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.

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.

Headgroup specificity for the interaction of the antimicrobial peptide tritrpticin with phospholipid Langmuir monolayers

We examined the interaction of the cationic antimicrobial peptide (AMP) tritrpticin (VRRFPWWWPFLRR, TRP3) with Langmuir monolayers of zwitterionic (dipalmitoyl phosphatidylcholine, DPPC, and dipalmitoyl phosphatidylethanolamine, DPPE) and negatively charged phospholipids (dipalmitoyl phosphatidic acid, DPPA, and dipalmitoyl phosphatidylglycerol, DPPG). Both surface pressure and surface potential isotherms became more expanded upon addition of TRP3 (DPPE similar to DPPC << DPPA < DPPG). The stronger interaction with negatively charged phospholipids agrees with data for vesicles and planar lipid bilayers, and with AMPs greater activity against bacterial membranes versus mammalian cell membranes. Considerable expansion of negatively charged monolayers occurred at 10 and 30 mol% TRP3, especially at low surface pressure. Moreover, a difference was observed between PA and PG, demonstrating that the interaction, besides being modulated by electrostatic interactions, displays specificity with regard to headgroup, being more pronounced in the case of PG, present in large quantities in bacterial membranes. In previous studies, it was proposed that the peptide acts by a toroidal pore-like mechanism [1,2]. Considering the evidence from the literature that PG shows a propensity to form a positive curvature as do toroidal pores, the observation of TRP3's preference for the PG headgroup and the dramatic increase in area promoted by this interaction represent further support for the toroidal pore mechanism of action proposed for TRP3. (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.

Langmuir and Langmuir-Blodgett films of a quinoline-fluorene based copolymer

The fabrication of Langmuir-Blodgett (LB) films of synthetic polymers allows the control of molecular architecture in order to optimize physical properties. In this paper, the surface chemistry of a quinoline-fluorene based copolymer spread on the air-water interface is investigated. Surface pressure-area isotherms as well as Polarization-Modulation Infrared Reflection-Absorption Spectroscopy (PM-IRRAS) were employed to characterize the films, which could be transferred to solid supports by the LB technique. Atomic force microscopy as well as UV-Vis and fluorescence spectroscopies have shown a regular deposition of the polymers, and the luminescence properties could be controlled with the number of layers deposited on the solid support. As a result, the photoluminescence of the LB films was considerably higher than that observed for the spin coated film, and the maximum emission peak was shifted to higher energies, which is attributed to the molecular-level interactions within the layer-ordered structure of the LB film. The luminescence response would possibly be tuned to approach the highest level, which allows the films to be employed in future applications in efficient optical devices such as organic light-emitting diodes (OLEDs). (C) 2011 Elsevier B.V. All rights reserved.

Immbolization of uricase enzyme in Langmuir and Langmuir-Blodgett films of fatty acids: Possible use as a uric acid sensor

Preserving the enzyme structure in solid films is key for producing various bioelectronic devices, including biosensors, which has normally been performed with nanostructured films that allow for control of molecular architectures. In this paper, we investigate the adsorption of uricase onto Langmuir monolayers of stearic acid (SA), and their transfer to solid supports as Langmuir Blodgett (LB) films. Structuring of the enzyme in beta-sheets was preserved in the form of 1-layer LB film, which was corroborated with a higher catalytic activity than for other uricase-containing LB film architectures where the beta-sheets structuring was not preserved. The optimized architecture was also used to detect uric acid within a range covering typical concentrations in the human blood. The approach presented here not only allows for an optimized catalytic activity toward uric acid but also permits one to explain why some film architectures exhibit a superior performance. (C) 2011 Elsevier Inc. 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.

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.

Synthesis of a functionalized europium complex and deposition of luminescent Langmuir-Blodgett (LB) films

The synthesis, characterization and formation of Langmuir-Blodgett (LB)films for the luminescent [(C12H25)(2)(CH3)(2)N][Eu(tta)(4)] complex, where [(C12H25)(2)(CH3)(2)](N+) is didodecyldimethylammonium and the tta ligand is thenoyltrifluoroacetone, are reported. The coordination of tta ligands to the Eu3+ ion was confirmed by FTIR spectroscopy and the emission spectrum comprised bands corresponding to D-5(0) -> F-7(0-4) transitions. The lifetime (tau) from the emission state (D-5(0))was 0.41 ms, measured by monitoring the hypersensitive D-5(0) -> F-7(2) transition, with the curve being fitted with a first-order exponential function. The surface pressure-area isotherm indicated that the anionic complex may form condensed structures at the air-water interface due to the amphiphilic properties of the counter ion and the beta-diketone ligand. Y-type LB films of [(C12H25)(2)(CH3)(2)N][Eu(tta)(4)] were deposited on quartz substrates, with preserved luminescence and a band assigned to the D-5(0) -> F-7(2) transition. The molecular arrangement at the air/water interface and the preserved luminescence in LB films are consistent with theoretical predictions using a semi-empirical Sparkle/AM1 calculation method for the molecule in vacuum. These tools were used for the first time to predict the behavior of organized films.

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.

Molecular organization and doping in poly(2-methoxyaniline)/Ni(dmit)(2) films obtained with the Langmuir-Blodgett technique

The control of the properties of materials at the molecular level is pursued for many applications, especially those associated with nanostructures. In this paper, we show that the coordination compound [Ni(dmit)(2)], where (dmit) is the 1,3-dithiole-2-thione-4,5-dithiolate ligand, can induce doping of poly(2-methoxyaniline) (POMA) in molecularly ordered Langmuir and Langmuir-Blodgett (LB) films. Doping was associated with interactions between the components and the compression of the Langmuir film at the air-water interface, according to polarization-modulated infrared reflection-absorption spectroscopy (PM-IRRAS) data. Taking these results together with in situ UV-Vis absorption measurements, we could identify the molecular groups involved in the interaction, including the way they were reoriented upon film compression. The Langmuir films were sufficiently stable to be transferred as Y-type LB films, while the hybrid POMA/[Ni(dmit)(2)] films remain doped in the solid state. As expected, the molecular charges affected the film morphology, as observed from combined atomic and electric force microscopy measurements. In summary, with adequate spectroscopy and microscopy tools we characterized molecular-level interactions, which may allow one to design molecular electronic devices with controlled electrical properties.

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)