Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A generalized alternating-direction implicit scheme for incompressible magnetohydrodynamic viscous flows at low magnetic Reynolds number

This paper presents numerical simulations of incompressible fluid flows in the presence of a magnetic field at low magnetic Reynolds number. The equations governing the flow are the Navier-Stokes equations of fluid motion coupled with Maxwell's equations of electromagnetics. The study of fluid flows under the influence of a magnetic field and with no free electric charges or electric fields is known as magnetohydrodynamics. The magnetohydrodynamics approximation is considered for the formulation of the non-dimensional problem and for the characterization of similarity parameters. A finite-difference technique is used to discretize the equations. In particular, an extension of the generalized Peaceman and Rachford alternating-direction implicit (ADI) scheme for simulating two-dimensional fluid flows is presented. The discretized conservation equations are solved in stream function-vorticity formulation. We compare the ADI and generalized ADI schemes, and show that the latter is more efficient in simulating low Reynolds number and magnetic Reynolds number problems. Numerical results demonstrating the applicability of this technique are also presented. The simulation of incompressible magneto hydrodynamic fluid flows is illustrated by numerical solution for two-dimensional cases. (c) 2007 Elsevier B.V. All rights reserved.

Generalized point interactions in one-dimensional quantum mechanics

There is a four-parameter family of point interactions in one-dimensional quantum mechanics. They represent all possible self-adjoint extensions of the kinetic energy operator. If time-reversal invariance is imposed, the number of parameters is reduced to three. One of these point interactions is the familiar delta function potential but the other generalized ones do not seem to be widely known. We present a pedestrian approach to this subject and comment on a recent controversy in the literature concerning the so-called delta' interaction. We emphasize that there is little resemblance between the delta' interaction and what its name suggests.

A homological version of the implicit function theorem

Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X is an open topological group in X and we use the classical topological group theory to conclude that this set is a Lie group.

Kinetics of the polarization reversal process in a non-constant applied electric field and the generalized superposition principle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Generalized polarizabilities and electroexcitation of the nucleon

Generalized nucleon polarizabilities for virtual photons can be defined in terms of electroproduction cross sections as function of the 4-momentum transfer Q2. In particular, the sum of the generalized electric and magnetic polarizabilities ∑ = α + β and the spin polarizability γ can be expressed by virtual photon absorption cross sections integrated over the excitation energy. These quantities have been calculated within the framework of the recently developed unitary isobar model for pion photo- and electroproduction on the proton, which describes the available experimental data up to an excitation energy of about 1 GeV. Our results have been compared to the predictions of chiral perturbation theory. © 1999 Elsevier Science B.V. All rights reserved.

Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a simpler version of the algebra G,(Ω). Although this subalgebra does not contain, in canonical way, the space D′(Ω) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

On the resolution of the generalized nonlinear complementarity problem

Minimization of a differentiable function subject to box constraints is proposed as a strategy to solve the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone. It is not necessary to calculate projections that complicate and sometimes even disable the implementation of algorithms for solving these kinds of problems. Theoretical results that relate stationary points of the function that is minimized to the solutions of the GNCP are presented. Perturbations of the GNCP are also considered, and results are obtained related to the resolution of GNCPs with very general assumptions on the data. These theoretical results show that local methods for box-constrained optimization applied to the associated problem are efficient tools for solving the GNCP. Numerical experiments are presented that encourage the use of this approach.

Necessary and sufficient condition for generalized passivity, passification and application to multivariable adaptive systems

Recently, a generalized passivity concept for linear multivariable systems was obtained which allows circumventing the restrictiveness of the usual passivity concept. The latter is associated with the classical SPR (Strictly Positive Real) condition whereas the new concept of passivity is associated with the so called WSPR condition and its advantage in multivariable systems is that it does not require a restrictive symmetry condition of SPR systems. As a result, it allows the design of multivariable adaptive control that, unlike some existing factorization approaches, does not imply in additional overparameterization of the adaptive controller. In this paper, we complete a previously established WSPR sufficient condition and prove that it is also necessary. We also propose some methods of passification by either premultiplying the system output tracking error vector or the system input vector by an adequate passifying matrix multiplier, so that the resulting input/output transfer function becomes WSPR. The efficiency of our proposals are illustrated by simulation utilizing a well known robotics adaptive visual servoing problem. © 2011 IFAC.

Batalin-Fradkin-Vilkovisky quantization of the generalized scalar electrodynamics

This work comprises a study upon the quantization and the renormalizability of the generalized electrodynamics of spinless charged particles (mesons), namely, the generalized scalar electrodynamics (GSQED4). The theory is quantized in the covariant framework of the Batalin-Fradkin-Vilkovisky method. Thereafter, the complete Green's functions are obtained through functional methods and a proper discussion on the theory's renormalizability is also given. Next, we present the computation and further discussion on the radiative correction at α order; and, as it turns out, an unexpected mP-dependent divergence on the mesonic sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory, we also give a diagrammatic discussion on the photon self-energy at α2 order, where we observe contributions from the meson self-energy function. Afterwards, we present the expressions of the counterterms and effective coupling of the theory, obtaining from the latter an energy range where the theory is defined by m2≤k2

A Spatial and Temporal Prediction Model of Corn Grain Yield as a Function of Soil Attributes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Higher order turán inequalities for the Riemann ξ-function

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