Stability of layered coatings under biaxial thermomechanical loading

The three-dimensional problem of stability of layered coatings at normal and high temperatures and small precritical strains is formulated and solved and the characteristic equations are derived. The temperature dependence of the physical and mechanical parameters of specific layered coatings is established experimentally. Three-layer coatings on a homogeneous substrate at different temperatures are considered as an example. Recommendations for establishing the optimal service conditions for layered structural members with coatings are formulated.     

Genus-One Correction to Multicut Matrix Model Solutions

We calculate genus-one corrections to the Hermitian one-matrix model solution with an arbitrary number of cuts based on the loop equation, confirming the answer previously obtained from algebro-geometric considerations and generalizing it to the case of arbitrary potentials.     

Absorption UV spectroscopy and electronic structure of ionic and tautomeric forms of hydroxy and methoxy derivatives of cytosine and adenine,and of some 5-substituted analogs of pyrimidines

The individual absorption spectra of various ionic and tautomeric species of some derivatives of nucleic-acid components have been determined by computer handling of the summary spectra of these compounds measured at different pH values. These individual spectra have been decomposed into separate bands represented by log-normal curves and corresponding to different electronic transitions. Using the parameter system calculated earlier for the molecules of the vitamin B₆ family, the calculation of the electronic spectra and electronic structure of various ionic and tautomeric species of the molecules studied have been carried out in the π-electron approximation. These properties have also been calculated by the all-valence electronic method CNDOS . The calculated results correlate well with both approximations and with our experimental spectral data. The localization of the molecular electronic excitation studied on the transition to the S₁ and T₁ states is considered in connection with the reactivity in these states.     

Variational method of investigating the stability of laminar semiinfinite media

International Applied Mechanics -     

Representation of Solutions to the Equations of Statics for Transversely Isotropic Mildly Sloping Shells

A representation of solutions to the system of differential equations for the statics of elastic, transversely isotropic, mildly sloping shells is found in the form of a series in terms of a parameter that characterizes the difference of the median surface from spherical. Recurrence relations are obtained that can be used for solving boundary value problems by expansion in terms of a small parameter to arbitrary approximations.     

AdS3/CFT2 on a Torus in the Sum over Geometries

We investigate the AdS₃/CFT₂ correspondence for the Euclidean AdS₃ space compactified on a solid torus with the CFT field on the regularizing boundary surface in the bulk. Correlation functions corresponding to the bulk theory at a finite temperature tend to the standard CFT correlation functions in the limit of removed regularization. In the sum over geometries in both the regular and the ℤ _N orbifold cases, the two-point correlation function for massless modes transforms into a finite sum of products of the conformal-anticonformal CFT Green's functions up to divergent terms proportional to the volume of the SL(2, ℤ)/ℤ group. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 17–30, January, 2006.     

Surface instability of a homogeneous half-space coupled with a finite number of laminas

In the context of the model of a piecewise-homogeneous medium in three-dimensional formulation we study the problem of the surface loss of stability in laminated semi-bounded media with a finite number of laminas. For the study we invoke a version of three-dimensional stability theory constructed for small pre-critical deformations when the pre-critical state is determined from the geometrically linear theory. To construct the resolvent characteristic equations we use the matrix representation of the basic relations. Using a computer we carry out a numerical study of the stability of a homogeneous half-space coupled to various numbers of laminas, and we conduct a comparative analysis of the results. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 8–13.