On the group extension of the transformation associated to non-archimedean continued fractions

Summary Let F_q be a finite field with q elements. We consider formal Laurent series of F_q -coefficients with their continued fraction expansions by F_q -polynomials. We prove some arithmetic properties for almost every formal Laurent series with respect to the Haar measure. We construct a group extension of the non-archimedean continued fraction transformation and show its ergodicity. Then we get some results as an application of the individual ergodic theorem. We also discuss the convergence rate for limit behaviors.     

Synthesis of 3-hydroxyindolin-2-one alkaloids, (±)-donaxaridine and (±)-convolutamydines A and E, through enolization-Claisen rearrangement of 2-allyloxyindolin-3-ones

Claisen rearrangement triggered by enolization of 2-allyloxyindolin-3-ones with DBU was performed in order to prepare 3-allyl-3-hydroxyindolin-2-ones. Total synthesis of 3-hydroxyindolin-2-one alkaloids, (±)-donaxaridine, as well as (±)-convolutamydines A and E, was achieved by transformation of the allyl moiety of 3-allyl-3-hydroxyindolin-2-ones.     

On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

 We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond–J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Perron algorithm. Received September 30, 2001; in revised form January 8, 2002     

Improvement of Dispersion and Release Properties of Nifedipine in Suppositories by Complexation with 2-Hydroxypropyl-β-cyclodextrin

Geometries, electronic properties and NMR-shielding of cucurbit[5]uril, decamethylcucurbit[5]uril, cucurbit[6]uril, cucurbit[7]uril, and cucurbit[8]uril are investigated with DFT calculations. All molecules are highly symmetrical with a distinct geometric flexibility. In addition with a characteristic partial charge distribution these findings account for their chemical complex building ability.     

Tetraarylester der μ-Imidodiphosphorsäure und ihre Thioderivate — Strukturuntersuchungen

Tetraarylesters of μ-Imido-Diphosphoric Acid and its Thio Derivatives — Structure Investigations New O,O′,O″,O?-tetratolyl- and ditolyl-diphenylesters of the μ-imido-diphosphoric acid and its mono and dithio derivatives were synthesized, compared with the corresponding tetraphenylesters and investigated by ¹H, ¹³C, and ³¹P NMR spectroscopy and X-ray crystal structure analysis. Structures of the O,O′,O″,O?-tetrakis-(2-methyl-phenyl)-μ-imidodiphosphate, 1b , as well as of the corresponding ortho-, meta- and para-tolylesters of the μ-imido-monothiodiphosphoric acid ( 2a , 2b , 2c ) were determined. All the compounds form dimers via N? H…?O hydrogen bonds in the crystal as well as in nonpolar solvents. The distances around the phosphorus atoms rise with decreasing electronegativity of the phosphorus substituents. Signs of the ²J_{P? N? P} coupling constants were determined by ¹³C{¹H, ³¹P} triple resonance experiments for some compounds. These constants become more negative owing to substitution of a phosphoryl by a thiophosphoryl group.     

Synthesis of PI-88 analogue using novel O-glycosidation of exo-methylenesugars

Acid-promoted α-stereoselective O-glycosidation of 1-exo-methylenesugars was successfully applied to the synthesis of a PI-88 analogue. By using methanesulfonic acid as a promoter, 1′-C-methyl-α-disaccharides with p-methoxybenzyl protection were obtained in high yield. The sequence of selective deprotection and glycosidation provided 1-C-methyl-pentasaccharide efficiently.     

A New Approach to the Construction of BEDT-TTF Derivatives Condensed with Heterocycles via BF3-promoted Reactions of Organotin Thiolates

The synthesis of BEDT-TTF derivatives fused with heterocycles (3–7) has been accomplished via the BF₃-promoted reaction of organotin thiolates (8 and 9) with electrophiles (10 and 11). Electrical conductivities of radical cation salts derived from some of them were also investigated.     

Diastereoselective synthesis of 2-aminoalkyl-3-sulfonyl-1,3-oxazolidines on solid support

Herein we report our investigation on the oxidation of solid-support-bound amino alcohols to their corresponding aldehydes. These aldehydes were converted into diastereomerically pure (>10:1) 2,4-cis-2-aminoalkyl-3-sulfonyl-1,3-oxazolidines using optically pure 1,2-amino alcohols. The relative configuration was determined using the nuclear Overhauser effect (NOE). The synthesized oxazolidines, which were obtained in high purities, represent a new, diverse scaffold for the solid-phase synthesis of libraries directed toward a pharmacological target.     

Study of flow rate in pressurized gradient capillary electrochromatography using splitter and separation of peptides using an Amide stationary phase

A pressurized gradient capillary electrochromatograph using a splitter was constructed. The variation in flow rate during gradient elution was investigated and separations of peptides using an Amide stationary phase were demonstrated. The flow rate, which is one of the important factors to control chromatographic behavior, was increased during the gradient elution, and the mismatching of mobile phase between the column and the resistance tubing derived three variation patterns in the flow rate. The electrophoretic migration in electrochromatography could enhance in separation of peptides. The separated peak number of tryptic digest of bovine serum albumin was increased from 30 to 40 by the application of +5 kV.     

An investigation on a broad infrared band with the maximum at approximately 1300 cm(-1) in magnesia cement,phase 3

In magnesia cement, phase 3, a broad and strong infrared band was observed with the maximum at approximately 1300 and 1050 cm(-1) in the H and D systems, respectively. To clarify the origin of the 1300 cm(-1) band the temperature dependency of the infrared spectra of the H system was observed and the spectra analyzed on the basis of a strong vibrational coupling of the OH stretching with lattice modes. The fitting was quite well, giving rise to the origin of the 1300 cm(-1) band of the OH stretching.