Shilnikov lemma for a nondegenerate critical manifold of a Hamiltonian system

Let M be a normally hyperbolic symplectic critical manifold of a Hamiltonian system. Suppose M consists of equilibria with real eigenvalues. We prove an analog of the Shilnikov lemma (strong version of the λ-lemma) describing the behavior of trajectories near M. Using this result, trajectories shadowing chains of homoclinic orbits to M are represented as extremals of a discrete variational problem. Then the existence of shadowing periodic orbits is proved. This paper is motivated by applications to the Poincaré’s second species solutions of the 3 body problem with 2 masses small of order µ. As µ → 0, double collisions of small bodies correspond to a symplectic critical manifold M of the regularized Hamiltonian system. Thus our results imply the existence of Poincaré’s second species (nearly collision) periodic solutions for the unrestricted 3 body problem.     

Complexation of heterocyclic ligands with DNA in aqueous solution

We have used spectrophotometry to study self-association and complexation with DNA by organic heterocyclic compounds in the acridine and phenothiazine series: proflavin, thionine, and methylene blue. Based on the experimental concentration dependences of the molar absorption coefficient of the molecules in an aqueous buffer solution (0.01 M NaCl, 0.01 M Na₂EDTA, 0.01 M Tris, pH 7.4, T = 298 K), we have determined the equilibrium dimerization constants for the dyes and the DNA complexation parameters using the Scatchard and McGhee-von Hippel models. The observed increase in the cooperativity parameters as the dimerization constants of the ligands increase allowed us to hypothesize that the same interactions occur between dye molecules adsorbed on DNA as in their self-association. The equilibrium DNA-binding constants for the ligands, obtained using the McGhee-von Hippel cooperative model, are (20.9 ± 2.7)·10³ M⁻¹ for proflavin and (33.8 ± 4.1)·10³ M⁻¹ for thionine. Using the Scatchard model, taking into account intercalation and “external” binding of ligands with DNA, we determined the DNA complexation constants for methylene blue: (26.4 ± 4.6)·10³ and (96 ± 17)·10³ M⁻¹ respectively. Based on analysis of the data obtained, we hypothesized that the predominant type of binding with DNA is intercalation binding in the case of proflavin and thionine, and “external” binding with the DNA surface in the case of methylene blue. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 2, pp. 242–249, March–April, 2008.     

Reactions of Amidoximes with Metal-Activated Nitriles

Metal-mediated reactions of amidoximes with nitrile ligands are discussed and recent works of the author are considered to allow the reader to better understand the amidoxime reactivity patterns. General routes of activation of amidoxime and nitrile substrates in the studied reactions are considered. Reactions employing amidoximes as HO- and HN-nucleophiles, as well as reactions of amidoximes with nitrile ligands leading to heterocyclic systems are discussed.     

Preparation and properties of silica gel with immobilized formazan group

A new sorption material, silica gel with covalently immobilized formazan group, was suggested and characterized. The material was prepared by coupling the immobilized aryldiazonium salt with benzaldehyde phenylhydrazone. The equilibrium and kinetic characteristics of the sorption of Cu(II), Co(II), Ni(II), and Cd(II) from solutions onto the modified silica gel were determined. The material proved to efficiently concentrate Cu(II) from multicomponent solutions. The coordination surrounding of Cu(II) in the complex on the sorbent surface was determined by ESR.     

Modifying the surface of a hydrogen permselective palladium–silver membrane

Thin films of Pd–23% Ag composition are obtained by means of magnetron sputter deposition. The surfaces of the films are modified via the electrolythic deposition of finely divided palladium. The hydrogen permeabilities of samples of membranes (both smooth and modified with palladium black) are compared. A marked increase in the hydrogen permeability of the modified membrane is observed, compared to the smooth membrane. The dependence of the rate of hydrogen fluence on the excess pressure is approximated by a curve of the first order, demonstrating the limitations of the process of hydrogen permeation by hydrogen superficial dissociation.     

On the multiplicity of periodic solutions of mountain pass type for a class of semilinear PDE’s

We prove the existence of many mountain pass periodic solutions for a semilinear elliptic PDE on a torus. The first author was supported by the National Science Foundation grant #0300319 and by the RFBR grant #050101119. The second author was supported by the NSF grant #MCS-8110556.     

Prediction of the growth of fatigue cracks taking environmental factors into account

A model of corrosion fatigue is proposed which takes into account the main phenomena of a mechanical nature, namely, the transfer of the active agent from the month of the crack to its tip, the accumulation of mechanical damage due to cyclic loads and the breakdown of the stability conditions in the body-with-cracks — load — environment system as the reason for the propagation of the crack tip. Particular attention is devoted to the mechanism by which active agent is transferred. In addition to diffusion, convective transfer as a consequence of the change in the shape and dimensions of the crack cavity is taken into account. The results of modelling are supplemented with diagrams, which relate the rate of growth of the crack with the range of the stress intensity factor, the concentration of the agent at the mouth of the crack and the characteristics of the cycle, equal to the ratio of the extremal values of the applied stresses in each cycle. The results are compared with experimental data.     

On the Influence of the Kinetic Energy¶on the Stability of Equilibria¶of Natural Lagrangian Systems

Natural Lagrangian systems (T,Π) on R ² described by the equation are considered, where is a positive definite quadratic form in and Π(q) has a critical point at 0. It is constructively proved that there exist a C ^∞ potential energy Π and two C ^∞ kinetic energies T and such that the equilibrium q(t)≡ 0 is stable for the system (T,Π) and unstable for the system . Equivalently, it is established that for C ^∞ natural systems the kinetic energy can influence the stability. In the analytic category this is not true. Accepted: October 20, 1999