Syntheses of Theaspirone and Vitispirane via Palladium(II)-Catalyzed Oxaspirocyclization

Total syntheses of theaspirone (A and B) and vitispirane (A and B) are described. The key step in the syntheses is the palladium(II)-catalyzed intramolecular oxaspirocyclization of diene alcohol 4 to either vitispirane or the allylic alcohol 9. The outcome of the oxaspirocyclization is very much dependent on the solvent employed. In water-acetic acid (4:1) a 1:1 mixture of the diastereomeric alcohols 9A and 9B was exclusively formed. In water with 8 equiv of a strong non-nucleophilic acid, vitispiranes A and B (1:1) were obtained. An alternative procedure to obtain vitispirane with the use of LiCl and K(2)CO(3) is described. In the latter reaction vitispirane B is formed preferentially. This result is explained by an equilibrium between the two possible pi-allyl complexes 5A and 5B, the kinetically favored 5B being transformed into vitispirane 3B before isomerization to 5A occurs.     

Asymmetric epoxidation of substituted chalcones and chalcone analogues catalyzed by α-d-glucose- and α-d-mannose-based crown ethers

The chiral monoaza-15-crown-5 lariat ethers annellated to methyl-4,6-O-benzylidene-α-d-glucopyranoside-1 or mannopyranoside 2 have been applied as phase-transfer catalysts in the epoxidation of substituted chalcones and chalcone analogues with tert-butylhydroperoxide resulting in significant asymmetric induction. It was found that the position of the substituents in the aromatic ring of the chalcone had an influence both on the chemical yields and enantiomeric excesses. The lowest enantioselectivities (62–83% ee) were found in the case of ortho-substituted model compounds. The highest ee values (ee of 83–97%) were obtained in the case of para-substituted models. From among the chalcone analogues, the maximum ee (90–92%) was detected for the model compound having α-tert-butyl- and β-aryl groups. Using glucose-based crown ether 1, formation of the (?)-enantiomer was preferred, while applying mannose-based 2 as the catalyst, the (+)-enantiomer was in excess.     

LC-UV Assay of Tolperisone HCl from Sustained Release Matrix Tablets

Tolperisone HCl is a central muscle relaxant, which was incorporated in a matrix system formulated with poly(ethylene oxide)–PEO, in order to achieve adequate gastric residence time. This tablet presents considerable analytical difficulties in the quantitative determination of the drug, because the PEO matrix causes significant increase of viscosity in the samples. Our purpose was to develop a reproducible sample preparation method, which is adapted from parameters of the in vitro dissolution test and validate an LC-UV analytical method, which allows good recovery of the drug (99.97%). The developed analytical method was suitable for quantitative analysis of tolperisone HCl in matrix tablets.     

Theoretical study of hyaluronan oligosaccharides

The structure and energetics of hyaluronan oligomers from di- to decasaccharides have been studied by density functional theory calculations at the B3LYP/6-31G** level. The study covered selected conformers of the sodium salt, anionic disaccharides, and neutral acids in the isolated state and in aqueous solution using the PCM model approach. We investigated the structural changes of the hyaluronan chain when the Na⁺ ion is removed or replaced by proton. These processes result in some characteristic changes in the glycosidic torsional angles and hydrogen bonding interactions. We evaluated the folding for the hyaluronan chains and obtained values between 2.2 and 3.2, somewhat smaller than reported for the crystals. We found a contraction of the hyaluronan chains upon enlargement in most derivatives attributed partly to the helical character of hyaluronan. The energy consequences of the enlargement have been modeled by isodesmic reactions. The enlargement processes proved to be exothermal and the energies consistent within the gradual enlargement.     

A polynomial time algorithm recognizing link trees

The link of a vertex v of a graph G is the subgraph induced by all vertices adjacent to v. If all the links of G are isomorphic to a finite graph L, then G is called a realization of L, and L is called a link graph. At the Smolenice symposium of 1963, Zykov posed the problem of recognizing link graphs. There are two versions of that problem, namely the finite (the existence of a finite realization is required) and the infinite one. Bulitko (see “On Graphs with Prescribed Links of Vertices” [in Russian], Trudy mat. inst. im. Steklova, Vol. 133, 1973, pp. 78-94) proved that the infinite version is algorithmically unsolvable. The solution of both versions is known only for special classes of graphs as paths, cycles, and graphs homeomorphic to a star (see M. Brown and R. Connelly, “On Graphs with a Constant Link I,” New Directions in the Theory of Graphs, Academic Press, New York, 1973, pp. 19-51; On Graphs with a Constant Link II, Discrete Mathematics, Vol. 11, 1975, pp. 199-232). The finite version for trees with less than 10 vertices has been solved by Blass, Harary, and Miller (see “Which Trees Are Link Graphs?” Journal of Combinatorics Theory Series B, Vol. 29, 1980, pp. 277-292). Trees that are link graphs are called link trees. Using some previous results of Bulitko (see “On a Recursive Property of Block-Complete Graphs” [in Russian], Proceedings of Czechoslovak Conference on Graphs, Zemplínska ?irava, 1978, p. 20-30), we present a polynomial time algorithm recognizing link trees. The applied methods have some remarkable consequences concerning the study of link graphs. © 1995 John Wiley & Sons, Inc.     

Enumerating transformation semigroups

We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation semigroups up to degree 4. Classification of these semigroups up to conjugacy, isomorphism and anti-isomorphism, by size and rank, provides a solid base for further investigations of transformation semigroups.     

Regularity of weakly subquadratic functions

Related to the theory of convex and subadditive functions, we investigate weakly subquadratic mappings, that is, solutions of the inequality

     

On biquadratic fields that admit unit power integral basis

We consider biquadratic number fields whose maximal orders have power integral bases consisting of units. We prove an effective and efficient criteria to decide whether the maximal order of a biquadratic field has a unit power integral basis or not. In particular we can determine all trivial biquadratic fields whose maximal orders have a unit power integral basis.