Periodic orbits in complex Abel equation

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On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator

The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.

The thermohydrodynamical picture of Brownian motion via a generalized Smoluchowsky equation

Via an operator continued fraction scheme, we expand Kramers equation in the high friction limit. Then all distribution moments are expressed in terms of the first momemt (particle density). The latter satisfies a generalized Smoluchowsky equation. As an application, we present the nonequilibrium thermodynamics and hydrodynamical picture for the one-dimensional Brownian motion. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q = 1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q not equal 1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.

On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Conditions for the validity of the quantum Langevin equation

From microscopic models, a Langevin equation can, in general, be derived only as an approximation. Two possible conditions to validate this approximation are studied. One is, for a linear Langevin equation, that the frequency of the Fourier transform should be close to the natural frequency of the system. The other is by the assumption of "slow" variables. We test this method by comparison with an exactly soluble model and point out its limitations. We base our discussion on two approaches. The first is a direct, elementary treatment of Senitzky. The second is via a generalized Langevin equation as an intermediate step.

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

Solvabilty of generalized Hammerstein integral equations on unbounded domains, with sign-changing kernels

In this work we study an Hammerstein generalized integral equation u(t)=∫_{-∞}^{+∞}k(t,s) f(s,u(s),u′(s),...,u^{(m)}(s))ds, where k:ℝ²→ℝ is a W^{m,∞}(ℝ²), m∈ℕ, kernel function and f:ℝ^{m+2}→ℝ is a L¹-Carathéodory function. To the best of our knowledge, this paper is the first one to consider discontinuous nonlinearities with derivatives dependence, without monotone or asymptotic assumptions, on the whole real line. Our method is applied to a fourth order nonlinear boundary value problem, which models moderately large deflections of infinite nonlinear beams resting on elastic foundations under localized external loads.

Modelos estatísticos indicadores de comportamentos associados a bem-estar térmico para matrizes pesadas

The study of female broiler breeders is of great importance for the country as poultry production is one of the largest export items, and Brazil is the second largest broiler meat exporter. Animal behavior is known as a response to the effect of several interaction factors among them the environment. In this way the internal housing environment is an element that gives hints regarding to the bird s thermal comfort. Female broiler breeder behavior, expresses in form of specific pattern the bird s health and welfare. This research had the objective of applying predictive statistical models through the use of simulation, presenting animal comfort scenarios facing distinct environmental conditions. The research was developed with data collected in a controlled environment using Hybro - PG® breeding submitted to distinct levels of temperature, three distinct types of standard ration and age. Descriptive and exploratory analysis were proceeded, and afterwards the modeling process using the Generalized Estimation Equation (GEE). The research allowed the development of the thermal comfort indicators by statistical model equations of predicting female broiler breeder behavior under distinct studied scenarios.

Quantum reflection: The invisible quantum barrier

We construct an invisible quantum barrier which represents the phenomenon of quantum reflection using available data on atom-wall and Bose-Einstein-condensate-wall reflection. We use the Abel equation to invert the data. The resulting invisible quantum barrier is double valued in both axes. We study this invisible barrier in the case of atom and Bose-Einstein condensate (BEC) reflection from a solid silicon surface. A time-dependent, one-spatial-dimension Gross-Pitaevskii equation is solved for the BEC case. We found that the BEC behaves very similarly to the single atom except for size effects, which manifest themselves in a maximum in the reflectivity at small distances from the wall. The effect of the atom-atom interaction on the BEC reflection and correspondingly on the invisible barrier is found to be appreciable at low velocities and comparable to the finite-size effect. The trapping of an ultracold atom or BEC between two walls is discussed.

THE INFLUENCE OF HIV-1 SUBTYPES C, CRF31_BC AND B ON DISEASE PROGRESSION AND INITIAL VIROLOGIC RESPONSE TO HAART IN A SOUTHERN BRAZILIAN COHORT

Background: Although most HIV-1 infections in Brazil are due to subtype B, Southern Brazil has a high prevalence of subtype C and recombinant forms, such as CRF31_BC. This study assessed the impact of viral diversity on clinical progression in a cohort of newly diagnosed HIV-positive patients. Methods: From July/2004 to December/2005, 135 HIV-infected patients were recruited. The partial pol region was subtyped by phylogeny. A generalized estimating equation (GEE) model was used to examine the relationship between viral subtype, CD4+ T cell count and viral load levels before antiretroviral therapy. Hazard ratio (Cox regression) was used to evaluate factors associated with viral suppression (viral load < 50 copies/mL at six months). Results: Main HIV-1 subtypes included B (29.4%), C (28.2%), and CRF31_BC (23.5%). Subtypes B and C showed a similar trend in CD4+ T cell decline. Comparison of non-B (C and CRF31_BC) and B subtypes revealed no significant difference in the proportion of patients with viral suppression at six months (week 24). Higher CD4+ T cell count and lower viral load were independently associated with viral suppression. Conclusion: No significant differences were found between subtypes; however, lower viral load and higher CD4+ T cell count before therapy were associated with better response.

Comparison of quality of life after stereotactic body radiotherapy and surgery for early-stage prostate cancer

Background: As the long-term efficacy of stereotactic body radiation therapy (SBRT) becomes established and other prostate cancer treatment approaches are refined and improved, examination of quality of life (QOL) following prostate cancer treatment is critical in driving both patient and clinical treatment decisions. We present the first study to compare QOL after SBRT and radical prostatectomy, with QOL assessed at approximately the same times pre- and post-treatment and using the same validated QOL instrument. Methods: Patients with clinically localized prostate cancer were treated with either radical prostatectomy (n = 123 Spanish patients) or SBRT (n = 216 American patients). QOL was assessed using the Expanded Prostate Cancer Index Composite (EPIC) grouped into urinary, sexual, and bowel domains. For comparison purposes, SBRT EPIC data at baseline, 3 weeks, 5, 11, 24, and 36 months were compared to surgery data at baseline, 1, 6, 12, 24,and 36 months. Differences in patient characteristics between the two groups were assessed using Chi-squared tests for categorical variables and t-tests for continuous variables. Generalized estimating equation (GEE) models were constructed for each EPIC scale to account for correlation among repeated measures and used to assess the effect of treatment on QOL. Results: The largest differences in QOL occurred in the first 16 months after treatment, with larger declines following surgery in urinary and sexual QOL as compared to SBRT, and a larger decline in bowel QOL following SBRT as compared to surgery. Long-term urinary and sexual QOL declines remained clinically significantly lower for surgery patients but not for SBRT patients. Conclusions: Overall, these results may have implications for patient and physician clinical decision making which are often influenced by QOL. These differences in sexual, urinary and bowel QOL should be closely considered in selecting the right treatment, especially in evaluating the value of non-invasive treatments, such as SBRT.