A Monte Carlo algorithm for solving systems of non-linear equations

A Monte Carlo method for solving systems of non-linear equations is presented and discussed. The method does not require the differentiation of left side functions of the system and provides the solution with arbitrary accuracy, although it may be applied only to systems with not too large a number of equations. Illustrative examples are given.     

Synchronous measurements of the atmospheric radio emission in the two and three millimeter wavelength regions

Apparatus and procedure of measuring the atmospheric radio emission simultaneously in two atmospheric windows are described. The results of measurements of the sky brightness temperature and obtained atmospheric optical depth values are reported. The diurnal and seasonal variations of the sky temperature and zenith absorption as well as their relation to weather parameters of nearsurface atmospheric layer are discussed.     

Synthesis and X-ray diffraction study of complex neptunium(VI) potassium chromate K2[(NpO2)2(CrO4)3(H2O)] · 3H2O

The crystal structure of the K₂[(NpO₂)₂(CrO₄)₃(H₂O)] · 3H₂O compound was established. The structure consists of anionic layers [(NpO₂)₂(CrO₄)₃(H₂O)] _n ²ⁿ , between which K+ ions and crystallization water molecules are located. The coordination polyhedra of Np atoms are distorted pentagonal bipyramids. All chromate ions are bound in a tridentate-bridging fashion. __________ Translated from Kristallografiya, Vol. 49, No. 4, 2004, pp. 676–680. Original Russian Text Copyright ? 2004 by Grigor’ev, Fedoseev, Budantseva, Bessonov, Krupa.     

On the exponential exponents of discrete linear systems

In this paper we introduce the concepts of exponential exponents of discrete linear time varying systems. It is shown that these exponents describe the possible changes in the Lyapunov exponents under perturbation decreasing at infinity at exponential rate. Finally we present formulas for the exponential exponents in terms of the transition matrix of the system.     

Periodic solutions of nonlinear hyperbolic evolution systems

We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation operator associated with the nonlinear evolution system, expressed in terms of the topological degree. The abstract results shall be applied to the damped hyperbolic partial differential equation.     

States of a supersaturated solution in limited-size systems

The features of phase transformations in limited-size systems have been described. The main specificity of small-size systems is the multivariance of equilibrium and metastable states whose stability and region of existence depend on the dimensions of the system, concentration, and temperature. A decrease in the dimensions of the system makes it possible to increase the solubility and to prevent the decay of the supersaturated solution. The properties described by the thermodynamic model are reproduced experimentally using the ensemble of evaporated drops of the solution.     

Usage and Experimental Tests of the Modified Waveguide Method for Measurement of the Complex Permittivity and Permeability of Materials

Physics of Wave Phenomena - Results of the numerical experiment are presented, which allow considerably extending the range of the waveguide method capabilities in determination of the complex...     

Heat-Resistant Epoxy Polymers of Anhydride Curing

The interaction of UP-643 epoxy-novolac resin with isomethyltetrahydrophthalic anhydride in the presence of the catalysts (azo-compounds of different structure) is studied. Latency of the catalysts is found. The possibility is shown of creating epoxy binders with a long lifetime (10–40 days) at room temperatures, cured at increased temperature up to heat-resistant polymers.     

Stratifying Polymer Solutions in Microsized Pores: Phase Transitions Induced by Deformation of a Porous Material

Technical Physics - Based on the thermodynamic approach, the influence of pore morphology on the phase equilibria in stratifying liquid solutions entrapped in a porous matrix is analyzed. As...