Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

Microvascular Lymphatic Density Analysis in Cutaneous Regressive and Nonregressive Superficial Spreading Melanomas Using the Lymphatic Marker D2-40

Background: The prognostic significance of spontaneous regression in melanoma, especially thin lesions, has been a controversial issue for the past 20 years, although recent studies suggest that extensive and late regression may be related to worse prognosis. Many data suggest that lymphangiogenesis predicts metastatic spread in melanoma. Methods: We have quantified lymphatic microvascular density (LMVD) in thin (<= 1.0 mm) superficial spreading melanomas comparing regressive and nonregressive melanomas, regressive and nonregressive areas from the same tumor, and early and late histological stages of regression in the same tumor. In addition, we tried to correlate lymphangiogenesis and tumor growth phase. We conducted histological examinations and immunohistochemical analyses using monoclonal antibody D2-40 with subsequent quantification by image analysis of 37 melanomas, 16 regressive and 21 nonregressive (controls). Results: We found higher LMVD in the late stage of regression compared with nonregressive area (internal control) of regressive melanomas. Conclusions: Our study suggest that the late stage of spontaneous regression in thin melanomas may be related to worse prognosis as it showed higher LMVD, and evidence shows that this is related with increased risk of metastatic spread. But this supposition must be confirmed by a longer follow-up for detection of lymph node metastases.

Electrical and chemical diagnostics of transformers insulation .A. Aged transformer samples

This paper describes the application of two relatively new diagnostic techniques for the determination of insulation condition in aged transformers. The techniques are (a) measurements of interfacial polarization spectra by a DC method and (b) measurements of molecular weight and its distribution by gel permeation chromatography. Several other electrical properties of the cellulose polymer were also investigated. Samples were obtained from a retired power transformer and they were analysed by the developed techniques. Six distribution transformers were also tested with the interfacial polarization spectra measurement technique, and the molecular weight of paper/pressboard samples from these transformers were also measured by the gel permeation chromatography. The variation of the results through different locations in a power transformer is discussed in this paper. The possible correlation between different measured properties was investigated and discussed in this paper.

Diffuse-regressive alterations and apoptosis of myocytes: Possible causes of myocardial dysfunction in HIV-related cardiomyopathy

Objective: To determine the frequency of cardiac alterations in necropsies of AIDS patients in pre-HAART era and better understand the pathogenesis of HIV-related cardiomyopathy. Design: Retrospective study of 94 complete necropsies. Method: Macroscopic, histopathologic (histochemical,immunohistochemical and in situ hybridization techniques) and ultra structural myocardial evaluation (23 cases). Results: Cardiac alterations were observed in 94.4%; 74% showed variable degrees of cardiac dilation not related to known cardiovascular diseases. Eighty-two percent (81.8%) of patients with biventricular dilation showed diffuse-regressive alterations (thinning and waving cardiomyocytes with increase of lipofuscin pigment granules). Myocarditis was diagnosed in 27 cases (28.7%), 16 (59.3%) of known etiology. The ultra structural study has revealed cardiomyocytes alterations (mitochondriosis, loss of myofibrils, increase in the amount of perinuclear-lipofuscin pigment granules) associated to activation signals of capillary-endothelial cells (enhancement of pseudopodia and transcellular channels). Cardiomyocytes` apoptosis was demonstrated at structural level in 10 (43.5%) patients; tumor necrosis factor alpha (TNF alpha) was detected in 17/18 cases. Conclusions: This pioneer study described the association of histopathological and ultra structural findings (thinning and waving cardiomyocytes with increase of lipofuscin pigment granules, mitochondriosis and loss of myofibrils) with different degrees of cardiac-chamber dilation probably representing a spectrum of alterations that would lead to myocardial dysfunction and development of HIV-related cardiomyopathy. Cardiomyocytes` apoptosis observed at ultra structural level and demonstration of TNF alpha associated to described alterations suggest that this cytokine plays an important role in both negative-inotropic effect and capacity to induce apoptosis through death receptor-controlled pathway. (C) 2008 Published by Elsevier Ireland Ltd.

Comparison of different nonlinear functions to describe Nelore cattle growth

This work aims to compare different nonlinear functions for describing the growth curves of Nelore females. The growth curve parameters, their (co) variance components, and environmental and genetic effects were estimated jointly through a Bayesian hierarchical model. In the first stage of the hierarchy, 4 nonlinear functions were compared: Brody, Von Bertalanffy, Gompertz, and logistic. The analyses were carried out using 3 different data sets to check goodness of fit while having animals with few records. Three different assumptions about SD of fitting errors were considered: constancy throughout the trajectory, linear increasing until 3 yr of age and constancy thereafter, and variation following the nonlinear function applied in the first stage of the hierarchy. Comparisons of the overall goodness of fit were based on Akaike information criterion, the Bayesian information criterion, and the deviance information criterion. Goodness of fit at different points of the growth curve was compared applying the Gelfand`s check function. The posterior means of adult BW ranged from 531.78 to 586.89 kg. Greater estimates of adult BW were observed when the fitting error variance was considered constant along the trajectory. The models were not suitable to describe the SD of fitting errors at the beginning of the growth curve. All functions provided less accurate predictions at the beginning of growth, and predictions were more accurate after 48 mo of age. The prediction of adult BW using nonlinear functions can be accurate when growth curve parameters and their (co) variance components are estimated jointly. The hierarchical model used in the present study can be applied to the prediction of mature BW in herds in which a portion of the animals are culled before adult age. Gompertz, Von Bertalanffy, and Brody functions were adequate to establish mean growth patterns and to predict the adult BW of Nelore females. The Brody model was more accurate in predicting the birth weight of these animals and presented the best overall goodness of fit.

Quantum nonlinear dynamics of continuously measured systems

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more diner comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system, in this paper we give a theory of such measurement and show that chaotic behavior in classical systems fan be reproduced by continuously measured quantum systems.

Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

Light guiding light: Nonlinear refraction in rubidium vapor

Recently there has been experimental and theoretical interest in cross-dispersion effects in rubidium vapor, which allows one beam of light to be guided by another. We present theoretical results which account for the complications created by the D line hyperfine structure of rubidium as well as the presence of the two major isotopes of rubidium. This allows the complex frequency dependence of the effects observed in our experiments to be understood and lays the foundation for future studies of nonlinear propagation.

Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.