Chaotic frictional vibrations excited by a quasiperiodic load

A Duffing oscillator frictionally interacting with a moving belt under a quasiperiodic load is studied. The multiple-scales method is used to derive a system of two nonautonomous equations with small parameters, which describes the modulation of vibrations. It is shown that the system of modulation equations has a heteroclinic structure. Melnikov functions are used to analyze the domain of heteroclinic chaos __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 127–133, September 2006.     

Class and rank of differential modules

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class – a substitute for the length of a free complex – and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over commutative noetherian rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.     

Vibrations of shallow shells rectangular in the horizontal projection with two freely supported opposite edges

The exact mode shapes of linear vibrations of a shallow shell rectangular in the horizontal projection with two freely supported opposite edges are obtained. These shapes are used to construct a discretemodel of vibrations of a shallow shell in geometrically nonlinear deformation. The harmonic balance method is used to study the free and forced nonlinear vibrations under internal resonance. The Lyapunov stability of the obtained periodic vibrations is analyzed.     

Modeling and calculations of the physicochemical parameters of diffusion of atomic hydrogen on the surface of differently sized nanotubes with different chiralities

This work is concerned with modeling the diffusion of atomic hydrogen on the surface of differently sized carbon nanotubes with different chiralities. The calculations were based on the estimation of activation energy by the density functional theory method and the use of transition state theory. Original Russian Text ? A.A. Kuzubov, R.P. Avramov, M.A. Raimova, M.N. Popov, Yu.M. Milyutina, T.A. Kozhevnikova, P.V. Artyushenko, 2009, published in Zhurnal Fizicheskoi Khimii, 2009, Vol. 83, No. 4, pp. 753–757.     

Free linear vibrations of thin axisymmetric parabolic shells

The Rayleigh–Ritz method is used to minimize the energy functional in order to calculate eigenfrequencies of parabolic shells. The properties of eigenfrequencies and eigenmodes of different heights parabolic shells are analyzed numerically.     

Homology algebra of the Koszul complex of a local Gorenstein ring

It is proved that local Gorenstein rings have the property that the homology algebra of their Koszul complex is a Poincaré algebra.Translated from Matematicheskie Zametki, Vol. 9, No. 1, pp. 53–58, January, 1971.