THE EFFECT OF THE FREEZE-OUT VOLUME IN THE MULTIFRAGMENTATION OF VERY HOT NUCLEAR REMNANT

In this paper a simplified method for the calculation of average Coulomb energy in statistical model of the disassembly processes of hot nuclei is proposed.The effect of freeze-out volume is studied based on the assumption of Gaussion-like distribution.It is indecated that the centre and dispersion of Gaussion-like distribution somewhat reflect the location and the renge of liquid-gas coexistence phase.     

Net Charge Fluctuation and String Fragmentation

We present the simulation results of the net charge fluctuation in Au Au collisions at √Snn=130 GeV from a dynamic model, JPCIAE, and its revisions. The simulations are done for the quark-gluon matter, the directly produced pions, the pion matter, and the hadron matter. The simulated net charge fluctuation of the quark-gluon matter is close to the thermal model prediction for the quark-gluon gas. However, the discrepancy exists comparing the simulated net charge fluctuation for directly produced pions and the pion matter with the thermal model prediction for pion gas and the resonance pion gas, respectively. The net charge fluctuation of hadron matter from default JPCIAE simulations is nearly 3.5 times larger than quark-gluon matter. A discussion is given for the net charge fluctuation as an evidence of QGP phase transition.     

Analysis of Fokker-Planck type stochastic equations with variable boundary conditions in an elementary process of collisional ionization

The diffusion model of ionization of Rydberg atoms in single collisions is formulated. The solution of kinetic equations describing nonstationary diffusion processes is discussed. Methods of analytical calculation of the effective times for the development of ionization in phase regions with moving boundaries are presented. An analytical method, going back to Weisskopf, for determining the corresponding cross sections for impact ionization in the adiabatic approximation is described. A numerical scheme for solving problems of stochastic movement of a Rydberg electron inside a Coulomb condensation of levels under conditions of time-variable ionization boundaries and region of development of stochastic instability is developed.     

Production of sapphire tubes for high-pressure sodium lamps using the stepanov method at high rates of growth

The process of the Stepanov growth of sapphire tubes is studied at the growth rates up to 20 mm · min⁻¹ in a Mo crucible with graphite succeptor. It is established that the main factor preventing the production of high-quality samples is contamination of the melt due to the gas transport reactions the growth chamber atmosphere and formation of oversaturated carbon solid solution in the Al₂O₃ matrix. The decomposition of this solid solution gives rise to the second-phase-particle precipitations. The production of highquality sapphire tubes at the growth rates up to 20 mm · min⁻¹ is possible with a careful elimination of water vapours and oxygen from the growth chamber atmosphere.     

Planar graphs without triangles adjacent to cycles of length from 4 to 7 are 3-colorable

It is known that planar graphs without cycles of length from 4 to 7 are 3-colorable (Borodin et al., 2005) [13] and that planar graphs in which no triangles have common edges with cycles of length from 4 to 9 are 3-colorable (Borodin et al., 2006) [11]. We give a common extension of these results by proving that every planar graph in which no triangles have common edges with k-cycles, where k∈{4,5,7} (or, which is equivalent, with cycles of length 3, 5 and 7), is 3-colorable.     

Distributions of the location of maximuma and minimuma for diffusions with jumps

The paper deals with methods of computation of distributions of location for maxima and minima for diffusions with jumps. As an example, we obtain explicit formulas for distributions of location for the maximum of the process which is equal to the sum of a Brownian motion and the compound Poisson process. Bibliography: 8 titles.     

Infinite-dimensional diffusions as limits of random walks on partitions

Starting with finite Markov chains on partitions of a natural number n we construct, via a scaling limit transition as n → ∞, a family of infinite-dimensional diffusion processes. The limit processes are ergodic; their stationary distributions, the so-called z-measures, appeared earlier in the problem of harmonic analysis for the infinite symmetric group. The generators of the processes are explicitly described.     

Effectiveness of linearization of calibration curves in Zeeman graphite furnace atomic absorption spectrometry

A theoretical analysis is made of the effect of analytical line broadening and of non-absorbable radiation in the light source on the shape of concentration curves in Zeeman graphite furnace atomic absorption spectrometry. These results have been used in a systematic study of the effect of spectrometer slit width and hollow-cathode lamp (HCL) current on linearization of calibration graphs for 11 elements: Ag, Au, Bi, Cd, Co, Cu, Fe, Mn, Ni, Pb, and Sb. The effectiveness of linearization throughout the analytical range covered was estimated experimentally on series of 25–30 solutions. Three solutions in each series were used as standards for constructing the calibration graph, the others serving to evaluate the linearization effectiveness. Increasing the slit width and decreasing the HCL current compared to the standard measurement conditions have permitted us to reach a sufficiently high effectiveness of linearization for all the elements studied, with the exception of Ni. The maximum deviation of experimental points from the linear graph under optimum conditions does not exceed 6%. The effect of the Δ parameter used in the computational algorithm on linearization effectiveness is investigated.