Fundamental groups of manifolds with <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>-category 2

A closed topological n-manifold M ⁿ is of S ¹-category 2 if it can be covered by two open subsets W ₁,W ₂ such that the inclusions W _i → M ⁿ factor homotopically through maps W _i → S ¹ → M ⁿ . We show that the fundamental group of such an n-manifold is a cyclic group or a free product of two cyclic groups with nontrivial amalgamation. In particular, if n = 3, the fundamental group is cyclic.      

Study of the morphological change of amorphous ITO films after temperature–humidity treatment

Amorphous indium tin oxide (ITO) thin films have been deposited on silicon and Corning 7059 glass substrates at room temperature (RT) and at 75 °C by direct-current magnetron sputtering method. After exposure of the two kinds of samples to the temperature–humidity (T–H) test, we find that there are two different types of circular structures are formed. RT ITO films are composed of granules, and 75 °C ITO films are composed of several different parts which have different Sn and In concentrations. Metallic ion concentration corrosion cells are used to explain the phenomena.     

Asymptotic regularity of solutions to Hartree–Fock equations with Coulomb potential

We study the asymptotic regularity of solutions to Hartree–Fock (HF) equations for Coulomb systems. To deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo‐differential operators on conical manifolds. First, the non‐self‐consistent‐field case is considered, which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator, which guarantee ellipticity for the local part of the Fock operator on the open stretched cone ?₊ × S². This proves the existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed‐point approach based on Cancès and Le Bris analysis of the level‐shifting algorithm, we show via another bootstrap argument that the corresponding self‐consistent‐field solutions to the HF equation have the same type of asymptotic regularity. Copyright © 2008 John Wiley & Sons, Ltd.     

Intramolecular Alkylation of Aromatic Compounds XXXVI [1]. Stereoselective Synthesis of C/D-cis-Configured Ergolines

Summary.  The stereoselective synthesis of cis-ergoline is presented. Starting from rac-N-benzoyl tryptophan methyl ester, the key compound indolinylmethylpyridin-3-one was prepared via a seven-step reaction in good yield. Since its cyclization to the desired ergolinone failed, the key compound was reduced to yield the two diastereomeric pyridin-3-ols; only one of them cyclized in trifluoromethanesulfonic acid, affording cis-ergoline. Catalytic hydrogenation of the latter gave N,N′-dimethyldihydroergoline, the X-ray crystallography of which revealed both the correct structure and identical relative configurations at C-5a and C-6a (SS or RR). Hydroboration and subsequent perruthenate oxidation of the Δ⁹-ergoline provided access to the regioisomeric ergolinols and ergolinones. Received December 27, 2001. Accepted January 15, 2002     

A convenient preparation of 8R,25-dihydroxy-9,10-seco-4,6,10(19)-cholestatrien-3-one

Summary The title compound was prepared in three steps from 25-hydroxyvitamin D₃. The keystep in this sequence is the transformation of3b to4 by means of the LiBr/HMPT complex.Dedicated to Prof. Dr. Karl Schlögl on the occasion of his 65th anniversary