Infinitesimale Deformationen von Kegeln über transkanonisch eingebetteten hyperelliptischen Kurven

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg -     

Solving Sequences of Refined Multistage Stochastic Linear Programs

Multistage stochastic programs with continuous underlying distributions involve the obstacle of high-dimensional integrals where the integrands' values again are given by solutions of stochastic programs. A common solution technique consists of discretizing the support of the original distributions leading to scenario trees and corresponding LPs which are – up to a certain size – easy to solve. In order to improve the accuracy of approximation, successive refinements of the support result in rapidly expanding scenario trees and associated LPs. Hence, the solvability of the multistage stochastic program is limited by the numerical solvability of sequences of such expanding LPs. This work describes an algorithmic technique for solving the large-scale LP of refinement ν based on the solutions at the previous ν?1 refinements. Numerical results are presented for practical problem statements within financial applications demonstrating significant speedup (depending on the size of the LP instances).     

2-Substituted 2-Propenoic Acid Esters via Reaction of a Masked Acrylate Ester with Carbonyl Compounds

β-Amino ester enolate reacts readily with selected aldehydes and ketones. Deprotection via the N-oxide provides good yields of the 2-substituted acrylate ester.     

Intramolecular Baylis-Hillman Reaction: A Pathway to Substituted Coumarins

The acrylate ester of salicylaldehyde, in the presence of DABCO, affords a crystalline coumarin salt. Formation of this derivative confirms a vital intermediate in the mechanism of the reaction. Salicylaldehyde, suitably protected, reacts with methyl acrylate to afford a novel coumarin not unlike the vasodilator chromonar.     

A series of novel lanthanide polyoxometalates: condensation of building blocks dependent on the nature of rare earth cations

A series of novel lanthanide polyoxomolybdates was synthesized by reaction of lanthanide cations with the Anderson type anion (TeMo(6)O(24))(6-). The polyoxometalates K(6n)(TeMo(6)O(24))(n)[(Ln(H(2)O)(7))(2)(TeMo(6)O(24))](n)[middle dot]16nH(2)O (Ln = Eu, Gd) and K(3n)[Ln(H(2)O)(5)(TeMo(6)O(24))](n)[middle dot]6nH(2)O (Ln = Tb, Dy, Ho, Er) were characterized by X-ray structure analysis, elemental analysis and IR spectroscopy. We found that the solid-state structures of Ln/(TeMo(6)O(24))(6-) compounds are strongly dependent on the lanthanide cations, and therefore represent a rare example for different arrangements of building units depending on the nature of the rare earth cations. While the Eu(3+) and Gd(3+) cations achieve ninefold coordination by seven water molecules and two terminal oxygen atoms of the (TeMo(6)O(24))(6-) anions, the Tb(3+), Dy(3+), Ho(3+) and Er(3+) cations are coordinated by five water molecules, two terminal oxygen atoms and one molybdenum-bridging oxygen atom belonging to the (TeMo(6)O(24))(6-) anion. The europium and gadolinium substituted compounds contain infinite one-dimensional [(Ln(H(2)O)(7))(2)(TeMo(6)O(24))](n) chains; the terbium, dysprosium, holmium and erbium compounds contain infinite one-dimensional [Ln(H(2)O)(5)(TeMo(6)O(24))](n)(3n-) chains.     

Azimuthal orientational correlations due to excluded volume epitaxy in growing anisotropic grains

The microstructure of anisotropically shaped grains can strongly influence a range of material properties, including transport, mechanical and electro-optical. A grain-structure-related phenomenon, known as excluded volume epitaxy (EVE), is reported in this study. EVE is a local, inter-grain orientational correlations effect, which results from a combination of continuous nucleation of anisotropic grains and impingement of growing grains. Due to EVE, anisotropically shaped grains have a tendency to be similarly aligned in a local neighbourhood, despite the absence of any forced global orientation in the sample. The effect has been repeatedly observed by the authors in block copolymers, as illustrated by a representative TEM image. Optical microscopy of anisotropically shaped non-polymeric crystals revealed the generality of this effect. The simulation study revealed a tendency for azimuthal, inter-grain orientational correlation and re-confirmed the experimental observation of EVE.     

Magnetization and magnetic excitations in HoAl2

The magnetization of HoAl₂ single crystals parallel and perpendicular to the applied field for three crystallographic directions has been measured between 4.2 and 300 K in fields up to 8 T. Further the spin wave excitations were investigated by inelastic neutron scattering at 5.2 K along <100>, <110> and <111> directions in reciprocal space. The results are interpreted consistently in terms of a cubic crystal field using a simple molecular field to calculate the magnetization and an isotropic Heisenberg exchange interaction to obtain the magnetic excitations.     

The Boltzmann equation from quantum field theory

We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff–Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff–Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.