Wellposedness of a Nonlinear, Logarithmic Schr?dinger Equation of Doebner–Goldin Type Modeling Quantum Dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schr?dinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schr?dinger equation somehow accounting for quantum Fokker–Planck effects, and see how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more easily achievable analysis regarding the local wellposedness of the initial-boundary value problem. This simplification requires the performance of the polar (modulus argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.     

Analysis of a model of phosphorus uptake by plant roots

In this paper, we consider a model of phosphorus uptake by plant roots, governed by a quasilinear parabolic equation. We first study the well posedness of the associated Cauchy problem. Then, we consider a shape optimization problem: how to deform the shape of the root in order to increase phosphorus uptake. Finally, we give some numerical results of the shape optimization process.     

Identification of a potential sex pheromone of the processionary moth, Thaumetopea pityocampa (lepidoptera,notodontidae)

The major component of the active fraction from the Thaumetopoea pityocampa (Denis and Schiff.) virgin female extract has been identified as (Z)-13-hexadecen-11-ynyl acetate on the basis of spectroscopic and microchemical reactions data. This is the first report of an acetylenic structure found in the insect pheromone field.     

Local exact controllability of the Navier–Stokes system

In this paper we deal with the local exact controllability of the Navier–Stokes system with distributed controls supported in small sets. In a first step, we present a new Carleman inequality for the linearized Navier–Stokes system, which leads to null controllability at any time T>0. Then, we deduce a local result concerning the exact controllability to the trajectories of the Navier–Stokes system.     

L?sungspolymerisation von 1,3,5-Trioxan und 1,3,5,7-Tetroxocan. 2. Mitt. Morphologie der so erhaltenen Polyoxymethylen-Kristalle

Ohne Zusammenfassung     

Deformation luminescence in KCl irradiated at room temperature

It has been found that there is a relationship between the thermoluminescence and the deformation luminescence of irradiated pure KCl samples. It is concluded that the luminescent process in the deformation luminescence is the recombination of interstitial halogen atoms with vacancy centres (F, M) as well as in the thermoluminescence.     

Integral transform solution of developing laminar duct flow in Navier-Stokes formulation

The generalized integral transform technique is employed in the hybrid numerical-analytical solution of the Navier-Stokes equations in streamfunction-only formulation, which govern the incompressible laminar flow of a Newtonian fluid within a parallel plate channel. Owing to the analytic nature of this approach, the outflow boundary condition for an infinite duct is handled exactly, and the error involved in considering finite duct lengths is investigated. The present error-controlled solutions are used to inspect the relative accuracy of previously reported purely numerical schemes and to compare Navier-Stokes and boundary layer formulations for various combinations of inlet conditions and Reynolds number.     

Characterization and sensor applications of polycarbonate optical fibers

Some of the optical, mechanical, thermal, and chemical tests performed on a polycarbonate optical fiber (Optipol) developed by BAYER AG are described in this paper. Allthe tests were mainly done in order to evaluate the performances of this optical fiber, looking for its application as light transmitter in Local Area Networks (LANs) and sensors manufacture in the automobile industry. Some sensors using this fiber are also described in this paper: one speedometer, one tachometer, and one magnetometer. The last two sensors are Faraday effect sensors and have been developed with polycrystalline Cd_1-xMn_x, Te. This low-cost Faraday rotator has been specially manufactured by the authors to be used in industrial applications.