Über die Berandung ebener und räumlicher Gebiete (Primendentheorie)

Ohne Zusammenfassung     

Cutting Triangular Cycles of Lines in Space

We show that n lines in 3-space can be cut into O(n^2-1/69log^16/69n) pieces, such that all depth cycles defined by triples of lines are eliminated. This partially resolves a long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics.     

Affine Kac-Moody algebras and semi-infinite flag manifolds

We study representations of affine Kac-Moody algebras from a geometric point of view. It is shown that Wakimoto modules introduced in [18], which are important in conformal field theory, correspond to certain sheaves on a semi-infinite flag manifold with support on its Schhubert cells. This manifold is equipped with a remarkable semi-infinite structure, which is discussed; in particular, the semi-infinite homology of this manifold is computed. The Cousin-Grothendieck resolution of an invertible sheaf on a semi-infinite flag manifold gives a two-sided resolution of an irreducible representation of an affine algebras, consisting of Wakimoto modules. This is just the BRST complex. As a byproduct we compute the homology of an algebra of currents on the real line with values in a nilpotent Lie algebra.Dedicated to Dmitry Borisovich Fuchs on his 50th birthdayAddress after September 15, 1989: Mathematics Department, Harvard University, Cambrdige, MA 02138, USA     

A Poisson–Lie Framework for Rational Reductions of the KP Hierarchy

We give a simple proof of I. Krichever's theorem on rational reductions of the Kadomtsev–Petviashvili hierarchy by using the Poisson–Lie structure on the group of pseudo-differential symbols.     

Influence of UV pretreatment on the abies wood catalytic delignification in the medium “acetic acid–hydrogen peroxide–TiO2”

Some regularities of abies-wood oxidative delignification by acetic acid–hydrogen peroxide mixture under the action of suspended TiO₂ catalyst and UV pretreatment of wood pulp were studied. The combined action of TiO₂ catalyst and of UV-pretreatment of abies-wood allow to produce at optimal conditions of the delignification process the chemically pure cellulose containing no residual lignin. The major characteristics of cellulose product obtained from abies-wood correspond to the characteristics of microcrystalline cellulose.     

Nonlinear wave interactions in patterned Silica and AlGaAs waveguides

We study nonlinear interactions between discrete optical solitons that propagate in different regimes of diffraction, and the nonlinear scattering of dispersive waves by local optical potentials. It is well known in optics that when linear coherent waves meet, they interfere without interactions. Linear waves also scatter through local optical structures not exchanging any power with the guided modes of these structures. As a focusing Kerr nonlinearity is present, such linearly-inhibited phenomena can exist. Our studies are performed in silica and AlGaAs nonlinear waveguides, excited by ultra-short pulses in the near infrared. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Pure Point Diffractive Substitution Delone Sets Have the Meyer Property

We prove that a primitive substitution Delone set, which is pure point diffractive, is a Meyer set. This answers a question of J.C. Lagarias. We also show that for primitive substitution Delone sets, being a Meyer set is equivalent to having a relatively dense set of Bragg peaks. The proof is based on tiling dynamical systems and the connection between the diffraction and dynamical spectra. The first author acknowledges support from the NSERC post-doctoral fellowship and thanks the University of Washington and the University of Victoria for being the host universities of the fellowship. The second author is grateful to the Weizmann Institute of Science where he was a Rosi and Max Varon Visiting Professor when this work was completed. He was also supported in part by NSF Grant DMS 0355187.     

Oxidation behaviour of uranium and neptunium in stabilised zirconia

Yttria stabilised zirconia (YSZ) based (Zr,Y,U)O_2−x and (Zr,Y,Np)O_2−x solid solutions with 6 and 20 mol% actinide were prepared with Y/Zr ratios ranging from 0.2 to 2.0 to investigate uranium and neptunium oxidation behaviour depending on the oxygen vacancies in the defect fluorite lattice. Sintering at 1600 °C in Ar/H₂ yields a cubic, fluorite-type structure with U(IV) and Np(IV). Annealing (Zr,Y,U)O_2−x with Y/Zr=0.2 at 800 °C in air results in a tetragonal phase, whereas (Zr,Y,U)O_2−x with higher Y/Zr ratios and (Zr,Y,Np)O_2−x retain the cubic structure. XANES and O/M measurements indicate mixed U(V)-U(VI) and Np(IV)-Np(V) oxidation states after oxidation. Based on X-ray diffraction, O/M and EXAFS measurements, different oxidation mechanisms are identified for U- and Np-doped stabilised zirconia. In contrast to U, excess oxygen vacancies are needed to oxidise Np in (Zr,Y,Np)O_2−x as the oxidation process competes with Zr for oxygen vacancies. As a consequence, U(VI) and Np(V) can only be obtained in stabilised zirconia with Y/Zr=1 but not in YSZ with Y/Zr=0.2.