Classification of bicovariant differential calculi on quantum groups of type A,B, C and D

Under the assumptions thatq is not a root of unity and that the differentialsdu _j ⁱ of the matrix entries span the left module of first order forms, we classify bicovariant differential calculi on quantum groupsA _n–1 ,B _n ,C _n andD _n . We prove that apart one dimensional differential calculi and from finitely many values ofq, there are precisely2n such calculi on the quantum groupA _n–1 =SL _q (n) forn3. All these calculi have the dimensionn ². For the quantum groupsB _n ,C _n andD _n we show that except for finitely manyq there exist precisely twoN ²-dimensional bicovariant calculi forN3, whereN=2n+1 forB _n andN=2n forC _n ,D _n . The structure of these calculi is explicitly described and the corresponding ad-invariant right ideals of ker are determined. In the limitq1 two of the 2n calculi forA _n–1 and one of the two calculi forB _n ,C _n andD _n contain the ordinary classical differential calculus on the corresponding Lie group as a quotient.     

New hardware for radio frequency powered glow discharge spectroscopies and its capabilities for analytical applications

A new radio frequency (rf) hardware is developed for glow discharge spectroscopic methods. The resulting features and its capabilities for analytical applications are discussed. The electrical equipment developed allows to work as quickly, stably, reliably and easily as known from the direct current (dc) mode. Moreover, the rf power measurement has been improved. The hardware has been developed, optimised and tested for glow discharge optical emission spectroscopy (GDOES), but nevertheless it is possible to use it for all procedures applying glow discharge sources.     

A quadratically convergent O(\sqrt n L)-iteration algorithm for linear programming

Recently, Ye, Tapia and Zhang (1991) demonstrated that Mizuno—Todd—Ye's predictor—corrector interior-point algorithm for linear programming maintains the O( L)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap to zero under the assumption of nondegeneracy. In this paper we establish the quadratic convergence result without any assumption concerning the convergence of the iteration sequence or nondegeneracy. This surprising result, to our knowledge, is the first instance of a demonstration of polynomiality and superlinear (or quadratic) convergence for an interior-point algorithm which does not assume the convergence of the iteration sequence or nondegeneracy.Supported in part by NSF Grant DDM-8922636 and NSF Coop. Agr. No. CCR-8809615, the Iowa Business School Summer Grant, and the Interdisciplinary Research Grant of the University of Iowa Center for Advanced Studies.Supported in part by NSF Coop. Agr. No. CCR-8809615, AFOSR 89-0363, DOE DEFG05-86ER25017 and ARO 9DAAL03-90-G-0093.Supported in part by NSF Grant DMS-9102761 and DOE Grant DE-FG05-91ER25100.     

Quantitative depth profiling in glow discharge spectroscopies – A new deconvolution technique to separate effects of an uneven erosion crater shape

An algorithm is presented as a concept for the quantification in direct current and radiofrequency glow discharge (GD) modes for GD optical emission spectroscopy. The algorithm is divided into excitation and sputtering part and thus it is possible to distinguish between the different excitation processes and to consider equivalent sputtering crater formations in both modes. Intensity-time profiles are affected corresponding to the method by several effects. One important effect is that sputtering occurs at a single time in different depths because of curved crater bottoms, this is usually called crater effect. The main purpose is to introduce an iterative deconvolution technique which for the quantification numerically takes into account the curved sputtering crater bottom. Input data for the deconvolution technique are the calibrated mass-time profile, the partial densities of the sample constituents and the measured final shape of the sputtering crater. Using a relatively simple model for ion sputtering the deconvolution technique improves iteratively the calculated layer structure by means of information on crater formation. The mathematical handling is illustrated for the quantification of a depth profile of a multilayer sample of ten 100 nm layers. The resulting concentration-depth profile reflects excellently the real elemental distribution of the multilayer system.     

Synthesen in der Pyridazin-Reihe, 26. Mitt.:

Zusammenfassung Es wird über die Synthese von verschiedenen methylsubstituiertens-Triazolo[4,3—b]pyridazinen berichtet. Außerdem wurdens-Triazolo[4,3—b]pyridazin und seine 7-Methyl- und 6-Chlor-Derivate der homolytischen Methylierung unterworfen, die Reaktionsgemische gaschromatographisch auf einzelne Methyl-s-triazolo[4,3—b]pyridazine aufgetrennt und die Verbindungen identifiziert.

