Splittings of Mapping Tori of Free Group Automorphisms

We present necessary and sufficient conditions for the existence of a splitting over nn3778v626/xxlarge8484.gif" alt="Zopf" align="BASELINE" BORDER="0"> of the mapping torus nn3778v626/10711_2004_Article_403441_TeX2GIFIE1.gif" alt=" $$M_\Phi = F \times _\Phi {\mathbb{Z}}$$ " align="middle" border="0"> of a free group automorphism nn3778v626/xxlarge934.gif" alt="PHgr" align="BASELINE" BORDER="0">.     

On σ-discrete borel mappings via quasi-metrics

Let X and Y be metrizable spaces. We show that, for a mapping f : X nn8717/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0"> Y, there exists a quasi-metric nn8717/xxlarge1009.gif" alt="rhov" align="MIDDLE" BORDER="0"> X inducing the topology of X such that f regarded as a mapping from (X, max{nn8717/xxlarge1009.gif" alt="rhov" align="MIDDLE" BORDER="0">, nn8717/xxlarge1009.gif" alt="rhov" align="MIDDLE" BORDER="0">^–1}) to Y is continuous if and only if f in the original topology of X is a nn8717/xxlarge963.gif" alt="sgr" align="BASELINE" BORDER="0">-discrete map of Borel class 1. Further, we prove that, for every nn8717/xxlarge963.gif" alt="sgr" align="BASELINE" BORDER="0">-discrete mapping f: X nn8717/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0"> Y of Borel class nn8717/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"> + 1, there exists a compatible quasi-metric nn8717/xxlarge1009.gif" alt="rhov" align="MIDDLE" BORDER="0"> on X such that f : (X, max{nn8717/xxlarge1009.gif" alt="rhov" align="MIDDLE" BORDER="0">, nn8717/xxlarge1009.gif" alt="rhov" align="MIDDLE" BORDER="0">^–1}) nn8717/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0"> Y is of Borel class nn8717/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">. We also investigate a more general situation when the range of the mapping under consideration is not necessarily metrizable. In passing, we obtain some results related to the behaviour of absolutely Borel sets and absolutely analytic spaces with respect to compatible quasi-metrics.     

γ(3S)→γ(1S)π~+π~-衰变及一个可能的bq态

利用手征幺正方法研究了衰变γ(3S)→γ(1S)π+π-,通过引入一个Jp=1+,I=1的中间态,该衰变的π+π-不变质量谱和cosθπ*角分布都能够得到很好的解释.同时,其他γ(nS)各态之间的π+π- 跃迁也能得到很好的描述,通过拟合CLEO的数据,对这个态的质量和宽度作了预言,该态的夸克组成应该是bbqq。     

Nichtflüchtige Inhaltsstoffe vonArtemisia afra

Summary From the pentane extract of the dried leaves ofArtemisia afra JACQ, an Asteraceae native in Southern Africa, the following non volatile constituents have been isolated: Cerylcerotinate, a wax ester, the hydrocarbon nonacosane and the triterpenes friedelin, nn68r313nq5778j7/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">- and nn68r313nq5778j7/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-amyrin. The relative high content of cerylcerotinate in this plant (0.25%) is noteworthy.

     

Intercalation ofn-alkylamines into α-titanium phosphate from aqueous solutions

The intercalation reactions betweenn-alkylamines and nn5472034903p252/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-titanium phosphate in aqueous media have been investigated. The compounds with the maximum intercalation have the formula nn5472034903p252/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-Ti(HOPO₃)₂ · 2 C _n H _2n+1 NH₂ · H₂O (n=1–10). Defined crystalline phases with lower amine content are described, the general formula being nn5472034903p252/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-Ti(HOPO₃)₂ · _m C _n H _2n+1 NH₂ ·pH₂O (m=1.0 1.3, 1.5, 1.7). Whenm=1.0 then-alkylamines form a monomolecular layer. Whenm>1.0 the layer is bimolecular. The inclination angle and the packing density of then-alkylamines in the interlayer space is determined.     

Zur Reaktion von Permethylcyclosilanen mit Halogenen

The series of nn11707672502m/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">,nn11707672502m/xxlarge969.gif" alt="ohgr" align="BASELINE" BORDER="0">-diiodopermethylpolysilanes, I(SiMe ₂) _n I, (n=4–6) andX(SiMe ₂)₄ X, (X=Cl, Br) has been prepared by the action of halogen on the corresponding cyclic compounds (SiMe ₂) _n . The mass spectra, NMR-, IR- andRaman-spectra of these compounds have been recorded.

Herrn Prof. Dr.Josef Schurz zum 60. Geburtstag gewidmet.     

Philipp Frank,Richard von Mises,and the Frank-Mises

The theoretical physicist Philipp Frank (1884–1966) and the applied mathematician Richard von Mises (1883–1953) both received their university education in Vienna shortly after 1900 and became friends at the latest during the Great War.They were attached to the Vienna Circle of Logical Positivists and wrote an influential two-part work on the differential and integral equations of mechanics and physics, the Frank-Mises, of 1925 and 1927, with its second edition following in 1930 and 1935.This work originated in the lectures that the mathematician Bernhard Riemann (1826–1866) delivered on partial differential equations and their applications to physical questions at the University of G?ttingen between 1854 and 1862, which were edited and published posthumously in1869 by the physicist Karl Hattendorff (1834–1882).The immediate precursor of the Frank-Mises, however, was the extensive revision of Hattendorff’s edition of Riemann’s lectures that the mathematician Heinrich Weber (1842–1913) published in two volumes, the Riemann-Weber, of 1900 and 1901, with its second edition following in 1910 and 1912. I trace this historical lineage, explore the nature and contents of the Frank-Mises, and discuss its complementary relationship to the first volume of the text that the mathematicians Richard Courant (1888–1972) and David Hilbert (1862–1943) published on the methods of mathematical physics in 1924, the Courant-Hilbert,which, when it and its second volume of 1937 were translated into English and extensively revised in 1953 and 1961, eclipsed the classic Frank-Mises.