Über Anzahl und Verteilung der Scheitel ebener Bogen

Zusammenfassung Seit der Entdeckung des 4-Scheitel-Satzes durch S. Mukhopadhaya (1909) und A. Kneser (1912) hat sich eine umfangreiche Literatur über Scheitel- und verwandte Sätze entwickelt. Unter anderem wurden ebene Bogen auf Scheitel hin untersucht bzgl. Charakteristiken, welche von k 1 Parametern stetig abhängen. Wir legen für die wichtigsten Sätze aus diesem Teil der Theorie überarbeitete Definitionen und Beweise unter vereinfachten Voraussetzungen vor.

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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     

Pore Structure Analysis of Porous Particles by Equivalent Model

Starting from Wheeler's composite theory, which takes both the multilayer adsorption and the capillary condensation into consideration, and assuming the equivalent cylindrical model, we have deduced a strict and relatively simpler formula for the calculation of pore size distribution by solving the integral equation directly. The formula is more convenient for application because of its recursion form. Following the same line of reasoning and using the mean value theorem of definite integrals under different conditions, we have unified the equations of Barrett-Joyner-Halenda, Dubinin, Cranston-Inkley, Dollimore-Heal and Roberts. A table of parameters which is required in the calculation is given. Besides the adsorption of nitrogen, the adsorption with water vapor as the adsorbate is investigated and the corresponding empirical equation of adsorption thickness is given.     

Umsetzung von hydrobromiertem 1,4-Polybutadien mit lithiumorganischen Verbindungen

Ohne ZusammenfassungMit 1 Abbildung und 1 Tabelle     

K2[(UO2)As2O7] – the First Uranium Polyarsenate

Yellowish crystals of K₂[(UO₂)As₂O₇] ( 1 ) have been synthesized by solid‐state reactions method. The structure of 1 [orthorhombic, Pmmn, a = 12.601(2), b = 13.242(2), c = 5.621(1) Å, V = 937.9(3) ų, Z = 4] has been solved by direct methods and refined to R₁ = 0.049, wR₂ = 0.1060 for 1059 observed reflections. The structure of 1 is based upon [(UO₂)As₂O₇]^2? sheets formed by corner sharing between [UO₆]^6? distorted octahedra and [As₂O₇]^4? polyarsenate groups. The K⁺ cations are either in eightfold or tenfold coordination and are located between the sheets. The topology of the uranyl arsenate sheet is related to silicate minerals of the melilite group and related synthetic silicate, aluminate and germanate compounds.     

Synthesis of a Stimuli‐Responsive P‐Chiral Polymer with Chiral Phosphorus Atoms and Azobenzene Moieties in the Main Chain

A reaction of the P‐chiral compound (S,S)‐1,2‐bis(boranato(tert‐butyl)methylphosphino)ethane with an azobenzene derivative gave stimuli‐responsive polymers with P‐chiral phosphines in the main chain. This is the first example of a stimuli‐responsive P‐chiral polymer. The polymer isomerized from the trans to the cis form upon UV irradiation and reverted to the trans form reversibly. The polymer was able to coordinate to platinum, and the resulting polymer complex exhibited the Cotton effect owing to the chirality of the phosphorus atoms. The structure of the P‐chiral polymer obtained could be changed reversibly by light and thermal stimuli, and the polymer chain was induced to rotate helically when complexed with transition metals through the chiral phosphorus atoms.     

One‐Dimensional,Cofacial Porphyrin Polymers Formed by Self‐Assembly of meso‐Tetrakis(ERE Donor) Zinc(II) Porphyrins

A series of meso‐tetrakis‐(ERE donor) zinc(II) porphyrins n Zn (ERE donor=4‐R‐3,5‐bis[(E)‐methyl]phenyl; 1 Zn: E=NMe₂, R=Br; 2 Zn: E=NMe₂, R=H; 3 Zn: E=OMe, R=Br; 4 Zn: E=OMe, R=H) have been synthesized in excellent yields. As a result of the combination of a Lewis acidic site and eight Lewis basic sites within one molecule, monomeric molecules of n Zn self‐assemble to form one‐dimensional porphyrin polymers [ n Zn]_∞ in the solid state, as confirmed for 1 Zn and 3 Zn by X‐ray crystallography. The coordination environment around the zinc(II) ions in these polymers is octahedral. They are ligated by four equatorial nitrogen atoms of the porphyrin and two apical E atoms (E=N, O) provided by the EBrE donor groups of adjacent n Zn molecules. Complexes 2 Zn and 4 Zn did not form single crystals, but solid‐state UV/Vis analysis points to the formation of similar structures. Solution UV/Vis and ¹H NMR spectroscopy indicated that interactions between 1 Zn and 2 Zn monomers in the polymers are stronger than between 3 Zn and 4 Zn monomers. Interestingly, they also revealed that the presence of a neighboring bromine atom in the EBrE donor groups has a considerable influence on the coordination properties of the benzylic N or O atoms. The zinc(II) ions of the porphyrins most likely adopt only hexacoordination in the solid state, owing to the unique predisposition of Lewis acidic and basic sites in the n Zn molecules. Several parameters of the aggregates, for example, the interplanar separation between porphyrins and the zinc–zinc distances, change as a function of the coordinating E groups. The high degree of modularity in their synthesis makes these zinc(II) porphyrins an interesting new entry in noncovalent multiporphyrin assemblies.     

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.     

Zur Kenntnis der Reaktionen von Carbonsäurechloriden in Lösungsmitteln mit Wolle

Zusammenfassung Wolle und-Keratose wurden mit Carbonsäure-chloriden in Dimethylsulfoxid mit Pyridinzusatz oder ohne Base bei 20–60 °C bis zu 4 Stunden umgesetzt. Die dabei eintretende Vernetzungsreaktion beruht auf der Bildung von Formaldehyd aus den Säurechloriden und Dimethylsulfoxid. Damit werden auch die Anafysendaten verständlich: geringe Gewichtsänderungen, Beteiligung des Lysins, keine Beteiligung der Carboxylgruppen, Verschwinden des Tyrosins erst nach saurer Totalhydrolyse. Läßt man Acylchloride in Dimethylformamid, Dimethylacetamid, Hexamethyl-phosphorsäuretriamid,-Butyrolacton und Methyl-pyrrolidon auf Wolle einwirken, so erfolgt N,O-Acylierung unter Gewichtszunahme.

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Summary Wool and -Keratose were reacted at 20–60° for 4 hours with acylchlorides in dimethylsulfoxide with addition of pyridine or without a base. The ensuing crosslinking reaction. was due to formation of formaldehyde by reaction of the acid chlorides with the solvent dimethylsulfoxide. This explains the analytical data found: small weight changes participation of lysine, no participation of the carboxylic groups, disappearance of tyrosine during the acid hydrolysis.If the acyl chlorides are reacted with wool in the solvents dimethylformamide, dimethylacetamide, hexamethyl-phosphortriamide,-butyrolacton and methyl-pyrrolidone, normal acylation and corresponding weight increases were found.

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Teil der DissertationH.-D. Scharf, RWTH Aachen, 1972; 21. Mitteilung über ,Reaktivität von Aminosäureseitenketten. 20. Mitteilung vgl.W. Wellner, D. Nissen und H. Zahn, Colloid u. Polymer Sci.255, 444 (1977).

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Jetzt Dynamit-Nobel AG., Troisdorf.

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Jetzt Wella AG, Darmstadt.

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Mit 4 Abbildungen und 8 Tabellen