Inclusion of Enantiomeric Carvones in β-Cyclodextrin: a Variable Temperature 1H NMR Study in Aqueous Solution

In aqueous solution, the apparent association constant at room temperature for the 1 : 1 inclusion of S-(+)-carvone in - cyclodextrin is double of that for R-(-)-carvone, whereas, at 45 °C, both enantiomers have association constants two orders of magnitude smaller, with the S-(+) inclusion being then slightly weaker than the R-(-) encapsulation. Calculations carried out at the molecular mechanics, AM1 and STO-3G levels confirm the preferential inclusion of the S-enantiomer and provide important clues for understanding chiral discrimination by -cyclodextrin.     

On Directly Infinite Rings

A ring R with identity 1 is said to be directly finite if for any a, b R, ab = 1 implies that ba = 1; otherwise R is directly infinite. With N the set of nonnegative integers, let B be the ring of N x N matrices over the ring of integers generated by two particular matrices. Properties of directly infinite rings are explored in relation to the ring B. This is made possible by various characterizations of the ring B one of which is that it is torsion free and generated by a bicyclic subsemigroup of its multiplicative semigroup. Some ideals and all idempotents of the ring B are constructed. The concepts of directly finite and chain finite idempotents are introduced in an arbitrary ring and applied to the ring B.     

About the definition of mass in (Machian) classical mechanics

We want in this note to clarify some aspects of the Machian foundation of the concept of mass in classical mechanics; specifically, we show how the relations of transitivity for the mass-ratios, necessary for a well grounded definition of mass, can be derived from Machian postulates.     

On a Fermat principle in general relativity. A Morse theory for light rays

In this paper an infinite dimensional Morse theory for lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds is developed under intrinsic assumptions. It yields applications to the gravitational lens effect. In particular we show that the number of images in the gravitational lens effect is infinite or odd.     

Lattice points

Journal of Fourier Analysis and Applications -     

Functional analysis concepts and Hartree-Fock instability conditions II: An analysis of the eight classes of solutions

The continuation of the previous work is presented. Here the instability matrices for the eight classes of HF solutions, considering time reversal and spin symmetries, are derived and explicitly shown. These matrices are expressed in terms of LCAO coefficients. Hence they are of immediate application to the verification of instabilities in HF calculations.