Isolation of singularities in the density and the kernel of a two-dimensional integral equation for complex boundary surfaces

We consider the solution of integral equations in problems of three-dimensional electromagnetic fields in piecewise-homogeneous media. An algorithm is proposed for analytical isolation of singularities in the kernel and the density of the integral equation of potential theory for the case of complex boundary surfaces.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 14–17, 1985     

Estimating a reduced rank regression model for non-normal variables

A method using third order moments for estimating the regression coefficients as well as the latent state scores of the reduced-rank regression model when the latent variable(s) are non-normally distributed is presented in this paper. It is shown that the factor analysis type indeterminacy of the regression coefficient matrices is eliminated. A real life example of the proposed method is presented. Differences of this solution with the reduced-rank regression eigen solution are discussed.     

Fluorescence spectra of different configurations of the diphenyl molecule in solid paraffin solutions

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 51, No. 2, pp. 212–217, August, 1989.     

Schmidt analysis of pure-state entanglement

We examine the application of Schmidt mode analysis to pure-state entanglement. Several examples permitting exact analytic calculation of Schmidt eigenvalues and eigenfunctions are included, as well as evaluation of the associated degree of entanglement.     

On the variational representation of solutions to some quasilinear equations and systems of hyperbolic type on the basis of potential theory

We demonstrate a method that permits to obtain generalized solutions for some quasilinear equations and systems of hyperbolic type. The corresponding variational principle is constructed using the theory of equilibrium of a potential in an external field. Dedicated to the memory of B. M. Levitan Supported by RFBR grants Nos. 05-01-00522 and NSh-1551.2003.1, by Program No. 1 of the Branch of Mathematics, Russian Academy of Sciences, and by INTAS project No. 03-51-6637.     

Observation of the nonlinear effect in relativistic Thomson scattering of electron and laser beams

Thomson scattering of high-power laser and electron beams is a good test of electrodynamics in the high-field region. We demonstrated production of high-intensity X-rays in the head-on collision of a CO₂ laser and 60-MeV electron beams at Brookhaven National Laboratory, Accelerator Test Facility. The energy of an X-ray photon was limited at 6.5 keV in the linear (lowest order) Thomson scattering, but the nonlinear (higher order) process produces higher energy X-rays. We measured the angular distribution of the high-energy X-rays and confirmed that it agrees with theoretical predictions.     

Advantages of NIR radiation use for optical determination of skin horny layer thickness with embedded TiO2 nanoparticles during tape stripping procedure

The tape stripping technique is an experimental method frequently used for reconstruction of the in-depth distribution of various topically administered substances within the horny layer of human skin, e.g., compounds contained in sunscreens. Titanium dioxide (TiO₂) nanoparticles (25–200 nm in diameter) are one such compound. Optical techniques which apply blue light are found to be suitable for reconstruction. However, the presence of particles affects the light propagation within the skin and therefore causes incorrect determination of strip thickness, leading to an improper reconstructed distribution of nanoparticle concentration revealed from the experimental data. This study evaluates the errors emerging from the use of blue (400 nm) and NIR (800 nm) radiation and finds the use of longer wavelength light more advantageous. Particles of different diameters are considered, and it is revealed that the application of small particles (25–60 nm) results in the lowest rate of error.     

Spatial structure of acousto-optic phase matching in uniaxial crystals

The spatial structure of Bragg angles and the transfer functions of an acousto-optic cell are calculated for the cases of isotropic and anisotropic light diffraction in a uniaxial crystal. Their change with ultrasound frequency is traced. The possibility of image processing by acousto-optic filtration of the spatial spectrum of an image is considered. The results of experimental visualization of the transfer functions of a calcium molybdate crystal cell are presented.