A note on the controllability for the wave equation in nonsmooth plane domains

We study exact boundary controllability for a two-dimensional wave equation in a region which is an angular sector of a circle or an angular sector of an annular region. The control, of Neumann type, acts on the curved part of the boundary, while in the straight part we impose homogeneous Dirichlet boundary condition. The initial state has finite energy and the control is square integrable. (c) 2005 Elsevier B.V. All rights reserved.

SURFACE PERTURBATIONS OF A SHALLOW VISCOUS-FLUID HEATED FROM BELOW AND THE (2+1)-DIMENSIONAL BURGERS-EQUATION

The (2 + 1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfies the condition R not-equal 30. A solution to this equation is explicitly exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink.

Effect of calcium ions on rat osseous plate alkaline phosphatase activity

Rat osseous plate alkaline phosphatase is a metalloenzyme with two binding sites for Zn2+ (sites I and III) and one for Mg2+ (site II). This enzyme is stimulated synergistically by Zn2+ and Mg2+ (Ciancaglini et al., 1992) and also by Mn2+ (Leone et al., 1995) and Co2+ (Ciancaglini et al., 1995). This study was aimed to investigate the modulation of enzyme activity by Ca2+. In the absence of Zn2+ and Mg2+, Ca2+ had no effects on the activity of Chelex-treated, Polidocanol-solubilized enzyme. However, in the presence of 10 mu M MgCl2, increasing concentration of Ca2+ were inhibitory, suggesting the displacement of Mg2+ from the magnesium-reconstituted enzyme. For calcium-reconstituted enzyme, Zn2+ concentrations Zip to 0.1 mu M were stimulatory, increasing specific activity from 130 U/mg to about 240 U/mg with a K-0.5 = 8.5 nM. Above 0.1 mu M Zn2+ exerted a strong inhibitory effect and concentrations of Ca2+ up to I mM were not enough to counteract this inhibition, indicating that Ca2+ was easily displaced by Zn2+. At fixed concentrations of Ca2+, increasing concentrations of Mg2+ increased the enzyme specific activity from 472 U/mg to about 547 U/mg, but K-0.5 values were significantly affected (from 4.4 mu M to 38.0 mu M). The synergistic effects observed for the activity of Ca2+ plus magnesium-reconstituted enzyme, suggested that these two ions bind to the different sites. A model to explain the effect of Ca2+ on the activity of the enzyme is presented. (C) 1997 Elsevier B.V.

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.

SUPERSYMMETRIC SOLUTION FOR 2-DIMENSIONAL SCHRODINGER-EQUATION

We use a non usual realization of the superalgebra to resolve certain two-dimensional potentials. The Hartmann and an anisotropic ring-shaped oscillator are explicitly solved.

Solving Schrödinger equation for two dimensional potential using supersymmetry

The formalism of supersymmetric Quantum Mechanics can be extended to arbitrary dimensions. We introduce this formalism and explore its utility to solve the Schodinger equation for a bidimensional potential. This potential can be applied in several systens in physical and chemistry context, for instance, it can be used to study benzene molecule.

OSSEOUS PLATE ALKALINE-PHOSPHATASE IS ANCHORED BY GPI

Alkaline phosphatase activity was released up to 100% from the membrane by using 0.1 U of phosphatidylinositol-specific phospholipase C from B. thuringiensis. The Mr of solubilized enzyme was 145,000 by Sephacryl S-300 gel filtration and 66,000 by SDS-PAGE, suggesting a dimeric structure. Solubilization of the membrane-bound enzyme with phospholipase C did not destroy its ability to hydrolyze p-nitrophenyl phosphate (PNPP) (264.3 mu mol min(-1) mg(-1)), ATP (42.0 mu mol min(-1) mg(-1)) and pyrophosphate (28.4 mu mol min(-1) mg(-1)). The hydrolysis of ATP and PNPP by solubilized enzyme exhibited ''Michaelian'' kinetics with K-0.5 = 70 and 979 mu M, respectively. For pyrophosphate, K-0.5 was 128 mu M and site-site interactions were observed (n = 1.4). Magnesium ions were stimulatory (K-d = 1.5 mM) but zinc ions were powerful non-competitive inhibitors (K-d = 6.2 mu M) of solubilized enzyme. Treatment of solubilized alkaline phosphatase with Chellex 100 reduced the original PNPPase activity to 5%. Cobalt (K-0.5 = 10.1 mu M), magnesium (K-0.5 = 29.5 mu M) and manganese ions (K-0.5 = 5 mu M) restored the activity of the apoenzyme with positive cooperativity, suggesting that phosphatidylinositol-specific phospholipase C-solubilized alkaline phosphatase is a metalloenzyme. The stimulation of the apoenzyme by calcium ions (K-0.5 = 653 mu M) was lower than that observed for the other ions (26%) and exhibited site-site interactions (n = 0.7). Zinc ions had no effect on the apoenzyme of the solubilized enzyme.

