Statistical hypersurfaces in the space of Hessian curvature zero

A rigidity theorem for a statistical hypersurface of Hesse–Einstein type is given.     

Synthesis of Sialic Acid Analogues with the Oxime Group at C-4 Or C-5 of KDN 1

Abstract

The readily available methyl (methyl 3-deoxy-5,8:7,9-di-O-isopropylidene-β-D-glycero-D-galacto-2-nonulopyranosid)onate (7) was converted in five synthetic steps into methyl (methyl 4-acetamido-3,4-dideoxy-β-D-glycero-D-talo-2-nonulopyranosid)onate (11). Selective protection of the C-4, C-7, C-8 and C-9 hydroxy groups of methyl (methyl 3-deoxy-8,9-O-isopropylidene-β-D-glycero-D-galacto-2-nonulpyranosid)onate (2) followed by oxidation of the C-5 hydroxy group and then its oximination gave 5-hydroxyimino derivatives (15 and 16).

     

A new strategy to sulfur heterocycles: Reactions of an allene episulfide with electrophiles

A variety of sulfur-containing five- and six-membered cyclic compounds was obtained by the acid-catalyzed and thermal reactions of an allene episulfide with various electrophiles.     

Drawing of ultrahigh-molecular-weight polyethylene single-crystal mats: The crystallinity

Single-crystal mats of ultrahigh-molecular-weight polyethylene can be drawn uniformly to high draw ratios, more than 20χ at the highest, after the necking process is completed. The dynamic mechanical modulus of the drawn mats increases markedly during the uniform drawing stage. The structural changes induced by the uniform drawing at 100°C have been followed by wide-angle and small-angle x-ray scattering, infrared absorption, differential scanning calorimetry, and birefringence. The crystallinity is estimated from the x-ray amorphous scattering intensity, the IR absorbance of gauche bands, the heat of fusion from DSC, and the density. The estimated crystallinities of the drawn mats are all very high and increase slightly and monotonically with increased drawing after necking, though the values of the crystallinity depend on the method of estimation. IR gauche bands and the SAXS peak due to the long period disappear at a draw ratio of about 80χ. All the results suggest that the uniform drawing after necking destroys the two-phase structure made up of alternately stacked crystalline and amorphous regions and then reorganizes it into a single-phase crystalline structure.     

A sensor for adenosine triphosphate fabricated by laser-induced forward transfer of luciferase onto a poly(dimethylsiloxane) microchip

Laser-induced forward transfer (LIFT) of the enzyme luciferase was explored as a potential technique to be used in the fabrication of a microchip adenosine triphosphate (ATP) sensor. Poly(dimethylsiloxane) (PDMS) was selected as the substrate for deposition of the luciferase. In comparison with other solid substrates, such as glass and polystyrene, it was found that the flexibility of PDMS made it a superior substrate for the immobilization of micro-spots of luciferase. LIFT of luciferase onto a PDMS substrate using a 355 nm laser was successfully carried out, while the bioactivity of the enzyme was maintained. Yellow luminescence ascribed to luciferase was observed from a transferred spot on the PDMS chip from the enzymatic reaction between luciferin and ATP. A microchip ATP sensor was also fabricated by attaching a small photodiode to the PDMS chip. On the basis of the fabricated microchip, the Michaelis-Menten relation between the luminescence intensity from the spot, and the ATP concentration was confirmed. The potential for fabricating biosensors using a combination of the LIFT technique with a PDMS substrate was shown to be very good.     

Studies on sialic acids I. Determination of anomeric configuration of neuraminic acid derivatives by circular dichroism

CD spectra were recorded for methyl α- and β-glycosides of $\text{D}$-neuraminic acid, and the band at the wave-length lower than 200 nm was attributed to the acetamido group. The Cotton effect at higher wave-length around 220 nm arose from the n-π^x transition of the carboxyl group. Thus α-linked glycosides snowed a negative band, while β-glycosides gave arise to a positive band.     

A Cylinder Theorem for Isometric Pluriharmonic Immersions

We prove a cylinder theorem for isometric pluriharmonic immersions of complete Kähler manifolds into semi-Euclidean spaces under an assumption concerning the index of relative nullity.     

Holomorphic centroaffine immersions and the Lelieuvre correspondence

The rigidity and intrinsic characterization of holomorphic centroaffine immersions are given. We also obtain a method to construct nondegenerate holomorphic affine hypersurfaces from centroaffine immersions and metrics satisfying some conditions. Mathematics subject classification: 53A15.