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.     

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.

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61. Mitt. über Ferrocenderivate

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

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

Wirkungsgrade in der Welt des Lebens und der Technik

Zusammenfassung Um der oft gehörten Meinung entgegenzutreten, die energetischen Wirkungsgrade lebender Organismen seien wesentlich höher als die technischer Verfahren, werden entsprechende Werte miteinander verglichen. Der sehr niedrige Wirkungsgrad der Photosynthese zusammen mit der kleinen Energiedichte der Sonnenstrahlung erzwang ab einer kritischen Größe die Aufspaltung in Energiesammler, die Pflanzen, und Verbraucher chemischer Energie, den Tieren. Dank den 10 mal höheren Wirkungsgraden in der Technik, lassen sich Solarmobile bauen, die von der auf sie fallenden Sonnenstrahlung angetrieben werden. Wegen des Multiplikationsgesetzes der Teilwirkungsgrade ergeben sich sowohl für die Speicherung der Sonnenenergie in den fossilen Brennstoffen wie in der Nahrungskette extrem niedrige Wirkungsgrade.

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Efficiencies in the world of life and in engineering

One often hears the opinion, that the efficiencies in the world of life are higher than in engineering. To disprove this, many values of efficiency of corresponding processes are compared. The very low efficiency of photosynthesis in living plants together with the low density of solar radiation has led the world of life to split into collectors of energy, the plants, and consumers of chemical energy, the animals. Thanks to the ten times higher efficiencies of solar cells, it is possible, to produce solar mobiles, vehicles that move driven by solar radiation.

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Herrn Prof. Dr.-Ing. U. Grigull zum 75. Geburtstag gewidmet     

Umsetzung von hydrobromiertem 1,4-Polybutadien mit lithiumorganischen Verbindungen

Ohne ZusammenfassungMit 1 Abbildung und 1 Tabelle     

Die Schmelzdiagramme der Systeme CsN3/Zn(N3)2 und KN3/Zn(N3)2

The phase diagrams of the systems CsN₃/Zn(N₃)₂ and KN₃/Zn(N₃)₂ have been obtained employing the microscopic technique ofL. Kofler andA. Kofler. Within the system CsN₃/Zn(N₃)₂ three eutectics at 148°C, 142°C, and 210°C were found. Besides Cs₂Zn(N₃)₄, melting incongruently in the interval 153°C to 170°C, there exist two further compounds of the most probable composition Cs₃Zn₂(N₃)₇ and CsZn₂(N₃)₅, melting congruently at 170°C and 210°C, resp. In the system KN₃/Zn(N₃)₂ there exist two eutectics at 203°C and 172°C and two compounds, one of them, i.e. K₂Zn(N₃)₄, melting congruently at 206°C, the other one, with composition KZn₃(N₃)₇ or KZn₄(N₃)₉, melting incongruently at 210°C.

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Mit 8 Abbildungen

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Herrn Professor Dr.Heribert Grubitsch zum 70. Geburtstag gewidmet.     

Mechanism of the oxidation of cycloheptanone by chloramine-T

The oxidation kinetics of cycloheptanone by chloramine-T in alkaline media has been investigated. A mechanism involving the formation of an intermediate by the interaction between the enolic anion of cycloheptanone and chloramine-T in a slow step followed by its interaction with another molecule of chloramine-T in a fast step leading to products has been proposed. The scheme satisfactorily accords with the observed stoichiometry, negligible influence of ionic strength and a positive dielectric effect. Various rate parameters have been computed and 1.2-cycloheptanedione identified as the end product.With 2 Figures     

Anwendung mikroanalytischer Methoden zur Lösung kunst- und kulturgeschichtlicher Probleme

Zusammenfassung Mit bekannten mikroanalytischen Arbeitsmethoden — Oberflächenreaktionen, Abstrichuntersuchungen mit dem Korundstäbchen, Schutzschichtreaktionen sowie dem Abdruckverfahren — lassen sich archaeometrische Probleme einer Lösung näherbringen. Die Art der Korrosion kupferhaltiger Oberflächen wurde diskutiert.

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Application of microanalytical methods to the solution of artistic- and cultural historical problems

Summary Archeometrical problems are brought closer to a solution by means of known microanalytical procedures-surface reactions, surface scraping studies with the corundum rod, protective layer reactions as well as the imprint method. A discussion of the corrosion of copper-bearing surfaces is included.

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Vortrag anläßlich der Tagung Chemische Analysen — Kunst- und Kulturwissenschaften im Reiß-Museum in Mannheim, 19.–21. September 1974.     

A new technique for the identification of chloride ions by the formation of chromyl chloride

Summary A new technique is described for the identification of the chloride ion through the formation of chromyl chloride, based on the extraction of the latter with carbon tetrachloride. The identification limit is 2g of chloride. It is possible to carry out the test in the presence of many other anions, including fluoride, which cannot be present when the traditional distillation technique is employed.

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Zusammenfassung Vorgeschlagen wird eine neue Technik zum Chloridnachweis durch Bildung von Chromylchlorid. Dieser Nachweis beruht auf der Extraktion des Chromylchlorids mit Tetrachlorkohlenstoff. Die Nachweisgrenze liegt bei 2g Chlorid, wobei die Möglichkeit besteht, den Test auch in Gegenwart von Fluorid durchzuführen, das bei Anwendung der üblichen Destillationsmethoden nicht anwesend sein darf.

     

Darstellung und Reaktionen des 3-Ethinyl-2,4-diformyl-pentandials

Preparation and physical and chemical properties of 3-ethinyl-2,4-diformyl-pentandial (3 a) and its salts are described.3 a contains 2 malonaldehyde groups. Starting from3 a, 4H-pyranes, 4H-dihydropyridines, dipyrazoles, diisoxazoles, bisdiazepines and vinamidine derivates are obtained.

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Mit 1 Abbildung