Dynamical Characteristics of Traveling Wave Packets of Total Electron Content Disturbances

Using the COPHASE method and the GPS interferometry method for travelling ionospheric disturbances, we analyze in detail the spatio-temporal properties of travelling wave packets (TWP) of total electron content (TEC) disturbances. The analysis is performed on the example of a clearest TWP manifestation observed in California, USA, in October 18, 2001, using the GLOBDET technique, developed at the Institute of Solar-Terrestrial Physics of the Siberian Branch of RAS for global detection and monitoring of natural and technogenic ionospheric disturbances on the basis of TEC variations retrieved from the global network of GPS receivers. In the time domain, TWPs are quasi-periodic TEC oscillations of duration about 1 h, period of 10–20 min, and amplitude exceeding that of the background TEC fluctuations by at least one order of magnitude. The velocity and direction of TWP motion are similar to those of mid-latitude mesoscale travelling ionospheric disturbances, as obtained earlier from the analysis of phase parameters of HF radio signals and the signals of geostationary satellites and discrete space radio sources.     

Asymptotics of solutions of a linear singularity perturbed system with degeneracy

Asymptotic expansions with respect to a small parameter e are constructed for a fundamental system of solutions of a linear singularity perturbed system of equations of the form

Construction of asymptotic solutions of linear singularly perturbed systems of second order with degeneracy

The paper discusses the asymptotic behavior of the general solution of a linear singularly perturbed system

Asymptotic solutions of a singularly perturbed linear system of differential equations with irregular singular point

We consider a singularly perturbed system of differential equations with irregular singular point. We prove that, in the general case of multiple elementary divisors, the corresponding asymptotic expansions can be constructed in the form of double series in fractional powers of the parameter and the ratio of the independent variable to the parameter.     

On the Existence and Asymptotics of a Periodic Solution of a Degenerate Singularly Perturbed System of Differential Equations in the Case of Multiple Elementary Divisors

We consider a linear inhomogeneous singularly perturbed system of differential equations with -periodic coefficients and identically degenerate matrix with the derivative. We establish sufficient conditions for the existence and uniqueness of an -periodic solution of this system in the case where the main pencil of matrices has multiple spectrum. We construct asymptotics of this solution.     

On some properties of degenerate linear systems

For a linear system of ordinary differential equations with degenerate matrix of derivatives, we find conditions of reducibility to the central canonical form. We also establish the structure of the general solution and conditions of solvability of the Cauchy problem, and study the problem of periodic solutions. Nezhin Pedagogic Institute, Nezhin. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1278–1296, September, 1997.     

Construction of an asymptotic solution of the Cauchy problem for a degenerate linear system in the singular case

We propose an algorithm for the construction of an asymptotic solution of the Cauchy problem for a singularly perturbed linear system of differential equations with degenerate matrix of coefficients of derivatives in the case where the limit pencil of matrices is singular. __________ Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 271–288, April–June, 2008.     

Absorption of Radiation by ITO Semiconductor Nanoparticles in Plasmon Resonance Region

The radiation absorption cross section of indium–tin oxide (ITO) semiconductor nanoparticles of various sizes placed in various media is calculated in the region of plasmon resonance. The photoabsorption cross sections calculated within the framework of the Mie theory and in the dipole approximation are compared with each other and with the available experimental data. The limits of applicability of the dipole approximation are determined. The prospects of using these nanoparticles as an active material in optical plasmon sensors are assessed.     

Scattering of Electromagnetic Radiation by ITO Nanoparticles with Various Doping Levels

The process of scattering of radiation by indium?tin oxide (ITO) nanoparticles is theoretically studied at various degrees of doping and for different radii of nanoparticles. Qualitative conclusions are made about the character of the dependence of the scattering cross section on the frequency with variation of the particle size and the percentage content of tin. The prospects of using ITO nanoparticles as an active substance in optical sensors are estimated.