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     

Development and application of high strength ternary boride base cermets

Reaction boronizing sintering is a novel strategy to form a ternary boride coexisting with a metal matrix in a cermet during liquid phase sintering. This new sintering technique has successfully developed world first ternary boride base cermets with excellent mechanical properties such as Mo₂FeB₂, Mo₂NiB₂ and WCoB base ones.In these cermets Mo₂FeB₂ and Mo₂NiB₂ base ones consist of a tetragonal M₃B₂ (M: metal)-type complex boride as a hard phase and a transition metal base matrix. The cermets have already been applied to wear resistant applications such as injection molding machine parts, can making tools, and hot copper extruding dies, etc.This paper focuses on the characteristics, effects of the additional elements on the mechanical properties and structure, and practical applications of the ternary boride base cermets.     

Thermolysis of reactive oligo(p-phenylene sulfide) containing disulfide bond

Oligo(phenylene sulfide) (OPS) containing one disulfide bond at the end of the chain, which was obtained by the oxidative polymerization of diphenyl disulfide, had a relatively low Td_10%(temperature for 10% weight loss) of 412 °C because of degradation of the disulfide bond. But this thermal cleavage of the disulfide bond promoted the curing reaction through thiophenoxy radical formation. OPS was allowed to react with diiodobenzene at 220 °C. The thermal stability of OPS was improved through the consumption of the disulfide bond and the coupling of the chain.     

Stability of porphyrin-calix[4]arene complexes analyzed by electrospray ionization mass spectrometry

The stability of some porphyrin-calix[4]arene sodium-ion complexes were determined by a collision-activated decomposition (CAD) method utilizing electrospray ionization mass spectrometry (ESI-MS). Comparing the values of E(1/2), the collision energy at which the relative intensity of the complex ion is 0.5, we found that the porphyrin-calix[4]arene complex with the higher value of E(1/2) corresponded to that with the larger association constant (Kass), as measured by 1H-NMR in CDCl3. Both our ESI-MS and NMR studies proved that the number of hydrogen bonds and the rigidity of the calix[4]arene stabilized the complex. The ESI-MS technique could be successful in screening the binding affinity in host-guest systems with a small amount of sample.     

Ruthenium-catalyzed one-pot hydroformylation of alkenes using carbon dioxide as a reactant

A new hydroformylation of alkenes using carbon dioxide as a reactant is shown to take place in the presence of ruthenium cluster complexes and halide salts. Similar or even better yields of alcohols were formed as compared to the conventional hydroformylation with CO under the same reaction conditions. The reaction proceeded in three steps: CO₂ is first converted to CO; then it is used as a reagent for hydroformylation to give aldehyde; subsequently, it is hydrogenated to alcohol. ESI-mass spectrometric analyses of the reaction solutions indicated formation of four kinds of ruthenium anionic complexes including tetra-, tri-, and mononuclear species. On the basis of experimental findings, possible roles of these complexes are discussed.     

Time evolution of density fluctuation in the supercritical region. 2. Comparison of hydrogen- and non-hydrogen-bonded fluids

The time evolution of the density fluctuation of molecules is investigated by dynamic light scattering in six neat fluids in supercritical states. This study is the first to compare the dynamics of density inhomogeneity between hydrogen- and non-hydrogen-bonded fluids. Supercritical methanol and ethanol are used as hydrogen-bonded fluids, whereas four non-hydrogen-bonded fluids were used: CHF(3), C(2)H(4), CO(2), and Xe. We measure the time correlation function of the density fluctuation of each fluid at the same reduced temperatures and densities and investigate the relationship between the dynamic and static density inhomogeneities of those supercritical fluids. In all cases, the profile of the time correlation function of the density fluctuation is characterized by a single-exponential function, whose decay is responsible for the dynamics characterized by hydrodynamic conditions. We obtain correlation times from the time correlation function and discuss dynamic and static inhomogeneity using the Kawasaki theory and the Landau-Placzek theory. While the correlation times in the six fluids show noncoincidence, those values agree well with each other except for the supercritical alcohols when scaled to a dimensionless parameter. Although the principle of corresponding state is observed in the non-hydrogen-bonded fluids, both the supercritical methanol and ethanol deviate from that principle. This deviation is attributed to the presence of hydrogen bonding among alcohol molecules at high temperature and low density. The average cluster size of each fluid is estimated under the same thermodynamic conditions, and it is shown that the clusters of supercritical alcohols are on average 1.5-1.7 times larger than those of the four non-hydrogen-bonded fluids. Moreover, the thermal diffusivity of each neat fluid is obtained over wide ranges of density and temperature.