Violation of the virial theorem and generalized equipartition theorem for logarithmic oscillators serving as a thermostat

Generalized equipartition theorem and confining walls

GENERALIZATION OF TITCHMARSH'S THEOREM FOR THE GENERALIZED FOURIER-BESSEL TRANSFORM

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.

GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES

The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.

Violation of the Equipartition Theorem for Thermally Insulated Clusters of Atoms with Different Masses

An expression is derived for calculating microcanonical-ensemble averages of the kinetic energies of atoms of different types in clusters isolated from the environment. This expression is a natural generalization of the solution to the problem of hard spheres with different masses to a system with a many-particle interatomic interaction potential. The dynamics of a C8H8 cubane is simulated nume...

A Sharp Form of the Virial Theorem

In its classical form the Virial Theorem concerns the behavior of a system S of n mass particles acting under Newtonian attraction in such a fashion that the center of mass 0 remains fixed and the potential energy V satisfies V> — <*> for all positive time t. The latter condition, which is not always stated explicitly, guarantees the analyticity of the coordinates of the particles in the indepe...