Proof of the Mixing Theorem for Statistical Systems in Classical Physics

In a general measure-theoretic context, it is proved that the action of a stochastic map on a pair of probability distributions can be characterized by the criterion of decreasing mixing distance.     

Scalar-type spectral operators andC(Ω)-operational calculi

It is shown that a continuous linear operatorT in a locally convex spaceX is a scalar-type spectral operator if and only if it admits aC((T))-operational calculus of a certain kind. This is a genuine extension of previous results of this type since we allow for the case when (T){} is an unbounded set in the complex planeC, a phenomenon which occurs often for continuous operatorsT defined in non- normable spacesX.     

Ab initio calculations of small hydrides including electron correlation

Five different structures of CH₅ ⁺ and one structure of CH₅ ^– are calculated using a gaussian basis both in the SCF approximation and with the inclusion of electron correlation in the independent electron pair approximation (IEPA). While on SCF level the C _sstructure of CH₅ ⁺ has to lowest energy, the energy difference between the C _sand C _2vstructures becomes negligible if correlation is included. In contrast to this the approach of a proton to CH₄ at large and intermediate distances is most favorable towards a corner of the CH₄ tetrahedron which means a structure. The decomposition of CH₅ ⁺ into CH₃ ⁺ and H₂ requires 20kcal/mol on SCF level and 40 kcal/mol if correlation is included.     

Über Pterinchemie. 79. Mitteilung. 13C-und 15N-NMR.-spektroskopische Untersuchungen an der (6RS)-5, 10-Methylen-5, 6, 7, 8-tetrahydro-L-folsäure; eindeutiger Beweis ihrer Struktur

¹³C- and ¹⁵N-NMR.-Spectroscopic Studies on (6RS)-5, 10-Methylene-5, 6, 7, 8-tetrahydro-L -folic Acid; Unequivocal Proof of thier Structure The existence of a 5, 10-methylene bridge in the title compound has been established with the help of ¹⁵N-NMR, and ¹³C-NMR. spectroscopy. The simultaneous coupling of ¹³C(11) with ¹⁵N(5) and ¹⁵N(10) proves that C(11) must be bound as a methylene bridge to both N-atoms. Some other aspects of the NMR. spectra of the compound are discussed. Synthesis of the title product with the label ¹⁵N is described.     

The Absolute Configuration of 1-Methylindane

It is shown unequivocally by chemical correlations (cf. Schemes 1--3) and Raman optical activity spectra (cf. Fig. 1 and 2) that the (R)-configuration has to be attributed to (+)-1-methylindane ((+)- 1 ). This is in contradiction to an earlier assignment of the (R)-configuration to (?)- 1 [2] which was based on the (R)-configuration of (+)-indane-1-carboxylic acid ( 3 ) [11].     

Sorptionseffekte an Eisen(III)-hydroxid-F?llungen

Zusammenfassung Um Material zur Deutung des Mechanismus der Sorption von Sr²⁺-Ionen an Eisen(III)-hydroxid zu gewinnen, werden Meßreihen mitgeteilt, in denen die pH-Abhängigkeit der Sorption sowie deren Beeinflussung bei Fällung mit verschiedenen Basen (NaOH, Ammoniak, Trimethylamin, Benzylamin) untersucht wird. Aus den charakteristischen Unterschieden der Sorptionskurven muß gefolgert werden, daß die Art der Base für die Sorption eine wichtige Rolle spielt.

---

Summary The sorption of Sr²⁺ ions on iron(III) hydroxide was studied as a function of the pH, of the precipitating reagent (NaOH, ammonium hydroxide, benzylamine, trimethylamine), of the temperature and of the total concentration.The curves of the relative sorption vs. pH are found to show characteristic differences which have to be explained in a detailed theory of the mechanism.