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Recent numerical and theoretical studies have demonstrated that the modes at threshold of a random laser are in direct correspondence with the resonances of the same system without gain, a feature which is well known in a conventional laser…
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…
A three-point iterative method for solving scalar non-linear equations was selected and then adapted to solve systems of non-linear equations. Subsequently, by applying Taylor's theorem to functions of $\R^{n}$ in $\R^{n}$, it is shown that…
Considerable progress has recently been made in controling the motion of free atomic particles by means of light pressure exerted by laser radiation. The free fall of atoms and bouncing on a reflecting surface made from evanescent wave…
Kinetic model of three component, weakly ionized, collisional plasma with a beam of neutral particles is developed. New dispersion relations for linear perturbations are derived and analyzed in various limiting cases.
A brief survey of nuclide abundances in the solar-system and in cosmic rays and of the believed mechanisms of their synthesis is given. The role of spallation processes in nucleosynthesis is discussed. A short review of recent measurements,…
A disordered structure embedding an active gain material and able to lase is called random laser (RL). The RL spectrum may appear either like a set of sharp resonances or like a smooth line superimposed to the fluorescence. A recent letter…
This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…
Suppose we are given an environment consisting of axis-parallel and diagonal line segments with integer endpoints, each of which may be reflective or non-reflective, with integer endpoints, and an initial position for a light ray passing…
We present a theoretical study of strong laser-atom interactions, when the laser field parameters are subjected to random processes. The atom is modelled by a two-level and three-level systems, while the statistical fluctuations of the…
This paper, the first of two, introduces an observational study of spiral structure in galaxies chosen from the SINGS survey. Near infrared (NIR) and optical data are used to produce mass surface density maps, and from these the morphology…
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
Let X be a scroll over a rational surface. We construct a linear system of surfaces in P^3 yielding a birational map from P^3 to X. We apply this construction to the scrolls of Bordiga and Palatini.
A scheme for polarization control using two laser beams in a non-linear optical medium is studied using both co- and counter-propagating beam geometries. In particular, we show that under certain conditions it is possible for two laser…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
Self-focusing instability is a well-known phenomenon of nonlinear optics, which is of great importance in the field of laser-plasma interactions. Self-focusing instability leads to beam focusing and, consequently, breakup into multiple…
The interaction between a large number of laser filaments brought together using weak external focusing leads to the emergence of few filamentary structures reminiscent of standard filaments, but carrying a higher intensity. The resulting…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In…
We study numerical methods of tomography in domains with a reflecting obstacle. It will be shown that tomography with sets containing both broken rays, i.e. rays reflecting at the obstacle, as well as unbroken rays, has a smaller error…