Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page

Spectral Asymptotics for Perturbed Spherical Schr\"odinger Operators and Applications to Quantum Scattering

We find the high energy asymptotics for the singular Weyl--Titchmarsh m-functions and the associated spectral measures of perturbed spherical Schr\"odinger operators (also known as Bessel operators). We apply this result to establish an improved local Borg-Marchenko theorem for Bessel operators as well as uniqueness theorems for the radial quantum scattering problem with nontrivial angular momentum.Comment: 20 page

Biodegradables composites : prepration and characterization

This study focuses on the polystyrene matrix composites and micro loads of vegetable origin: spruce sawdust and celelulose microcrystal. The latter are obtained by extracting the cellulose from flour spruce. The composite samples were prepared by injection. The particle size analysis made it possible to determine the size of the charges and to highlight the effectiveness of treatment extraction. Analysis of microstructural changes was followed by Fourier transform inefrared spectroscopy and morphology by scanning electron microscopy. The mechanical behaviour and tensile strength were studied before and after hydrothermal agin

Analysis of parameters effects on crack breathing and propagation in shaft of rotor dynamic systems

In this paper the design of experiment method is used to investigate and explain the effects of the rotor parameters on crack breathing and propagation in the shaft. Three factors are considered which have an influence on the behavior and the propagation of the crack: the rotational speed, the length of the rotor and the diameter of the shaft. The elaborated mathematical model allows determining the effects and interaction of speed, diameter and length on crack breathing mechanism.The model also determines the optimal values of the parameters to achieve high performance

Modeling of Cracked Beams by the Experimental Design Method

Abstract The understanding of phenomena, no matter their nature is based on the experimental results found. In the most cases, this requires an important number of tests in order to put a reliable and useful observation served into solving the technical problems subsequently. This paper is based on independent and variables combination resulting from experimentation in a mathematical formulation. Indeed, mathematical modeling gives us the advantage to optimize and predict the right choices without passing each case by the experiment. In this work we plan to apply the experimental design method on the experimental results found by (Deokar, A, 2011), concerning the effect of the size and position of a crack on the measured frequency of a beam console, and validating the mathematical model to predict other frequencie

Investigation of Ga substitution in ZnO powder and opto-electronic properties

Two sets of Ga-doped ZnO powders were synthesized via solid-state and Pechini routes with a substitution rate varying from 0 to 4 mol %. The gallium solubility limit is strongly dependent on the synthesis history. Indeed, a low temperature annealing allows incorporating about 1.5 mol % (X-ray diffraction (XRD), inductive coupled plasma spectroscopy (ICP), optical properties) whereas under 0.1% of dopant is introduced after thermal treatment at high temperature: 1500 °C (from XRD and pellets conductivity). The incorporation of gallium leads to an anisotropic distortion of the zincite crystal lattice (a and c parameters increase and decrease, respectively, versus the Ga content leading to a decrease of the c/a ratio) which can be explained from the valence bond model. XRD analysis, chemical titration by ICP, and conductivity measurements (on pellets obtained at high temperature) allow determining accurately the maximum Ga content in the zincite. The optical properties (IR absorption efficiency) linked to electron carriers are directly correlated to the gallium rate introduced in ZnO oxide; nevertheless, the non linear correlation between these two parameters tends to show that the concentration of charge carriers in the system is not equal to the amount of Ga3+ atoms inserted per ZnO volume unit. A saturation regime is observed and was here explained once again on the basis of the valence band model by the increase of inhibiting p type defects with the increase of (n-type donors) Ga3+ concentration