Berger-Shaw's theorem forp-hyponormal operators

For an-multicyclicp-hyponormal operatorT, we shall show that |T|^2p –|T ^*|^2p belongs to the Schatten and that tr Area ((T)).     

Residues of $q$-Hypergeometric Integrals and Characters of Affine Lie Algebras

We study certain subspaces of solutions to the sl₂ rational qKZ equation at level zero. Each subspace is specified by the vanishing of the residue at a certain divisor which stems from models in two dimensional integrable field theories. We determine the character of the subspace which is parametrized by the number of variables and the sl₂ weight of the solutions. The sum of all characters with a fixed weight gives rise to the branching functions of the irreducible representations of sl₂ in the level one integrable highest weight representations of . It is written in the fermionic form.     

Donor-substituted cyanoethynylethenes: powerful chromophores for opto-electronic applications

Donor-substituted cyanoethynylethenes (CEEs) were synthesised, structurally characterised and investigated for their electronic and two-photon absorption properties, revealing exceptionally strong intramolecular charge-transfer interactions.     

Asymmetric autocatalysis induced by chiral hydrocarbon [2.2]paracyclophanes

Chiral hydrocarbon [2.2]paracyclophanes act as chiral initiators in asymmetric autocatalysis in the addition of diisopropylzinc to pyrimidine-5-carbaldehyde and give highly enantiomerically enriched 5-pyrimidyl alkanol with a reversed sense of the enantioselectivity to that of other [2.2]paracyclophanes with heteroatoms.     

Characterization of sulfur exchange reaction between polysulfides and elemental sulfur using a 35S radioisotope tracer method

A sulfur exchange reaction between di-tert-butylpolysulfides and elemental sulfur was examined using a 35S tracer method and the reaction mechanism was discussed.     

Reaction pathways of the Simmons-Smith reaction

The cyclopropanation reaction of an alkene with a metal carbenoid has been studied by means of the B3LYP hybrid density functional method. The cyclopropanation of ethylene with a lithium carbenoid or a zinc carbenoid [Simmons-Smith (SS) reagent] goes through two competing pathways, methylene transfer and carbometalation. Both processes are fast for the lithium carbenoid, while, for the zinc carbenoid, only the former is fast enough to be experimentally feasible. The reaction of an SS reagent (ClZnCH(2)Cl) with ethylene and an allyl alcohol in the presence of ZnCl(2) was also studied. The allyl alcohol reaction was modeled with an SS reagent/alkoxide complex (ClCH(2)ZnOCH(2)CH=CH(2)) formed from the SS reagent and allyl alcohol. Two modes of acceleration were found. The first involves the well-accepted mechanism of 1,2-chlorine migration, and the second involves a five-centered bond alternation. The latter was found to be more facile than the former and to operate equally well both with ethylene and with aggregates of SS reagent/alkoxide complexes. Calculations on the SS reaction with 2-cyclohexen-1-ol offer a reasonable model for the hydroxy-directed diastereoselective SS reaction, which has been used for a long time in organic synthesis.     

Polarographic study on poly alpha-L-glutamic acid-Cd2+,Co2+ complexes in the helix-coil pH region

Interactions between poly alpha- L-glutamic acid (PGA) and metal ions Cd(2+), Co(2+) were studied by direct current polarography. The diffusion currents of these ions decreased sharply in the presence of PGA in the pH region from 5.0 through neutral. A corresponding increase in the helix content of the PGA-metal ion complex was revealed by CD measurements on the same solutions. Helix contents determined by polarography were in good agreement with those by CD in the neutral pH region. On the contrary, the decrease of current in lower acidic pH regions was independent of helix formation and suggested that metal ions coordinate to sporadically-dissociated carboxylate groups to cause aggregation of the intra and/or inter polymer chains. The diffusion current of the ions, therefore, is a parameter sensitive to the conformational changes of PGA from acidic through neutral pH region.     

The Toda molecule equation and the -algorithm

One of the well-known convergence acceleration methods, the -algorithm is investigated from the viewpoint of the Toda molecule equation. It is shown that the error caused by the algorithm is evaluated by means of solutions for the equation. The acceleration algorithm based on the discrete Toda molecule equation is also presented.