Classification of the space spanned by theta series and applications

We determine a class of functions spanned by theta series of higher degree. We give two applications: A simple proof of the inversion formula of such theta series and a classification of skew-holomorphic Jacobi forms.

     

Some time change representations of stable integrals, via predictable transformations of local martingales

From the predictable reduction of a marked point process to Poisson, we derive a similar reduction theorem for purely discontinuous martingales to processes with independent increments. Both results are then used to examine the existence of stochastic integrals with respect to stable Lévy processes, and to prove a variety of time change representations for such integrals. The Knight phenomenon, where possibly dependent but orthogonal processes become independent after individual time changes, emerges as a general principle.     

Random time change and an integral representation for marked stopping times

Summary Consider the set of all possible distributions of triples (, , ), such that is a finite stopping time with associated mark in some fixed Polish space, while is the compensator random measure of (, ). We prove that is convex, and that the extreme points of are the distributions obtained when the underlying filtration is the one induced by (, ). Moreover, every element of has a corresponding unique integral representation. The proof is based on the peculiar fact that EV _, =0 for every predictable processV which satisfies a certain moment condition. From this it also follows thatT _, isU(0, 1) wheneverT is a predictable mapping into [0, 1] such that the image of , a suitably discounted version of , is a.s. bounded by Lebesgue measure. Iterating this, one gets a time change reduction of any simple point process to Poisson, without the usual condition of quasileftcontinuity. The paper also contains a very general version of the Knight-Meyer multivariate time change theorem.Research supported by NSF grant DMS-8703804     

Synthesis and X-ray crystal structures of six [TeL4][MF6] salts, where L is ethylene- or trimethylene-thiourea, and M is Si, Ge or Sn. Five Te(II) complexes with a novel type of structure linked together by unusual N–HF hydrogen bonds

The complexes [Te(etu)₄][SiF₆] (1), [Te(etu)₄][SiF₆] · H₂O (2), [Te(trtu)₄][SiF₆] (3), [Te(etu)₄][GeF₆] · H₂O (4), [Te(trtu)₄][GeF₆] (5) and [Te(etu)₄][SnF₆] (6) (etu = ethylenethiourea, trtu = trimethylenethiourea) have been prepared and their crystal structures determined by X-ray crystallographic methods. The crystals of 1, 3 and 5 are tetragonal; space groups P4cc (No. 103) with Z = 4 for 1, P4nc (No. 104) with Z = 2 for 3, and I4 (No. 79) with Z = 2 for 5. The crystals of 2, 4 and 6 are orthorhombic, space group Pccn (No. 56) with Z = 8 for 2 and 4 and Z = 4 for 6; those of 2 and 4 being isomorphous. The cations contain square planar or slightly distorted square planar TeS₄ coordination groups. In 1, 3 and 5 the Te atoms are located on fourfold rotation axes; the cations have fourfold rotational symmetry and the four thiourea ligands extend to the same side of the TeS₄ plane. These are the first examples of [TeL₄]²⁺ conformers of this type. In 2 and 4 the Te atoms lie on general positions; the cations are distorted versions of those in 1, and also in these the four ligands extend to the same side of the TeS₄ plane. In 6 the Te atoms are located on twofold rotation axes, the conformation of the cations corresponds to the point group C₂ with two neighbouring ligands extending to one side of the coordination plane and the remaining two to the opposite side. In 1–5 each of the four ligands forms a N–HF bond to the same F atom in the counter ion. The crystals of 1–5 are red, and those of 6 are yellow. The red colour is attributed to interactions of Te and S lone electron pairs caused by ligand TeS₄/TeSC tilt angles markedly different from 90°.     

Structural changes by sulfoxidation of phenothiazine drugs

Summary The side-chain conformations of psychoactive phenothiazine drugs in crystals are different from those of biologically inactive ring sulfoxide metabolites. This study examines the potential energies, molecular conformations and electrostatic potentials in chlorpromazine, levomepromazine (methotrimeprazine), their sulfoxide metabolites and methoxypromazine. The purpose of the study was to examine the significance of the different crystal conformations of active and inactive phenothiazine derivatives, and to determine why phenothiazine drugs lose most of their biological activity by sulfoxidation. Quantum mechanics and molecular mechanics calculations demonstrated that conformations with the side chain folded over the ring structure had lowest potential energy in vacuo, both in the drugs and in the sulfoxide metabolites. In the sulfoxides, side chain conformations corresponding to the crystal structure of chlorpromazine sulfoxide were characterized by stronger negative electrostatic potentials around the ring system than in the parent drugs. This may weaken the electrostatic interaction of sulfoxide metabolites with negatively charged domains in dopamine receptors, and cause the sulfoxides to be virtually inactive in dopamine receptor binding and related pharmacological tests.     

A new interpretation of Hund's first rule

The diagonal elements of the first and second order spinless density matrices have been calculated for the lowest excited¹ P and³ P terms of Be, B⁺ and C⁺⁺ using wavefunctions at different levels of approximations published in the literature. The analysis of these functions has resulted in a new interpretation of Hund's first rule in terms of an anisotropic screening effect.     

Ab initio study of the NMR shielding constants and spin-spin coupling constants in cyclopropene

Summary Ab initio calculations of parameters which characterize the NMR spectrum are presented for the cyclopropene molecule. The London orbitals CHF (or GIAO-CHF, Gauge-Independent Atomic Orbital Coupled Hartree-Fock) results for the shielding constants are in good agreement with the experimental data, accurately determined, and with otherab initio values. The calculations of the NMR spin-spin coupling constants have been performed using the Multiconfiguration Time-Dependent Hartree-Fock (MC TDHF) approach. Different basis sets and MC SCF wavefunctions were used to estimate the accuracy of the results. Good agreement is obtained with the coupling constants estimated using the available experimental data.Dedicated to Professor Werner Kutzelnigg on the occasion of his 60th birthday