Effect of trapping centers of luminescent properties of bismuth orthogermanate

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 6, pp. 970–975, June, 1991.     

Free and nonsteady-state oscillations of elastic fluid-filled systems situated on an elastic base

We develop a method of computing the nonsteady-state and free oscillations of a framed elastic structure situated on an elastic base and containing an ideal compressible fluid. The solution uses the method of integral transforms in conjunction with the method of orthogonal polynomials. In the transform space the problem reduces to systems of linear algebraic equations. The Fourier transform is applied to return to the original space. Examples of the computation are given.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 69–72.     

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.     

IFS attractors and Cantor sets

We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R³ such that every homeomorphism f of R³ which preserves K coincides with the identity on K.     

Direct Renormalizations of the One-Dimensional Torus

Renormalization formulas connecting the points of the orbits O ₀ ^± , i.e., the sequences generated by an irrational shift on the half-open interval [0, 1) or (0, 1], and the points of the orbits' derivatives d^mO ₀ ^± , i.e., the sequences obtained by restricting O ₀ ^± to half-open intervals of smaller length, are obtained. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 142–154.     

Noiselike magnetic resonance fine structure for ferromagnetic powders: Dipole-dipole interaction effects

A noiselike fine structure of ferromagnetic resonance spectra in magnetic powders was investigated after ultrasonic treatment. Magnetic interactions between particles are proved to have an influence upon the fine structure formation. After decreasing dipole-dipole magnetic interactions in dilute suspension a special order appears in fine-structure spectra, which is generally the same for different systems.     

Coherent Type-B e + e- Pair Production by Photons in a Crystal

An overview of theoretical and experimental studies of the coherent type-B e ⁺ e-pair production by photons in aligned crystals performed at Nuclear Physics Institute at Tomsk Polytechnic University is given.     

On the Determination of the Absolute Intensities of Vibrational-Rotational Lines of XY3 Molecules with C 3v Symmetry

Analytical formulas are derived that describe the dependences of the transition probabilities in vibrational-rotational spectra of XY₃-type molecules with C _3v symmetry on the rotational quantum numbers.     

Christoffel-Darboux-type formulae and a recurrence for biorthogonal polynomials

It is proved that biorthogonal polynomials obey two different kinds of Christoffel-Darboux-type formulae, one linking polynomials with a different parameter and one combining polynomials with different degrees. This is used to produce a mixed recurrence relation, which is valid for all biorthogonal polynomials. This recurrence relation establishes several results on interlacing property of zeros of successive biorthogonal polynomials and leads to a new result on the interlace of zeros of orthogonal polynomials (of equal degrees) with respect to two distributionsdψ(x) andx ^p dψ(x), 0<p≤1, with support in either [0, 1] or [1, ∞).