Über die Anwendung algebraischer Methoden in der Deformationstheorie komplexer Räume

Es handelt sich um einen Beweis der folgenden Sätze, die zuerst von Grauert angegeben wurden (Publ. Math. I.H.E.S. No. 5, 1960; vgl. dies Zbl.100, 80 (1963)):Es seif:X Y eine eigentliche holomorphe Abbildung komplexer Räume, sei einef-platte kohärente analytische Garbe überX; es bezeichneX _y die Faser vonf über einem Punkty Y und die analytische Einschränkung von aufX _y . Dann gilt: (I) Die Funktionend _q (y)=dimH _q (X _y , sind halbstetig nach oben. (II) Ist für einq die Funktiond _q (y) konstant undY reduziert, so ist dieq-te direkte Bildgarbe von unterf lokal frei überY. (III) Die Euler-Poincaré-Charakteristikx(y)=(–1) ^q dimH _q (X _y ,) ist lokal konstant überY. — Der Beweis benutzt systematisch den Begriff des Steinschen Kompaktums (= kompakte semianalytische Menge mit Steinscher Umgebungsbasis). Mit Hilfe der von Frisch bewiesenen Tatsache, daß die Algebra der Schnitte in der Strukturgarbe eines komplexen Raumes über einem Steinschen Kompaktum noethersch ist (Invent. Math.4, 118–138 (1967); vgl. dies Zbl.167, 68 (1969)), gelingt es, die Grothendieckschen Methoden im algebraischen Fall (EGA III) auf die analytische Situation zu übertragen.     

Polarization of 22 MeV neutrons elastically scattered from liquid tritium

The asymmetries from elastic scattering of 22.1 MeV incident neutrons was measured for 11 laboratory angles between 40° and 118.5°. The extrema are −60% at 85° (lab) and +98% at 110° (lab).     

Completely normal matrices

Normal matrices in which all submatrices are normal are said to be completely normal. We characterize this class of matrices, determine the possible inertias of a particular completely normal matrix, and show that real matrices in this class are closed under (general) Schur complementation. We provide explicit formulas for the Moore–Penrose inverse of a completely normal matrix of size at least four. A result on irreducible principally normal matrices is derived as well.     

Weakly first-order or nearly second-order phase transitions in ammonium halides

This work is mainly concerned with the application to the ammonium chloride system of the model that was developed by Yurtseven (1993).

Using the model, which is an Ising model superimposed on an Einstein and/or Debye model, the specific heat C _v has been calculated in the vicinity of the λ-phase transition in NH₄Cl.

Our calculated C _v values give a reasonable fit to the observed more recent C _p data from the literature.

The model predictions applicable to the ammonium halides are discussed.     

Isolation of a new indoxyl alkaloid,Amoenamide B,from Aspergillus amoenus NRRL 35600: Biosynthetic implications and correction of the structure of Speramide B

A new prenylated indoxyl alkaloid, Amoenamide B (1), was isolated from Aspergillus amoenus NRRL 35600 along with Asperochramide A (2). Although many prenylated oxindole alkaloids, containing bicyclo[2.2.2]diazaoctane cores, have been isolated from the fungus of the genera Aspergillus and Penicillium to date, 1 is the fourth compound with the indoxyl unit containing the cores. During the structure elucidation of 1, we found that the planar structure matched to that of Speramide A (3), isolated from A. ochraceus KM007, but the reported structure of 3 was incorrect and turned out to be that of Taichunamide H (4), recently isolated from A. versicolor HDN11-84.     

Vector subdivision schemes and multiple wavelets

We consider solutions of a system of refinement equations written in the form

where the vector of functions is in and is a finitely supported sequence of matrices called the refinement mask. Associated with the mask is a linear operator defined on by . This paper is concerned with the convergence of the subdivision scheme associated with , i.e., the convergence of the sequence in the -norm.

Our main result characterizes the convergence of a subdivision scheme associated with the mask in terms of the joint spectral radius of two finite matrices derived from the mask. Along the way, properties of the joint spectral radius and its relation to the subdivision scheme are discussed. In particular, the -convergence of the subdivision scheme is characterized in terms of the spectral radius of the transition operator restricted to a certain invariant subspace. We analyze convergence of the subdivision scheme explicitly for several interesting classes of vector refinement equations.

Finally, the theory of vector subdivision schemes is used to characterize orthonormality of multiple refinable functions. This leads us to construct a class of continuous orthogonal double wavelets with symmetry.

     

Biomimetic total synthesis of malbrancheamide and malbrancheamide B

The biomimetic total syntheses of both malbrancheamide and malbrancheamide B are reported. The synthesis of the two monochloro species enabled the structure of malbrancheamide B to be unambiguously assigned. The syntheses each feature an intramolecular Diels-Alder reaction of a 5-hydroxypyrazin-2(1H)-one to construct the bicyclo[2.2.2]diazaoctane core, which has also been proposed as the biosynthetic route to these compounds.