Applications of Clifford’s Geometric Algebra

We survey the development of Clifford’s geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly demonstrate the benefit of developing problem solutions in a unified framework for algebra and geometry with the widest possible scope: from quantum computing and electromagnetism to satellite navigation, from neural computing to camera geometry, image processing, robotics and beyond.     

Synthese von 2.4-Dibrom-3-Thiapentan

Abstract

The reaction of bromine with trimeric thioacetic aldehyde leads to the formation of the title compound which may be used as starting material for the synthesis of new methyl-substituted cyclic and linear thioalkanes.     

Charge carrier mobility,photovoltaic, and electroluminescent properties of anthracene‐based conjugated polymers bearing randomly distributed side chains

This article reports on the synthesis, characterization, and properties of various anthracene‐containing poly (p‐phenylene‐ethynylene)‐alt‐poly(p‐phenylene‐vinylene) (PPE‐PPV) polymers (AnE‐PVs) bearing statistical distributions of various side chains. Primarily, the ratio of linear octyloxy and branched 2‐ethylhexyloxy side chains at the poly(p‐phenylene vinylene) (PPV) parts was varied, leading to the polymers stat, stat1, and stat2. Furthermore, polymers also containing asymmetric substituted PPV and poly(p‐phenylene ethynylene) units (bearing methoxy and 2‐ethylhexyloxy side chains) were prepared yielding stat3, stat4, and stat5. These materials exhibit a broad variation in their photovoltaic properties. It is once more shown that side chains and their distribution can crucially affect the photovoltaic device performance. The introduction of units with asymmetric substitution into these systems seems to be harmful for their utilization in photovoltaic applications. Organic field‐effect transistors were fabricated to investigate hole mobilities in these new materials. Large variance was observed, falling in the range of almost two orders of magnitude, indicating rather different π–π stacking behavior of the polymer backbones owing to side‐chain modifications. Moreover, a selection of the new polymeric systems was investigated regarding their potential for light‐emitting diode (LED) applications. Polymer LEDs using the polymers AnE‐PVstat, ‐stat3, ‐stat4, and ‐stat5, as the active layer showed turn‐on voltage of ～2 V and exhibited red light emission. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Real-World Forward Rate Dynamics With Affine Realizations

We investigate the existence of affine realizations for Lévy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral approach concerning the existence of affine realizations are transferred to the general case. A similar result holds true for models driven by compound Poisson processes with finite jump size distributions. However, in the presence of jumps with infinite activity we obtain severe restrictions on the structure of the market price of risk; typically, it must even be constant.     

1‐Factor and Cycle Covers of Cubic Graphs

Let G be a bridgeless cubic graph. Consider a list of k 1‐factors of G. Let be the set of edges contained in precisely i members of the k 1‐factors. Let be the smallest over all lists of k 1‐factors of G. Any list of three 1‐factors induces a core of a cubic graph. We use results on the structure of cores to prove sufficient conditions for Berge‐covers and for the existence of three 1‐factors with empty intersection. Furthermore, if , then is an upper bound for the girth of G. We also prove some new upper bounds for the length of shortest cycle covers of bridgeless cubic graphs. Cubic graphs with have a 4‐cycle cover of length and a 5‐cycle double cover. These graphs also satisfy two conjectures of Zhang 18 . We also give a negative answer to a problem stated in 18 .     

Analysis of hydrothermally formed corrosion layers in Ni‐base alloy 625 by combined FE‐SEM and EDXS

During experiments simulating the destruction of organic waste or the conversion of biomass with water at supercritical water conditions (SCW, T > 374 °C, p > 22.1 MPa), severe corrosion phenomena were observed. Depending on the experimental conditions applied, scale formation and precipitation of corrosion products occurred. The harsh conditions and the chemical properties of the feed solutions lead to consecutive chemical reactions with the materials involved. To study such hydrothermal reactions on simplified model systems, tubular reactors made of Ni‐based alloys were exposed to feed solutions composed of water, methanol and alkaline salts. After each experiment, the reaction tubes were cut and examined by optical microscopy. Hydrothermally formed corrosion layers were studied by field emission electron microscopy and combined energy dispersive X‐ray spectroscopy. Element line scans and mappings were performed which depicted selective dissolution of alloying elements (dealloying of Ni, Fe, Mo). The formation of the corrosion layers was accompanied by a subsequent reduction of the tube wall diameter. Atomic force microscopy gained additional morphological information; a Monte Carlo programme was applied to simulate X‐ray line scans. Copyright © 2011 John Wiley & Sons, Ltd.