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.     

Effects of the architecture and environment on polymeric molecular assemblies of novel amphiphilic diblock copolynorbornenes with narrow polydispersity via living ring‐opening metathesis polymerization

Diblock copolymers of 5‐(methylphthalimide)bicyclo[2.2.1]hept‐2‐ene (NBMPI) and 1,5‐cyclooctadiene were synthesized by living ring‐opening metathesis polymerization with a well‐defined catalyst {RuCl₂(CHPh)[P(C₆H₁₁)₃]₂}. Unhydrogenated diblock copolymers showed two glass transitions due to poly(NBMPI) and polybutadiene segments, such as two glass‐transition temperatures at ?86.5 and 115.3 °C for poly 1a and ?87.2 and 115.3 °C for poly 1b . However, only one melting temperature could be observed for hydrogenated copolymers, such as 119.8 °C for poly 2a and 121.7 °C for poly 2b . The unhydrogenated diblock copolymer with the longer poly(NBMPI) chain (poly 1a ; temperature at 10% mass loss = 400 °C) exhibited better thermal stability than the one with the shorter poly(NBMPI) chain (poly 1b ; temperature at 10% mass loss = 385 °C). Two kinds of hydrogenated diblock copolymers, poly 2a and poly 2b , exhibited relatively poor solubility but better thermal stability than unhydrogenated diblock copolymers because of the polyethylene segments. Poly[(hydrochloride quaternized 2‐norbornene‐5‐methyleneamine)‐b‐butadiene]‐1 (poly 3a ) was obtained after the hydrolysis and quaternization of poly 1a . Dynamic light scattering measurements indicated that the hydrodynamic diameters of the cationic copolymer (poly 3a ) in water (hydrodynamic diameter = 1580 nm without salt), methanol/water (4/96 v/v; hydrodynamic diameter = 1500 nm without salt), and tetrahydrofuran/water (4/96 v/v; hydrodynamic diameter = 1200 nm without salt) decreased with increasing salt (NaCl) concentration. The effect of temperature on the hydrodynamic diameter of hydrophobically modified poly 3a was also studied. The inflection point of the hydrodynamic diameter of poly 3a was observed at various polymer concentrations around 30 °C. The critical micelle concentration of hydrophobically modified poly 3a was observed at 0.018 g dL^?1. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2901–2911, 2006     

Viscometric study of gelatin in dilute aqueous solutions

The viscosities of aqueous solutions of gelatin at different temperatures were carefully measured in a common glass‐capillary Ubbelohde viscometer at dilute to extremely dilute concentrations. The adsorption effect that occurred in the viscosity measurements was theoretically analyzed and discussed. A theory based on Langmuir isotherms could adequately describe the existing data. Some structural information was obtained by the use of an iterative fitting procedure to treat the reduced viscosity data, which disclosed that individual gelatin chains underwent a coil‐to‐helix transition as the solution cooled from 40 to 15 °C. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1804–1812, 2006     

Preparation and characterization of rigid poly(vinyl chloride)/MMT nanocomposites. II. XRD,morphological and mechanical characteristics

A Haake torque rheometer equipped with an internal mixer is used to study the influence of the amount of sodium montmorillonite (Na⁺‐MMT) and organically modified MMT (O‐MMT) on X‐ray diffraction (XRD), morphology, and mechanical characteristics of rigid poly (vinyl chloride) (PVC)/Na⁺‐MMT and PVC/O‐MMT nanocomposites, respectively. Results of XRD and transmission electron microscopy (TEM) indicate that MMT is partially encapsulated and intercalated in the rigid PVC/Na⁺‐MMT nanocomposites. However, results of XRD and TEM show MMT is partially intercalated and exfoliated in the rigid PVC/O‐MMT nanocomposites. Tensile strength, yield strength, and elongation at break of the rigid PVC/MMT nanocomposites were improved simultaneously with adding 1–3 wt % Na⁺‐MMT or O‐MMT with respect to that of pristine PVC. However, the addition of Na⁺‐MMT or O‐MMT should be kept as not more than 3 wt % to optimize the mechanical properties and the processing stability of the rigid PVC/MMT nanocomposites. SEM micrographs of the fractured surfaces of the rigid PVC/Na⁺‐MMT and PVC/O‐MMT nanocomposites both before and after tensile tests were also illustrated and compared. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2145–2154, 2006     

4-Amino-imidazole durchThorpe-Cyclisierung

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.     

The electrocapillarity of polyacrylates

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     

Stereochemie von Metallocenen, 40. Mitt.

Starting from optically active methylferrocene-- and--carboxylic acids (1 a and1 b) of known absolute configuration and enantiomeric purity about 15 chiral ferrocenes (of each isomeric series— and ) were obtained by suitable ligand transformations. Thereby (almost) all possible chiral combinations of the ligands CH₃, COOH (COO^–), COOCH₃, CN and NH₂ (NH₃ ⁺) were accessible which are necessary for a potential test of approximations of chirality functions for compounds with basic symmetry C_5v. The chiroptical properties of these disubstituted ferrocenes are recorded.Preliminary tests using a shortened Ansatz revealed large discrepancies between calculated () and found [M]_D-values. Possible reasons for this failure are discussed.

---

---

61. Mitt. über Ferrocenderivate

---

39. Mitt.:A. Meyer, H. Neudeck undK. Schlögl, Chem. Ber.110, 1403 (1977).

---

60. Mitt.:V. Rapi, K. Schlögl undB. Steinitz, J. Organometal. Chem.94, 87 (1975).