Temperature and concentration dependences of the electronic etructure of copper oxides in the generalized tight binding method

The electronic structure of p-type doped HTSC cuprates is calculated by explicitly taking into account strong electron correlations. The smooth evolution of the electronic structure from undoped antiferro-magnetic to optimally and heavily doped paramagnetic compositions is traced. For a low doping level, in-gap impurity-type states are obtained, at which the Fermi level is pinned in the low-doping region. These states are separated by a pseudogap from the valence band. The Fermi surfaces calculated for the paramagnetic phase for various concentrations of holes are in good agreement with the results of ARPES experiments and indicate a gradual change in the Fermi surface from the hole type to the electron type.     

Using Pseudoperiodicity for Polycrystal XRD Determination of the General Structural Motif of Coordination Compounds

This review summarizes experience in polycrystal diffractogram analysis for 100 coordination compounds using the translation sublattice isolation technique. The most widespread cases are described, and the general strategy of analysis is proposed. Conditions for transition from a rhombohedral sublattice to cubic lattices with different centerings are discussed.     

Adsorption of hydrophobic polyelectrolytes onto oppositely charged surfaces

We present a scaling theory for the adsorption of a weakly charged polyelectrolyte chain in a poor solvent onto an oppositely charged surface. Depending on the fraction of charged monomers and on the solvent quality for uncharged monomers, the globule in the bulk of the solution has either a spherical conformation or a necklace structure. At sufficiently high surface charge density, a chain in the globular conformation adsorbs in a flat pancake conformation due to the Coulombic attraction to the oppositely charged surface. Different adsorption regimes are predicted depending on two screening lengths (the Debye screening length monitored by the salt concentration and the Gouy-Chapman length monitored by the surface charge density), on the degree of ionization of the polymer and on the solvent strength. At low bulk ionic strength, an increase in the surface charge density may induce a transition from an adsorbed necklace structure to a uniform pancake due to the enhanced screening of the intra-chain Coulombic repulsion by the counterions localized near the surface. Received 12 April 2001     

Efficiency of the production of γ families with halos and the fraction of protons at an energy of 10<Superscript>16</Superscript> eV

γ Families with halos detected in the “Pamir” experiment have been analyzed. Comparison of the experimental data with the results of calculation within the quark-gluon string model (MC0 code) made it possible to determine the efficiency of halo formation by protons, α particles, and heavy nuclei, as well as the fraction of protons in the mass composition of primary cosmic rays at an energy of 10¹⁶ eV. It is shown that halos are formed predominantly by protons. The fraction of protons in the mass composition of primary cosmic rays at an energy of 10¹⁶ eV is 20%.     

Optimal synthesis in an infinite-dimensional space

For a class of optimal control problems and Hamiltonian systems generated by these problems in the space l ₂, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space l ₂ forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.     

Asymptotic behavior of singular solitons and the inverse scattering method for solving boundary value problems

We solve the boundary value problems for the sine-Gordon equation and the elliptic Toda lattice in the framework of the inverse scattering method. This approach allows incorporating the singular soliton solutions of the spiral vortex form. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 2, pp. 279–291, August, 2000.     

Rational-exponential solutions of nonlinear equations

A new, straightforward and systematic approach to construct rational-exponential solutions is proposed. The method is based on the formal perturbation theory. Explicit rational-exponential solutions for the two-dimensional elliptic sine-Gordon and Korteweg-de Vries equations are constructed. The method used is quite general and applicable to most nonlinear evolution equations, including certain multidimensional equations.