Optimal uniform approximation on angles by entire functions

The paper discusses the best or optimal uniform approximation problem by entire functions on a closed angle Δ. This problem has been studied by M.V. Keldysch in [4], under the assumption that the functions ? subject to approximation are holomorphic in a larger angle containing Δ and there is no restriction on the growth of ? at infinity. In [8], the problem was investigated for a wider class of functions ? continuously complex differentiable on Δ, with sharper estimates on the growth of approximating entire functions, linked with the growth of ? on Δ and the differential properties of ? on the boundary of Δ. In this paper, we improve some of the results on entire approximation on angles, using new approximation ideas partially presented in [9] and [10].     

Experimental study of laser-induced processes on the surfaces of carbonaceous materials with simultaneous measuring of their temperatures

Results are presented from experiments on monitoring laser-induced processes (heating, melting, and ablation) on surfaces of carbonaceous materials (glassy carbon, pyrocarbon) using a laser display and according to the brightness temperature determined during these processes with a high-temperature pyrometer. The melting brightness temperature of glassy carbon (2720 ± 15 K) is determined using a continuouswave fiber laser. Some wave structures are revealed. No melting of pyrocarbon was observed over the range of powers and temperatures. The surfaces ablated after heating.     

Drop deposition of thin nanostructured coatings of lead telluride

The current-voltage relationships of deposited structures are measured for cluster structures consisting of nanoparticles of lead telluride. Variation in the value of the tunnel current is shown. Optimum conditions for the possible emergence of quantum-hopping conductivity due to carrier tunneling (the characteristic sizes of the nanoclusters and the distances between them) are determined.     

Propagation of Smallness for Harmonic and Analytic Functions in Arbitrary Domains

In this paper the authors develop a new approach to the problemof ‘propagation of smallness’ for harmonic functionsin arbitrary domains, in Rⁿ (n 2). The main result of thispaper is a certain logarithmic-convexity relation for the L²-normsof harmonic functions. As a consequence, new kinds of uniquenessresults for harmonic functions are obtained. The method worksalso for analytic functions in C, with L^p-norms (p > 0).1991 Mathematics Subject Classification 31B05.     

Josephson dynamics for coupled polariton modes under the atom–field interaction in the cavity

We consider a new approach to the problem of Bose–Einstein condensation (BEC) of polaritons for atom–field interaction under the strong coupling regime in the cavity. We investigate the dynamics of two macroscopically populated polariton modes corresponding to the upper and lower branch energy states coupled via Kerr-like nonlinearity of atomic medium. We found out the dispersion relations for new type of collective excitations in the system under consideration. Various temporal regimes like linear (nonlinear) Josephson transition and/or Rabi oscillations, macroscopic quantum self-trapping (MQST) dynamics for population imbalance of polariton modes are predicted. We also examine the switching properties for time-averaged population imbalance depending on initial conditions, effective nonlinear parameter of atomic medium and kinetic energy of low-branch polaritons. PACS 03.75.Lm; 71.36.+c; 42.50.Fx     

Studying the structure and electrical conductivity of thin granulated bimetallic films

The surface resistance of bimetallic granular films prepared by means of laser-induced deposition is studied. The possibility of modeling their conductivity is demonstrated, depending on their morphological properties.     

Frobenius nonclassicality of Fermat curves with respect to cubics

For Fermat curves F: aX ⁿ + bY ⁿ = Z ⁿ defined over F _q , we establish necessary and sufficient conditions for F to be F _q -Frobenius nonclassical with respect to the linear system of plane cubics. In the new F _q -Frobenius nonclassical cases, we determine explicit formulas for the number N _q (F) of F _q -rational points on F. For the remaining Fermat curves, nice upper bounds for N _q (F) are immediately given by the Stöhr–Voloch Theory.     

High-temperature Bose-Einstein condensation of photonlike atom-light polaritons

We propose a method for obtaining a Bose-Einstein condensate of an ideal one-dimensional gas of atom-light polaritons of the lower branch in a trap at high temperatures (on the order of room temperature or higher). The system under consideration is an atomic ensemble that interacts with a single-mode quantum electromagnetic field in the presence of optical collisions with a high-pressure buffer gas. The possibility of using biconical waveguides for revealing the predicted phenomenon is discussed. The dynamics of the polariton condensate in the trap is investigated on the basis of the variational approach.