Exact boundary control for the wave equation in a polyhedral time-dependent domain

We establish exact boundary controllability for the wave equation in a polyhedral domain where a part of the boundary moves slowly with constant speed in a small interval of time. The control on the moving part of the boundary is given by the conormal derivative associated with the wave operator while in the fixed part the control is of Neuman type. For initial state H-1 x L-2 we obtain controls in L-2. (C) 1999 Elsevier B.V. Ltd. All rights reserved.

KINETIC-PROPERTIES OF OSSEOUS PLATE ALKALINE-PHOSPHATASE FROM DIABETIC RATS

1. Increased levels of bone alkaline phosphatase activity were observed in diabetic rats. These animals exhibited impaired bone development without concomitant alterations of the sequence of cellular transformations.2. Alkaline phosphatase activity was delayed in diabetic rats but the kinetic parameters for the hydrolysis of p-Nitrophenylphosphate (PNPP) were virtually the same observed for controls (N = 1.2 and K0.5 = 43 muM).3. Alkaline phosphatase from diabetic rats had a better affinity (K0.5 = 38 muM) for magnesium ions than controls (K0.5 = 9 1 muM).4. Zinc ions affected alkaline phosphatase activity from control and diabetic rats in the same way (K0.5 = 10 muM).

Non-linear boundary element analysis of floor slabs reinforced with rectangular beams

In this work, a numerical model to perform non-linear analysis of building floor structures is proposed. The presented model is derived from the Kirchhoff-s plate bending formulation of the boundary element method (BENI) for zoned domains, in which the plate stiffness is modified by the presence of membrane effects. In this model, no approximation of the generalized forces along the interface is required and the compatibility and equilibrium conditions along interfaces are imposed at the integral equation level. In order to reduce the number of degrees of freedom, the Navier Bernoulli hypothesis is assumed to simplify the strain field for the thin sub-regions (rectangular beams). The non-linear formulation is obtained from the linear formulation by incorporating initial internal force fields, which are approximated by using the well-known cell sub-division. Then, the non-linear solution of algebraic equations is obtained by using the concept of the consistent tangent operator. The Von Mises criterion is adopted to govern the elasto-plastic material behaviour checked at points along the plate thickness and along the rectangular beam element axes. The numerical representations are accurately obtained by either computing analytically the element integrals or performing the numerical integration accurately using an appropriate sub-elementation scheme. (C) 2007 Elsevier Ltd. All rights reserved.

THE ALGEBRA OF NONLOCAL CHARGES IN NONLINEAR SIGMA-MODELS

We obtain the exact classical algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, now containing a calculable correction of order one unit lower. The relation with Yangians and the role of the results in the context of Lie-Poisson algebras are also discussed.

A well-balanced flow equation for noise removal and edge detection

In this paper, an anisotropic nonlinear diffusion equation for image restoration is presented. The model has two terms: the diffusion and the forcing term. The balance between these terms is made in a selective way, in which boundary points and interior points of the objects that make up the image are treated differently. The optimal smoothing time concept, which allows for finding the ideal stop time for the evolution of the partial differential equation is also proposed. Numerical results show the proposed model's high performance.

Dirac equation in magnetic-solenoid field

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)