Straight chains of interconnected mass points under the action of non-symmetric dry friction

The motion of a chain of interconnected equal material points placed on a rough straight line and connected by equal kinematical constraints is considered. It is supposed that the system experiences a small non-symmetric Coulomb dry frictional force acting from the line side upon each mass point and opposite to the direction of motion. The magnitude of this force depends on the direction of motion. To the equation of motion the procedure of averaging is applied. The expression for the stationary “on the average” velocity of the motion of the system as a single whole is found. The obtained theoretical results can be used for the design of worm-like vibration robots. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Metallation of poly(1-trimethylsilyl-1-prop-1-yne) and poly(vinyltrimethylsilane) with superbases

The pathway and degree of metallation of polymers were studied depending on the the conditions (temperature, concentration, nature, and component ratio) of metallation of poly(1-trimethylsilylprop-1-yne) (PTMSP) and poly(vinyltrimethylsilane) (PVTMS) by superbases, viz., BuⁿLi and Bu^sLi, in combination with potassium tert-pentyl oxide (Pe^tOK). For the BuⁿLi—Pe^tOK system (1 : 3), the yield of modified PTMSP reached 90%. In the case of PTMSP, only the Me groups at the double bonds and at the Si atoms undergo metallation, whereas only the Me groups at the Si atoms are metallated in PVTMS. The kinetics of metallation with the BuⁿLi—Pe^tOK system was studied.     

Electronic excitation energy transfer in solid solution of 7-diethylamino-3,4-benzophenoxazine-2-one (Nile Red dye) in bis[N-2-(oxybenzylidene)-4-tert-butylaniline]zinc

Transfer of electronic excitation energy from the host material to guest molecules was studied taking the solid-phase system bis[N-(2-oxybenzylidene)-4-tert-butylaniline]zinc + 7-diethylamino-3,4-benzophenoxazine-2-one (the guest compound) as an example. The luminescence excitation spectra and the concentration quenching of green fluorescence of the host compound and the excitation of sensitized red fluorescence of the guest molecules were studied. Among the exciton mechanism of energy migration and Förster"s long-range, single-jump mechanism, the former dominates. The number of jumps (m) and the mean diffusion length of the singlet exciton (l), calculated in the framework of the model of partially delocalized, randomly hopping exciton, were estimated at 1.5·10³ and 450 , respectively.     

A central limit theorem for projections of the cube

We prove a central limit theorem for the volume of projections of the cube \([-1,1]^N\) onto a random subspace of dimension \(n\) , when \(n\) is fixed and \(N\rightarrow \infty \) . Randomness in this case is with respect to the Haar measure on the Grassmannian manifold.     

Quantum effects for parametric X-ray radiation during channeling: Theory and first experimental observation

The theory of X-ray radiation from relativistic channeled electrons at the Bragg angles—parametric X-ray radiation (PXR) during channeling (PXRC)—is developed while accounting for two quantum effects: the initial population of bound states of transverse motion and the transverse “form-factor” of channeled electrons. An experiment was conducted using a 255 MeV electron beam from a linac at the SAGA Light Source. We have identified a difference in the angular distributions of PXR and PXRC and obtained a fairly good agreement between the theoretical and experimental results.     

Nonstationary interference wave fields of SV type in a free elastic layer and the problem of ultrasonic simulation of plane seismic fields by using plate models

The problem of quantitatively studying wave fields in a free elastic layer excited by a nonstationary point source is discussed. Much attention is given to the low-frequency part of the Fourier spectrum. The roots of the dispersion equation of the layer are studied comprehensively, and on this basis efficient methods of quantitatively estimating interference wave modes are developed. Particular attention is given to the ultralow-frequency band of the spectrum. This allows us to make progress toward the mathematical justification of methods of seismic modeling of plane wave fields on plate models. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 225, 1997, pp. 121–239. Translated by N. S. Zabavnikova.