Virasoro Action on Imaginary Verma Modules and the Operator Form of the KZ-Equation

We define the Virasoro algebra action on imaginary Verma modules for affine and construct an analogue of the Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a realization of imaginary Verma modules in terms of sums of partial differential operators.

Equation of Motion Governing the Dynamics of Vertically Collapsing Buildings

The present paper aims at contributing to a discussion, opened by several authors, on the proper equation of motion that governs the vertical collapse of buildings. The most striking and tragic example is that of the World Trade Center Twin Towers, in New York City, about 10 years ago. This is a very complex problem and, besides dynamics, the analysis involves several areas of knowledge in mechanics, such as structural engineering, materials sciences, and thermodynamics, among others. Therefore, the goal of this work is far from claiming to deal with the problem in its completeness, leaving aside discussions about the modeling of the resistive load to collapse, for example. However, the following analysis, restricted to the study of motion, shows that the problem in question holds great similarity to the classic falling-chain problem, very much addressed in a number of different versions as the pioneering one, by von Buquoy or the one by Cayley. Following previous works, a simple single-degree-of-freedom model was readdressed and conceptually discussed. The form of Lagrange's equation, which leads to a proper equation of motion for the collapsing building, is a general and extended dissipative form, which is proper for systems with mass varying explicitly with position. The additional dissipative generalized force term, which was present in the extended form of the Lagrange equation, was shown to be derivable from a Rayleigh-like energy function. DOI: 10.1061/(ASCE)EM.1943-7889.0000453. (C) 2012 American Society of Civil Engineers.

Testing allele homogeneity: the problem of nested hypotheses

Background: The evaluation of associations between genotypes and diseases in a case-control framework plays an important role in genetic epidemiology. This paper focuses on the evaluation of the homogeneity of both genotypic and allelic frequencies. The traditional test that is used to check allelic homogeneity is known to be valid only under Hardy-Weinberg equilibrium, a property that may not hold in practice. Results: We first describe the flaws of the traditional (chi-squared) tests for both allelic and genotypic homogeneity. Besides the known problem of the allelic procedure, we show that whenever these tests are used, an incoherence may arise: sometimes the genotypic homogeneity hypothesis is not rejected, but the allelic hypothesis is. As we argue, this is logically impossible. Some methods that were recently proposed implicitly rely on the idea that this does not happen. In an attempt to correct this incoherence, we describe an alternative frequentist approach that is appropriate even when Hardy-Weinberg equilibrium does not hold. It is then shown that the problem remains and is intrinsic of frequentist procedures. Finally, we introduce the Full Bayesian Significance Test to test both hypotheses and prove that the incoherence cannot happen with these new tests. To illustrate this, all five tests are applied to real and simulated datasets. Using the celebrated power analysis, we show that the Bayesian method is comparable to the frequentist one and has the advantage of being coherent. Conclusions: Contrary to more traditional approaches, the Full Bayesian Significance Test for association studies provides a simple, coherent and powerful tool for detecting associations.

Three dimensional Lifshitz black hole and the Korteweg-de Vries equation

We consider a solution of three dimensional New Massive Gravity with a negative cosmological constant and use the AdS/CTF correspondence to inquire about the equivalent two dimensional model at the boundary. We conclude that there should be a close relation of the theory with the Korteweg-de Vries equation. (C) 2012 Elsevier B.V..All rights reserved.

