On the diameter of planar curves and Fourier coefficients

Summary LetF denote a complex valued function on , which is absolutely continuous and periodic with a period 2. Its complex Fourier coefficientsc _n satisfy the inequality 2|c _n |d,n0, whered denotes the diameter of the closed planar curve defined byF. In this paper those functionsF are considered, which give equality for a specificn.

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Zusammenfassung Es seiF eine komplexwertige Funktion auf , die absolut stetig und periodisch ist mit einer Periode 2. Sie definiert eine geschlossene ebene Kurve. Zwischen ihrem Durchmesserd und den komplexen Fourierkoeffizientenc _n besteht die Ungleichung 2|c _n |d fürn0. Es werden jene FunktionenF betrachtet, für die in dieser Ungleichung, für ein gegebenesn, Gleichheit besteht.

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Dedicated to my colleague for many years, Professor Eduard Stiefel

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This research was supported in part by the National Research Council of Canada A-7339     

Fluorescence studies and semiempirical calculations on alkali ion indicators

Two newly synthesized cryptands act as sensitive Na⁺- and K⁺-selective indicators for cation concentrations above 20 M. The fluorescence properties change markedly upon cation binding. In addition, the free ligands exhibit a pronounced sensitivity to pH, which is considerably lower for the cation complexes. Time resolved fluorescence is characterized by a decay time of about 5 ns that is attributed to the diprotonated protolytic state of the uncomplexed ligands. Semiempirical calculations show the systematic influence of the nitrogen lone pairs or the N–H bond on the stability of the system. The cause of the strong fluorescence intensity increase observed upon protonation of the fluorescent cryptands may be attributed to an increase in the S₁–T _x energy gap as a consequence of bridgehead nitrogen protonation.This is a peer-reviewed conference proceeding article from the Third Conference on Methods and Applications of Fluorescence Spectroscopy, Prague, Czech Republic, October 18–21, 1993.     

Quantitative Elektronenstrahlmikroanalyse und Zyklotronresonanzmessungen an Wismut-Antimon (Bi1−xSbx)

For the investigation of the electronic properties of bismuth-antimony single crystals the analysis of their chemical composition is important. For this te Electron Microprobe Analysis is a suitable method. In general the quantitative Elektron Microprobe Analysis requires to take into account various influences. This is possible by correcting calculations on the basis of theoretical models. For the reproducibility and the comparability of analytical results information is necessary on conditions of measurement and on theoretical corrections. In this paper an investigation is made, under which conditions in the analysis of bismuth-rich bismuth-antimony alloys the correction can be neglected. The successful utilization of the Electron Microprobe Analysis for the investigation of the dependence of the band structure of Bi_1−xSb_x on the antimony concentration x is shown by the example of the measurements of cyclotron resonance.     

Zur quantitativen Auswertung von Mikro-Autoradiogrammen mit dem Densitron

Die vorliegende Arbeit beschāftigt sich mit der Answertung von Autoradiogrammen inhomogen markierter mikroskopischer Strukturen am Densitron. Dazu fertigten wir von herkömmlichen Stripping-Filmen (z. B. ORW O K 106) Mikro-Stufengraukeile an und bestimmten die Schwärzung S_ijeder Stufe photometrisch. Graukeile geeigneten Schwärzungsumfangs dienten dann zur Einstellung der Farbtrigger des Densitrons, so daß sich die bei dieser Einstellung gemessenen Farbflächen F_i des jeweiligen Objektes bestimmten Schwärzungswerten zuordnen ließen.

Als Modellobjekte verwendelen wir erstens Autoradiogramme von ³H-Thymidin-markierten Tumorzellen. Vergleichsmessungen an unterschiedlich lange exponierten, sonst aber identischen Präparaten ergaben eine gute Reproduzierbarkeit der Meßergebnisse. Als zweites Testobjekt dienlen Autoradiogramme einer nur schwach markierten Struktur im Gehirn von Fröschen. Die an diesem Grenzfall erhaltenen Ergebnisse werden mit Meßwerten verglichen, die vom gleichen Objekt mittels Scanning-Photometrie an einem. Mikroskop-Photometer SMP 01 (OPTON, Oberkoches, BRD) gewonnen wurden.     

