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     

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.     

Uniformization of Riemann surfaces revisited

Annals of Global Analysis and Geometry - We give an elementary and self-contained proof of the uniformization theorem for noncompact simply connected Riemann surfaces.     

Effects of molecular structure and environment on the photodimerization of substituted anthracenes

Photochemical and photophysical studies of a number of 9-substituted anthracene sandwich pairs in their corresponding photodimer crystal matrices have been carried out. Corresponding studies have also been made in methylcyclohexane matrices at 6 K. Photodimerization of the 9-methyl, 9-chloro and 9-cyano derivatives in the photodimer matrices occurs at 6 K with unit quantum yield. The presence of excimer fluorescence from sandwich pairs indicates the lack of a perfect topochemical orientation while activation processes, leading to photodimerization, involve molecular re-orientation from more stable ground state configurations which are achieved within the constraints imposed by the solvent or crystalline cage.     

Determination of alachlor and two metabolites in groundwater using solid phase and a new micro-liquid-liquid extraction method

Two different extraction procedures to determine alachlor (2-chloro-2,6-diethyl-N-methoxymethyl-acetanilide) and its metabolites 2,6-diethylaniline (DEA) and 2-chloro-2,6-diethylacetanilide (CDEA) at very low concentration levels in groundwater are compared. Both methods were performed during a field leaching study and laboratory soil column experiments. Solid phase extraction (SPE) is characterized by the enrichment of 11 water samples at 1 g RP-C18 material, while micro liquid/liquid extraction (MLLE) means that 400 ml water samples saturated with sodium chloride were extracted once with 500 l of toluene. Both methods differ in their concentration factors, i.e. 5000 for SPE and 800 for MLLE. The determination limits for alachlor determined as the lowest spiked concentration analyzed are 10 ng/l with SPE and 25 ng/l with MLLE. Even though the determination limits of the two methods are similar, the volatile metabolite 2,6-diethylaniline was not sufficiently recovered by SPE. Furthermore, SPE is more expensive and time consuming than MLLE. The latter is simple in use, rapidly performed and needs no evaporation step and clean-up before GC analysis. This is of special advantage for the analysis of 2,6-diethylaniline. The determination limits of the metabolites CDEA and DEA analyzed by MLLE are 25 ng/l. The extracts from both methods were directly analyzed by gas chromatography using electron capture and nitrogen-phosphorus detection.     

Novel Copolymers of 4-Fluorostyrene. 11. Some Ring-substituted 1,1-dicyano-2-(1-naphthyl)ethylenes

Novel copolymers of trisubstituted ethylene monomers, ring-substituted 1,1-dicyano-2-(1-naphthyl)ethylenes, RC₁₀H₆CH?C(CN)₂ (where R is H, 2-OCH₃, 4-OCH₃) and 4-fluorostyrene were prepared by solution copolymerization in the presence of a radical initiator (ABCN) at 70°C. The composition of the copolymers was calculated from nitrogen analysis, and the structures were analyzed by IR, ¹H and ¹³C-NMR. The order of relative reactivity (1/r ₁) for the monomers is (5.86) > 2-CH₃O (4.28) > 4-CH₃O (2.87). Relatively high T_g of the copolymers in comparison with that of poly(4-fluorostyrene) indicates a decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer unit. Decomposition of the copolymers in nitrogen occurred in two steps, first in the 200–500°C range with residue (7.3–7.7% wt.), which then decomposed in the 500–800°C range.     

Simultaneous acquisition of magnetic resonance spectroscopy (MRS) data and positron emission tomography (PET) images with a prototype MR-compatible, small animal PET imager

Multi-modality imaging (such as PET-CT) is rapidly becoming a valuable tool in the diagnosis of disease and in the development of new drugs. Functional images produced with PET, fused with anatomical images created by MRI, allow the correlation of form with function. Perhaps more exciting than the combination of anatomical MRI with PET, is the melding of PET with MR spectroscopy (MRS). Thus, two aspects of physiology could be combined in novel ways to produce new insights into the physiology of normal and pathological processes. Our team is developing a system to acquire MRI images and MRS spectra, and PET images contemporaneously. The prototype MR-compatible PET system consists of two opposed detector heads (appropriate in size for small animal imaging), operating in coincidence mode with an active field-of-view of approximately 14 cm in diameter. Each detector consists of an array of LSO detector elements coupled through a 2-m long fiber optic light guide to a single position-sensitive photomultiplier tube. The use of light guides allows these magnetic field-sensitive elements of the PET imager to be positioned outside the strong magnetic field of our 3T MRI scanner. The PET scanner imager was integrated with a 12-cm diameter, 12-leg custom, birdcage coil. Simultaneous MRS spectra and PET images were successfully acquired from a multi-modality phantom consisting of a sphere filled with 17 brain relevant substances and a positron-emitting radionuclide. There were no significant changes in MRI or PET scanner performance when both were present in the MRI magnet bore. This successful initial test demonstrates the potential for using such a multi-modality to obtain complementary MRS and PET data.