Elastic arches with large elevation. Singularly perturbed problem of nonlinear elasticity

In this paper we examine the asymptotic expansion of a three-dimensional displacement field defined over a slender, bowlike domain whose shape corresponds to a thin arch. We show that it is possible to derive from the principles of virtual work two families of arch equations whose forms vary with the scale of external forces and the curvature of the arch. The first family of models, for relatively small curvatures, is described by singularly perturbed ordinary differential equations. The second family, when the curvature of the original arch is large, is described by two-dimensional partial differential equations whose form depends on the shape of the cross-section of the solid arch.     

A numerical method for separation of overlapping components of a spectral line

A simple method for separation of two overlapping spectral lines with the same intensity distribution is given. The method covers the case of spectrometers with periodical instrumental functions and gives explicit formulae for the intensity distribution of the components in selected points.     

Consequence of hydrogen atom abstraction from 5’-hydroxyl group of 2’-deoxyadenosine. Theoretical quantum mechanics study

Reactive oxygen species (ROS) may generate different nucleoside/nucleotide radicals in a cell environment. In this study, the possibility of cyclic-2’-deoxyadenosines formation by a rearrangement of their free radicals was investigated. It seems that for cyclic-nucleosides formation, adoption of an O4’-exo conformation by the sugar moiety is necessary. However, this is the energetically unfavoured form of the 2-deoxyribose ring. Moreover, the creation of a O5’, C8 bond in purine deoxy-nucleosides/nucleotides leads to the termination of the DNA elongation process.      

Mössbauer studies of Soltmany and Shisr 176 meteorites – comparison with other ordinary chondrites

Two ordinary chondrites type L6: Soltmany and Shisr 176, were recently investigated in our laboratory. The distribution of iron in the 4 main iron bearing mineral phases (olivine, pyroxene, kamacite and troilite) determined by Mössbauer spectroscopy in Soltmany and Shisr 176 meteorites was very different from that in the Baszkowka meteorite (type L5). To explain the cause of this difference, a comparison of the distribution of iron among the main mineral phases present in other type L and H meteorites was performed. Our studies have shown that the Baszkowka meteorite is not a good point of reference for Soltmany and Shisr 176 meteorites.     

Dynamical models for plates and membranes. An asymptotic approach

We examine the asymptotic expansion of a time-dependent displacement field defined over a three-dimensional elastic body whose shape corresponds to a thin plate. We show that under simple assumptions it is possible to derive from the principles of virtual work two known plate equations and three membrane models. Our results modify the displacement-stress method used by P.G. Ciarlet to derive von-Kárman plate equations. The modified algorithm allows one to employ techniques of algebraic geometry which simplify the computational aspects of the analysis.     

On the definition of singular bilinear forms and singular linear operators

We analyze various definitions of the concepts of a singular operator and a singular bilinear form and propose the most suitable ones. We also study the simplest properties of these objects.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 8, pp. 1084–1089, August, 1993.     

Ground-state energies of closed-shell atoms

Ground-state energies of He, Be, and Ne isoelectronic series have been calculated. The Dirac–Hartree–Fock energy values have been corrected by adding Breit, vacuum polarization, self-energy, nuclear mass, and electron correlation corrections. The resulting energies are compared with the experimental values. As a result, an estimate of the correlation-relativistic cross-term energy is obtained. The effect, for large-Z atoms, proves to be quite substantial.     

Symmetric‐group‐based methods in quantum chemistry

The eigenvalue problem of a Hamiltonian represented in a finite-dimensional model space being the N-electron subspace of the 2K-spinorbital Fock space is analyzed. It is pointed out that the permutation group S _N is a very convenient framework for this analysis. The resulting approach is known as the symmetric group approach to the N-electron problem. Its applications to construction of a basis in the model space, to the evaluation of matrix elements of spin‐independent and of spin‐dependent operators and, finally, to solution of the eigenvalue problem of the Hamiltonian are briefly reviewed. Recently developed applications of the symmetric group to studies of the Heisenberg Hamiltonian spectra and to evaluation of spectral density distribution moments are also dicussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Symmetric group graphical approach to the direct configuration interaction method

An approach to the configuration interaction method based on symmetric groups (SGA ) is developed. The formalism is an alternative of the unitary group approach (UGA ). In many aspects the present formulation seems to be superior to UGA . In particular, in SGA the orbital and the spin parts of the configuration state functions may be processed separately. In consequence its graphical formulation is much simpler and the coupling constant expressions are more compact than the UGA analogs. A special emphasis is put on direct CI implementations. In addition to formulas for coupling constants, explicit expressions allowing for separation of external and internal space contributions are also presented.