Über die Synthese von 5-(o-Trifluormethylphenyl)-1H-thieno[3,4—e]-1,4-diazepin-2(3H)-onen

The synthesis of 5-(o-trifluoromethylphenyl)-1H-thieno-[3,4-e]1,4-diazepin-2(3H)-one (7) and its nitration and chlorination in pos. 8 are described.     

Observations on the swelling characteristics of the zwitterionic hydrogel of poly(1-3-sulfopropyl)-2-vinyl-pyridinium-betaine hydrogel

Samples of poly[1-(3-sulfopropyl)-2-vinyl-pyridinium-betaine] (PSPV) have been synthesized to high conversion by free radical polymerization in aqueous solution of the zwitterionic monomer SPV with several concentrations of the crosslinker N,N′-methylene-bis-acrylamide (MBA). The densities of the resultant xerogels increased regularly with the content of MBA. Hydrogels obtained by swelling them in water and aqueous KSCN solution were examined by gravimetric and dimensional analysis. The water contents increased with decreasing content of MBA, the value of 92.7 wt% at the lowest MBA content being higher than that for other zwitterionic hydrogels. Enhanced swelling occurred in 1 M aq. KSCN at each MBA content, the total swelling being 98.1 wt% at the lowest crosslinker content. Swelling increased with increasing temperature. An approximate procedure to formulating swelling equilibrium in term of the volume fraction of water in hydrogel, in conjunction with the van’t Hoff equation, yields a small positive value for the enthalpy of swelling. This is compared with values derived similarly for other hydrogels.     

Berechnung von mittleren Schwingungsamplituden einiger tetraedrischer Moleküle und Ionen nach der Methode der charakteristischen Schwingungen

Mean amplitudes of vibration of a series of tetrahedralXY ₄ molecules and ions (hydrides, halides, oxides and oxoanions) have been calculated using the “Method of the Characteristic Vibrations” ofA. Müller. The results indicate that this method leads to very good values for most of the investigated species, and especially in the cases of highM _X/M_Y mass ratio.     

Supramolecular framework adducts constructed of hexamethylenetetramine,aquated alkali metal cationic clusters,and hexacyanoferrates(II/III)

The reaction of alkali metal hexacyanoferrate(II/III) with (CH₂)₆N₄ (hexamethylenetetramine, abbreviated HMT) in an acidic medium yielded crystalline compounds of stoichiometries HK₂[Fe¹¹¹(CN)₆]·2HMT·4H₂O, H₂K₂[Fe¹¹(CN)₆]·2HMT·4H₂O, and HNa₂[Fe¹¹¹(CN)₆]· 2HMT·5H₂O. Their crystal structures are based on a packing of three molecular components: neutral and/orprotonated HMT, hexacyanoferrate, and an alkali metal ion-water cluster. The resulting three-dimensional supramolecular framework is constructed from the coordination of the alkali metal ion by aqua ligands as well as [Fe(CN)₆]{n–} and HMT units, and further stabilization is achieved by hydrogen bonding between water molecules and the noncoordinated nitrogen atoms of HMT and hexacyanoferrate.     

Die Hydrohalogenierung von Hexaphenyldigerman und die Schwingungsspektren einiger Ge2(C6H5) n X6−n -Verbindungen

The reactions of Ge₂(C₆H₅)₆ with HCl and HBr lead in nearly quantitative yields to the 1,1,2,2-tetrahalo derivatives Cl₂(C₆H₅)GeGe(C₆H₅)Cl₂ (I) and Br₂(C₆H₅)GeGe(C₆H₅)Br₂ (II), resp. The Si?Ge bond of (C₆H₅)₃SiGe(C₆H₅)₃ is cleaved under the conditions of hydrohalogenation. The vibrational spectra of Ge₂Br₆, Ge₂(C₆H₅)₆, I, and II are reported. The influence of vibrational coupling on ν GeGe in these compounds is discussed in detail, including vibrational calculations.     

Gleichverteilung und Quadratwurzelschnecke

A new proof of a theorem of W. Neiss is given that the rays of the Quadratwurzelschnecke are uniformly distributed mod 2 . The exact order of the discrepancy of the sequence is determined. Multidimensional generalizations of this sequence are also considered. It is shown that the Quadratwurzelschnecke is something like a roulette.

---

---

Mit 2 Abbildungen

---

Herrn Prof. R. M. Redheffer in Freundschaft zum 60. Geburtstag gewidmet     

Eine Topologie auf der Menge der endlichdimensionalen nichtassoziativen Algebren über einem lokalen Körper

Motivated by an investigation ofKuz'min [2], in this note we introduce a topology on the set of nonassociative algebras of a fixed dimensionr< over a local fieldF. We obtain a space, which is notT ₁. If the trivial algebra is removed, the remaining subspace is quasicompact. The space is homeomoprhic to the group of square classes ofF ^*; forr3 the space is notT ₁. The set of division algebras is open in.     

Maße für gerichtete Geraden und nicht-symmetrische Pseudometriken in der Ebene II

We continue our investigations started in a paper with the same title. The -length of a curve defined in this paper can be written as an integral along the curve. Furthermore, we determine necessary and sufficient conditions for the existence of a measure of orientated lines which generates a given non-symmetric pseudo-metric.

---

---

Herrn Prof. Dr. H.-J. Kanold zum 65. Geburtstag gewidmet     

Ein asymptotischer Ausdruck für eine zahlentheoretische Funktion

Arithmetic formulae and an asymptotic expression for the order of magnitude of the arithmetic function ged (s, n) and of a generalisation of it are derived.     

LP-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen II

This paper deals with the global classical solvability of the Cauchy problem for nonlinear wave equations of higher order of the following form where denotes the Laplacian, a real constant, m a positive integer, and f the nonlinearity. Using results of the first part [6] concerning estimations for the kernel of the associated integral equation a priori estimates for certain L^P-norms of the local regular solution are established for higher space dimensions and for a class of nonlinearities satisfying certain growth and positivity conditions. This leads to completely regular solutions by means of the Sobolev embedding theorems.