets and fixed point sets. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Effect of maltodextrin on the freezing point and thermal conductivity of uvaia pulp (Eugenia piriformis Cambess)

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

Karyotype description of two Neotropical Psittacidae species: the endangered Hyacinth Macaw, Anodorhynchus hyacinthinus, and the Hawk-headed Parrot, Deroptyus accipitrinus (Psittaciformes: Aves), and its significance for conservation plans

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Short term hydroelectric scheduling combining network flow and interior point approaches

In this paper, short term hydroelectric scheduling is formulated as a network flow optimization model and solved by interior point methods. The primal-dual and predictor-corrector versions of such interior point methods are developed and the resulting matrix structure is explored. This structure leads to very fast iterations since it avoids computation and factorization of impedance matrices. For each time interval, the linear algebra reduces to the solution of two linear systems, either to the number of buses or to the number of independent loops. Either matrix is invariant and can be factored off-line. As a consequence of such matrix manipulations, a linear system which changes at each iteration has to be solved, although its size is reduced to the number of generating units and is not a function of time intervals. These methods were applied to IEEE and Brazilian power systems, and numerical results were obtained using a MATLAB implementation. Both interior point methods proved to be robust and achieved fast convergence for all instances tested. (C) 2004 Elsevier Ltd. All rights reserved.

CURRENT-ALGEBRA OF SUPER WZNW MODELS

We derive the current algebra of supersymmetric principal chiral models with a Wess-Zumino term. At the critical point one obtains two commuting super-affine Lie algebras as expected, but, in general, them are intertwining fields connecting both right and left sectors, analogously to the bosonic case. Moreover, in the present supersymmetric extension we have a quadratic algebra, rather than an affine Lie algebra, due to the mixing between bosonic and fermionic fields; the purely fermionic sector displays an affine Lie algebra as well.

Evaluation of shear bond strength at the interface of two porcelains and pure titanium injected into the casting mold at three different temperatures

Statement of problem. Titanium has physical and mechanical properties, which have led to its increased use in dental prostheses despite casting difficulties due to high melting point and formation of oxide layers which affect the metal-ceramic bond strength.Purpose. This in vitro study evaluated the shear bond strength of the interface of 2 dental porcelains and pure titanium injected into a mold at 3 different temperatures.Material and methods. Using commercially pure (cp) titanium bars (Titanium, Grade I) melted at 1668degreesC and cast at mold temperatures of 430degreesC, 700degreesC or 900degreesC, 60 specimens were machined to 4 x 4 mm, with a base of 5 x 1 mm. The 4-mm surfaces were airborne-particle abraded with 100 mum aluminum oxide before applying and firing the bonding agent and evaluating the 2 porcelains (Triceram/Triline ti and Vita Titankeramik). Ten specimens were prepared for each temperature and porcelain combination Shear bond testing was performed in a universal testing machine, with a 500-kg load cell and crosshead speed of 0.5 mm/min. The specimens were loaded until failure. The interfaces of representative fractured specimens of each temperature were examined with a scanning electron microscope (SEM) and energy dispersive spectrometer (EDS). Data for shear bond strength (MPa) were statistically analyzed by 2-way ANOVA and the Tukey test (alpha = .05).Results. The results showed significant differences for the metal/porcelain interaction effect (P = .0464). There were no significant differences for the 2 porcelains (P = .4250). The Tukey test showed a significant difference between the pair cp Ti 430degreesC Triceram and cp Ti 900degreesC Triceram, with respective mean values and SDs of 59.74 +/- 11.62 and 34.03 +/- 10.35 MPa.Conclusion. Triceram porcelain showed a bond strength decrease with an increase in the mold temperature for casting titanium. The highest bond strength for Vita porcelain and the best metal-ceramic interface observed with the SEM were found with the mold temperature of 700degreesC.