Qualitative analysis of finite-gap solutions of the KgΦ equation by the automorphic approach

By the automorphic approach and the use of computer graphics, we carry out a qualitative analysis of finite-gap periodic solutions of the Kg equation. Graphs are constructed for multiphase solutions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 165, pp. 31–41, 1987.     

Solution of the inverse problem for an evolution equation in a Banach space

For the equationdy (t)/dt=Ay(t) + p, t [0, ), where A is a closed linear operator on a Banach space , p is an unknown parameter from , we consider the problem

Nonlinear properties of surface “screw” instability in symmetric semiconductor plates

For the first time we study the nonlinear properties of the surface screw instability (SSI) when waves are excited at both faces of a plate and the interaction between them must be taken into account. The nature of the SSI development and the stability of surface screw waves against modulation are examined. Diagrams of the regions where the SSI development is soft and explosive as well as the regions of modulated waves are given in the space of parameters characterizing the electro-hole plasma and external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–34, April 1990.     

Behavior of effective charges in e6 grand unification theory in curved spacetime

The behavior of effective charges _i(t) corresponding to the parameters of nonminimal coupling of scalar and gravitational fields in E₆ Grand Unification Theory (GUT) in curve spacetimes is studied. It is shown that in a strong gravitational field ¦_i(t)¦ grows indefinitely.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 74–11, September, 1990.     

Crystal structure oftrans-[PtCl2(Me2PhP)(cis-2,5-dimethylpyrrolidine)]

The complextrans-[PtCl₂ (Me₂PhP)(cis-2,4-dimethylpyrrolidine)] has been characterized by X-ray crystallography. It crystallizes in the monoclinic space group P 2₂/c witha=8.762(3),b=16.034(5),c=12.600(4)Å,=93.43(3)° andZ=4. The structure was solved by heavy atom method and refined toR=0.052 for 3251 observed counter reflections. The coordination sphere of the Pt atom is square-planar with a geometry very similar to that of the studied complexes of the type trans-[PtCl₂(R₃P)L] whereL is either one of the possible isomers of theC,C-dimethylpyrrolidine or the unsubstituted pyrrolidine. In the present complex the puckered five-membered ring of the dimethylpyrrolidine ligand assumes an envelope conformation with the maximum puckering at the N atom.     

Relaxation methods in control theory

Two different relaxed problems associated with a problem of optimal control theory, governed by an ODE, are considered: the first is obtained by Young's methods and the second by semicontinuity arguments. A formula which relates the two relaxed functionals to each other is given.     

Entropy dissipation rate and convergence in kinetic equations

We give a lower bound of the entropy dissipation rate of Ka, Boltzmann and Fokker-Planck-Landau equations. We apply this estimate to the problem of the speed of convergence to equilibrium in large time for the Boltzmann equation.     

Precipitation structure in an Al-2·0 at. % Zn-1·0 at. % Mg alloy within and close to the grain boundaries and its effects on mechanical properties

During ageing the Al-2·0 at. %Zn-1·0 at. % Mg alloy at elevated temperatures the width of the precipitation free zone (PFZ) at both sides of the grain boundaries (GB) is identical with that free of quenched-in dislocation loops (DL). After sufficiently long ageing a band of precipitates is growing inside the former PFZ and the DLs in the midgrain regions act as sites for the heterogeneous nucleation of the-phase. Two precipitation processes significantly affect the mechanical properties. TEM correlates grain boundary precipitate density and morphology with grain boundary misorientation.