ESR microscopy

New spatial imaging methods to determine the microscopic concentration of unpaired electron spins or paramagnetic ions (ESR microscopy methods) have been developed (a) with an intense magnetic field gradient method based on conventional magnetic resonance imaging (MRI) using field gradient coils in a cavity, (b) by scanning the localized magnetic field or modulation field mechanichally or electronically, and (c) by use of the scanning localized microwave field. Some examples of fossil imaging and of microdosimetry in this laboratory are reviewed briefly.     

Uniqueness and nonuniqueness of static black holes in higher dimensions

We prove a uniqueness theorem for asymptotically flat static charged dilaton black-hole solutions in higher-dimensional space-times. We also construct infinitely many nonasymptotically flat regular static black holes on the same space-time manifold with the same spherical topology. An application to the uniqueness of a class of flat p-branes is also given.     

Renormalization Group Analysis of the Self-Avoiding Paths on the d-Dimensional Sierpiński Gaskets

Notion of the renormalization group dynamical system, the self-avoiding fixed point and the critical trajectory are mathematically defined for the set of self-avoiding walks on the d-dimensional pre-Sierpiski gaskets (n-simplex lattices), such that their existence imply the asymptotic behaviors of the self-avoiding walks, such as the existence of the limit distributions of the scaled path lengths of canonical ensemble, the connectivity constant (exponential growth of path numbers with respect to the length), and the exponent for mean square displacement. We apply the so defined framework to prove these asymptotic behaviors of the restricted self-avoiding walks on the 4-dimensional pre-Sierpiski gasket.     

Investigation of the possibility of geometrical electrophoresis

We investigate the possibility of geometrical electrophoresis, which is based on nanofabrication techniques. (GEE) utilizes geometrical effects during electrophoresis, which are generated by physical interactions between walls and a macromolecule confined in spaces smaller than the Flory radius. When a polymer is injected into a small space, confinement energy is usually required. However, the confinement energy form depends on the geometry of the space. In the case of electrophoresis, the electric field itself changes depending on the geometry. Using a nanofabricated quartz chip with a curved channel, we investigated electrophoretic behavior of high molecular weight DNA based on the curvature effect.     

Synthetic procedure for various selenium-containing electron donors of the bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) type

Six selenium variants of BEDT-TTF have been successfully synthesized by a newly developed synthetic method that involves a combination of two key reactions for the construction of two kinds of heterocyclic rings: the first is a one-pot formation of 1,3-dichalcogenole-2-chalcogenones from a common starting material, THP-protected 2-(ethynylthio)ethanol, leading to the inner five-membered rings, and the other is the annelation of the outer six-membered heterocyclic ring onto the inner ring by an intramolecular transalkylation reaction on a chalcogen atom. This method turned out to be widely applicable to the syntheses of the electron donors of bis(ethylenedithio)- and bis(ethyleneselenothio)-substituted types. However, synthetic attempts to form analogous donors of the bis(ethylenediseleno)-substituted type from THP-protected 2-(ethynylseleno)ethanol were unsuccessful. This is attributable to the predominance of side-reactions via a seleniranium (episelenonium) salt over the desired six-membered ring formation by transalkylation via a seleninium salt.     

Use of chirally modified zeolites and crystals in photochemical asymmetric synthesis

Three different approaches to asymmetric induction in the cis-to-trans photoisomerization of a number of 1-benzoyl-2,3-diphenylcyclopropane derivatives are reported: the use of chiral inductors and covalent chiral auxiliaries in MY zeolites and the use of ionic chiral auxiliaries in crystals. High levels of asymmetric induction were achieved using the latter two methods-up to 71% through the use of covalent chiral auxiliaries in zeolites and a remarkable 99% via the solid state ionic chiral auxiliary approach. In the zeolite method, the diastereomeric excess was found to depend strongly on the nature of the zeolite cation, M(+), and in the ionic chiral auxiliary approach, evidence is presented that it is the fixed orientation of the benzoyl group with respect to the cyclopropane ring that controls enantioselectivity in the crystalline state-a finding that is directly relevant to theoretical work on this topic.     

Shintani functions on

In this paper, in analogy to the real case, we give a formulation of the Shintani functions on , which have been studied by Murase and Sugano within the theory of automorphic -functions. Also, we obtain the multiplicity one theorem for these functions and an explicit formula in a special case.