Studien über Kernalkylierung

Ohne Zusammenfassung     

Gray code for derangements

We give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no fixed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of fixed points bounded between two constants.     

On the construction of 2-substituted 1,4-diacetoxybutadiene moiety: application to the synthesis of (±)-caulerpenyne

The synthesis of 2-substituted 1,4-diacetoxybutadiene derivatives with a partial control of stereochemistry is described from two potentially precursor enals by a judicious choice of experimental conditions (Ac₂O/DMAP in Et₃N). These conditions have been successfully applied in the first total synthesis of caulerpenyne.     

Spray thermometry using thermographic phosphors

In this study a novel technique for 2D spray temperature measurement is presented. For this purpose the thermographic phosphor (TP) Mg₄GeO_5.5F:Mn was dispersed in n-dodecane and atomised using a conventional semi solid-cone nozzle. The thermographic phosphor was excited electronically by a frequency tripled Nd:YAG laser (355 nm). An ICCD-camera in combination with an image doubler detected the subsequently emitted phosphorescence at both peak emission wavelengths located at 633 nm and 659 nm, respectively. Utilising suitable calibration measurements, the local spray temperature was determined by evaluating the intensity ratio of both emission wavelengths. To the knowledge of the authors this is the first approach of spray temperature measurement exploiting the temperature dependent intensity ratio of thermographic phosphors. PACS 07.20.Dt; 32.50.+d     

Problems, Models and Complexity. Part II: Application to the DLSP

In Part I of this study, we suggest to identify an operations research (OR) problem with the equivalence class of models describing the problem and enhance the standard computer-science theory of computational complexity to be applicable to this situation of an often model-based OR context. The Discrete Lot-sizing and Scheduling Problem (DLSP) is analysed here in detail to demonstrate the difficulties which can arise if these aspects are neglected and to illustrate the new theoretical concept. In addition, a new minimal model is introduced for the DLSP which makes this problem eventually amenable to a rigorous analysis of its computational complexity.     

Idempotency of Extensions via the Bicompletion

Let Top ₀ be the category of topological T ₀-spaces, QU ₀ the category of quasi-uniform T ₀-spaces, T : QU ₀ → Top ₀ the usual forgetful functor and K : QU ₀ → QU ₀ the bicompletion reflector with unit k : 1 → K. Any T-section F : Top ₀ → QU ₀ is called K-true if KF = FTKF, and upper (lower) K-true if KF is finer (coarser) than FTKF. The literature considers important T-sections F that enjoy all three, or just one, or none of these properties. It is known that T(K,k)F is well-pointed if and only if F is upper K-true. We prove the surprising fact that T(K,k)F is the reflection to Fix(TkF) whenever it is idempotent. We also prove a new characterization of upper K-trueness. We construct examples to set apart some natural cases. In particular we present an upper K-true F for which T(K,k)F is not idempotent, and a K-true F for which the coarsest associated T-preserving coreflector in QU ₀ is not stable under K. We dedicate this paper to the memory of Sérgio de Ornelas Salbany (1941–2005).     

Une nouvelle définition de l'entropie dynamique des systèmes non commutatifs

An alternative definition of entropy for non-commutative systems, equivalent to the one by A. Connes, H. Narnhofer, and W. Thirring, is given. It is based on the concepts of conditional entropy, and stationary couplings with classical systems. It allows to prove that any quantum dynamical system with singular spectrum has zero entropy.     

Stochastic Arithmetic: s-spaces and Some Applications

It has been recently shown that computation with stochastic numbers as regard to addition and multiplication by scalars can be reduced to computation in familiar vector spaces. In this work we show how this can be used for the algebraic solution of linear systems of equations with stochastic right-hand sides. On several examples we compare the algebraic solution with the simulated solution using the CADNA package.