Derivatives of isoquinoline. 30. Synthesis of 4-spirosubstituted dioxenoisoquinolines

Methods have been developed for the synthesis of 1,4-benzodioxanyl-6-ethylamine with cyclopentyl and tetrahydropyranyl substituents in the -position. These compounds have been used as starting materials for the synthesis of new heterocyclic systems, the 4-spirocyclosubstituted dioxinoisoquinolines.For Communication 29, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 677–680, May, 1993.     

Characterisation of chlorinated hydrocarbons in a third generation candidate fish reference material (Limanda limanda) prepared under cryogenic conditions

Summary This paper describes the cryogenic preparation of 50 individual specimens of dab (Limanda limanda) from the Baltic Sea to produce a homogeneous fish material. 950 subsamples (8 g each) are stored in the gaseous phase over liquid nitrogen. Five series of analyses were randomly selected out of store. The results show that the obtained precision of 8 to 9% could be used as an indication unit for the deviation of the mean values of CHC concentrations from true values. If the analytical variability is 5%, the maximum inhomogeneity in the subsamples is 3–4%. It may be concluded that the subsamples of the candidate fish reference material (RM) are homogeneous enough for analytical purposes. Thus ESB (German Environmental Specimen Bank) material prepared in accordance with the standard operating procedure (SOP) [1] are valuable and appropriate reference materials. The prepared fish RM is suitable for the analysis of chlorinated hydrocarbons in fat containing marine samples.     

Synthesis of derivatives of ketocarboxylic acids by the decomposition of 1,4-cyclohexanedione monoethyleneketal hydroperoxide

The decomposition of 1,4-dihydroxy-1,4-dihydroperoxycyclohexane under the action of FeSO₄ and the decomposition of 1,4-cyclohexanedione monoethyleneketal hydroperoxide under the action of Fe^II salts in the presence of various ligands or under the action of Cu^II sulfate have been studied. A preparative method for the synthesis of derivatives of diketodicarboxylic or -functionally substituted ketocarboxylic acids from 1,4-cyclohexanedione monoethyleneketal has been developed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1231–1235, July, 1993.     

Algebraic version of extension theory for a quantum system with internal structure

An explicit two-channel matrix representation is obtained for the Hamiltonians of systems with internal structure in the framework of the theory of extensions of symmetric operators. Generalized potentials that are equivalent to zero-range interactions with internal structure and automatically reproduce the boundary conditions that correspond to them asx0 are constructed.St. Petersburg State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 2, pp. 163–181, November, 1993.     

A note on the illumination of convex bodies

LetKE ^d be a convex body and letl _r(K) denote the minimum number ofr-dimensional affine subspaces ofE ^d lying outsideK with which it is possible to illuminateK, where 0rd–1. We give a new proof of the theorem thatl _r(K)(d+1)/(r+1) with equality for smoothK.The work was supported by Hung. Nat. Found. for Sci . Research No. 326-0213 and 326-0113.     

Reaction-diffusion model for combustion with fuel consumption: II. Robin boundary conditions

A model, derived in a previous paper, for the reaction betweena gaseous oxidant and a solid porous fuel is analysed furtherfor general Robin boundary conditions. Numerical solutions areobtained and the effects of varying the dimensionless parameters,particularly the Frank-Kamenetskii parameter and the Lewisnumber L, are discussed in detail and compared with resultsobtained previously when Dirichlet boundary conditions are applied.Analytic solutions are obtained for the small-time developmentand for large values of . This latter solution shows the existenceof a propagating reaction-diffusion burning wave, and has featureswhich are qualitatively different to those derived earlier.     

Matching the Kerr solution on the surface of a rotating perfect fluid

We investigate the possible shapes of the surface of a rigidly rotating perfect fluid on which is matched the Kerr metric, using the Boyer (1965) surface condition. The solution, given in Figures 1 to 5, depends on three parameters, = qK, q = a/m, - (a/gwc), wherem denotes the mass of the source, a its angular momentum per unit mass, the angular velocity of rotation, andK is an integration constant appearing in Boyer's surface condition. When < 1, as in Figures 1 to 3, there are, for givenq and, two possible surfaces, of which the smaller one touches the ring-singularity at = a, z = 0. When > 1, as in Figures 4 and 5, there is only one possible surface of kidney-shaped tori, which also touch the ring singularity. In the case of a differentially rotating perfect fluid, we find a variety of possible strictly spheroidal surfaces, depending on the choice of an arbitrary integration function() of the angular velocity . If we choose() so that, at each point on the surface, is single-valued, then the resulting distribution exhibits an equatorial acceleration, similar to what is observed on the surface of the sun. This angular velocity distribution turns out to be identical with Thorne's (1971) angular velocity of cumulative dragging.