Nonlinear equations of flexural-flexural-torsional oscillations of rotating beamswith arbitrary cross-section

A system of three nonlinear partial differential equations describing the flexural-flexural-torsional vibrations of a rotating slender cantilever beam of arbitrary cross-section is derived using Hamilton’s principle. It is assumed that the center of gravity and the shear center are at different points. The interaction between flexural and torsional vibrations is accounted for in the linear and nonlinear parts of model Published in Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 123–132, May 2008.     

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.     

Reduction of derived Hochschild functors over commutative algebras and schemes

We study functors underlying derived Hochschild cohomology, also called Shukla cohomology, of a commutative algebra S essentially of finite type and of finite flat dimension over a commutative noetherian ring K. We construct a complex of S-modules D, and natural reduction isomorphisms for all complexes of S-modules N and all complexes M of finite flat dimension over K whose homology H(M) is finitely generated over S; such isomorphisms determine D up to derived isomorphism. Using Grothendieck duality theory we establish analogous isomorphisms for any essentially finite-type flat map of noetherian schemes, with f^!OY in place of D.     

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.     

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.     

Kinetic study of thermal decomposition of CoOOH

The kinetics of the thermal decomposition of CoOOH powder has been studied isothermally in a temperature range of 260—310°C in air. The reaction was found to proceed by the advance of a two-dimensional reaction interface. The kinetics results indicate that there are two phases in the decomposition in this temperature range: up to 280°C with an activation energy E₁ = 34.75 kcal mol⁻¹ and above 280°C with E₂ = 18.91 kcal mol⁻¹. A reaction mechanism is proposed to account for these observations.     

Thermal stability of the amorphous system Ge20As14(SexS1−x)52I14

Results of thermal investigations of the amorphous five-component chalcogenide system Ge₂₀As₁₄(Se_xS_1?x)₅₂I₁₄ are presented. Differential thermal analysis (DTA), derivative differential thermal analysis (DDTA), and dilatometry were employed to determine the temperatures of softening and partial crystallization of the samples. Thermal treatment of the samples at 1000°C and recording of the corresponding thermogravimetric (TG) and derivative thermogravimetric (DTG) curves allowed an elucidation of the full mechanism of their decomposition, which proceeds via seven characteristic phase transitions.