On the Theory of Gravitational Field in Finsler Spaces

Some structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as g_λχ(x, y) = γ_λχ(x) + h_λχ(x, y) is proposed, where γ_λχ denotes the Riemann metric of Einstein's gravitational field, while hλχ the Finsler metric induced by the Riemann metric h_ij(y) of the internal field; The intrinsic behaviour of the internal variable y, which is expressed as ?ⁱ = K(x, y) y^j in the internal field, is grasped by the Finslerian parallelism δyⁱ (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δy^χ = e(x) δyⁱ. The whole metrical Finsler connection D for g_λχ(i.e., Dg_λχ = 0) is determined by taking account of the intrinsic behaviour δy^χ.     

Study of a high-dimensional chaotic attractor

The nature of a very high-dimensional chaotic attractor in an infinite-dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high-dimensional attractor in the phase space. We introduce two complementary bases from which the attractor is observed, one the Lyapunov basis composed of the Lyapunov vectors and the another the Fourier basis composed of the Fourier modes. We introduce the exterior subspaces on the basis of the Lyapunov vectors and observe the chaotic motion projected onto these exteriors. It is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace goes out of the attractor. The origin of such a phenomenon is attributed to more fundamental features of our attractor, which become manifest when the attractor is observed from the Lyapunov basis. A counterpart of the phenomenon can be observed also on the Fourier basis because there is a statistical one-to-one correspondence between the Lyapunov vectors and the Fourier modes. In particular, a statistical property of the high-pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor.     

Novel synthesis of macrocycles with 1,1′-binaphthalene-2,2′-diol using intramolecular oxidative coupling

A new series of BINOL-based macrocycles with two phenolic protons have been synthesized via oxidative coupling reaction using CuCl(OH)-TMEDA.     

A novel synthesis of (+)-biotin from L-cysteine

(+)-Biotin (1) was synthesized in 25% overall yield over 11 steps from L-cysteine. The contiguous asymmetric centers at C-3a and C-6a were formed through a novel and highly stereoselective Lewis base-catalyzed cyanosilylation of alpha-amino aldehyde 3 to provide anti-O-TMS-cyanohydrin 4 with high stereoselectivity and in high yield (anti/syn = 92:8, 96%). Treatment of 4 with a di-Grignard reagent, 1,4-bis(bromomagnesio)butane, followed by carbon dioxide, efficiently installed the 4-carboxybutyl chain at C-4 to give keto acid 5. The final cyclization to bicyclic compound 7b, a precursor to 1, was realized by a palladium-catalyzed intramolecular allylic amination of cis-allylic carbonate 6b that was elaborated from 5.     

Fluorometric sensing of alkaline Earth metal cations by new lariat ethers having plural pyrenylmethyl groups on the electron-donating sidearms

[structure: see text] New fluorescent compounds (1), lariat ethers having plural pyrenylmethyl groups on the sidearms, were prepared, and their complexation behavior with alkaline earth metal cations was examined by fluorescence spectrometry. The pyrene excimer emission decreased accompanied with an increase in the monomer emission upon complexation with the metal ion. This finding is ascribed to the cooperative participation of one of the two sidearms in the complexation of the crown ring with the metal ion.     

Measurement of acid-catalyzed isomerization of unsaturated aldehyde-2,4-dinitrophenylhydrazone derivatives by high-performance liquid chromatography analysis

Aldehyde-2,4-dinitrophenylhydrazones exist as (E)- and (Z)-geometrical isomers, and adventitious isomerization during sample preparation can cause analytical errors. Purified alkenal-2,4-dinitrophenylhydrazone derivatives comprise only the (E)-isomer. However, partial isomerization to the (Z)-isomer occurs upon addition of acid to attain an equilibrium isomer ratio. The UV-visible spectral properties of the isomers differ; the (Z)-isomer exhibiting a 6-10 nm lower absorption maximum compared to the (E)-isomer. Alkenal-2,4-dinitrophenylhydrazones having a CC double bond at the 2- or 3-position of the alkenal exhibited similar absorption maxima with an equilibrium isomer ratio (0.035) that was much lower than those of other alkenals. The CC double bond at the 3-position migrates to a position of conjugation with the CN double bond during hydrazone synthesis to form a stabilized molecular structure. Alkenal-2,4-dinitrophenylhydrazones having a double bond at the 4-position or greater exhibited a similar absorption maxima equilibrium isomer ratio (0.14) to alkanal-2,4-dinitrophenylhydrazones. The quantitative analysis of carbonyl compounds in air or water using DNPH is usually conducted in the presence of an acid catalyst. Consequently, the solution of the direct extract prepared for HPLC or GC analysis contains both (E)- and (Z)-isomers.     

PICOSECOND LASER PHOTOLYSIS STUDIES OF FLUORESCENCE QUENCHING MECHANISMS OF FLAVIN: A DIRECT OBSERVATION OF INDOLE-FLAVIN SINGLET CHARGE TRANSFER STATE FORMATION IN SOLUTIONS and FLAVOENZYMES

Formation of singlet charge transfer (heteroexcimer) states in the course of the fluorescence quenching of lumiflavin and riboflavin tetrabutyrate by indole and N-methylindole have been directly observed by means of time-resolved absorption spectral measurements using a picosecond laser photolysis method. Similar transient spectra have been observed also in the case of a flavoenzyme, D-amino acid oxidase.     

Preparation and reaction of 2-aryl-3-silyl-1,3-butadiene

[reaction: see text] A conjugated pi-electron compound, 2-aryl-3-silyl-1,3-butadiene, was easily prepared from 1-benzyloxy-3-silyl-2-propyne, bis(iodozincio)methane, and an aryl halide in the presence of nickel catalyst. A subsequent cross-coupling reaction of the product with another aryl halide gave an unsymmetrical 2,3-diaryl-1,3-butadiene efficiently.     

Simultaneous polymerization and formation of polyacetylene film on the surface of concentrated soluble Ziegler-type catalyst solution

A direct method of simultaneously polymerizing and forming acetylene monomer to produce uniformly thin films of polyacetylene was investigated in terms of catalyst system, catalyst concentration, and polymerization temperature. The best catalyst was a Ti(OC₄H₉)₄–Al(C₂H₅)₃ system (Al/Ti = 3–4) and the critical concentration was 3 mmole/l. of Ti(OC₄H₉)₄. Below the critical concentration, only a solid or a powder was obtained. The configuration of the polymers obtained depends strongly upon the polymerization temperature. Thus an all-cis polymer was obtained at temperatures lower than ?78°C, whereas an all-trans polymer resulted at temperatures higher than 150°C. Observations either in an electron microscope by direct transmission or in a scanning electron microscope showed that the film is composed of an accumulation of fibrils about 200–300 Å in width and of indefinite length.