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Syntheses of pyridazines, XXVI: Synthesis and homolytic methylation of s-triazolo[4.3—b]pyridazines

The syntheses of some methyl substituteds-triazolo[4,3—b]-pyridazines are reported.s-Triazolo[4.3—b]pyridazine and its 7-methyl and 6-chloro analogs were submitted to homolytic methylations and the obtained reaction mixtures were separated by gas chromatography into particular components which were then identified.

     

The Adsorption of Polyvinylpyrrolidone on Kaolinite Saturated with Sodium Chloride

The adsorption of two different molecular weights of polyvinylpyrrolidone (PVP) (M(w)=44,000 and M(w)=360,000 g mol(-1)) from water on kaolinite saturated with sodium chloride has been studied. The adsorption of PVP increases slowly as temperature increases. The adsorption of PVP on the kaolinite was studied by considering Fourier transform infrared (FTIR) spectra, X-ray diffraction patterns, and dielectric constants. During the adsorption process, PVP interacts with saturating sodium cations and possibly forces some of them onto the edges of the kaolinite; thus, the dielectric constant of saturated kaolinite is reduced after PVP adsorption. Copyright 2001 Academic Press.     

Determination of Aroma Compounds from Alcoholic Beverages in Spiked Blood Samples by Means of Dynamic Headspace GC–MS

Some aroma compounds found in alcoholic beverages are characteristic of a certain beverage (i.e. 2,4-decadienoic acid ethyl ester is characteristic of pear spirit and 5-butyltetrahydro-4-methylfuran-2-on “whiskey lactone” is characteristic of aged spirits like whiskey). These substances were detectable in beverages but not in blood samples. The aim of this investigation was to find a sensitive sampling technique for aroma compounds in whole blood samples. This technique may be used in forensic toxicology for examination of drinking claims. The method comprises dynamic headspace sampling using a purge and trap concentrator, followed by quantitative gas chromatography–mass spectrometry (dynamic HS–GC–MS). The influence of sample preparation, trap adsorbents and sample temperature as well as desorption time and purge time on the quality of the analytical results were investigated. The following optimal parameters were determined: stirred and diluted whole blood sample without salt addition, use of Carbotrap C as trap material, sample temperature at 80 °C, desorption time 20 min and purge time 30 min. These optimal parameters were used for the determination of detection limits (LOD). The LOD of aroma compounds by means of dynamic headspace sampling were compared with the results of conventional sampling: the static headspace technique. Limits of detection for the aroma compounds with conventional static headspace GC are in the range 400–10,000 μg L^?1. Dynamic headspace–GC was found to be a more sensitive sampling technique for most of the aroma compounds investigated (e.g. C₄–C₈ ethyl esters, benzoic acid ethyl ester, linalool oxide and 4-ethylguaiacol) with detection limits between 1 and 50 μg L^?1, but there were also limits to the sampling of substances with lower volatility like decanoic acid ethyl ester, 2,4-decadienoic acid ethyl ester, eugenol and whiskey lactone with detection limits of about 1,000 μg L^?1.     

TheSemmler-Wolff aromatization andSchmidt reaction applied to some pyrido[2′,3′:3,4]pyrazolo[5,1-c][1,2,4]benzotriazines

Pyrido[2,3:3,4]pyrazolo[5,1-c][1,2,4]benzotriazin-4(1H)ones were transformed via their oximes in aSemmler-Wolff aromatization process in the tetracyclic heteroaromatic amines4 or bySchmidt reaction into a mixture of the same amine4 and a ring enlarged lactam3. Syntheses of some halo pyrazolo[3,4-b]pyridines and a photochemical transformation of 3-azidopyrazolo[3,4-b]pyridine are also described.

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Über dieSemmler-Wolff- undSchmidt-Reaktion einiger Pyrido[2,3:3,4]pyrazolo[5,1-c][1,2,4]benzotriazine

Zusammenfassung Pyrido[23:3,4]pyrazolo[5,1-c][1,2,4]benzotriazin-4(1H)one werden über Oxime in einerSemmler-Wolff-Reaktion in die tetracyklischen aromatischen Amine4 umgewandelt. In einerSchmidt-Reaktion wurden dieselben Ketone in ein Gemisch aus Amin4 und Lactam3 übergeführt. Synthesen von halogensubstituierten Pyrazolo[3,4-b]pyridinen und photochemische Umwandlung von 3-Azidopyrazolo[3,4-b]pyridin werden beschrieben.