PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

We consider the family of singularly nonautonomous plate equation with structural dampingu(tt) + a(t, x)u(t) - Delta u(t) + (-Delta)(2)(u) + lambda u = f(u),in a bounded domain Omega subset of R(n), with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in H(0)(2)(Omega) x L(2)(Omega) and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

LOWER SEMICONTINUITY of PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Experimental study of the conventional equation to determine a plate's moment of inertia

In this work, we describe an experimental setup in which an electric current is used to determine the angular velocity attained by a plate rotating around a shaft in response to a torque applied for a given period. Based on this information, we show how the moment of inertia of a plate can be determined using a procedure that differs considerably from the ones most commonly used, which generally involve time measurements. Some experimental results are also presented which allow one to determine parameters such as the exponents and constant of the conventional equation of a plate's moment of inertia.

Vortices in nonlocal Gross-Pitaevskii equation

We consider vortices in the nonlocal two-dimensional Gross-Pitaevskii equation with the interaction potential having Lorentz-shaped dependence on the relative momentum. It is shown that in the Fourier series expansion with respect to the polar angle, the unstable modes of the axial n-fold vortex have orbital numbers l satisfying 0 < \l\ < 2\n\, as in the local model. Numerical simulations show that nonlocality slightly decreases the threshold rotation frequency above which the nonvortex state ceases to be the global energy minimum and decreases the frequency of the anomalous mode of the 1-vortex. In the case of higher axial vortices, nonlocality leads to instability against splitting with the creation of antivortices and gives rise to additional anomalous modes with higher orbital numbers. Despite new instability channels with the creation of antivortices, for a stationary solution comprised of vortices and antivortices there always exists another vortex solution, composed solely of vortices, with the same total vorticity but with a lower energy.

Exponential decay for Kirchhoff wave equation with nonlocal condition in a noncylindrical domain

In this paper, we prove the exponential decay as time goes to infinity of regular solutions of the problem for the Kirchhoff wave equation with nonlocal condition and weak dampingu(tt) - M (\\delU\\(2)(2)) Deltau + integral(0)(t) g(t - s)Deltau(.,s) ds + alphau(t) = 0, in (Q) over cap,where (Q) over cap is a noncylindrical domain of Rn+1 (n greater than or equal to 1) with the lateral boundary (&USigma;) over cap and alpha is a positive constant. (C) 2004 Elsevier Ltd. All rights reserved.

The higher grading structure of the WKI hierarchy and the two-component short pulse equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Transient non-Darcy forced convective heat transfer from a flat plate embedded in a fluid-saturated porous medium

Transient non-Darcy forced convection on a flat plate embedded in a porous medium is investigated using the Forchheimer-extended Darcy law. A sudden uniform pressure gradient is applied along the flat plate, and at the same time, its wall temperature is suddenly raised to a high temperature. Both the momentum and energy equations are solved by retaining the unsteady terms. An exact velocity solution is obtained and substituted into the energy equation, which then is solved by means of a quasi-similarity transformation. The temperature field can be divided into the one-dimensional transient (downstream) region and the quasi-steady-state (upstream) region. Thus the transient local heat transfer coefficient can be described by connecting the quasi-steady-state solution and the one-dimensional transient solution. The non-Darcy porous inertia works to decrease the velocity level and the time required for reaching the steady-state velocity level. The porous-medium inertia delays covering of the plate by the steady-state thermal boundary layer. © 1990.

Allosteric modulation of pyrophosphatase activity of rat osseous plate alkaline phosphatase by magnesium ions

