Measures of inset information on the open domain — I: Inset entropies and information functions of all degrees

This is one in a series of papers studying measures of information in the so-called mixed theory of information (i.e. considering the events as well as their probabilities) on the open domain (i.e. without empty sets and zero probabilities). In this paper we find all-recursive, 3-semisymmetric inset entropies on the open domain. We do this by solving the fundamental equation of inset information of degree () on the open domain.Dedicated to Professor János Aczél on his 60th birthday.     

Invertomers at nitrogen in aziridine carboxylates by mltltinuclear (1H,13C,17O,and15N) NMR study

A confrgurational and conformational study of NH, N-acetyl- and N-sulfonylaziridine carboxylates is performed by¹H ,¹³C,¹⁷O, and¹⁵N NMR spectroscopy. The presence of acetyl and su fonyl groups on the ring nitrogen atom seems to reduce greatly the configurational stability at nitrogen.Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1226–1234, September, 1995.     

Assignment of the relative configuration of spiro[4.5]decanes by 13C, 15N and 17O NMR

The relative configuration of 11 1,4-diazaspiro[4.5]decanes (1a-1j and 1m), 15 1,4-oxazaspiro[4.5]decanes (2a-2o) and 10 1,4-dioxaspiro[4.5]decanes (3a-3n) substituted at the 2-, 6-, 7- or 8-position by a methyl group or using the tert-butyl group as a model for the ananchomeric structure is reported. The relative stereochemistry was analyzed by 1H, 13C, 15N and 17O NMR and all isomers present were characterized spectroscopically. Compounds with a methyl group in the six-membered ring show a chair conformation preference with the methyl group in the equatorial position. Compounds with one or two nitrogens exhibit a tautomeric equilibrium between the imine-diazolidine forms, as demonstrated by IR and 13C NMR.     

Crystal Structure of (6S,9S,13R,14S)-7,8-Didehydro-3,7-dimethoxy-17-methylmorphinan-4,6-diol

1 INTRODUCTION (9S,13R,14S)-7,8-Didehydro-3,7-dimethoxy-4-hydroxy-17-methylmorphinan-6-one I is an impor- tant natural product that was used to ease pain, decrease blood pressure and diminish inflammation. In order to study the stereochemistry of the reduction of I with potassium boronhydride, the crystal structure of the title compound II was determined by X-ray diffraction method. 2 EXPERIMENTAL 2. 1 Instrument The melting point was measured on a Yanagimoto MP-500 apparatus…     

Polyhydroxy pregnanes from Dregea volubilis

Three new polyhydroxy pregnanes named dregealol (1), volubilogenone (2) and volubilol (3) were isolated from the flowers of Dregea volubilis, and their structures elucidated from extensive 2D NMR analysis. The structure of volubilol (3) was confirmed by X-ray crystallographic studies. The known pregnane derivatives drevogenin D, iso-drevogenin P and 17α-marsdenin were also isolated.     

On the occupation times of cones by Brownian motion

Summary We study some features concerning the occupation timeA _t of a d-dimensional coneC by Brownian motion. In particular, in the case whereC is convex, we investigate the asymptotic behaviour ofP(A₁u0, when the Brownian motion starts at the vertex ofC. We also give the precise integral test, which decides whether a.s., lim inf _t A _t/(tf(t))=0 or for a decreasing functionf.     

Free-field realization of theWKP(N) algebra

TheW _KP ^(N) algebra has been identified with the second Hamiltonian structure in theNth Hamiltonian pair of the KP hierarchy. In this Letter, by constructing the Miura map that decomposes the second Hamiltonian structure in theNth pair of the KP hierarchy, we show thatW _KP ^(N) can also be decomposed toN independent copies ofW _KP ⁽¹⁾ algebras, therefore its free-field realization can be worked out by constructing free fields for each copy ofW _KP ⁽¹⁾ . In this way, the free fields may consist ofN + 2n number of bosons, among them, 2n are in pairs, wheren is an arbitrary integer between 1 andN. We also express the currents ofW _KP ^(N) in terms of the currents ofN —n copies of U(1) andn copies of SL(2,R) _k algebras with levelk = 1. By reductions, we give similar results forW ^(N) andW ₃ ⁽²⁾ algebra.     

Symmetries and generalizedW∞ algebra of the modified KP equation

The infinitely many symmetries with arbitrary functions of timet for the potential modified Kadomtsev-Petviashvilli equation are obtained by using a simple direct method. These symmetries constitute a generalization of the well-knownW algebra.     

Alkylation of cyclododecanone with α,ω-dibromoalkanes under conditions of phase-transfer catalysis

Alkylation of cyclododecanone with ,-dibromoalkanes Br(CH) _n Br (n=3, 4, 5) under conditions of phase-transfer catalysis in the presence of KOH results in the formation of either bicyclic ketones forn=3 and 5 or a mixture of bicyclic and spirocyclic ketones forn=4.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1436–1438, August, 1994.