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Gallin Peter Prof. Dr. 《ZDM》2003,35(3):110-119
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 17th century.  相似文献   
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The article referenced above was first published online on 7 August 2007 with incorrect pagination; the pagination has now been corrected online and in print. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   
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In this contribution, we demonstrate a new effective methodology for constructing highly efficient and durable poly(p‐phenyleneethynylene) (PPE) containing emissive material with nonaggregating and hole‐facilitating properties through the introduction of hole‐transporting blocks into the PPE system as the grafting coils as well as building the energy donor–acceptor architecture between the grafting coils and the PPE backbone. Poly(2‐(carbazol‐9‐yl)ethyl methacrylate) (PCzEMA), herein, is chosen as the hole‐transporting blocks, and incorporated into the PPE system as the grafting coils via atom transfer radical polymerization. The chemical structure of the resultant copolymer, PPE‐g‐PCzEMA, was characterized by NMR and gel permeation chromatography, showing that the desirable copolymer was obtained with the narrow polydispersity. The increased thermal stability of PPE‐g‐PCzEMA was confirmed by thermogravimetric analysis and differential scanning calorimetry along with its macroinitiator. The optoelectronic properties of this copolymer were studied in detail by ultraviolet‐visible absorption, photoluminescence emission and excitation spectra, and cyclic voltammogram (CV). The results indicate that PPE‐g‐PCzEMA exhibits the solid‐state luminescent property dominated by individual lumophores, and also the energy transfer process from the PCzEMA blocks to the PPE backbone with a relatively higher energy transfer efficiency in the solid‐state compared to that of the solution state. Additionally, the hole‐injection property is greatly facilitated due to the presence of PCzEMA, as confirmed by CV profiles. All these data indicate that PPE‐g‐PCzEMA is a good candidate for use in optoelectronic devices. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3776–3787, 2007  相似文献   
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A novel microphase‐inversion method was proposed for the preparation of TiO2–SiO2/poly(methyl methacrylate) core–shell nanocomposite particles. The inorganic–polymer nanocomposites were first synthesized via a free‐radical copolymerization in a tetrahydrofuran solution, and the poor solvent was added slowly to induce the microphase separation of the nanocomposite and result in the formation of nanoparticles. The average particle sizes of the microspheres ranged from 70 to 1000 nm, depending on the reaction conditions. Transmission electron microscopy and scanning electron microscopy indicated a core–shell morphology for the obtained microspheres. Thermogravimetric analysis and X‐ray photoelectron spectroscopy measurements confirmed that the surface of the nanocomposite microspheres was polymer‐rich, and this was consistent with the core–shell morphology. The influence of the synthetic conditions, such as the inorganic composition and the content of the crosslinking monomer, on the particle properties was studied in detail. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3911–3920, 2006  相似文献   
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Polycarbonate (PC) was melt blended with small amount of liquid‐crystalline polymer (LCP) and various contents of glass beads (GB) having different diameters. The rheological measurements indicated that the GB addition increased the viscosity ratio and seemed unfavorable to the LCP fibrillation. However, the morphological observation showed that the LCP fibrillation was promoted by the GB addition and varied with the GB packing. With the increased GB packing by increasing the GB content and/or decreasing the GB diameter, LCP deformed from spheres and ellipsoids into stretched ellipsoids at lower shear rates and into long fibrils at higher shear rates. Although higher content of smaller GB jammed into the larger LCP droplets and inhibited the LCP fibrillation, very long LCP fibrils formed at higher shear rates at a high enough packing of GB. The relationship between GB packing and LCP fibrillation revealed two kinds of hydrodynamic effects of GB promoting the LCP fibrillation: at lower GB packing, the shear flow was enhanced by the high local shear between GB, in quantity; and for a high enough GB packing, the shear flow was changed, in quality, into elongational flow, which was more effective for the LCP fibrillation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1020–1030, 2006  相似文献   
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The alkylation of arylaminomethylenecyanamides1 or cyano-imidothiocarbamates2 with -halogen carbonyl compounds followed by base catalysed cyclization yields substituted 4-amino-imidazoles4. Imidazo[4,5-d]pyrimidones5, 6 and imidazo[4,5-b]pyridines7 can be obtained from4.  相似文献   
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Summary The electrocapillary properties of polyacrylic acid have been studied by two methods. Exploratory measurements have been made of the effect of the polymer on the differential capacity of a mercury drop in 0.1 m sodium perchlorate. They showed that the polymer was strongly adsorbed over a wide range of potentials but that it did not appear to form a monolayer. The surface excess of polymer obtained from drop weight data showed a maximum at very low concentrations and then a decline at higher concentrations. The bulk of the work was carried out by making surface tension measurements, using a sessile mercury drop, in solutions of a fraction of polyacrylic acid (mol. wt. 7.02×104) in potassium chloride at 0.01, 0.1, 0.2, and 0.5 m at 25°C.The data have been used to evaluate the surface excesses of the polymer and of the inorganic ions. The distribution of K+ and Cl in the electrical double layer and the contact adsorption of Cl on the mercury were very little affected by the presence of the polymer. The surface excess of polymer was always found to be greatest at low concentrations, to decrease steeply at first as the concentration was increased and then to decrease more slowly at higher concentrations.Possible explanations of this behaviour are discussed and it is concluded that the rapid decrease is a consequence of molecular weight dispersion and the stronger adsorption of high molecular weight polymer. The slow decrease in surface excess at higher concentrations may be a result of configurational changes of the polymer molecules.Surface pressure data show that, despite this decrease in the surface excess, the surface coverage reaches a high level at very low polymer concentrations and then continues to increase slowly as the concentration of polymer is increased. This apparent contradiction is due to changes in configuration of the adsorbed polymer molecules. At higher bulk concentrations the chain configurations are more compact and each adsorbed molecule makes more contacts with and so occupies a greater area of the mercury surface than at low concentrations.The conclusion is reached that the surface excess of polymer is mostly contained in a layer probably more than 1000 Å thick. It consists of a concentrated and entangled mass of polymer chains. Relatively few of these chains are in contact with the mercury at any istant. The concentration in this surface layer decreases steadily with increasing distance from the mercury surface and it merges without discontinuity into the bulk solution.With 10 figures in 22 details  相似文献   
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