Discretization of the dynamic problem of elasticity theory with a discontinuous solution

A discretization algorithm for initial boundary-value problems is developed for systems of two linear equations of hyperbolic type with discontinuous solutions. A Crank—Nicholson scheme is constructed for discretization of the Cauchy problem and error bounds are obtained for the approximate solution. A model example is solved.Institute of Cybernetics of the Ukrainian Academy of Sciences. Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 75–83, 1991.     

Mathematical modelling of actinide extraction equilibria and extraction processes

Progress is reviewed in the authors' works on actinide extraction equilibria (including activity coefficient evaluation from extraction data) and their mathematical modelling (including Tc influence on Pu/U separation).     

Swell wave propagation in an inhomogeneous ice sheet

The propagation of surface waves beneath a periodically inhomogeneous ice sheet is considered. Areas of broken ice and hummock ridges are considered as irregularities. It is shown that waves with frequencies corresponding to wind and swell waves are strongly scattered by the irregularities and are damped exponentially as they propagate beneath the ice.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 162–169, September–October, 1996.     

A study of the interaction between polyelectrolyte-coated nanostructured CaCO<Subscript>3</Subscript> particles and a stearic acid monolayer spread at the water/air interface

The influence of nanostructured CaCO₃ particles, both uncoated and coated with a polyelectrolyte (poly(diallyldimethylammonium chloride), polyethyleneimine, fluorescein-5-isothiocyanate-labeled poly(allylamine hydrochloride), or sodium polystyrene sulfonate), on a stearic acid monolayer spread on the surface of an aqueous subphase has been studied. The interaction of the particles present in the subphase with the monolayer as depending on the presence and composition of a polymer coating has been estimated with the help of compression isotherms and the Brewster angle microscopy. The monolayers were transferred from the aqueous subphase onto a solid substrate and studied by scanning electron microscopy. Strong interaction has been revealed between the calcium carbonate particles and the stearic acid monolayer. It has been shown that the transfer of the monolayer from the aqueous suspension surface onto the solid substrate may be accompanied by the detachment of the polymer coating from the surface of CaCO₃ particles or their transfer together with the monolayer.     

Modal control of hybrid differential-difference systems and associated delay systems of neutral type in scales of differential-difference controllers

We study the statements and solvability of the modal control problem (the pole assignment problem) for linear time-invariant hybrid difference-differential systems in symmetric form and for the associated delay systems of neutral type. We obtain constructive necessary and sufficient parametric conditions for the modal controllability of the systems in question in various scales of difference-differential controllers. Methods for the construction of such controllers solving the corresponding modal controllability problem are indicated. The results are illustrated by examples and counterexamples.     

Plane Collision Problem for Two Identical Elastic Parabolic Bodies—Direct Central Impact

A direct central collision of two identical infinite cylindrical bodies is studied. A nonstationary plane elastic problem is solved. The variable boundary of the contact area is determined. A mixed boundary problem is formulated. Its solution is represented by Fourier series. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying boundary conditions. The basic characteristics of the collision process are determined numerically depending on the curvature of the frontal surface of the bodies     

Resonant inelastic x-ray scattering at the limit of subfemtosecond natural lifetime

We present measurements of the resonant inelastic x-ray scattering (RIXS) spectra of the CH(3)I molecule in the hard-x-ray region near the iodine L(2) and L(3) absorption edges. We show that dispersive RIXS spectral features that were recognized as a fingerprint of dissociative molecular states can be interpreted in terms of ultrashort natural lifetime of ～200 attoseconds in the case of the iodine L-shell core-hole. Our results demonstrate the capacity of the RIXS technique to reveal subtle dynamical effects in molecules with sensitivity to nuclear rearrangement on a subfemtosecond time scale.     

Synthesis and stereoisomerism of the decahydroquinoline series N-oxides 6. X-ray diffraction study of 1,2e-dimethyl-4a-ethynyl-4e-hydroxy-trans-decahydroquinoline N-oxide hydrobromide

The results of x-ray diffraction analysis on 1,2e-dimethyl-4a-ethynyl-4e-hydroxy-trans-decahydroquinoline N-oxide hydrobromide corroborated the orientation of the substituents at the nitrogen atom that was determined previously from PMR data.For Communication 5, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 82–85, January, 1993.