Regiospecific synthesis of cepanolide,a cancer chemoprotective micronutrient found in green onions

The naturally occurring γ-hydroxy-β-sulfanylbutenolide cepanolide and a range of new analogues were synthesized in concise, regiospecific manner through the combined use of 2-silyloxyfuran oxyfunctionalization and tandem thio-Michael addition/elimination.     

Lanthanide Identity Governs Guest-Induced Dimerization in LnIII[15-MC N(L-pheHA)-5])3+ Metallacrowns

Series of lanthanide-containing metallic coordination complexes are frequently presented as structurally analogous, due to the similar chemical and coordinative properties of the lanthanides. In the case of chiral (Ln^III[15-MC _N(L-pheHA)-5])³⁺ metallacrowns (MCs), which are well established supramolecular hosts, the formation of dimers templated by a dicarboxylate guest (muconate) in solution of neutral pH is herein shown to have a unique dependence on the identity of the MC's central lanthanide. Calorimetric data and nuclear magnetic resonance diffusion studies demonstrate that MCs containing larger or smaller lanthanides as the central metal only form monomeric host-guest complexes whereas analogues with intermediate lanthanides (for example, Eu, Gd, Dy) participate in formation of dimeric host-guest-host compartments. The driving force for the dimerization event across the series is thought to be a competition between formation of highly stable MCs (larger lanthanides) and optimally linked bridging guests (smaller lanthanides).     

The gas phase oxidation of HCOOH by Cl and NH2 radicals. Proton coupled electron transfer versus hydrogen atom transfer*

ABSTRACT

The reaction of formic acid (HCOOH) with chlorine atom and amidogen radical (NH₂) have been investigated using high level theoretical methods such BH&HLYP, MP2, QCISD, and CCSD(T) with the 6–311?+?G(2df,2p), aug-cc-pVTZ, aug-cc-pVQZ and extrapolation to CBS basis sets. The abstraction of the acidic and formyl hydrogen atoms of the acid by the two radicals has been considered, and the different reactions proceed either by a proton coupled electron transfer (pcet) and hydrogen atom transfer (hat) mechanisms. Our calculated rate constant at 298?K for the reaction with Cl is 1.14?×?10^?13?cm³?molecule^?1?s^?1 in good agreement with the experimental value 1.8?±?0.12/2.0?×?10^?13?cm³?molecule^?1?s^?1 and the reaction proceeds exclusively by abstraction of the formyl hydrogen atom, via hat mechanism, producing HOCO+ClH. The calculated rate constant, at 298?K, for the reaction with NH₂ is 1.71?×?10^?15?cm³?molecule^?1?s^?1, and the reaction goes through the abstraction of the acidic hydrogen atom, via a pcet mechanism, leading to the formation of HCOO+NH₃.     

Addition reaction and characterization of chlorotris(triphenylphosphine)iridium(I) on silicon(1 1 1) surfaces

Studies were performed to determine the chemical addition of a metal complex molecule, chlorotris(triphenylphosphine)iridium(I), on hydrogen passivated Si(1 1 1) surfaces to form a self-assembled monolayer (SAM). The iridium complex was synthesized prior to chemical addition, for which modified reaction conditions were chosen. Following addition, the silicon surfaces were characterized with X-ray photoelectron spectroscopy (XPS) and cyclic voltammetry (CV). The XPS results revealed that the surfaces consisted of the expected elemental percentages and that the iridium has a slightly higher success rate at attaching to oxide-free surfaces. XPS data also strongly indicate that the iridium complex remained intact upon chemisorption and did not decompose during the addition reaction. CV data show a difference between iridium treated surfaces and control samples. Hydrogen passivated wafers with iridium complex were much more conductive than those which were terminated with just an oxide or with an oxide and iridium complex. Furthermore, no free iridium reagent was detected as an additional feature in the current profile, indicating there was no physisorbed layer.