Die Strommer-Zykliden des Flaggenraumes

According to H. BRAUNER a flag space is a three-dimensional affine space with an absolute {,f,F}, wheref is a line in the plane of infinity andF a point onf. A cyclide is a surface of order 4 that intersects only atf. A STROMMER-cyclide is a cyclide generated by translation of a circle in an isotropic plane. In this paper we proof that all STROMMER-cyclides can be generated by translation of an isotropic circle along a divergent Newton-parabola or a conic in a full isotropic plane. We give normal-forms and CAD-pictures of these surfaces. Finaly some geometrical results about STROMMER-cyclides are developed.

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Herrn o.Prof. Dr. Gy. Strommer zum 70. Geburtstag gewidmet.     

Density fluctuations in amorphous and semicrystalline polymers

Summary The small-angle scattering of amorphous and semicrystalline polymers contains an intensity component due to density fluctuations within the crystalline and amorphous domains.For amorphous polymers, the density fluctuations aboveT _g correspond to the theoretical value for a fluid system in thermodynamic equilibrium. BelowT _g , a temperature dependence proportional to T is observed over a range of about 50°. At lower temperatures, a linear relationship with a smaller slope has been found which extrapolates to a non-zero value at 0 °K. This value corresponds to the frozen-in disorder, the slope at low temperatures is related to thermal vibrations and can be evaluated in terms of photon-phonon scattering.Semicrystalline polymers show a temperature dependence of the density fluctuation similar to that of the amorphous polymers. At constant temperature the density fluctuations vary linearly with crystallinity.Natural rubber shows an increase of the density fluctuations with increasing cross-linking densities from which information on the density changes in the vicinity of a cross-link and on the statistics of the distribution of cross-linking can be obtained.

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Zusammenfassung Die Kleinwinkelstreuung amorpher und teilkristalliner Polymere besitzt eine Intensitätskomponente, die von Dichtefluktuationen innerhalb der kristallinen und amorphen Bezirke herrührt. Für amorphe Polymere entspricht die Dichtefluktuation oberhalb vonT _g dem theoretischen Wert für ein fluides System im thermodynamischen Gleichgewicht. UnterhalbT _g wird eine Temperaturabhängigkeit proportional zuT über einen Bereich von etwa 50° beobachtet. Bei tieferen Temperaturen wird eine lineare Beziehung mit einer geringeren Steigung gefunden, welche zu einem endlichen Wert bei 0 °K extrapoliert werden kann. Dieser Wert bezieht sich auf die eingefrorene Fehlordnung, die Steigung bei tiefen Temperaturen ist auf thermische Schwingungen zurückzuführen und kann als Photon-Phonon-Streuung ausgewertet werden.Teilkristalline Polymere zeigen eine Temperaturabhängigkeit der Dichtefluktuation, die der von amorphen Polymeren ähnlich ist. Bei konstanter Temperatur ändert sich die Dichtefluktuation linear mit der Kristallinität.Naturkautschuk zeigt eine mit der Vernetzungsdichte ansteigende Dichtefluktuation, aus der man Information über die Dichteänderung in der Umgebung eines Netzpunktes und die Statistik der Netzpunktverteilung erhalten kann.

     

Absolute infrared intensities of hydrocarbons

Dipole-moment derivatives, calculated by both the CNDO/2 method with different parameterizations and the INDO method, are compared to the experimental values determined from absolute infrared intensity measurements for the IR active modes of methane, ethane, ethylene and acetylene. A parameter refinement procedure is introduced in which the CNDO/2 molecular orbital parameters are adjusted through a damped least-squares treatment to give best agreement with the observed dipole-moment derivatives. It is found that the refinement does not substantially improve the agreement obtained with the original CNDO/2 parameterization. The INDO method gives somewhat poorer agreement than the CNDO/2 calculations. As an example of the applicability of the molecular orbital methods toward reproducing relative infrared intensities, the spectrum of cyclopropane in the gasphase is examined.

