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.     

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.     

Ligand Substitution Reaction of Bis(ethylenediamine)glycinatocobalt(III) Complex with Ethylenediamine Catalyzed by the Photo-excited Tris(2,2′-bipyridine)ruthenium(II) Complex

Substitution reaction with ethylenediamine of coordinated glycinate ligand in bis(ethylenediamine)-glycinatocobalt(III) complex has been studied in the presence of photo-excited tris(2,2′-bipyridine)ruthenium(II) complex in alkaline aqueous solution (buffered around pH 12) containing 1.0M chloride ion at 25°C. VIS absorption and CD spectra were used for the racemate and the optically active isomers of the Co(III) complexes, respectively. The reaction was catalyzed by the excited Ru(II) complex to give tris(ethylenediamine)cobalt(III) complex. Mechanism of the ligand-substitution reaction and role of the excited Ru(II) complex were discussed.     

Chiral ligand-controlled asymmetric conjugate addition of lithium amides to enoates

The external chiral ligand-controlled asymmetric conjugate addition reaction of lithium amides with alpha,beta-unsaturated esters provided beta-amino esters in high yields and high enantioselectivities.     

Preparation and gas separation properties of zeolite T membrane

Zeolite T membranes were synthesized on tubular porous mullite tubes by hydrothermal synthesis. The membranes selectively permeated carbon dioxide from CO2/CH4 and CO2/N2 mixtures with high separation performances, which were due to combined effects of molecular sieving and competitive adsorption.