1-Meixner Random Vectors

Journal of Theoretical Probability - A definition of d-dimensional n-Meixner random vectors is given first. This definition involves the commutators of their semi-quantum operators. After that we...     

Boundary conditions in quantum field theories

Several interesting and important quantum field theories must contain the coupling constant in the boundary conditions. The theories considered include quantum electrodynamics of spin-1/2 fermions and gauge field theories.     

A Galois Connection

The connection presented in this paper mirror-links two metamathematical structures, the finitary closure operators, and the compact consistency properties, in such a way that a specification of one structure induces a provably equivalent specification of the other. Mathematics Subject Classification (2000): Primary 06A15, Secondary 28E10 03B22     

Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.     

Chlorokomplexe von Cu2+ und Ni2+ in Dimethylformamid

Zusammenfassung Durch spektrophotometrische Messungen in Dimethylformamid (DMF) werden die Koordinationsformen [CuCl]⁺ und [CuCl₃]^– sowie [NiCl]⁺, [NiCl₃]^– und [NiCl₄]^2– nachgewiesen. Bei Nickel(II)-chlorid und Kupfer(II)-chlorid wird Autokomplexbildung diskutiert. Die Solvate [Cu(DMF)₄] (ClO₄)₂ und [Ni(DMF)₆] (ClO₄)₂ werden isoliert.Im Zuge der Untersuchungen über Chlorokomplexe von Ionen der Übergangsmetalle^{1, 2} in nichtwäßrigen Lösungsmitteln wurden die Spektren der Lösungen von Kupfer(II)- und Nikkel(II)-perchlorat inDMF in Gegenwart verschiedener Mengen Tetraäthylammoniumchlorid aufgenommen.Mit 5 Abbildungen     

Modeling of serine protease prototype reactions with the flexible effective fragment potential quantum mechanical/molecular mechanical method

A complete cycle of chemical transformations for the serine protease prototype reaction is modeled following calculations with the flexible effective fragment quantum mechanical/molecular mechanical (QM/MM) method. The initial molecular model is based on the crystal structure of the trypsin–bovine pancreatic trypsin inhibitor complex including all atoms of the enzyme within approximately 15–18 Å of the oxygen center O of the catalytic serine residue. Several selections of the QM/MM partitioning are considered. Fractions of the side chains of the residues from the catalytic triad (serine, histidine and aspartic acid) and a central part of a model substrate around the C–N bond to be cleaved are included into the QM subsystem. The remaining part, or the MM subsystem, is represented by flexible chains of small effective fragments, whose potentials explicitly contribute to the Hamiltonian of the QM part, but the corresponding fragment–fragment interactions are described by the MM force fields. The QM/MM boundaries are extended over the C–C bonds of the peptides assigned to the QM subsystem in the enzyme, C–C and C–N bonds in model substrates. Multiple geometry optimizations have been performed by using the RHF/6-31G method in the QM part and OPLSAA or AMBER sets of MM parameters, resulting in a series of stationary points on the complex potential-energy surfaces. All structures generally accepted for the serine protease catalytic cycle have been located. Energies at the stationary points found have been recomputed at the MP2/6-31+G^* level for the QM part in the protein environment. Structural changes along the reaction path are analyzed with special attention to hydrogen-bonding networks. In the case of a model substrate selected as a short peptide CH₃(NHCO-CH₂)₂ – HN–CO–(CH₂–NHCO)CH₃ the computed energy profile for the acylation step shows too high activation energy barriers. The energetics of this rate-limiting step is considerably improved, if more realistic model for the substrate is considered, following the motifs of the ThrI11–GlyI12–ProI13-–CysI14–LysI15–AlaI16–ArgI17–IleI18–IleI19 sequence of the bovine pancreatic trypsin inhibitor.     

De novo structural prediction of transition metal complexes: application to technetium

De novo structural prediction of transition metal complexes is investigated. Technetium complexes are chosen given their importance in medical imaging and nuclear waste remediation and for the chemical diversity they display. A new conformational searching algorithm (LIGB) for transition metals is described that allows one to search for different conformational and geometric isomers within a single simulation. In the preponderance of cases, both conformational searching techniques (LIGB and high-temperature molecular dynamics/simulated annealing) provide comparable results, while LIGB is superior for macrocyclic complexes. A genetic algorithm-optimized PM3(tm) parametrization for Tc is compared with the standard implementation and found to yield a significant improvement in predictive ability for the most prevalent Tc structural motifs. The utility of a coupled molecular mechanics-semiempirical quantum mechanics protocol is demonstrated for very rapid, efficient, and effective de novo prediction of transition metal complex geometries.     

Size exclusion chromatographic characterization of sodium hyaluronate fractions prepared by high energetic sonication

Summary A high molecular weight sodium hyaluronate isolated from rooster combs was degraded by ultrasonication. High-performance size exclusion chromatography allowed rapid and accurate determination of molecular weight parameters (M_z, M_w, M_n) and distributions. The time dependence of hyaluronan ultrasonication to the molecular characteristics of the polymer was investigated. A non-random nature of the degradation process was demonstrated and the reciprocal M_n value was found to be linearly proportional to the time of ultrasonication.     

Kontinuierliche Messung von 14C-markierten Aminos?uregemischen mit Hilfe eines Scintillatorschlauches nach der Trennung an Ionenaustauschers?ulen

Zusammenfassung Es wird eine Methode beschrieben, die es gestattet, während einer automatischen Aminosäuretrennung an Ionenaustauschersäulen die Radioaktivität der einzelnen ¹⁴C-markierten Aminosäuren zu messen. Die aufgetrennten Fraktionen werden unmittelbar am Säulenausgang durch eine Meßanordnung geschickt, bestehend aus einem Scintillatorschlauch, der sich zwischen zwei in Koinzidenz geschalteten Photomultipliern befindet. Anschließend wird mit Ninhydrin angefärbt. Die Nachweisgrenze beträgt 2 · 10^–3 C. Die Methode ist einfach zu handhaben, die Meßgeräte, einschließlich der Meßzelle, sind im Handel erhältlich.

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Summary A method is described for the continuous measurement of ¹⁴C-labelled amino-acids during automatic separation by ion-exchanger columns. Immediately after emerging from the column the single fractions are passed through a measuring device consisting of a plastic scintillator between two photomultipliers in a coincidence circuit. Subsequently the eluate is reacted with ninhydrin. The limit of detection is 2 · 10^–3 C. The procedure is simple and the measuring device is commercially available.

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Die Untersuchungen wurden durch den Minister für Atomkernenergie gefördert. Hierfür danken wir auch an dieser Stelle verbindlich.

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Am Ausbau der Methode waren zeitweilig die Herren Dr. Ing. W. Heptner und Dr. Ing. S. Vierkötter beteiligt.