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Zusammenfassung Die Ableitungen des Dipol-Moments, die nach der CNDO/2-Methode mit verschiedenen Parametrisierungen sowie der INDO-Methode berechnet wurden, werden mit den experimentellen Ergebnissen aus Messungen der absoluten Infrarot-Intensitäten für die IR-aktiven Schwingungen von Methan, Äthan, Äthylen und Azetylen verglichen. Die CNDO/2-Parameter werden mit einer Methode der kleinsten Quadrate den beobachteten Dipol-Moment-Ableitungen angepaßt. Die Ergebnisse sind jedoch nicht wesentlich von denen der ursprünglichen CNDO/2-Methode verschieden. Die INDO-Ergebnisse sind nicht so gut wie die CNDO/2-Ergebnisse. Als Beispiel der Anwendbarkeit der MO-Methoden zur Berechnung von relativen IR-Intensitäten wird das Spektrum des Cyclopropans in der Gasphase untersucht.

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Résumé Les dérivées du moment dipolaire, calculées par la méthode CNDO/2 avec différentes paramétrisations et par la méthode INDO, sont comparées aux valeurs expérimentales déterminées à partir de mesures d'intensité absolue pour les modes actifs dans l'infra-rouge dans le méthane, l'éthane, l'éthylène et l'acétylène. Les paramètres sont ajustés de manière à donner le meilleur accord avec les dérivées du moment dipolaire. Cet ajustement n'améliore pas sensiblement l'accord obtenu avec la paramétrisation CNDO/2 originale. La méthode INDO donne des résultats moins bons que les calculs CNDO/2. Le spectre du cyclopropane en phase gazeuse est étudié comme exemple de l'applicabilité de la méthode des orbitales moléculaires au calcul des intensités relatives infra-rouge.

     

A dual-electrode approach for highly selective detection of glucose based on diffusion layer theory: experiments and simulation

A dual-electrode configuration for the highly selective detection of glucose in the diffusion layer of the substrate electrode is presented. In this approach, a glassy carbon electrode (GCE, substrate) modified with a conductive layer of glucose oxidase/Nafion/graphite (GNG) was used to create an interference-free region in its diffusion layer by electrochemical depletion of interfering electroactive species. A Pt microelectrode (tip, 5 microm in radius) was located in the diffusion layer of the GNG-modified GCE (GNG-G) with the help of scanning electrochemical microscopy. Consequently, the tip of the electrode could sense glucose selectively by detecting the amount of hydrogen peroxide (H2O2) formed from the oxidization of glucose on the glucose oxidase layer. The influences of parameters, including tip-substrate distance, substrate potential, and electrolyzing time, on the interference-removing efficiency of this dual-electrode approach have been investigated systematically. When the electrolyzing time was 30 s, the tip-substrate distance was 1.8 a (9.0 microm) (where a is the radius of the tip electrode), the potentials of the tip and substrate electrodes were 0.7 V and 0.4 V, respectively, and a mixture of ascorbic acid (0.3 mM), uric acid (0.3 mM), and 4-acetaminophen (0.3 mM) had no influence on the glucose detection. In addition, the current-time responses of the tip electrode at different tip-substrate distances in a solution containing interfering species were numerically simulated. The results from the simulation are in good agreement with the experimental data. This research provides a concept of detection in the diffusion layer of a substrate electrode, as an interference-free region, for developing novel microelectrochemical devices.     

Chiral separation of amino acids derivatized with fluoresceine-5isothiocyanate by capillary electrophoresis and laser-induced fluorescence detection using mixed selectors of beta-cyclodextrin and sodium taurocholate