Additional scaled solutions to Richards' equation for infiltration and drainage

Warrick and Hussen developed in the nineties of the last century a method to scale Richards' equation (RE) for similar soils. In this paper, new scaled solutions are added to the method of Warrick and Hussen considering a wider range of soils regardless of their dissimilarity. Gardner-Kozeny hydraulic functions are adopted instead of Brooks-Corey functions used originally by Warrick and Hussen. These functions allow to reduce the dependence of the scaled RE on the soil properties. To evaluate the proposed method (PM), the scaled RE was solved numerically using a finite difference method with a fully implicit scheme. Three cases were considered: constant-head infiltration, constant-flux infiltration, and drainage of an initially uniform wet soil. The results for five texturally different soils ranging from sand to clay (adopted from the literature) showed that the scaled solutions were invariant to a satisfactory degree. However, slight deviations were observed mainly for the sandy soil. Moreover, the scaled solutions deviated when the soil profile was initially wet in the infiltration case or when deeply wet in the drainage condition. Based on the PM, a Philip-type model was also developed to approximate RE solutions for the constant-head infiltration. The model showed a good agreement with the scaled RE for the same range of soils and conditions, however only for Gardner-Kozeny soils. Such a procedure reduces numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils. (C) 2011 Elsevier B.V. All rights reserved.

Invariant Solutions of Richards' Equation for Water Movement in Dissimilar Soils

Scaling methods allow a single solution to Richards' equation (RE) to suffice for numerous specific cases of water flow in unsaturated soils. During the past half-century, many such methods were developed for similar soils. In this paper, a new method is proposed for scaling RE for a wide range of dissimilar soils. Exponential-power (EP) functions are used to reduce the dependence of the scaled RE on the soil hydraulic properties. To evaluate the proposed method, the scaled RE was solved numerically considering two test cases: infiltration into relatively dry soils having initially uniform water content distributions, and gravity-dominant drainage occurring from initially wet soil profiles. Although the results for four texturally different soils ranging from sand to heavy clay (adopted from the UNSODA database) showed that the scaled solution were invariant for a wide range of flow conditions, slight deviations were observed when the soil profile was initially wet in the infiltration case or deeply wet in the drainage case. The invariance of the scaled RE makes it possible to generalize a single solution of RE to many dissimilar soils and conditions. Such a procedure reduces the numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils.

RegCM3 nested in HadAM3 scenarios A2 and B2: projected changes in extratropical cyclogenesis, temperature and precipitation over the South Atlantic Ocean

The RegCM3 (Regional Climate Model-version 3) was nested in HadAM3 model to simulate present (1975-1989, referred hereafter as RegHad) and two future climate scenarios (A2 and B2 from 2071 to 2085, referred as RegA2 and RegB2) over the South America (SA) and South Atlantic Ocean (SAO). Projected changes in the air temperature, precipitation, low level circulation and cyclogenesis climatology were investigated. The cyclogenesis were identified using an automatic scheme for tracking based on the minimum of relative vorticity (zeta) from 10-m height wind. During summer, a general decrease (increase) in the precipitation is projected by RegA2 and RegB2 over the northeastern SA (center-west and south Brazil, north Argentina and Uruguay). For winter, an anomalous low level anticyclonic circulation is associated with the reduction in the rainfall over the central part of southern Brazil in RegA2 and RegB2 scenarios. Similar to HadAM3, RegCM3 projects larger warming in A2 scenario. For the present climate, when compared to HadAM3, RegHad defines better both the location of the main cyclogenetic areas and its annual cycle near southwestern SAO. The projections indicate a reduction in the total number of cyclones of -7.2% and -4.7% for RegA2 and RegB2, respectively, while HadAM3 reduction is -4.5% for both scenarios. The decrease is larger for initially intense cyclones (zeta <=-<= 2.5 x 10(-5) s-(1)): -20.9% (RegA2) and -11.3% (RegB2). For the lifetime, distance traveled and mean velocity of the cyclones, the A2 and B2 scenarios present mean values close to the present climate ( 3 days, 1900 km, and 9 m s(-1), respectively). Regarding the initial mean vorticity of the systems, RegB2 simulates values similar to the present climate, but they are initially weaker in RegA2. In general, RegA2 and RegB2 show a large decrease in the number of cyclones over the southern SAO due to an anticyclonic anomaly covering SAO between 30-55A degrees S. The reduction is larger in the scenario with higher concentrations of greenhouse gases (RegA2).

