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     

Spectrophotometric determination of anthracycline anticancer agents with aluminum(III) and chromazurol S in a nonionic surfactant micellar medium.

A simple and highly sensitive spectrophotometric method for the determination of anthracycline anticancer agents, such as Daunorubicin hydrochloride (DAU), was established by using aluminum(III) and Chromazurol S (CAS) in a nonionic surfactant micellar medium. In the case of determination of DAU, the apparent molar absorptivity was 1.3 x 10(5) dm3 mol(-1) cm(-1) at 615 nm. Beer's law was obeyed in the concentration range of 0.028 - 2.82 microg ml(-1) for DAU. Owing to no need for solvent extraction, this method could be applied to assays of DAU and related drugs in pharmaceutical preparations.     

Establishment of hybrid-derived offspring populations in the Ohomopterus ground beetles through unidirectional hybridization

An approach to deduce the mechanism of stabilization of the hybrid-derived populations in the Ohomopterus ground beetles has been made by comparative studies on the phylogenetic trees of the mitochondrial and nuclear DNA. A phylogenetic tree based on the internal transcribed spacer (ITS) of nuclear ribosomal gene roughly reflects the relations of morphological species group, while mitochondrial NADH dehydrogenase subunit 5 (ND5) gene shows a considerable different topology on the tree; there exist several geographically-linked lineages, most of which consist of more than one species. These results suggest that the replacement of mitochondria has occurred widely in the Ohomopterus species. In most cases, hybridization is unidirectional, i.e., the species A (♂) hybridized with another species B (♀) and not vice versa, with accompanied replacement of mitochondria of A by those of B. The results also suggest that partial or complete occupation of the distribution territory by a hybrid-derived morphological species. The morphological appearance of the resultant hybrid-derivatives are recognized as that of the original species A. Emergence of a morphological new species from a hybrid-derived population has been exemplified.     

Diamagnetic muon yields of metal acetylacetonates

Diamagnetic muon yields /P_D/ in various metal acetylacetonates were measured at room temperature by the muon spin rotation technique. We have found a clear difference in P_D between complexes of typical elements and those of transition elements. We suggest that partially filled inner orbitals play some important role in determining the diamagnetic yield in these complexes.     

Mössbauer and ESR study of the formation of phthalocyanineiron(II) pyridine adduct in the supercage of NaY,KY, and RbY zeolite

Phthalocyanineiron(II) (FePc) and phthalocyaninato[(2-)bispyridine]iron(II) (FePc(py)₂) synthesized in supercage of NaY, KY and RbY zeolite have been characterized by Mössbauer and ESR spectroscopy. The yield of formation of the pyridine adduct depends on the ionic radius of the alkali ions introduced into the supercage, but not on the number of iron ions trapped in the cages, suggesting that free space in the supercage was the most important factor for the formation of the FePc-py-adducts.