Soliton-cuspon interaction for the Camassa-Holm equation

The interaction of different kinds of solitary waves of the Camassa-Holm equation is investigated. We consider soliton-soliton, soliton-cuspon and cuspon-cuspon interactions. The description of these solutions had previously been shown to be reducible to the solution of an algebraic equation. Here we give explicit examples, numerically solving these algebraic equations and plotting the corresponding solutions. Further, we show that the interaction is elastic and leads to a shift in the position of the solitons or cuspons. We give the analytical expressions for this shift and represent graphically the coupled soliton-cuspon, soliton-soliton and cuspon-cuspon interactions.

Darboux-Egoroff metrics, rational Landau-Ginzburg potentials and the Painleve VI equation

We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.

A general treatment for the conductivity of electrolytes in the whole concentration range in aqueous and nonaqueous solutions

Despite the great importance of ion transport, most of the widely accepted models and theories are valid only in the not very practical limit of low concentrations. Aiming to extend the range of applicability to moderate concentrations, a number of modified models and equations (some approximate, some fundamented on different assumptions, and some just empirical) have been reported. In this work, a general treatment for the electrical conductivity of ionic solutions has been developed, considering the electrical conductivity as a transport phenomenon governed by dissipation and feedback. A general expression for the dependence of the specific conductivity on the solution viscosity (and indirectly on concentration), from which the whole conductivity curve can be obtained, has been derived. The validity of this general approach is demonstrated with experimental results taken from the literature for aqueous and nonaqueous solutions of electrolytes.

Bayesian approximations in randomized response model

Practical Bayesian inference depends upon detailed examination of posterior distribution. When the prior and likelihood are conjugate, this is easily carried out; however, in general, one must resort to numerical approximation. In this paper, our aim is to solve, using MAPLE, the Bayesian paradigm, for a very special data collecting procedure, known as the randomized-response technique. This allows researchers to obtain sensitive information while guaranteeing privacy to respondents. This approach intends to reduce false responses on sensitive questions. Exact methods and approximations will be compared from the accuracy point of view as well as for the computational effort.

A Bayesian Analysis of Spectral ARMA Model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Gel'fand-Levitan equation for deletion of states from Coulomb spectra

The Gel'fand-Levitan formalism is used to study how a selected set of bound states can be eliminated from the spectrum of the Coulomb potential and also how to construct a bound state in the Coulomb continuum. It is demonstrated that a sizeable quantum well can be produced by deleting a large number of levels from the s spectral series and the edge of the Coulomb potential alone can support the von Neumann-Wigner states in the continuum. © 1998 Elsevier Science B.V.

Two-dimensional integrable generalization of the Camassa-Holm equation

In this letter we discuss the (2 + 1)-dimensional generalization of the Camassa-Holm equation. We require that this generalization be, at the same time, integrable and physically derivable under the same asymptotic analysis as the original Camassa-Holm equation. First, we find the equation in a perturbative calculation in shallow-water theory. We then demonstrate its integrability and find several particular solutions describing (2 + 1) solitary-wave like solutions. © 1999 Published by Elsevier Science B.V. All rights reserved.

Galilean covariance and the Duffin-Kemmer-Petiau equation

We use a five-dimensional approach to Galilean covariance to investigate the non-relativistic Duffin-Kemmer-Petiau first-order wave equations for spinless particles. The corresponding representation is generated by five 6 × 6 matrices. We consider the harmonic oscillator as an example.

Inferences about the coefficient of correlation in the standard bivariate normal distribution

The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

A sub-national public-private strategic alliance for innovation and export development: the case of the Canadian province of Alberta's oil sands

Includes bibliography

The impact of structural reforms on growth in Latin America and the Caribbean: an empirical estimation

Includes bibliography

Measuring supply chain management practices

Purpose: This paper aims to perform an empirical investigation about the constructs and indicators of the supply chain management practices framework. Design/methodology/approach: The measuring framework proposed is based on a survey that was carried out on 107 Brazilian companies. Statistical techniques were employed to verify, validate, and test the reliability of the constructs and their indicators. To validate this framework principal component analysis and structural equation modeling techniques were used. Findings: In general, previous studies suggest six constructs for measuring the supply chain management practices framework. However, in this study a framework was achieved with four constructs of supply chain management practices, namely, supply chain (SC) integration for production planning and control (PPC) support, information sharing about products and targeting strategies, strategic relationship with customer and supplier, and support customer order. This framework has adequate levels of validity and reliability. Research limitations/implications: The main limitation of this study was that only a small sample of companies in a single sector and country were surveyed, and therefore there needs to be further research considering the special conditions in other countries. Originality/value: This study investigated statistically set indicators to discuss the topic supply chain management practices. The framework obtained has good quality of validity and reliability indicators. Thus, an alternative framework has been added to measure supply chain management practices, which is currently a popular topic in the supply chain mainstream literature. Both defined constructs and the validated indicators can be used in other studies on supply chain management. © Emerald Group Publishing Limited.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

A simple derivation of the Lindblad equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The algebraic structure behind the derivative nonlinear Schrödinger equation

The Kaup-Newell (KN) hierarchy contains the derivative nonlinear Schrödinger equation (DNLSE) amongst others interesting and important nonlinear integrable equations. In this paper, a general higher grading affine algebraic construction of integrable hierarchies is proposed and the KN hierarchy is established in terms of an Ŝℓ2Kac-Moody algebra and principal gradation. In this form, our spectral problem is linear in the spectral parameter. The positive and negative flows are derived, showing that some interesting physical models arise from the same algebraic structure. For instance, the DNLSE is obtained as the second positive, while the Mikhailov model as the first negative flows. The equivalence between the latter and the massive Thirring model is also explicitly demonstrated. The algebraic dressing method is employed to construct soliton solutions in a systematic manner for all members of the hierarchy. Finally, the equivalence of the spectral problem introduced in this paper with the usual one, which is quadratic in the spectral parameter, is achieved by setting a particular automorphism of the affine algebra, which maps the homogeneous into principal gradation. © 2013 IOP Publishing Ltd.