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.

Exponential stability for a plate equation with p-Laplacian and memory terms

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, utt+?2u-?pu+?0tg(t-s)?u(s)ds-?ut+f(u)=0inOXR+, with simply supported boundary condition, where O is a bounded domain of RN, g?>?0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows.

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.

Estimating total body fat using a skinfold prediction equation in Brazilian children

Background: The double burden of obesity and underweight is increasing in developing countries and simple methods for the assessment of fat mass in children are needed. Aim: To develop and validate a new anthropometric predication equation for assessment of fat mass in children. Subjects and methods: Body composition was assessed in 145 children aged 9.8 +/- 1.3 (SD) years from Sao Paulo, Brazil using dual energy X-ray absorptiometry (DEXA) and skinfold measurements. The study sample was divided into development and validation sub-sets to develop a new prediction equation for FM (PE). Results: Using multiple linear regression analyses, the best equation for predicting FM (R-2 - 0.77) included body weight, triceps skinfold, height, gender and age as independent variables. When cross-validated, the new PE was valid in this sample (R-2 = 0.80), while previously published equations were not. Conclusion: The PE was more valid for Brazilian children that existing equations, but further studies are needed to assess the validity of this PE in other populations.

New Equation for Prediction of Reverse Remodeling after Cardiac Resynchronization Therapy

Objectives: To integrate data from two-dimensional echocardiography (2D ECHO), three-dimensional echocardiography (3D ECHO), and tissue Doppler imaging (TDI) for prediction of left ventricular (LV) reverse remodeling (LVRR) after cardiac resynchronization therapy (CRT). It was also compared the evaluation of cardiac dyssynchrony by TDI and 3D ECHO. Methods: Twenty-four consecutive patients with heart failure, sinus rhythm, QRS = 120 msec, functional class III or IV and LV ejection fraction (LVEF) = 0.35 underwent CRT. 2D ECHO, 3D ECHO with systolic dyssynchrony index (SDI) analysis, and TDI were performed before, 3 and 6 months after CRT. Cardiac dyssynchrony analyses by TDI and SDI were compared with the Pearson's correlation test. Before CRT, a univariate analysis of baseline characteristics was performed for the construction of a logistic regression model to identify the best predictors of LVRR. Results: After 3 months of CRT, there was a moderate correlation between TDI and SDI (r = 0.52). At other time points, there was no strong correlation. Nine of twenty-four (38%) patients presented with LVRR 6 months after CRT. After logistic regression analysis, SDI (SDI > 11%) was the only independent factor in the prediction of LVRR 6 months of CRT (sensitivity = 0.89 and specificity = 0.73). After construction of receiver operator characteristic (ROC) curves, an equation was established to predict LVRR: LVRR =-0.4LVDD (mm) + 0.5LVEF (%) + 1.1SDI (%), with responders presenting values >0 (sensitivity = 0.67 and specificity = 0.87). Conclusions: In this study, there was no strong correlation between TDI and SDI. An equation is proposed for the prediction of LVRR after CRT. Although larger trials are needed to validate these findings, this equation may be useful to candidates for CRT. (Echocardiography 2012;29:678-687)

STRUCTURE AND BIFURCATION OF PULLBACK ATTRACTORS IN A NON-AUTONOMOUS CHAFEE-INFANTE EQUATION

The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, u(t) = u(xx) + lambda(xx) - lambda u beta(t)u(3), and investigate the bifurcations that this attractor undergoes as A is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case.

EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.

STRUCTURE OF THE ELECTROMAGNETIC FIELD ALLOWING EXACT SOLUTION OF THE SCHRODINGER EQUATION IN SUPERPOSITION WITH AN AHARONOV-BOHM FIELD

A charged particle is considered in a complex external electromagnetic field. The field is a superposition of an Aharonov-Bohm field and some additional field. Here we describe all additional fields known up to the present time that allow exact solution of the Schrodinger equation in a complex field.