Approximate Toeplitz Matrix Problem Using Semidefinite Programming

Given a data matrix, we find its nearest symmetric positive-semidefinite Toeplitz matrix. In this paper, we formulate the problem as an optimization problem with a quadratic objective function and semidefinite constraints. In particular, instead of solving the so-called normal equations, our algorithm eliminates the linear feasibility equations from the start to maintain exact primal and dual feasibility during the course of the algorithm. Subsequently, the search direction is found using an inexact Gauss-Newton method rather than a Newton method on a symmetrized system and is computed using a diagonal preconditioned conjugate-gradient-type method. Computational results illustrate the robustness of the algorithm.     

The Knizhnik-Zamolodchikov equations associated with the root system <Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript>

At the end of the twentieth century, in mathematical physics, the Knizhnik-Zamolodchikov equations for the root systems A _n and their generalizations for the root systems of types B _n , C _n , and D were constructed. For the root system of type G ₂, the vector version of the Knizhnik-Zamolodchikov equations was obtained by M. P. Zamakhovskii and V. P. Leksin. However, the tensor version of these equations has remained unstudied. In this paper, the Knizhnik-Zamolodchikov equations associated with the root system of type G ₂ are considered. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal Conference-2004, Part 3, 2006.     

Stress monitoring in a Guinness 10-day scuba dive

Nowadays, there is high demand for sensitive gas sensors both for human and environmental monitoring. This paper deals with a high-resolution (0.2 ppb) laser-based photoacoustic spectroscopic system realized at ENEA Frascati, Italy, applied for monitoring stress in scuba divers during sustained immersion by analyzing breath samples. Blood tests and psychometric tests for scuba divers were performed at Catholic University in Rome. Results will be reported and discussed.     

Conditions of stability of magnetic sublattices at exchange mixing of states with different spins

The conditions of compatibility of the magnetic sublattice hypothesis with the requirements of quantum theory have been derived. These conditions imply the presence of (even weak) magnetic anisotropy and a macroscopic number of spins in the sublattice.     

Effect of oxygen stoichiometry and microstructure on superconducting properties of YBaCuO films

Microstructure and oxygen stoichiometry of YBaCuO films manufactured by laser ablation are investigated. Dependence of the specific electrical resistivity and superconducting parameters of films on microstructure and oxygen stoichiometry is demonstrated. Conditions of deposition are determined, under which films with minimum microstructure defects and good conducting properties are formed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 41–45, February, 2007.     

Electro-absorption and refraction in Fabry-Perot quantum well modulators: a general discussion

Fabry-Perot resonators have long been advocated to improve the limited contrast ratio of multiple quantum well optical modulators used in photonic switches based on self electrooptic effect devices (SEEDs) and in other array based optical interconnection schemes. Using data on field dependent GaAs/AlGaAs quantum well absorption and refraction, we have modelled the reflectivity, modulation depth and contrast ratio of resonant modulators. Our results are generally valid for any quantum well modulator and demonstrate 23the important role played by electro-refraction even in regions of strong absorption. Resonators give large contrast ratios but there are trade-offs in the maximum reflectivity change achievable with Fabry-Perot resonators compared to simple modulators. The model gives the optimum number of quantum wells and reflectivity values required to make a resonator at any wavelength for a given quantum well structure. Understanding the limits of Fabry-Perot quantum well modulator performance is important for their application in symmetric self electrooptic effectiveness for photonic switching where modulation and detection properties are both used and for optical interconnection systems.