Intermolecular Interactions in 8-Aza-D-Homogonane Crystals and their Manifestation in the IR Spectra

Crystalline modifications of 8-aza-D-homogon-1,3,5(10),13-tetraen-12,17a-dione have been investigated by IR spectroscopy and x-ray structural analysis. It is shown that this compound crystallizes from solutions of chloroform with hexane in the form of a solvate comprised of chelate hydrogen bonds between the hydrogen atom of the chloroform molecule and the oxygen atoms of the carbonyl groups of the 8-azasteroid molecule. A relation between the changes in the characteristic absorption bands of the CH₂-, C=O-, and I=C groups and the structure of the crystalline modifications has been established.     

N identical particles under quantum confinement: a many-body dimensional perturbation theory approach

Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrödinger equation, the spatial dimension D→∞ equilibrium (D⁰) structure, and the normal-mode (D⁻¹) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose-Einstein condensate with a repulsive hard-core potential.     

Extremal Convex Planar Sets

Each convex planar set K has a perimeter C, a minimum width E, an area A, and a diameter D. The set of points (E,C, A^1/2, D) corresponding to all such sets is shown to occupy a cone in the non-negative orthant of R⁴with its vertex at the origin. Its three-dimensional cross section S in the plane D = 1 is investigated. S lies in a rectangular parallelepiped in R³. Results of Lebesgue, Kubota, Fukasawa, Sholander, and Hemmi are used to determine some of the boundary surfaces of S, and new results are given for the other boundary surfaces. From knowledge of S, all inequalities among E, C ,A, and D can be found.     

Commuting Rank 2 Differential Operators Corresponding to a Curve of Genus 2

We construct commuting rank 2 formally self-adjoint ordinary differential operators corresponding to a curve of genus 2.     

Raman echo under medium excitation by extremely short pulses

A generalization of the Bloembergen-Shen model to Raman active molecules with an arbitrary number of normal modes was suggested. The generalized model was used to study Raman echo signal characteristics when a system of molecules was excited by pulses of widths up to one period of optical oscillations. It was shown that a large number of echo responses on Stokes and anti-Stokes components could arise even under a two-pulse action in a continuous monochromatic pumping field. The number of echo responses depended on the number of molecular normal modes and the geometry of measurements. At small exciting pulse “areas,” the echo responses whose Stokes and anti-Stokes components corresponded to normal vibrational modes of a molecule had the highest intensity, whereas the components formed by normal mode combinations were strongly suppressed.     

Groups in which every non-abelian subgroup is permutable

A subgroupH of a groupG is said to bepermutable ifHX=XH for every subgroupX ofG. In this paper the structure of groups in which every subgroup either is abelian or permutable is investigated. This work was done while the last author was visiting the University of Napoli Federico II. He thanks the “Dipartimento di Matematica e Applicazioni” for its financial support.     

Creation, Dissipation and Recycling of Resources in Non-Equilibrium Systems

In this article, we define stochastic dynamics for a system coupled to reservoirs. The rules for forward and backward transitions are related by a generalized detailed balance identity involving the system and its reservoirs. We compare the variation of information and of entropy. We define the Carnot dissipation and prove that it can be expressed in terms of cyclic transformations. Lower bounds for partial dissipations are also studied, as well as the effect of switching off certain reservoirs. We also study the near degeneracy of the stochastic matrix, relate it to phase transitions and we show that the reduced dynamics on the set of phases is a permutation. Finally, we relate these concepts to heat, work and more generally to the dissipation and creation of resources, in general systems.     

Weak density of smooth maps for the Dirichlet energy between manifolds

We prove that given a simply connected compact manifold M and a closed manifold N, any map in the Sobolev space W ^1,2(M,N) can be approximated weakly by smooth maps between M and N. Submitted: September 2002, Final version: November 2002.     

Lasing of iodine in the fullerene-oxygen-iodine system

The possibility of lasing in the fullerene-oxygen-iodine system with optical excitation of fullerene is studied. Laser radiation with an energy of 25 mJ and a pulse duration of 5–10 ms is obtained.     

Three methods for analyzing forced vibration of a fluid-filled cylindrical shell

The forced vibration of an infinite elastic circular cylindrical shell filled with fluid is studied. Three methods are employed to analyze the forced vibration problem of this shell-fluid coupled system, that is, wave propagation approach (wave mode superposition), theorem of residues and a numerical integral method. In order to explain these methods more explicitly, before being used to investigate the vibration of an infinite fluid-filled elastic circular cylindrical shell, all these three methods are employed firstly to analyze the forced vibration problem of an infinite beam and an infinite elastic circular cylindrical shell in vacuo. Advantage and disadvantage of these three methods are discussed and their interesting relationship is revealed. That is, to any circumferential wavenumber and frequency of the external force, there is an unchangeable relationship between the general coordinates of various waves in the wave propagation approach and the residuals in the theorem of residues.