Molecular orbital studies on the conformation of GABA (γ-aminobutyric acid)

In distinction to Extended Hückel Theory which predicts as the most stable conformation of free zwitterionic GABA a totally extended form, PCILO and SCF ab initio studies show that the intrinsically preferred conformation of the isolated molecule is a highly folded one, resulting from strong interactions between the two charged ends. Computations are also carried out for hydrated GABA in the supermolecule approach allowing moreover for the flexibility of binding of some of the water molecules of the first hydration shell. They predict the coexistence in solution of a large number of conformations showing different degrees of folding (or extension), a result confirmed by recent NMR studies. This and a number of similar results show that we have to adapt our thinking on the role of conformations in pharmacological activity to this situation, which was frequently obscured by the more abundant results of X-ray crystallography yielding a single conformation.     

Studies into the Diels-Alder reactions of 5-trimethylsilylthebaine

The introduction of a 5-trimethylsilyl group on the least hindered face of the diene thebaine was anticipated to favor attack by dienophiles from the alternate face, but only gave rise to a rearrangement product when treated with 3-butene-2-one at 110 °C. Reaction with the more reactive benzoquinone at lower temperature gave rise to a very slow reaction from the same face as the silyl group, indicating that a trimethylsilyl group does not sufficiently hinder this face to achieve reaction at the other face.     

Non planéité de cyclopenténones substituées analyse conformationnelle par résonance magnétique nucléaire

The stereochemistry of substituted cyclopent-2-en-1-ones was studied by NMR. The existence of non-planar rings is indicated and conformational analysis, based principally upon examination of the coupling constants enables the conformational population to be estimated; trans dihalogeno derivatives, for example, occur predominantly in the diaxial form.     

Sodium-23 Nuclear Magnetic Resonance Spectroscopy

With the availability of Fourier transform spectrometers, ²³Na-NMR spectroscopy has become an important tool. It affords direct insight into solvation and ion pairing phenomena, both in organic and in bio-inorganic systems. Monitoring the chemical shifts and linewidths of ²³Na signals gives access to binding constants, reorientational correlation times and the microdynamics of the sodium coordination shell. The binding of other cations can also be studied by ²³Na-NMR spectroscopy, in competition experiments.     

An electronic structure investigation of the BNO-BON-NBO system

The potential energy hypersurface of the ground triplet states of the BNO-BON-NBO system has been investigated using traditional ab initio electronic structure theory. The molecules studied have the molecular formula BON and include three linear and three angular species, and two transition states for the isomerization of an angular N-B-O to an angular B-O-N and a linear B-NO, respectively. All stationary points on the BNO-BON-NBO isomerization potential energy surface have been characterized employing UMP2, UMP4, and Gaussian-2 (G2) theory with the 6-311G(d), 6-311G(2d), and TZ2P basis sets. The isomerization for an angular N-BO to the linear B-NO has a lower energy barrier than that of the former to an angular B-ON. Energetics are presented with G2 energies. Two sets of resonance structures for both bent B-NO (boron nitrosyl) and B-ON (boron isonitrosyl) were proposed and the bonding in the two species was analyzed. For the purpose of comparison, the density functional theory based hybrid methods B3LYP/6-311G(d) and B3LYP/TZ2P have also been applied to both geometry optimization and single-point calculations. It is found that the B3LYP prediction of the nature of the linear B-O is contradictory to that made by all MPn(n = 2 and 4) calculations. The cause for this contradiction is discussed.     

An indexed set of density bounds on lattice packings

It has long been known that the admissibility of a lattice with respect to a symmetric convex bodyB is equivalent to being a packing lattice for 1/2B. This fact is the basis of the interplay between the classical theory of the arithmetic minima of positive definite quadratic forms, on the one hand, and the dense lattice packing of spheres inR ⁿ , on the other.We give an indexed set of bounds _L (B) a _j , where 0 j n/2, on the lattice packing density ofB. The casej=0 reduces to the aforementioned long-known fact, andj=1 was proved by Elkies, Odlyzko, and Rush, and was used to obtain record high packing densities for various superballs. The new cases make possible the use of smaller primes in the construction of these dense packings.Supported by National Science Foundation grant DMS-9103233.     

Über lineare Unabhängigkeit

It is the aim of the present work to prove, under appropriate conditions, lower estimates for the dimension of w ₁ + ... + w _m over , wherew ₁,...,w _m are given real numbers. In particular, if this dimension ism, i.e. ifw ₁,...,w _m are linearly independent over , we are also interested in a quantitative version of this fact. Our qualitative theorems generalize a result of Nesterenko. Its formulation is quite similar to the axiomatization of methods for algebraic independence, as it became usual during the last decade.

     

The invertibility of the product of unbounded Toeplitz operators

In this note I give necessary and sufficient conditions on outer functionsf andg for the operator to be bounded and invertible on H². I also discuss the relationship of this question to two open questions in operator theory and weighted norm inequalities.     

On nonnegative solvability of linear operator equations

LetE be a Banach lattice having order continuous norm. Suppose, moreover,T is a nonnegative reducible operator having a compact iterate and which mapsE into itself. The purpose of this work is to extend the previous results of the authors, concerning nonnegative solvability of (kernel) operator equations on generalL ^p-spaces. In particular, we provide necessary and sufficient conditions for the operator equation x=T x+y to possess a nonnegative solutionxE wherey is a given nonnegative and nontrivial element ofE and is any given positive parameter.     

Incomplete idempotent Schröder quasigroups and related packing designs

Summary In this paper it is proved that, for any positive integern 2, 3 (mod 4),n 7, there exists an incomplete idempotent Schröder quasigroup with one hole of size two IISQ(n, 2) except forn = 10. It is also proved that for any positive integern 0, 1 (mod 4), there exists an idempotent Schröder quasigroup ISQ(n) except forn = 5 and 9. These results completely determine the spectrum of ISQ(n) and provide an application to the packing of a class of edge-coloured block designs.Research supported by NSERC grant A-5320.Research supported by NSFC grant 19231060-2.