Synthesis and characterization of novel polyimides with 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein‐3′,5′‐bis(trifluoromethyl)anilide

2,2‐Bis[4(4‐aminophenoxy)phenyl]phthalein‐3′,5′‐bis(trifluoromethyl)anilide (6FADAP), containing fluorine and phthalimide moieties, was synthesized via the Williamson ether condensation reaction from 1‐chloro‐4‐nitrobenzene and phenolphthalein‐3′,5′‐bis(trifluoromethyl)anilide, which was followed by hydrogenation. Monomers such as 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein‐anilide containing phthalimide groups and 2,2‐bis[4(4‐aminophenoxy)phenyl]phthalein containing only phthalein moieties were also synthesized for comparison. The monomers were first characterized by Fourier transform infrared (FTIR), ¹H NMR, ¹⁹F NMR, elemental analysis, and titration and were then used to prepare polyimides with 2,2‐bis(3,4‐dicarboxyphenyl)hexafluoropropane dianhydride. The polyimides were designed to have molecular weights of 20,000 g/mol via off‐stoichiometry and were characterized by FTIR, NMR, gel permeation chromatography (GPC), differential scanning calorimetry, and thermogravimetric analysis. Their solubility, water absorption, dielectric constant, and refractive index were also evaluated. The polyimides prepared with 6FADAP, containing fluorine and phthalimide moieties, had excellent solubility in N‐methylpyrrolidinone, N,N‐dimethylacetamide, tetrahydrofuran, CHCl₃, tetrachloroethane, and acetone, and GPC analysis showed a molecular weight of 18,700 g/mol. The polyimides also exhibited a high glass‐transition temperature (290 °C), good thermal stability (～500 °C in air), low water absorption (1.9 wt %), a low dielectric constant (2.81), a low refractive index, and low birefringence (0.0041). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3361–3374, 2003     

Untersuchungen über Papaverin

Ohne Zusammenfassung     

Vacuum expectation values from fusion of vertex operators

The algebra of fused vertex operators for the ABF model is defined and studied in the free fields approach. Vacuum expectation values of local operators in the scaling theory are reproduced from the matrix elements of the fused vertex operators.     

Dispersion analysis of the least‐squares finite‐element shallow‐water system

The frequency or dispersion relation for the least‐squares mixed formulation of the shallow‐water equations is analysed. We consider the use of different approximation spaces corresponding to co‐located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd.     

Prädikatives und funktionales Denken in der Wahrscheinlichkeitsrechnung

In order to emphasize functional thinking in mathematical education, arguments are brought forward for an early and frequent use of tree diagrams in teaching stochastics. Since set and tree diagrams can be regarded as two sides of the same matter, Bayes’ theorem, which is strongly associated with predicative set diagrams, need not be dealt with explicitly any longer. Set diagrams are replaced by tree diagrams that are labelled in detail and by tree inversion as a functional instrument of dealing with conditioned probabilities. This technique is demonstrated by three typical problems in the context of conditioned probability. Finally, two letters by Pascal to Fermat are analysed in order to illustrate that predicative and functional approaches were already pursued in the early stages of probability calculus in the 17^th century.     

Use of reference materials in coastal monitoring quality assurance

The NOAA National Status and Trends (NS&T) Program determines the current status of, and changes over time in the environmental health of U.S estuarine and coastal waters. Concentrations of organic and inorganic contaminants are determined in bivalves, bottom-dwelling fish and sediments. The quality of the analytical data generated by the NS&T Program is over-seen by the performance-based Quality Assurance Project, which is designed to document sampling protocols, analytical procedures, and laboratory performance, and to reduce intralaboratory and interlaboratory variation. All NS&T cooperating laboratories are required to participate in yearly intercomparison exercises. The analysis of reference materials, such as the National Research Council of Canada's Certified Reference Materials (CRMs) and National Institute of Standards and Technology's (NIST) Standard Reference Materials (SRMs), and of control materials, is required. Because of the need for marine matrix reference materials and standards, NOAA contributed to the production of eight NIST SRMs and seven internal standard solutions. Analytical data from all control materials and all matrix reference materials are reported to the Program office.     

Decomposition methods: A new proof of convergence

We propose a new convergence proof of Adomian's technique based on properties of convergent series. Then we deduce some results about the speed of convergence of this method allowing us to solve nonlinear functional equations.