Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting

In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions (RBFs). These estimates include situations in which the target function does not belong to the native space of the RBF.

     

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.