On Generating Discrete Orthogonal Bivariate Polynomials

In this paper we present an algorithm for recursively generating orthogonal bivariate polynomials on a discrete set S ². For this purpose we employ commuting pairs of real symmetric matrices H, K ^n×n to obtain, in a certain sense, a two dimensional Hermitian Lanczos method. The resulting algorithm relies on a recurrence having a slowly growing length. Practical implementation issues an applications are considered. The method can be generalized to compute orthogonal polynomials depending on an arbitrary number of variables.     

Partition coefficients of organic molecules in squalane and water/ethanol mixtures by molecular dynamics simulations

Accurate partition coefficient data of migrants between a polymer and a solvent are of paramount importance for estimating the migration of the migrant over time, including the concentration of the migrant at infinite time in the two solvents. In this article it is shown how this partition coefficient can be estimated for both a small hydrophilic and a hydrophobic organic molecules between squalane (used here to mimic low density poly ethylene) and water/ethanol solutes using thermodynamic integration to calculate the free energy of solvation. Molecular dynamics simulations are performed, using the GROMACS software, by slowly decoupling of firstly the electrostatic and then the Lennard-Jones interactions between molecules in the simulation box. These calculations depend very much on the choice of force field. Two force fields have been tested in this work, the TraPPE-UA (united-atom) and the OPLS-AA (all-atom). The computational cheaper TraPPE-UA force field showed to be more accurate over the whole range of systems compared to the OPLS-AA force field. Moreover, some of the calculations were done with five different water models to investigate the influence of the specific water model on the calculations. It was found that the combination of the TraPPE-UA force field and the TIP4p water model gave the best results. Based on the methodology proposed in this article, it is possible to obtain good partition coefficients only knowing the chemical structure of the molecules in the system.     

Ranking Beta Sheet Topologies with Applications to Protein Structure Prediction

One reason why ab initio protein structure predictors do not perform very well is their inability to reliably identify long-range interactions between amino acids. To achieve reliable long-range interactions, all potential pairings of β-strands (β-topologies) of a given protein are enumerated, including the native β-topology. Two very different β-topology scoring methods from the literature are then used to rank all potential β-topologies. This has not previously been attempted for any scoring method. The main result of this paper is a justification that one of the scoring methods, in particular, consistently top-ranks native β-topologies. Since the number of potential β-topologies grows exponentially with the number of β-strands, it is unrealistic to expect that all potential β-topologies can be enumerated for large proteins. The second result of this paper is an enumeration scheme of a subset of β-topologies. It is shown that native-consistent β-topologies often are among the top-ranked β-topologies of this subset. The presence of the native or native-consistent β-topologies in the subset of enumerated potential β-topologies relies heavily on the correct identification of β-strands. The third contribution of this paper is a method to deal with the inaccuracies of secondary structure predictors when enumerating potential β-topologies. The results reported in this paper are highly relevant for ab initio protein structure prediction methods based on decoy generation. They indicate that decoy generation can be heavily constrained using top-ranked β-topologies as they are very likely to contain native or native-consistent β-topologies.     

Wasser

Analytical and Bioanalytical Chemistry -     

Non-linear dynamic phenomena in the behaviour of a railway wheelset model

A dicone moving on a pair of cylindrical rails can be considered as a simplified model of a railway wheelset. Taking into account the non-linear friction laws of rolling contact, the equations of motion for this non-linear mechanical system result in a set of differential-algebraic equations. Previous simulations performed with the differential-algebraic solver DASSL, [2], and experiments, [7], indicated non-linear phenomena such as limit-cycles, bifurcations as well as chaotic behaviour. In this paper the non-linear phenomena are investigated in more detail with the aid of special in-house software and the path-following algorithm PATH [10]. We apply Poincaré sections and Poincaré maps to describe the structure of periodic, quasiperiodic and chaotic motions. The analyses show that part of the chaotic behaviour of the non-linear system can be fully understood as a non-linear iterative process. The resulting stretching and folding processes are illustrated by series of Poincaré sections.     

Ring Opening of Pymisyl‐Protected Aziridines with Organocuprates

The pyrimidine‐2‐sulfonyl (pymisyl) group is introduced as a new protecting group that can be used to activate aziridines towards ring opening. It is readily introduced and removed under mild conditions. Regioselective ring opening of pymisyl‐protected 2‐methyl‐aziridine with organocuprates gives the corresponding sulfonamides in high yields, and the pymisyl group can subsequently be removed upon treatment with a thiolate. The versatility of this new nitrogen protecting group is illustrated with a new synthesis of Selegiline, a monoamine oxidase‐B inhibitor marketed for the treatment of Parkinson’s disease.     

Chemometric quality control of chromatographic purity

It is common practice in chromatographic purity analysis of pharmaceutical manufacturing processes to assess the quality of peak integration combined by visual investigation of the chromatogram. This traditional method of visual chromatographic comparison is simple, but is very subjective, laborious and seldom very quantitative. For high-purity drugs it would be particularly difficult to detect the occurrence of an unknown impurity co-eluting with the target compound, which is present in excess compared to any impurity. We hypothesize that this can be achieved through Multivariate Statistical Process Control (MSPC) based on principal component analysis (PCA) modeling. In order to obtain the lowest detection limit, different chromatographic data preprocessing methods such as time alignment, baseline correction and scaling are applied. Historical high performance liquid chromatography (HPLC) chromatograms from a biopharmaceutical in-process analysis are used to build a normal operation condition (NOC) PCA model. Chromatograms added simulated 0.1% impurities with varied resolutions are exposed to the NOC model and monitored with MSPC charts. This study demonstrates that MSPC based on PCA applied on chromatographic purity analysis is a powerful tool for monitoring subtle changes in the chromatographic pattern, providing clear diagnostics of subtly deviating chromatograms. The procedure described in this study can be implemented and operated as the HPLC analysis runs according to the process analytical technology (PAT) concept aiming for real-time release.     

The K-theoretical range of Cuntz–Krieger algebras

We augment Restorff's classification of purely infinite Cuntz–Krieger algebras by describing the range of his invariant on purely infinite Cuntz–Krieger algebras. We also describe its range on purely infinite graph C^?$C^{?}$-algebras with finitely many ideals, and provide ‘unital’ range results for purely infinite Cuntz–Krieger algebras and unital purely infinite graph C^?$C^{?}$-algebras.     

Untersuchung von Fetten und ?len

Ohne Zusammenfassung     

Methane as a Selectivity Booster in the Arc‐Discharge Synthesis of Endohedral Fullerenes: Selective Synthesis of the Single‐Molecule Magnet Dy2TiC@C80 and Its Congener Dy2TiC2@C80

The use of methane as a reactive gas dramatically increases the selectivity of the arc‐discharge synthesis of M‐Ti‐carbide clusterfullerenes (M=Y, Nd, Gd, Dy, Er, Lu). Optimization of the process parameters allows the synthesis of Dy₂TiC@C₈₀‐I and its facile isolation in a single chromatographic step. A new type of cluster with an endohedral acetylide unit, M₂TiC₂@C₈₀, is discovered along with the second isomer of M₂TiC@C₈₀. Dy₂TiC@C₈₀‐(I,II) and Dy₂TiC₂@C₈₀‐I are shown to be single‐molecule magnets (SMM), but the presence of the second carbon atom in the cluster Dy₂TiC₂@C₈₀ leads to substantially poorer SMM properties.