Pyrophosphatase activity of rat osseous plate alkaline phosphatase was studied at different concentrations of calcium and magnesium ions. with the aim of characterizing the modulation of enzyme activity by these metals. In the absence of metal ions, the enzyme hydrolysed pyrophosphate following Michaelian kinetics with a specific activity of 36.7 U/mg and K-0.5 = 88 mu M. In the presence of low concentrations (0.1 mM) of magnesium (or calcium) ions, the enzyme also exhibited Michaclian kinetics for the hydrolysis of pyrophosphate, but a significant increase in specific activity (123 U/mg) was observed. K-m values remained almost unchanged. Quite different behavior occurred in the presence of 2 mM magnesium (or calcium) ions. In addition to low-affinity sites (K-0.5 = 40 and 90 mu M, for magnesium and calcium, respectively), high-affinity sites were also observed with K-0.5 values 100-fold lower. The high-affinity sites observed in the presence of calcium ions represented about 10% of those observed for magnesium ions. This was correlated with the fact that only magnesium ions triggered conformational changes yielding a fully active enzyme. These results suggested that the enzyme could hydrolyse pyrophosphate, even at physiological concentrations (4 mu M), since magnesium concentrations are high enough to trigger conformational changes increasing the enzyme activity. A model, suggesting the involvement of magnesium ions in the hydrolysis of pyrophosphate by rat osseous plate alkaline phosphatase is proposed. (C) 1998 Published by Elsevier B.V. Ltd. All rights reserved.

Inorganic pyrophosphate-phosphohydrolytic activity associated with rat osseous plate alkaline phosphatase

Purified membrane-bound alkaline phosphatase from rat osseous plate hydrolyzed pyrophosphate in the presence of magnesium ions, with a specific activity of 92.7 U/mg. Optimal apparent pH for pyrophosphatase activity was 8.0 and it remained unchanged on increasing the pyrophosphate concentration. In the absence of magnesium ions the enzyme had a K-m = 88 mu M and V = 36.7 U/mg for pyrophosphate and no inhibition by excess substrate was observed. Pyrophosphatase activity was rapidly destroyed at temperatures above 40 degrees C, but magnesium ions apparently protected the enzyme against danaturation. Sodium metavanadate (Ki = 1.0 mM) was a competitive inhibitor of pyrophosphatase activity, while levamisole (Ki = 8.2 mM) and theophylline (Ki = 7.4 mM) were uncompetitive inhibitors. Magnesium ions (K-0.5 = 1.7 mu M) stimulated pyrophosphatase activity, while cobalt (Ki = 48.5 mu M) and zinc (Ki = 22.0 mu M) ions were non-competitive inhibitors. Manganese and calcium ions had no effect on pyrophosphatase activity. The M-w of the pyrophosphatase: protein was 130 kDa by gel filtration, but a value of 65 kDa was obtained by dissociative gel electrophoresis, suggesting that it was a dimer of apparently identical subunits. These results suggested that pyrophosphatase activity stems from the membrane-bound osseous plate alkaline phosphatase and not from a different protein.

Kinetic characterization of a membrane-specific ATPase from rat osseous plate and its possible significance on endochondral ossification

Treatment with phosphatidylinositol-specific phospholipase C of rat osseous plate membranes released up to 90-95% of alkaline phosphatase, but a specific ATPase activity (optimum pH = 7.5) remained bound to the membrane. The hydrolysis of ATP by this ATPase was negligible in the absence of magnesium or calcium ions. However, at millimolar concentrations of magnesium and calcium ions, the membrane-specific ATPase activity increased to about 560-600 U/mg, exhibiting two classes of ATP-hydrolysing sites, and site-site interactions. GTP, UTP, ITP, and CTP were also hydrolyzed by the membrane-specific ATPase. Oligomycin, ouabain, bafilomycin A(1), thapsigargin, omeprazole, ethacrynic acid and EDTA slightly affected membrane-specific ATPase activity while vanadate produced a 18% inhibition. The membrane-specific ATPase activity was insensitive to theophylline, but was inhibited 40% by levamisole. These data suggested that the membrane-specific ATPase activity present in osseous plate membranes, and alkaline phosphatase, were different proteins. (C) 1998 Elsevier B.V. B.V.

Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

About the Use of the HdHr Algorithm Group in Integrating the Movement Equation with Nonlinear Terms

This work summarizes the HdHr group of Hermitian integration algorithms for dynamic structural analysis applications. It proposes a procedure for their use when nonlinear terms are present in the equilibrium equation. The simple pendulum problem is solved as a first example and the numerical results are discussed. Directions to be pursued in future research are also mentioned. Copyright (C) 2009 H.M. Bottura and A. C. Rigitano.

Some exact solutions of the Dirac equation

Exact analytic solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions.