Polymerabwandlung und Synthese mit Sulfenylderivaten. 5. Mitt. Addukte mit cis-1,4-Polybutadien

Ohne Zusammenfassung     

Spherical functions and invariant differential operators on complex Grassmann manifolds

Proofs are given of two theorems of Berezin and Karpelevič, which as far as we know never have been proved correctly. By using eigenfunctions of the Laplace-Beltrami operator it is shown that the spherical functions on a complex Grassmann manifold are given by a determinant of certain hypergeometric functions. By application of this result, it is proved that a certain system of operators, fow which explicit expressions are given, generates the algebra of radial parts of invariant differential operators.     

Unbounded convex mappings of the ball in

In this paper, we study univalent holomorphic mappings of the unit ball in that have the property that the image contains a line for some , . We show that under certain rather reasonable conditions, up to composition with a holomorphic automorphism of the ball, the mapping is an extension of the strip mapping in the plane to higher dimensions.

     

Low temperature survival of slender naiad (Najas flexilis) seeds

The response to drying and storage at -20 degrees C or in liquid nitrogen was studied in seeds of the freshwater aquatic plant Najas flexilis. The seeds of this species show some desiccation sensitivity, although post-harvest storage in water at 16 degrees C resulted in improvements in desiccation tolerance. There was 63% germination of seeds dried to 9.5% moisture content (30% RH) following this maturation period. Optimum moisture contents for seeds stored at -20 degrees C for 3 months and in liquid nitrogen for 1 week were ~11% and ~15%, respectively.     

Structure of a styrylbenzoselenazole platinum(II) complex: [NEt4][Pt(nsbse)Br3]

Tetraethylammonium tribromo[2-(2-chloro-5-nitrostyryl)benzoselenazole] platinate (II), [(C₂H₅)₄N][PtBr₃(C₁₅H₉ClN₂O₂Se)], is monoclinic, in space groupP2₁/c, witha=9.496(2),b=20.321(7),c=15.166(3)Å,=100.18(1)°,V=2880(2)ų,M _r =928.72,Z=4,D _x =2.141 g cm^–3, (MoK)=0.71073 Å,=104.1 cm^–1,F(000)=1752,T=298 K. The structure was solved by direct methods and refined toR=0.032 for 2626 unique observed reflections withI>3(I). The [Pt(nsbse)Br₃)] unit has square-planar geometry about the Pt atom, with the nsbse coordinated to the Pt through the N of the selenazole ring. The ligand molecule is non-planar, with a dihedral angle of 61.6(2)° between the benzoselenazole and phenyl rings. The dihedral angles between the PtBr₃ plane and the benzoselenazole and phenyl planes are 105.2(1) and 80.7(1)°, respectively.     

Symmetry and Resonance in Periodic FPU Chains

The symmetry and resonance properties of the Fermi Pasta Ulam chain with periodic boundary conditions are exploited to construct a near-identity transformation bringing this Hamiltonian system into a particularly simple form. This “Birkhoff–Gustavson normal form” retains the symmetries of the original system and we show that in most cases this allows us to view the periodic FPU Hamiltonian as a perturbation of a nondegenerate Liouville integrable Hamiltonian. According to the KAM theorem this proves the existence of many invariant tori on which motion is quasiperiodic. Experiments confirm this qualitative behaviour. We note that one can not expect this in lower-order resonant Hamiltonian systems. So the periodic FPU chain is an exception and its special features are caused by a combination of special resonances and symmetries. Received: 25 July 2000 / Accepted: 20 December 2000     

Minimality and other properties of the width- nonadjacent form

Let be an integer and let be the set of integers that includes zero and the odd integers with absolute value less than . Every integer can be represented as a finite sum of the form , with , such that of any consecutive 's at most one is nonzero. Such representations are called width- nonadjacent forms (-NAFs). When these representations use the digits and coincide with the well-known nonadjacent forms. Width- nonadjacent forms are useful in efficiently implementing elliptic curve arithmetic for cryptographic applications. We provide some new results on the -NAF. We show that -NAFs have a minimal number of nonzero digits and we also give a new characterization of the -NAF in terms of a (right-to-left) lexicographical ordering. We also generalize a result on -NAFs and show that any base 2 representation of an integer, with digits in , that has a minimal number of nonzero digits is at most one digit longer than its binary representation.

     

ELLIPSOMETRY OF BLACK LIPID MEMBRANES OF EGG LECITHIN AND CHLOROPLAST EXTRACTS

Abstract— Ellipsometric angles and reflectivity of black lipid membranes containing either egg lecithin or chloroplast extracts were measured at a wavelength of 6328 Å. Evidence was found for positive uniaxial anisotropy in membranes of lecithin. If the thickness of those films is assumed to be 62 Å, the refractive index normal to the film surface is 1.471 ± 0.004, and the refractive index parallel to the film surface is 1.454 ± 0.003. The results for membranes of chloroplast extracts also indicate a positive anisotropy in the indices of absorption.     

Hearing loss from interrupted, intermittent, and time varying Gaussian noise exposures: the applicability of the equal energy hypothesis

Eight groups of chinchillas (N=74) were exposed to various equivalent energy [100 or 106 dB(A) sound pressure level (SPL)] noise exposure paradigms. Six groups received an interrupted, intermittent, time varying (IITV) Gaussian noise exposure that lasted 8 h/d, 5 d/week for 3 weeks. The exposures modeled an idealized workweek. At each level, three different temporal patterns of Gaussian IITV noise were used. The 100 dB(A) IITV exposure had a dB range of 90-108 dB SPL while the range of the 106 dB(A) IITV exposure was 80-115 dB SPL. Two reference groups were exposed to a uniform 100 or 106 dB(A) SPL noise, 24 h/d for 5 days. Each reference group and the three corresponding IITV groups comprised a set of equivalent energy exposures. Evoked potentials were used to estimate hearing thresholds and surface preparation histology quantified sensory cell populations. All six groups exposed to the IITV noise showed threshold toughening effects of up to 40 dB. All IITV exposures produced hearing and sensory cell loss that was similar to their respective equivalent energy reference group. These results indicate that for Gaussian noise the equal energy hypothesis for noise-induced hearing loss is an acceptable unifying principle.