Remarks on unit indices of imaginary abelian number fields II

Satz 41 in Hasse's monograph [4] is modified because of the incorrectness of Satz 29. We investigate unit indices of imaginary abelian number fields of type (2,2) and (2,2, 2), some of which give counterexamples to Satz 41. We moreover give a relation between unit indices of certain imaginary fields of type (2,2²) and those of their real cyclic subfields.     

Covering vertices of a graph by k disjoint cycles

Let d, k and n be three integers with k3, d4k−1 and n3k. We show that if d(x)+d(y)d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d,n} vertices of G.     

Buchsbaum homogeneous algebras with minimal multiplicity

In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous k-algebras A in terms of the dimension d, the codimension c, the initial degree q, and the length of the local cohomology modules of A. Next, we introduce the notion of Buchsbaum k-algebras with minimal multiplicity of degree q, and give several characterizations for those rings. In particular, we will show that those algebras have linear free resolutions. Further, we will give many examples of those algebras.     

Some Recent Progress and Applications in Graph Minor Theory

In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough' structure of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some of these along with some other recent advances on graph minors are surveyed. Research partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Grant number 16740044, by Sumitomo Foundation, by C & C Foundation and by Inoue Research Award for Young Scientists Supported in part by the Research Grant P1–0297 and by the CRC program On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia     

Simple and convenient synthesis of a fluorinated GM4 analogue

A series of fluorinated galactosides, dodecyl 2-deoxy-2-fluoro-β-d-galactopyranoside (2F Gal), dodecyl 4-deoxy-4-fluoro-β-d-galactopyranoside (4F Gal) and dodecyl 6-deoxy-6-fluoro-β-d-galactopyranoside (6F Gal), was chemically synthesized and introduced to B16 cells to serve as scaffolds for cellular enzyme glycosylation. Results showed that the presence of fluorine exercised significant effects on cell viability. Among the fluorinated galactosides used, 2F Gal was glycosylated to afford a GM4 analogue.     

The chemical synthesis of a cyclic oligosaccharide derivative with branching

A cyclic oligosaccharide derivative was synthesized by cationic ring-opening polymerization of an anhydrodisaccharide derivative under high vacuum in dichloromethane with 20 mol% of PF₅ as initiator. Analysis of the spectral results showed that the oligomer chain is composed of only 3 glucose units connected by -1,6 linkages with a glucopyranosyl branching unit at C-4 of each sugar residue in the main chain.     

Stable isotope dilution mass spectrometry for the simultaneous determination of cortisol, cortisone, prednisolone and prednisone in plasma.

A capillary gas chromatographic-mass spectrometric method for the simultaneous determination of cortisol, cortisone, prednisolone and prednisone in human plasma is described. [1,1,19,19,19-2H5]Cortisol, [1,1,19,19,19-2H5]cortisone, [1,19,19,19-2H4]prednisolone and [1,19,19,19-2H4]prednisone were used as internal standards. Formation of the bismethylenedioxy-3-heptafluoro-n-butyryl (BMD-HFB) derivatives made possible the separation of the four corticosteroids with good gas chromatographic behaviour. The new double derivatization has been demonstrated to be of value for sensitive and selective quantification by this technique. Detection was performed by monitoring the molecular ion (M+) of the BMD-HFB derivatives for cortisone and prednisolone, the [M - 18]+ ion for cortisol, and the [M - 30]+ ion for prednisone. The method requires no complex corrections for contributions and provides good accuracy and precision.     

Towards the selective formation of specific isomers of fullerenes: T - and p-dependence in the yield of various isomers of fullerenes C60–C84

Systematic fractional change in the yield of various isomers of fullerenes was revealed to strongly depend on temperature of a buffer gas. A new kinetic consideration is proposed for understanding the observed temperature- and pressure-dependence of yield of fullerenes. The model consists of three competitive reactions in consideration of plausible behaviors of a precursor, (1) decomposition into smaller fragments, (2) isomerization leading to formation of a stable fullerene cage, and (3) growth into a larger carbon cluster. Arrhenius activation energy of formation of stable fullerenes was determined to be 0.8 eV for both C₆₀ and C₇₀, while a higher energy of 2.0?3.3 eV for seven different isomers of higher fullerenes ranging from C₇₆ to C₈₄. Correlation in the activation energy is noted for a series of higher fullerenes with different sizes, suggesting the existence of a specific precursor in their formation processes.     

Interactions between temperature-sensitive hydrogel microspheres and granulocytes

Poly(N-isopropylacrylamide) (PNIPAM) has a low critical solution temperature (LCST) at 32°C in water and the hydrophilicity changes through the LCST. The microspheres whose surface was composed of PNIPAM exhibited phase transition behavior around 32°C. Therefore, the interactions between PNIPAM micropheres and granulocytes depended on the temperature. That is, the oxygen consumption and active oxygen production by cells in contact with PNIPAM-containing microspheres and adhesion of the microspheres to the cell surface were more enhanced above the LCST of PNIPAM than below it, whereas no significant temperature dependence of cell–microspheres interaction was observed in nonthermosensitive microsphere systems. It was suggested that the function of cells could be controlled with temperature using the temperature-sensitive microspheres.