Whitham's dynamical principle for parabolic equations and its proof

A generalization of Whitham's asymptotic principle for parabolic equations is stated. An application of this principle to Fisher's one-dimensional nonlinear equation is considered.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 179, pp. 46–51, 1989.     

Construction of asymptotic solutions for weakly nonlinear Hamiltonian systems

A change of variables is constructed for a class of weakly nonlinear Hamiltonian systems which makes it possible to reduce the order of the nonlinearity from O() to O(²) and to construct asymptotic solutions. The results can be applied to some nonlinear partial differential equations of interest in physics.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 140, pp. 36–40, 1984.The author thanks V. M. Babich, V. F. Lazutkin, and I. A. Molotkov for useful remarks.     

Model compounds of caged capsaicin: design, synthesis, and photoreactivity

Molecules were prepared with substituted nitrobenzyl groups covalently bonded to N-(4-hydroxy-3-methoxybenzyl)acetamide (2) by ether or carbonate linkages. These compounds decomposed under irradiation at 363 nm. Those with carbonate linkages decomposed at slower rates than those with ether linkages. Molecules with dimethoxy-substituted benzyl groups decomposed more slowly than monomethoxy-substituted benzyl groups due to the electronic characteristics of the benzylic carbon.     

Crystal structure of di (1-n-dodecylpyridine) decahydro-closo-decaborate(2-) (C5H5N-C12H25)2[B10H10]

Using X-ray analysis, we have determined the crystal structure of di(1-n-dodecylpyridine) decahydrocloso-decaborate(2-), (py-C₁₂H₂₅)₂[B₁₀H₁₀] (I), a yellow salt-like substance obtained by reaction of (py-C₁₂H₂₅)Br and K₂[B₁₀H₁₀] in an aqueous solution. Compound I melts at 125⁰ without decomposition and luminesces under ultraviolet radiation (λ_max=555 nm at 298 K). In I, quaternary pyridine bases, containing a hydrocarbon radical with the C₁₂ chain, are combined with the closo-cluster hydroborate anion [B₁₀H₁₀]^2-. This results in a charge transfer structure having shortened nonvalent (equatorial B) H.…H(C of pyridine) contacts of 2.41(8) Å. Crystals I are orthorhombic with a=8.584 (1), b=7.739(1), c=31.183(5) Å, V_cell=2071.4(5) ų, space group Pnmm, Z=2, d_calc=0.986 g/cm³ (a Syntex P2₁ automatic diffractometer, λCUK_α, N_msd/used=1654/711, R_aniso=0.076, R_w=0.080, w=1/(σ(F_obs)²+0.0007·F _obs ² ). Substantial changes are observed in the vibration range of the valent B?H bonds in the IR spectrum of I as compared to that of pure ionic K₂[B₁₀H₁₀], confirming the interaction.     

A condition for the absence of the singular continuous spectrum in the Friedrichs model. II

One considers a self-adjoint operator H for which one has a unitary group U such that the operator H UHU ^–1 is analytic with respect to . Under certain additional restrictions on H, one proves the absence of the singular continuous spectrum of H. In this connection one admits such a behavior of the essential spectrum of H for Im 0 which excludes the application of the method of analytic dilatations. In our analysis, analogies with the method of the inverse scattering problem play an important role.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 127, pp. 3–6, 1983.     

Justification of an asymptotic formula for solutions of the perturbed Klein-Fock-Gordon equation

A problem with periodic boundary conditions is considered for the Fock-Klein-Gordon equation perturbed by a small nonlinear operator R[t, u, u_x, u_xx]:. It is shown that under certain conditions the solution exists and is close to the known asymptotic solution on the interval 0 t l/.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 104, pp. 84–92, 1981.In conclusion, the author wishes to thank I. A. Molotkov, V. M. Babich, Ya. V. Kurylev, M. M. Popov, V. B. Filippov, and all the participants in the seminar on wave diffraction (LOMI) for valuable advice, pointers, and discussions.     

Formation of vortex flows in thin nematic cells

The director field reorientation and the formation of steady vortex flows in doubly and obliquely oriented thin liquid-crystal cells under the temperature gradient have been theoretically described within the nonlinear generalization of the classical Ericksen-Leslie theory for describing liquid crystal hydrodynamics. This generalization allowing the consideration of thermomechanical contributions to the shear stress and to the entropy balance equation has made it possible to describe the formation of a steady two-vortex flow in doubly oriented liquid-crystal cells.     

Structural Basis for Carbapenemase Activity of the OXA-23 β-Lactamase from Acinetobacter baumannii

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Dissipative and Hamiltonian Systems with Chaotic Behavior: An Analytic Approach

Some classes of dissipative and Hamiltonian distributed systems are described. The dynamics of these systems is effectively reduced to finite-dimensional dynamics which can be unboundedly complex in a sense. Yarying the parameters of these systems, we can obtain an arbitrary (to within the orbital topological equivalence) structurally stable attractor in the dissipative case and an arbitrary polynomial weakly integrable Hamiltonian in the conservative case. As examples, we consider Hopfield neural networks and some reaction–diffusion systems in the dissipative case and a nonlinear string in the Hamiltonian case.     

Surface tension of free-standing smectic films

A generalized mean-field model, which takes into account the anisotropic interactions between the nearest neighbor molecules (forming free-standing smectic films (FSSFs)) and the stabilizing effect of smectic-air interfaces, has been used for numerically studying the structural and thermodynamic properties of these systems during their layer-by-layer thinning. The results of calculating the surface tension γ of a partially fluorinated liquid-crystal compound formed by 5-n-alkyl-2-(4-n-(perfluoroalkyl-methyleneoxy))pentyl (H10F5MOPP) molecules have demonstrated that the value of γ per FSSF molecule undergoes a stepwise increase during layer-by-layer thinning of the film. The dimensional surface tension during the layer-thinning of a 25 layer FSSF formed by H10F5MOPP molecules varies insignificantly within ∼19 dyn/cm, which agrees with the experimental value (∼14 dyn/cm) for this liquid-crystal compound.