NMR kinetic studies on the decomposition of beta-amidozinc reagents: optimization of palladium-catalyzed cross-coupling with acid chlorides

The decomposition of beta-amidozinc reagent 4 by beta-elimination has been shown to be a unimolecular process in both THF and DMF as solvent, with relative rates of 4:1 at room temperature, and activation parameters have been determined. These results indicate the beta-elimination is a syn-process. NMR experiments reveal that as little as 2 equiv of DMF can have a significant stabilizing influence on reagent 4. Use of a mixture of DMA and toluene as the bulk solvent, in place of DMF, has allowed successful palladium-catalyzed cross-coupling reactions of both 4 and the homologous reagent 5 with acid chlorides to yield unsymmetrical ketones (nine examples).     

Quasilinear resolutions of non-linear equations

By analogy with the linear vector bundle case, a non-linear partial differential equation on a manifold can be defined as a fibred submanifold R_k of a k-jet bundle. By observing that under natural conditions the first prolongation gives rise to a vector bundle over R_k, (that is, a quasilinear equation), techniques of the linear case are adapted to establish conditions for the formal integrability of the equation.     

Induced torque of sodium measured by a modulation method

The induced torque in sodium detected by a new modulation method is anisotropic with twofold anisotropy at low fields. Fourfold torque does not develop in magnetic fields up to 2 T as is observed in potassium. The results are not explained completely by the theory of Lass assuming ellipsoidal boundary conditions or by the theory of Bishop and Overhauser for the charge density wave model.     

On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems,including inequalities for log concave functions,and with an application to the diffusion equation

We extend the Prékopa-Leindler theorem to other types of convex combinations of two positive functions and we strengthen the Prékopa-Leindler and Brunn-Minkowski theorems by introducing the notion of essential addition. Our proof of the Prékopa-Leindler theorem is simpler than the original one. We sharpen the inequality that the marginal of a log concave function is log concave, and we prove various moment inequalities for such functions. Finally, we use these results to derive inequalities for the fundamental solution of the diffusion equation with a convex potential.     

A general rearrangement inequality for multiple integrals

In this paper we prove a rearrangement inequality that generalizes inequalities given in the book by Hardy, Littlewood and Pólya¹ and by Luttinger and Friedberg.² The inequality for an integral of a product of functions of one variable is further extended to the case of functions of several variables.     

The complement: a solution to liquid drop finite size effects in phase transitions

The effects of the finite size of a liquid drop undergoing a phase transition are described in terms of the complement, the largest (but mesoscopic) drop representing the liquid in equilibrium with the vapor. Vapor cluster concentrations, pressure, and density from fixed mean density lattice gas (Ising) calculations are explained in terms of the complement generalization of Fisher's model. Accounting for this finite size effect is important for extracting the infinite nuclear matter phase diagram from experimental data.     

Organic homojunction diodes with a high built-in potential: interpretation of the current-voltage characteristics by a generalized Einstein relation

We realize p- and n-type doping of the organic semiconductor zinc-phthalocyanine using a novel strong organic donor. This allows us to demonstrate the first stable and reproducible organic p-n homojunctions. The diodes show very high built-in potentials, attractive, e.g., for organic solar cells. However, the diode characteristics cannot be described by the standard Shockley theory of the p-n junction since the ideality factor strongly increases with decreasing temperature. We show that this behavior can be explained by deviations from the Einstein relation for disordered materials.     

Limit on the electron electric dipole moment in gadolinium-iron garnet

A new method for the detection of the electron electric dipole moment (EDM) using a solid is described. The method involves the measurement of a voltage induced across the solid by the alignment of the sample's magnetic dipoles in an applied magnetic field, H. A first application of the method to GdIG has resulted in a limit on the electron EDM of 5 x 10(-24)e cm, which is a factor of 40 below the limit obtained from the only previous solid-state EDM experiment. The result is limited by the imperfect discrimination of an unexpectedly large voltage that is even upon the reversal of the sample magnetization.