A new one-dimensional model, the multicomponent Calogero model of B N-type confined in the harmonic potential, is introduced. The Lax pair of this model is determined, and then a set of functionally independent conserved operators are constructed. Moreover, the energy spectrums of the above model are obtained by three different methods.

Two equations are constructed which reflect, for fermions moving independently in a spherical harmonic potential, a differential virial theorem and a relation between the turning points of kinetic energy and particle densities. These equations are used to derive a differential equation for the particle density and a non-local kinetic energy functional.

A catalog record for this book is available from the British Library. Harmonic mappings in the plane / Peter Duren. Includes bibliographical references and index.

Predictions of the CMB spectrum from a bimetric gravity theory (BGT) [1] are presented. The initial inflationary period in BGT is driven by a vanishingly small speed of gravitational waves vg in the very early universe. This initial inflationary period is insensitive to the choice of scalar field potential and initial values of the scalar field. After this initial period of inflation, vg will i...

We study the renormalized energy-momentum tensor (EMT) of cosmological scalar fluctuations during the slow-rollover regime for chaotic inflation with a quadratic potential and find that it is characterized by a negative energy density which grows during slow-rollover. We also approach the back-reaction problem as a second-order calculation in perturbation theory finding no evidence that the bac...

which is a symplectic analog of the well-known de Rham–Hodge ∗operator on oriented Riemannian manifolds: one should use the symplectic form instead of the Riemannian metric. Going further, one can define operator δ = ± ∗ d∗, δ = 0. The form α is called symplectically harmonic if dα = 0 = δα. However, unlike de Rham–Hodge case, there exist simplectically harmonic forms which are exact. Because o...

Following the analytic approach to thermodynamics developed by Stückelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations describing the mechanical and the thermal evolution of the system. The coupling between these evolution equations is due to the action of a viscous friction ter...

Recently there has been much interest in the Liouville type theorems for harmonic maps. For a detailed survey and progress in this direction, see the works by Hildebrandt [4], Eells and Lemaire [2]. Here we would like to mention that for all known results, the conditions on the harmonic maps can be divided into two kinds. The first of these conditions concerns the finiteness of the energy of th...

Vibrational dynamics of folded proteins is studied using a Gaussian model in which the protein is viewed as a network, residues representing the junctions, and the connectivity being established by a single parameter harmonic potential. Application to seven proteins showed that the local packing density plays a major role in determining the vibrational spectrum at time scales of picoseconds. At...

We develop a new method of implementing the Hartree-Fock calculations. A class of Gaussian bases is assumed, which includes the Kamimura-Gauss basis-set as well as the set equivalent to the harmonic-oscillator basis-set. By using the Fourier transformation to calculate the interaction matrix elements, we can treat various interactions in a unified manner, including finite-range ones. The presen...