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).     

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.     

Stigmergy in comparative settlement choice and palaeoenvironment simulation

Decisions on settlement location in the face of climate change and coastal inundation may have resulted in success, survival or even catastrophic failure for early settlers in many parts of the world. In this study, we investigate various questions related to how individuals respond to a palaeoenvironmental simulation, on an interactive tabletop device where participants have the opportunity to build a settlement on a coastal landscape, balancing safety, and access to resources, including sea and terrestrial foodstuffs, while taking into consideration the threat of rising sea levels. The results of the study were analyzed to consider whether decisions on settlement were predicated to be near to locations where previous structures were located, stigmergically, and whether later settler choice would fare better, and score higher, as time progressed. The proximity of settlements was investigated and the reasons for clustering were considered. The interactive simulation was exhibited to thousands of visitors at the 2012 Royal Society Summer Science Exhibition at the “Europe's Lost World” exhibit. 347 participants contributed to the simulation, providing a sufficiently large sample of data for analysis. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–73, 2016     

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.     

Chain homogeneous Souslin algebras

Assuming Jensen's principle ?⁺ we construct Souslin algebras all of whose maximal chains are pairwise isomorphic as total orders, thereby answering questions of Koppelberg and Todor?evi?.