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.     

On-line determination of organophosphorus pesticides in water by solid-phase microextraction and gas chromatography with thermionic-selective detection

This paper describes the extraction of 49 organophosphorus pesti-cides (OPPs) from water samples using solid-phase microextraction (SPME). Three fibers, including a 15-μm XAD-coated fiber, a 85-μm polyacrylate-coated fiber, and a 30-μm polydimethylsilox-ane-coated fiber (PDMS), were evaluated here. The effects of stirring and the addition of NaCl to the sample were examined for the polyacrylate-coated fiber. The precision of the technique was examined for all three fibers and the extraction kinetics were investigated using the XAD- and polyacrylate-coated fibers. With some exceptions, the XAD- and polyacrylate-coated fibers performed better than the PDMS-coated fiber. The superiority of the XAD-nd polyacrylate-coated fiber. The superiority of the XAD- and polyacrylate-coated fibers over the PDMS-coated fibers can be attribuibuted to the aromatic functionalities of the XAD and the polar functionalities in the polyacrylate. The relatively high percent RSDs indicate that the SPME technique needs to be further refined before it can be used for anything other than screening. A more effective form of agitation than mechanical stirring may be neccessary to reduce variability and achieve a faster equilibrium between the sample and the SPME fiber.     

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].