Total synthesis and properties of the crambescidin core zwitterionic acid and crambescidin 359

The total synthesis of the crambescidin core acid 9, crambescidins 359 (8) and 431 (7), and the properties of the crambescidin core are described. A key step of the synthetic route to guanidinium carboxylate 9 is Pd(0) catalyzed cleavage of the ester side chain of pentacyclic cinnamyl ester 15. This ester is also employed to prepare a small library of crambescidin alkaloid analogues that differ in their C14 side chain. The zwitterionic guanidinium carboxylate 9 was shown to readily decarboxylate to form crambescidin 359 (8). Decarboxylation of crambescidin core acid 9 was fastest under basic conditions. In the presence of base, up to eight deuterium atoms can be incorporated into the pentacyclic crambescidin core. Both deuterium incorporation and decarboxylation of crambescidin core acid 9 are the result of facile ring opening of the spirocyclic ether rings of the pentacyclic guanidinium moiety.     

A multilinear Phelps' Lemma

We prove a multilinear version of Phelps' Lemma: if the zero sets of multilinear forms of norm one are `close', then so are the multilinear forms.

     

Behavior of entire functions on balls in a Banach space

In this paper we prove that given any two disjoint balls in an infinite dimensional complex Banach space, there exists an entire function which is bounded on one and unbounded on the other.     

Observation of soft magnetorotons in bilayer quantum Hall ferromagnets

Inelastic light-scattering measurements of low-lying collective excitations of electron double layers in the quantum Hall state at total filling nu(T)=1 reveal a deep magnetoroton in the dispersion of charge-density excitations across the tunneling gap. The roton softens and sharpens markedly when the phase boundary for transitions to highly correlated compressible states is approached. The findings are interpreted with Hartree-Fock evaluations that link soft magnetorotons to enhanced excitonic Coulomb interactions and to quantum phase transitions in the ferromagnetic bilayers.     

Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment

We study the influence of asymmetric coupling strengths on the onset of light intensity oscillations in an experimental system consisting of two semiconductor lasers cross coupled optoelectronically with a time delay. We discover a scaling law that relates the amplitudes of oscillations and the coupling strengths. These observations are in agreement with a theoretical model. These results could be applicable to the population dynamics of other systems, such as the spread of disease in human populations coupled by migration.     

Influence of the anion on lone pair formation in Sn(II) monochalcogenides: a DFT study

The electronic structure of SnO, SnS, SnSe, and SnTe in the rocksalt, litharge, and herzenbergite structures has been calculated using density functional theory. Comparison of the distorted and undistorted structures allows for an explanation of the unusual experimentally observed structural transitions seen along the Sn(II) monochalcogenides. Analysis of the electronic structure shows a strong anion dependence of the Sn(II) lone pair, with the Sn(5s) and Sn(5p) states too far apart to couple directly. However, the interaction of Sn(5s) with anion states of appropriate energy produce a filled antibonding Sn(5s)-anion p combination which allows coupling of Sn(5s) and Sn(5p) to occur, resulting in a sterically active asymmetric density on Sn. While the interaction between Sn(5s) and O(2p) is strong, interactions of Sn with S, Se, and Te become gradually weaker, resulting in less high energy 5s states and hence weaker lone pairs. The stability of the distorted structures relative to the symmetric structures of higher coordination is thereby reduced, which induces the change from highly distorted litharge SnO to highly symmetric rocksalt SnTe seen along the series.     

Chaotic advection,diffusion, and reactions in open flows

We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity. (c) 2000 American Institute of Physics.     

A model for the Schrödinger zitterbewegung and the plane monochromatic wave

The stochastic approach worked out in earlier papers is applied to the Dirac fluid. It gives a model of the Schrödinger zitterbewegung, from which, by the spinor-vector correspondence, a model of the plane monochromatic wave in the rest frame is derived. The relation of the scheme with quantization is found to have the same character as in the previous papers. The link of spin with relativity is explained.