Universal elementary constituents of potential transformations shifting waves (qualitative theory)

It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization of a chosen bound state in a potential well of finite width are as well applicable to the scattering functions if states of the continuous spectrum are considered as bound states normalized to unity but distributed on an infinite interval with vanishing density. The potential perturbations of the same type on the half-axis concentrate the scattering wave at the origin, thus creating a bound state embedded into the continuous spectrum (zero width resonance).     

The role of metallic palladium in the reductive decomposition of π-allyl palladium chloride in aqueous alkaline solutions

Russian Chemical Bulletin -     

Dynamic Bifurcation of Multibody Systems

In this paper, the process of loss of stability of multibody systems and structures is analyzed. A novel approach is presented and applied to the statically loaded spatial systems for the analysis of a dynamic response of systems imposed on impact, high velocity compulsive motion, or percussive forces. The analysis is based on the solution of the dynamic equations and eigenvalue problem of systems, and of the resultant motion simulation. The flexible systems are discretized using the finite element method. The dynamic equations are derived with respect to the relative coordinates of the finite elements. Large flexible deflections due to a loss of stability are simulated. The initial forms of the possible deformations are defined by the computed eigenvectors solving the eigenvalue problem for the system stiffness matrix. The critical forces and system deflections are then analyzed. Examples of bifurcation of beam and beam structure imposed on compulsive motion, percussive forces, and impact are presented.     

A rheological model of polymers and glass-reinforced plastics

Network polymers and the corresponding glass-reinforced plastics are investigated for a homogeneous uniaxial state of stress and constant temperature. A physical law relating the high-elastic strain and the stress in explicit form with once-determined structural constants is obtained for the damped (bounded) creep regime. The theoretical solutions are compared with the experimental data for a glass-reinforced plastic based on unsaturated polyester resin and glass mat reinforcement.Institute of Engineering Mechanics, Bulgarian Academy of Sciences, Sofia. Translated from Mekhanika Polimerov, No. 5, pp. 851–857, September–October, 1971.     

Nonlinear physical stress - strain relationship of cellular polymers and glass plastics under conditions of attenuating creep

The coupling equations of hard cellular polymers and glass plastics based on these are analyzed. The material is considered as an elastically relaxing medium for the case of small deformations. The physical relationship between the rubber-elastic stresses and strains is derived in explicit form for the case of attenuating creep and a uniform three-dimensional stressed state. The total deformations are described by the one-dimensional rheological model of a "typical body" with a reduced stress and an instantaneous elastic modulus, having the appropriately chosen viscosity of a non-Newtonian liquid.Institute of Technical Mechanics, Bulgarian Academy of Sciences, Sofia. Translated from Mekhanika Polimerov, No. 2, pp. 231–235, March–April, 1972.     

Multichannel and Multidimensional Bargmann Potentials

The class of potential matrices for which coupled channel Schrödinger equations have exact solutions is presented. This is achieved due to degeneration of the kernel of the inverse-problem integral equation with respect to the channel indices, in addition to separability of its coordinate dependence. No attention has been paid before to this fact. Maybe therefore there was no satisfactory multichannel generalization of Bargmann potentials. Partially nonlocal Bargmann potentials for multidimensional and many-particle systems are constructed. Examples of new transparent potentials are given.     

Combined theoretical and experimental deep-UV resonance raman studies of substituted pyrenes

The results of time-dependent density functional theory (TDDFT) calculations of resonance Raman intensities are combined with experimental deep-ultraviolet resonance Raman measurements at a single wavelength, i.e., 244 nm, in order to test the possibility to distinguish several very similar compounds. Pyrene and three of its substituted derivatives, in which a single hydrogen atom has been replaced by a halogen atom, are compared. The fixed 244 nm excitation wavelength overlapped with the same electronic transition of the four pyrenes. Ground-state calculations using the BP86 exchange-correlation functional were used to predict the Raman frequencies, whereas excited-state calculations have been carried out employing the "statistical averaging of (model) orbital potentials" (SAOP) potential within a linear-response TDDFT framework in combination with the short-time approximation of resonance Raman intensities. In view of the simplistic theoretical approach, we find a surprisingly good agreement between the simulated and measured resonance Raman spectra of pyrene and its substituted analogues in terms of frequencies and intensities, which shows that the calculations can be used reliably to interpret the experimental spectra. With this combined information, it is possible to find criteria to distinguish the compounds under investigation, although many features of their vibrational spectra are similar.     

Mathematical justification of a heuristic for statistical correlation of real-life time series

Many of the analyses of time series that arise in real-life situations require the adoption of various simplifying assumptions so as to cope with the complexity of the phenomena under consideration. Whilst accepting that these simplifications lead to heuristics providing less accurate processing of information compared to the solution of analytical equations, the intelligent choice of the simplifications coupled with the empirical verification of the resulting heuristic has proven itself to be a powerful systems modelling paradigm. In this study, we look at the theoretical underpinning of a successful heuristic for estimation of urban travel times from lane occupancy measurements. We show that by interpreting time series as statistical processes with a known distribution it is possible to estimate travel time as a limit value of an appropriately defined statistical process. The proof of the theorem asserting the above, supports the conclusion that it is possible to design a heuristic that eliminates the adverse effect of spurious readings without loosing temporal resolution of data (as implied by the standard method of data averaging). The original contribution of the paper concerning the link between the analytical modelling and the design of heuristics is general and relevant to a broad spectrum of applications.     

Three-body inverse scattering problem

Two methods are suggested to reconstruct three-body potentials from three-body scattering data. This was achieved by using the reduction of the corresponding Schrödinger equation to a system of ordinary differential equations (not integro-differential equations as usual in the direct problem). Exactly solvable three-body models are presented. A new simple method for solving the multi-dimensional inverse problem in a finite-difference approximation is considered in the Appendix.