Angular correlations in the inelastic-scattering process 24Mg(d, dγ)24Mg at E d = 15.3 MeV

The double-differential cross sections for the reaction ²⁴Mg(d, dγ _1.369)²⁴Mg at the projectiledeuteron energy of E _d = 15.3 MeV weremeasured for deuteron emission angles in the forward hemisphere. All even spin-tensor components of the density matrix for the 2⁺ state of the ²⁴Mg nucleus at 1.369 MeV were reconstructed, and its orientation properties were determined. These experimental results were compared with the results of calculations based on various versions of the coupled-channel method.     

Synthesis of nickel-doped alkali halide microcrystals and their spectral and structural analysis

Nickel-doped alkali halide microcrystals were obtained by various methods, including an original synthetic procedure. Their spectral and structural characteristics were investigated. The crystal field strength was calculated from the reflection spectra recorded for the microcrystals for different impurity concentrations. In contrast to single crystals, higher impurity concentrations can be obtained for lower degrees of aggregation in microcrystals.     

Synthesis and Crystal and Molecular Structure of 3,5-Dihydroxy-1-diphenylmethyleneamino-5-methoxycarbonyl-4-p-toluoyl-2,5-dihydro-2-pyrrolone

The reaction between methyl 2-diphenylmethylenehydrazino-4-oxo-4-p-tolyl-2-butenic ether and oxalyl chloride gave 1-diphenylmethyleneamino-5-methoxycarbonyl-4-p-toluoyl-2,3-dihydro-2,3-pyrroledione, which adds water to yield substituted 3,5-dihydroxy-2,5-dihydro-2-pyrrolone. The crystal and molecular structure of pyrrolone and the inter- and intramolecular hydrogen bonds in its crystals and solutions were investigated by IR spectroscopy and XRD analysis. The crystals of C₂₇H₂₂N₂O₆ are triclinic with cell dimensions a = 9.8540(10), b = 10.0880(10), c = 13.982(2) , = 69.820(10), = 110.57(10), = 91.350(10)°, V = 1213.8(2) ³, M = 470.47, d _calc = 1.287 g/cm³, Z = 2, space group P1. The data were collected on a KM-4 (KUMA DIFFRACTION) diffractometer, 3781 reflections with I> 2 (I). Direct methods, hydrogen atoms localized, least-squares refinement (in an anisotropic approximation for non-hydrogen atoms), R = 0.0454. The crystal is built from the centrosymmetric dimer associates of molecules bonded by strong (2.64 ) intermolecular hydrogen bonds (IMHB) of O–H...O type. The dimer associates are linked by weaker (2.82 ) centrosymmetric IMHB, forming an infinite chain of hydrogen-bonded molecules.     

Bubbles and droplets in nonlinear physics models: Analysis and numerical simulation of singular nonlinear boundary value problem

For a second-order nonlinear ordinary differential equation (ODE), a singular Boundary value problem (BVP) is investigated which arises in hydromechanics and nonlinear field theory when static centrally symmetric bubble-type (droplet-type) solutions are sought. The equation, defined on a semi-infinite interval 0 < r < ∞, possesses a regular singular point as r→ 0 and an irregular one as r→ ∞. We give the restrictions to the parameters for a correct mathematical statement of the limit boundary conditions in singular points and their accurate transfer into the neighborhoods of these points using certain results for singular Cauchy problems and stable initial manifolds. The necessary and sufficient conditions for the existence of bubble-type (droplet-type) solutions are discussed (in the form of additional restrictions to the parameters) and some estimates are obtained. A priori detailed analysis of a singular nonlinear BVP leads to efficient shooting methods for solving it approximately. Some results of the numerical experiments are displayed and their physical interpretation is discussed. This article was submitted by the author in English.     

Experimental investigations of nonresonance parametric interactions of elastic waves in solids

Results are presented of experimental investigations into nonresonance parametric interactions of elastic waves in isotropic solid media conducted on the base of audio modulation by sound in an aluminum alloy. It is shown that the experimental results agree well with the theory. Third-order elasticity constants and the absolute values of dynamic elastic fields are measured.     

Dynamical insurance models with investment: Constrained singular problems for integrodifferential equations

Previous and new results are used to compare two mathematical insurance models with identical insurance company strategies in a financial market, namely, when the entire current surplus or its constant fraction is invested in risky assets (stocks), while the rest of the surplus is invested in a risk-free asset (bank account). Model I is the classical Cramér–Lundberg risk model with an exponential claim size distribution. Model II is a modification of the classical risk model (risk process with stochastic premiums) with exponential distributions of claim and premium sizes. For the survival probability of an insurance company over infinite time (as a function of its initial surplus), there arise singular problems for second-order linear integrodifferential equations (IDEs) defined on a semiinfinite interval and having nonintegrable singularities at zero: model I leads to a singular constrained initial value problem for an IDE with a Volterra integral operator, while II model leads to a more complicated nonlocal constrained problem for an IDE with a non-Volterra integral operator. A brief overview of previous results for these two problems depending on several positive parameters is given, and new results are presented. Additional results are concerned with the formulation, analysis, and numerical study of “degenerate” problems for both models, i.e., problems in which some of the IDE parameters vanish; moreover, passages to the limit with respect to the parameters through which we proceed from the original problems to the degenerate ones are singular for small and/or large argument values. Such problems are of mathematical and practical interest in themselves. Along with insurance models without investment, they describe the case of surplus completely invested in risk-free assets, as well as some noninsurance models of surplus dynamics, for example, charity-type models.     

Luminescence of polymer composite materials with cadmium sulfide nanoparticles

The structure and optical characteristics of CdS nanoparticles synthesized in low-density polyethylene were studied. The particles have a hexagonal structure of the greenockite type; the presence of the cubic phase is also possible. The position of the absorption edge slightly depends on the average size of particles because of their polydispersity. It has been shown that the luminescence spectra of nanoparticles are strongly distorted by scattering and self-adsorption in the samples. To correct the spectra, a program for Monte-Carlo simulation of luminescence propagation in the samples was developed. It was shown that the luminescence band at 500–550 nm in the experimental spectra might be spurious because of luminescence absorption in the edge region.