Chiral separation of 20 pairs of amino acids derivatized with fluoresceine-5-isothiocyanate (FITC) by capillary electrophoresis and laser-induced fluorescence detection was studied using the mixture of beta-cyclodextrin (beta-CD) and sodium taurocholate (STC) as selector. Resolution was considerably superior to that obtained by using either beta-CD or STC alone. The molar ratio of beta-CD to STC of about 2:3 was found to be critical to achieve maximum separation. At this beta-CD-to-STC ratio, chiral separation occurred at really low total concentration of beta-CD and STC (<0.1 mM). Other impacting factors were investigated including the total concentration of beta-CD and STC, pH, and capillary conditioning procedure between two successive runs. Using a running buffer of 80 mM borate containing 20 mM beta-CD and 30 mM STC at pH 9.3, all of the 20 pairs of FITC-amino acid enantiomers were baseline resolved. The resolutions of the most pairs of the amino acid enantiomers (17 of 20) were higher than 3.0, only three pairs gave a resolution lower than 3.0 but higher than 1.90 (beta-phenylserine, pSer). The highest resolution reached 14.58 (Glu). Two derivatives of beta-CD, 2-hydroxypropyl-beta-CD (HP-beta-CD) and heptakis(2,6-di-O-methyl)-beta-CD (DM-beta-CD) were also explored. HP-beta-CD showed similar cooperative effect with STC, while DM-beta-CD together with STC led to poorer chiral separation.     

Electrostatic layer-by-layer assembled carbon nanotube multilayer film and its electrocatalytic activity for O2 reduction

Multilayer films of shortened multiwalled carbon nanotubes (MWNTs) are homogeneously and stably assembled on glassy carbon electrodes with the layer-by-layer (LBL) method, based on electrostatic interaction of positively charged poly(diallyldimethylammonium chloride) and negatively charged and shortened MWNTs. The film assembly and electrochemical property as well as the electrocatalytic activity toward O2 reduction of the MWNT multilayer film are studied. Scanning electron microscopy, the quartz crystal microbalance technique, ultraviolet-visible-near-infrared spectroscopy, and cyclic voltammetry are used for characterization of film assembly. Experimental results revealed that film growth is uniform, almost with the same coverage of the MWNTs in each layer, and that the assembled MWNTs are mainly in the form of small bundles or single tubes on the electrodes. Electrochemical studies indicate that the LBL assembled MWNT films possess a remarkable electrocatalytic activity toward O2 reduction in alkaline media. This property, combined with the well-dispersed, porous and conductive features of the MWNT film illustrated with the LBL method, suggests the potential application of the MWNT film for constructing an efficient alkaline air electrode for energy conversions.     

Oxidation resistant germanium nanowires: bulk synthesis, long chain alkanethiol functionalization, and Langmuir-Blodgett assembly

A simple method is developed to synthesize gram quantities of uniform Ge nanowires (GeNWs) by chemical vapor deposition on preformed, monodispersed seed particles loaded onto a high surface area silica support. Various chemical functionalization schemes are investigated to passivate the GeNW surfaces using alkanethiols and alkyl Grignard reactions. The stability of functionalization against oxidation of germanium for various alkyl chain lengths is elucidated by X-ray photoelectron spectroscopy. Among all schemes tested, long chain alkanethiols (> or = C12) are found to impart the most stable GeNW passivation against oxidation upon extended exposure to ambient air. Further, the chemically functionalized oxidation-resistant nanowires are soluble in organic solvents and can be readily assembled into close-packed Langmuir-Blodgett films potentially useful for future high performance electronic devices.     

121Sb-Mössbauer-Spektren von Antimon(V)-Verbindungen. II

¹²¹Sb Mössbauer Spectra of Antimony (V) Compounds. II The Mössbauer resonance effect of ¹²¹Sb has been studied at 4.2 K in a series of 11 antimony(V) compounds which are in most cases bridged. Isomer shift and quadrupole splitting variations are considered in the light of results of X-ray and vibrational spectroscopy. Preparation and the vibrational spectra of [NMe₄][SbCl₄(n₃)₂] are described. Within the limitations of available structural data related tin compounds are compared with those of corresponding ¹¹⁹Sn Mössbauer spectra.     

Sukzessive Minima mit und ohne Nebenbedingungen

Given semi-normsf andg on ⁿ and a real number >0. Then the successive minima off under the constraintg are defined by _j : = inf {: there existj linear independent vectors inZ ⁿ withf andg}. The main theorem of this paper (Lagrange multiplier theorem) states that the successive minima of a certainnorm h on ⁿ (without constraints) coincide with the _j 's up to bounded factors. Moreover, this norm is constructed explicitly. Using Minkowski's wellknown theorem on successive minima and our result certain inequalities on simultaneous Diophantine approximations are derived.