Matrix Entries of Real Representations of the Groups O(3) and SO(3)

We indicate bases for spinor representations of the groups O(3), SO(3), and SU(2) in which the representation matrices are real-valued. The matrix entries in these bases are calculated. We describe the transformation of classical orthogonal harmonic polynomials in three-dimensional space by these matrix entries.     

Excitation of low-lying nuclear states by the ion line emission in femtosecond laser plasma

A scheme of nuclear excitation by the ionic X-ray lines in laser plasma using two femtosecond laser pulses is proposed. The first pulse produces plasma with a given degree of ionization, allowing the X-ray line energies of the target ions to be tuned to resonance with the nuclear transition, while the second pulse generates hot electrons that are necessary for X-ray generation.     

Phase Composition of Coatings Formed on Titanium in Borate Electrolyte by Microarch Oxidation

The effect of oxidation conditions, temperature and concentration of the electrolyte, and its transformation from the true to colloidal solution on the phase composition and electrical resistance of coatings was studied.     

Polymerization of Acetylene in Liquid Crystal Media

The synthesis of polyacetylene in a new class of solvents - liquid crystals - will be reported. The effect of the solvent molecules orientation in the polymer's structure and its properties will be discussed.     

Invariant operators and separation of residual stresses

We consider the equations of linear theory of elasticity in stresses for the threedimensional space. Solutions are decomposed into sums of stationary solutions not satisfying the compatibility condition (residual stresses) and nonstationary solutions satisfying the compatibility condition and hence represented through the displacements. The construction of this decomposition is reduced to solving a series of Poisson equations.     

Excited Brownian motions as limits of excited random walks

We obtain the convergence in law of a sequence of excited (also called cookies) random walks toward an excited Brownian motion. This last process is a continuous semi-martingale whose drift is a function, say ??, of its local time. It was introduced by Norris, Rogers and Williams as a simplified version of Brownian polymers, and then recently further studied by the authors. To get our results we need to renormalize together the sequence of cookies, the time and the space in a convenient way. The proof follows a general approach already taken by Tóth and his coauthors in multiple occasions, which goes through Ray-Knight type results. Namely we first prove, when ?? is bounded and Lipschitz, that the convergence holds at the level of the local time processes. This is done via a careful study of the transition kernel of an auxiliary Markov chain which describes the local time at a given level. Then we prove a tightness result and deduce the convergence at the level of the full processes.