Theq-harmonic oscillator and the Al-Salam and Carlitz polynomials

One more model of aq-harmonic oscillator based on theq-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form ofq-creation andq-annihilation operators,q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed.     

Instability of the paramagnetic state towards incommensurate magnetic order in the 2-d Hubbard model

We determine the instability line separating the paramagnetic phase in the phase diagram of the 2-d Hubbard Model from a phase with incommensurate magnetic order. A mean-field approximation of the Kotliar-Ruckenstein slave boson representation is used to calculate the wave-vector dependent magnetic susceptibility. For largeU/t the instability occurs at a densityn0.37, and a wave-vector close toq=(0,). The dependence ofq onU andn is also given.     

Determination of platinum and palladium in strongly acid solution by means of flow injection analysis

Microamounts of Pt(II/IV) (0.25–800 μg/ml) and Pd(II) (5–600 μg/ml) in> 0.5 M hydrochloric acid can readily be determined by means of a simple FIA method based on the selective reaction of tin(II)chloride with these metals. The FIA method has a high linear dynamic range, and is relatively free from interferences of many transition metals, with the exception of Au and Rh; small amounts of other PGMs can be tolerated. Determination of Pt on a hydrogenation catalyst by this method compares well with that found by flame atomic absorption spectroscopy. By monitoring at two or more wavelengths, Pt and Pd can be determined in mixtures by this means, to yield a simple, cost-effective FIA method for possible on-line determinations and quality control of, in particular, Pt containing acidic refinery and other process streams.     

Total synthesis and properties of prostaglandins. 36. Condensation of (+)2-oxabicyclo[3.3.0]-6-octen-3-one with furylacrolein and furylpropionic aldehyde

A study was made of the condensation of bicyclic -lactone I with furylacrolein and furylpropionic aldehyde. Significant differences were observed in the reactivity of the aldols obtained, and in the stereochemical trend of their dehydration reaction.For Communication 35, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1035–1039, August, 1993.     

Polyfunctional macroheterocycles. 7. Synthetic enzyme analogs. synthesis of 16- and 22-membered nitrogen and sulfur crown compounds containing exocyclic histamine and histidine fragments and carboxyl groups

The acid hydrolysis of 9,14-bis(2-methoxycarbonylethyl)-11-12-benzo-3,4-(4,5-dimethylbenzo)-10,13-dioxo-1,6-dithia-9,14-diazacyclohexadeca-3,11-diene leads to the corresponding 9,14-biscarboxy derivative. The reaction of 4,9,15,20-tetrakis-(2-methoxycarbonylethyl)-6,7,17,18-dibenzo-5,8,16,19-tetraoxo-1,12-dithia-4,9,15,20-tetraazacyclodocosa-6,17-diene with hydrazine hydrate and subsequent treatment with NaNO₂ gave the corresponding tetraazide. The reaction of this tetraazide with histamine and histidine leads to macroheterocycles, containing exocyclic histamine and histidine fragments.For Communication 6, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 130–133, January, 1993.     

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.