Inversely symmetric interpolatory quadrature rules

We consider interpolatory quadrature rules with nodes and weights satisfying symmetric properties in terms of the division operator. Information concerning these quadrature rules is obtained using a transformation that exists between these rules and classical symmetric interpolatory quadrature rules. In particular, we study those interpolatory quadrature rules with two fixed nodes. We obtain specific examples of such quadrature rules.

Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.

The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

Quasi-homologous spherically symmetric branes and their symmetry breaking

We revisit the dynamical system-based approach of spherically symmetric vacuum braneworlds, pointing out and studying the existence of a transcritical bifurcation as the dark pressure parameter changes its sign, we analyze some consequences of not discard the brane cosmological constant. For instance, it is noteworthy that the existence of an isothermal state equation between the dark fluid parameters cannot be obtained via the requirement of a quasi-homologous symmetry of the vacuum. © 2013 Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica.

PT-symmetric coupler with chi((2)) nonlinearity

We introduce the notion of a PT-symmetric dimer with a chi((2)) nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain and loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear solutions occur in two different ways depending on whether the first-or the second-harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur, including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical time-evolution simulations exploring the evolution of the different configurations, when unstable.

Classic tests of General Relativity described by brane-based spherically symmetric solutions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Asymmetric and Symmetric Triazenido Cyclopalladated Complexes: Synthesis, Structural Analysis and DFT Calculations

The reaction of [Pd{dmba}(l-N3)]2 (dmba = N,N-dimethylbenzylamine) with 1-(2-fluorophenyl)-3-(4- nitrophenyl)triazenido (L1 ) or 1,3-bis(4-nitrophenyl)triazenido (L2 ) anions, in methanol, and subsequent treatment with pyridine (py) allows the preparation of the corresponding cyclopalladated compounds [Pd(dmba)(L1 )(py)] (1) and [Pd(dmba)(L2 )(py)]py (2). The acentric mononuclear entities of (1) and (2) are connected by weak intermolecular non-classical CAHC hydrogen bonds, which results in 2-D arrangements by translation, along the [1 0 0] and [0 01] crystallographic directions, respectively.

Bounds for the zeros of symmetric kravchuk polynomials

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

Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrodinger equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Integrable deformations of strings on symmetric spaces

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

Conservation laws for Z(N) symmetric quantum spin models and their exact ground state energies

We derive an infinite set of conserved charges for some Z(N) symmetric quantum spin models by constructing their Lax pairs. These models correspond to the Potts model, Ashkin-Teller model and the particular set of self-dual Z(N) models solved by Fateev and Zamolodchikov [6]. The exact ground state energy for this last family of hamiltonians is also presented. © 1986.

Quantum exchange interaction of spherically symmetric plasmoids

We study nano-sized spherically symmetric plasma structures which are radial nonlinear oscillations of electrons in plasma. The effective interaction of these plasmoids via quantum exchange forces between ions is described. We calculate the energy of this interaction for the case of a dense plasma. The conditions when the exchange interaction is attractive are examined and it is shown that separate plasmoids can form a single object. The application of our results to the theoretical description of stable atmospheric plasma structures is considered. (C) 2012 Elsevier Ltd. All rights reserved.

Local power properties of some asymptotic tests in symmetric linear regression models

In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of symmetric linear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2011 Elsevier B.V. All rights reserved.

The discriminants associated to isotropy representations of symmetric spaces

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.

Mixed-valence state of symmetric diruthenium complexes: synthesis, characterization, and electron transfer investigation

Complexes of the type {[(pyS)Ru(NH3)(4)](2)-mu-L}(n), where pyS = 4-mercaptopyridine, L = 4,4'-dithiodipyridine (pySSpy), pyrazine (pz) and 1,4-dicyanobenzene (DCB), and n = +4 and +5 for fully reduced and mixed-valence complexes, respectively, were synthesized and characterized. Electrochemical data showed that there is electron communication between the metal centers with comproportionation constants of 33.2, 1.30 x 10(8) and 5.56 x 10(5) for L = pySSpy, pz and DCB, respectively. It was also observed that the electronic coupling between the metal centers is affected by the p-back-bonding interaction toward the pyS ligand. Raman spectroscopy showed a dependence of the intensity of the vibrational modes on the exciting radiations giving support to the assignments of the electronic transitions. The degree of electron communication between the metal centers through the bridging ligands suggests that these systems can be molecular wire materials.