Molecular Structure of Phosphinidene Phosphates

Abstract

Alkalimetal diphenylphosphinites degrade (Ph-P)₅ and P₄ to give anions containing a chain of 2, 3 or 4 four- and two-coordinated phosphorus atoms. Representatives of the chain with two four-coordinated and one two-coordinated P atoms became first available from the aminolysis of tris (phosphoryl)phosphides¹.     

Structure and properties of Na-magadiite dependent on temperature

The mechanism of the thermal behaviour of Na-magadiite at a temperature range from 293–573 K was developed based on X-ray diffraction, DTA, DTL, Q-TG, and gravimetric measurements. A structure model (BRANDT et al.) previously proposed was additionally used. It is possible to show that there probably is a connection between the typical modifications of basal spacing and significant shiftings of silicate sheets. Different steps of dehydration, decrystallization and structure variations can be ascribed to the several thermal transitions. The results depend on sample treatment such as the existent or not existent solid-water vapour interaction and the establishment of equilibrium. It seems that there is a predominance of the first mentioned influence.     

Kriterien für das Fehlen quadratisch integrierbarer Lösungen der Differentialgleichung −Δv=f(x,v) in Außengebieten

Ohne Zusammenfassung     

Synthese und Reaktionen des 5-[p-(Dimethylamino)phenyl]-2,2-dimethyl-4-phenyl-3-oxazolins

Synthesis and Reactions of 5-[p-(Dimethylamino)phenyl]-2,2-dimethyl-4-phenyl-3-oxazoline The title compound 8 has been synthesized in a one-pot reaction of 4′-(dimethylamino)benzoin ( 4 ) with 2-propanone and NH₃. The preparation of the intermediate 4 from 3 is the first example of an acid-catalyzed transformation of the stable benzoin 3 into the corresponding less stable benzoin 4 . Structures and yields of various by-products occurring under different reaction conditions during the synthesis of 8 from 4 are given. The O-atom of the 3-oxazoline ring in 8 could be replaced by S from P₂S₅ yielding the 3-thiazoline 14 . Separation of the enantiomers of the racemate 8 could only be performed by transforming them into the trimethylanilinium salts 8b and 8c of (−)- and (+)-10-camphorsulfonic acid, respectively. Solid NaOAc in boiling toluene caused the precipitation of the 10-camphorsulfonic acids from the quaternary ammonium salts as sodium salts and the removing of the third methyl group from the quaternary ammonium salts as AcOMe to give the enantiomers (−)-(5S)- 8 and (+)-(5R)- 8 . Their absolute configurations are deduced from an X-ray analysis of 8b .     

Nichtlineare Tschebyscheff Approximation mit Nebenbedingungen: Anwendungen

Summary In this paper we give some applications resulting from the theory of nonlinear approximation under side-conditions developed in a preceding paper [3]. Particularly a necessary condition for best approximation in terms of a generalized alternant is discussed, the approximating functions having restricted ranges. As special cases of this kind we deduce theorems for one-sided approximation and for approximations by positive functions. We conclude with a result in the theory of nonlinear programming.

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Zweiter Teil einer gekürzten Fassung der Dissertation des Verfassers [3].