A Hopf type classification theorem for isovariant maps from free <Emphasis Type="Italic">G</Emphasis>-manifolds to representation spheres

An isovariant map is an equivariant map preserving the isotropy subgroups. In this paper, we develop an isovariant version of the Hopf classification theorem; namely, an isovariant homotopy classification result of G-isovariant maps from free G-manifolds to representation spheres under a certain dimensional condition, the so-called Borsuk-Ulam inequality. In order to prove it, we use equivariant obstruction theory and the multidegree of an isovariant map.     

Theoretical Investigation of Decay Process in a Doubly Excited 2s^2 ^1S0 State of He-Like Ions

In the framework of multi-configuration Dirac-Fock theory, a detailed calculation is performed for the decay rates and the energies of the doubly excited 2s^2 ^1So state of He-like ions, of which atomic number Z ranges from 6 to 92. The 2s^2 ^1So - ls ^2S1/2 Auger decay is predominant at low Z regime, whereas the 2s^2 ^1So - 1s2p ^1,3P1 two-electron one-photon transitions become quite important in moderate and high Z regimes. For heavy ions with Z ≥ 72, the contribution of 2s^2 ^1So - 1s2s ^3S1 M1 transition is significant. The Breit interaction considerably enhances the 2s^2 ^1So - 1s ^2S1/2 Auger rate at high Z regime.     

Development of an ultra-micro sample injector for gas chromatography using an ink-jet microchip.

An ultra-micro sample injector for gas chromatography (GC) was developed. An ink-jet microchip, originally used for industrial recorder, was modified at the edge near to an orifice, and fixed into the GC. In order to evaluate the characteristics of this injector, a sample injector and a thermal conductive detector (TCD) were connected directly, while water was used as the test sample. The volume of the droplet, the interval time and the back-pressure to the ink-jet microchip were investigated. Within the range of 1 - 5 nL volume injected sample, the TCD response according to the amount of the sample volume (the volume of one droplet from the ink-jet microchip was about 1 nL) was obtained. A good reproducibility of the peak area was obtained to be about 1.0% of the RSD value. In order to compare the injection method of the ink-jet chip with that using a micro-syringe, the method using the ink-jet chip could introduce 1/1000 of the amount of the sample and gave reproducible results.     

Essay: 2nd Award 2004: Probing Gravitational Interactions of Elementary Particles

The gravitational interactions of elementary particles are suppressed by the Planck scale M _* ~ 10¹⁸ GeV and are typically expected to be far too be weak to be probed by experiments. We show that, contrary to conventional wisdom, such interactions may be studied by particle experiments in the next few years. As an example, we consider conventional supergravity with a stable gravitino as the lightest supersymmetric particle. The next-lightest supersymmetric particle (NLSP) decays to the gravitino through gravitational interactions after about a year. This lifetime can be measured by stopping NLSPs at colliders and observing their decays. Such studies will yield a measurement of Newton's gravitational constant on unprecedentedly small scales, shed light on dark matter, and provide a window on the early universe.     

On the surface chemical reactions of metal and oxide XPS samples at 300–400° at a high vacuum produced by oil diffusion pumps

Metal and oxide surface reactions formed by heating in the spectrometer at 300–400° at a vacuum of ca. 10^?9 Torr (oil diffusion pumps) were studied. As a result of spectral observations before and after heating, the metals studied were classified into five groups. In the first group, oxide films on the metal surface are easily evaporated because of the high vapour pressure of oxide; in the second, the oxide films are easily reduced in the spectrometer; in the third, the oxide film formed on the metal is reduced but the bulk oxide is not easily reduced; in the fourth, very stable oxide films are formed and the bulk oxide is also stable; and finally in the fifth, the oxide film formed on the metal is apparently reduced, yet the bulk oxide is very stable.     

Zeta functions of prehomogeneous vector spaces with coefficients related to periods of automorphic forms

The theory of zeta functions associated with prehomogeneous vector spaces (p.v. for short) provides us a unified approach to functional equations of a large class of zeta functions. However the general theory does not include zeta functions related to automorphic forms such as the HeckeL-functions and the standardL-functions of automorphic forms on GL(n), even though they can naturally be considered to be associated with p.v.’s. Our aim is to generalize the theory to zeta functions whose coefficients involve periods of automorphic forms, which include the zeta functions mentioned above. In this paper, we generalize the theory to p.v.’s with symmetric structure ofK _ε-type and prove the functional equation of zeta functions attached to automorphic forms with generic infinitesimal character. In another paper, we have studied the case where automorphic forms are given by matrix coefficients of irreducible unitary representations of compact groups. Dedicated to the memory of Professor K G Ramanathan     

Synthetic studies of decursivine derivatives: preparation of key indole alkaloids via α-hydroxyalkylation

2-Hydroxyacetyl indole modified at C-3 position was prepared with an eye to developing a total synthesis of decursivine derivatives (decursivine, serotobenine, moschaminindolol, and flavumindole). The indole was prepared through a sequence of oxalyl chloride introduction at C-3 position of indole and acid chloride reduction with tributyltin hydride. In addition, we report a novel synthesis of fully functionalized Uhle's ketone via ortho-selective α-hydroxyalkylation.     

Automated extraction of chemical structure information from digital raster images

Background  

To search for chemical structures in research articles, diagrams or text representing molecules need to be translated to a standard chemical file format compatible with cheminformatic search engines. Nevertheless, chemical information contained in research articles is often referenced as analog diagrams of chemical structures embedded in digital raster images. To automate analog-to-digital conversion of chemical structure diagrams in scientific research articles, several software systems have been developed. But their algorithmic performance and utility in cheminformatic research have not been investigated.     

Synthetic studies toward miroestrols: trials for elongation of the methyl group of 5-substituted 2-methyl-2-cyclohexanone to 3-methyl-2-butenyl function

Toward total synthesis of miroestrols (miroestrol and deoxymiroestrol), 3-methyl-2-butenyl function (endo-C5 unit) on D ring as a carbon chain for C and E rings was prepared by elongation of the methyl group in α-methyl-α,β-unsaturated ketone unit, and 3,5-dinitrobenzoyl group was introduced as a potential leaving group for the construction of B ring. The former was accomplished through a sequence of epoxide ring-opening, microwave-irradiated siloxy-Cope rearrangement, and isomerization of 3-methyl-3-butenyl function (exo-C5 unit) to endo-C5 unit.     

Inhibitors of adhesion molecules expression; the synthesis and pharmacological properties of 10H-pyrazino[2,3-b][1,4]benzothiazine derivatives

During a search for novel, orally-active inhibitors of upregulation of adhesion molecules such as intercellular adhesion molecule-1 (ICAM-1), we found a new series of 10H-pyrazino[2,3-b][1,4]benzothiazine derivatives to be potent ICAM-1 inhibitors. Of these compounds, N-[1-(10H-Pyrazino[2,3-b][1,4]benzothiazin-8-ylmethyl)piperidin-4-yl]-N',N'-dimethylsulfamide 7p showed the potent oral inhibitory activities against neutrophil migration in a murine interleukin-1 (IL-1) induced paw inflammation model. The synthesis and structure-activity relationships of these amide derivatives are described.