Large deviation for stochastic line integrals as L p -currents

The large deviation principle for stochastic line integrals along Brownian paths on a compact Riemannian manifold is studied. We regard them as a random map on a Sobolev space of 1-forms. We show that the differentiability order of the Sobolev space can be chosen to be almost independent of the dimension of the underlying space by assigning higher integrability on 1-forms. The large deviation is formulated for the joint distribution of stochastic line integrals and the empirical distribution of a Brownian path. As the result, the rate function is given explicitly.     

Total synthesis of xanthanolides

The total synthesis and determination of the absolute configuration of (+)- and (−)-sundiversifolide have been achieved via intramolecular acylation and Wittig-lactonization as the key steps. The xanthanolide sesquiterpene lactones, 8-epi-xanthatin (1), dihydroxanthatin (2), and xanthatin (3) were also prepared, starting from a common intermediate derived from the synthesis of sundiversifolide.     

Imaging,Chemical and Spectroscopic Studies of the Methylation-induced Decomposition of Melanosomes†

The morphological and chemical changes associated with the exposure of melanosomes to methyl iodide are assessed by a variety of analytical, imaging and spectroscopic methods. Scanning electron microscopy, light scattering and N₂ adsorption measurements all indicate significant changes in the morphology of the pigment following methylation. Solid-state nuclear magnetic resonance (SS-NMR) spectroscopy and chemical degradation analysis reveals the methylation results in the introduction of ester groups into the pigment structures. Amino acid analysis further reveals that Arg, Cys, His, Ser and Tyr undergo methylation; the SS-NMR data provide additional evidence for the methylation of the sulfur of Cys. Methylation results in increased solubility of the melanosome; the absorption properties of the dissolved material are characterized by an absorption maximum at 225 nm, with a long tail throughout the UV-A and UV-B, indicating that the solubilized material is a combination of protein and pigment. The methylation-induced decomposition of the melanosomes provides new insights into both the observed increase in O-methyl derivatives of the indolic precursor to eumelanin in the urine of melanoma patients and how increased levels of biologic methylating agents in the brain induce symptoms that resemble Parkinson’s disease.     

Formation and structures of mercury complexes of 18-membered unsaturated and saturated thiacrown ethers

The complexation of 18-membered unsaturated thiacrown ether, 18-UT-6, with 1 equiv of HgCl(2) in acetone afforded mercury complex Hg(II)(18-UT-6)Cl(2). The complexations of 18-membered saturated thiacrown ether, 18S6, with 1 equiv each of HgCl(2) and CdCl(2) in acetone afforded Hg(II)(18S6)Cl(2) and Cd(II)(18S6)Cl(2), respectively. The crystal structure of Hg(II)(18-UT-6)Cl(2) revealed that the mercury atom was inside the cavity of the macrocycle and the geometry around the mercury atom was an eight-coordinate hexagonal bipyramidal arrangement. ORTEP drawing of Hg(II)(18S6)Cl(2) revealed the existence of the mercury atom outside the cavity of the ring, as well as a polymeric chain structure. (1)H NMR study of Hg(II)(18-UT-6)Cl(2) in acetone-d(6) indicated that the interconversion between free 18-UT-6 and pure complex was slower than the NMR time scale. The titration experiment by (1)H NMR revealed that 18-UT-6 had inclusion selectivity for the number of mercury atoms. The electrochemical behavior of complexes Hg(II)(18-UT-6)Cl(2) and Hg(II)(18S6)Cl(2) was also examined.     

On the topological complexity of DC-sets

A DC-set is a set defined by means of convex constraints and one additional inverse convex constraint. Given an arbitrary closed subsetM of the Euclideann-space, we show that there exists a DC-set in (n+1)-space being homeomorphic to the given setM. Secondly, for any fixedn2, we construct a compactn-dimensional manifold with boundary, which is a DC-set and which has arbitrarily large Betti-numbersr _k fork n–2.     

Highly stereoselective synthesis of homoallylic amines based on addition of allyltrichlorosilanes to benzoylhydrazones

Allyltrichlorosilanes reacted with benzoylhydrazones in DMF without the use of any catalyst to afford the corresponding homoallylic benzoylhydrazines in good to high yields. The reactions proceeded at 0 degrees C to room temperature under mild conditions. In addition, it was found that the reactions tolerated well the steric hindrance of hydrazones and allyltrichlorosilanes. Indeed, ketone-derived benzoylhydrazones reacted with allyltrichlorosilane smoothly to afford the corresponding N'-tert-alkyl-N-benzoylhydrazines in high yields. In crotylation with (E)- and (Z)-crotyltrichlorosilanes, syn- and anti-adducts were stereospecifically obtained, respectively. These reactions are most likely to proceed via a cyclic chairlike transition state where the R group takes an axial position. When alpha-heteroatom-substituted chiral benzoylhydrazones were used, high anti-diastereoselectivities were observed. These adducts can be readily converted to homoallylic amines in high yields without epimerization.