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.

Refining specifications to logic programs

The refinement calculus provides a framework for the stepwise development of imperative programs from specifications. In this paper we study a refinement calculus for deriving logic programs. Dealing with logic programs rather than imperative programs has the dual advantages that, due to the expressive power of logic programs, the final program is closer to the original specification, and each refinement step can achieve more. Together these reduce the overall number of derivation steps. We present a logic programming language extended with specification constructs (including general predicates, assertions, and types and invariants) to form a wide-spectrum language. General predicates allow non-executable properties to be included in specifications. Assertions, types and invariants make assumptions about the intended inputs of a procedure explicit, and can be used during refinement to optimize the constructed logic program. We provide a semantics for the extended logic programming language and derive a set of refinement laws. Finally we apply these to an example derivation.

Model for Differential Nursing Diagnosis of Alterations in Urinary Elimination Based on Fuzzy Logic

Nursing diagnoses associated with alterations of urinary elimination require different interventions, Nurses, who are not specialists, require support to diagnose and manage patients with disturbances of urine elimination. The aim of this study was to present a model based on fuzzy logic for differential diagnosis of alterations in urinary elimination, considering nursing diagnosis approved by the North American Nursing Diagnosis Association, 2001-2002. Fuzzy relations and the maximum-minimum composition approach were used to develop the system. The model performance was evaluated with 195 cases from the database of a previous study, resulting in 79.0% of total concordance and 19.5% of partial concordance, when compared with the panel of experts. Total discordance was observed in only three cases (1.5%). The agreement between model and experts was excellent (kappa = 0.98, P < .0001) or substantial (kappa = 0.69, P < .0001) when considering the overestimative accordance (accordance was considered when at least one diagnosis was equal) and the underestimative discordance (discordance was considered when at least one diagnosis was different), respectively. The model herein presented showed good performance and a simple theoretical structure, therefore demanding few computational resources.

Developing logic programs from specifications using stepwise refinement

In this paper we demonstrate a refinement calculus for logic programs, which is a framework for developing logic programs from specifications. The paper is written in a tutorial-style, using a running example to illustrate how the refinement calculus is used to develop logic programs. The paper also presents an overview of some of the advanced features of the calculus, including the introduction of higher-order procedures and the refinement of abstract data types.

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.