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     

Bis(pentafluorophenyl) disulfide as a hydrogen abstractor and an electron acceptor from the resulting radical intermediate

The pentafluorobenzenethiyl radical is an efficient hydrogen abstractor from an activated methylene or methine group and bis(pentafluorophenyl) disulfide is an efficient electron acceptor from the resulting radical intermediate. Thus benzyl-OTBS ether was easily converted into the corresponding pinacol, and 2-phenyl-1,3-dioxanes are converted into the monobenzoates of diols.     

Development of measuring magnetic Compton profiles by grazing incidence geometry

A novel technique of measuring a magnetic Compton profile using the grazing angle geometry against a sample surface (Grazing Incidence Magnetic Compton Profile) has been successively developed. Measurements of a magnetic moment and a magnetic Compton profile are possible for a Fe 200 nm film on a thick glass substrate. The estimated thinnest limit for measurements is 100 nm for a Fe film.     

Method of observation of low density interface states by means of X-ray photoelectron spectroscopy under bias and passivation by cyanide ions

X-ray photoelectron spectroscopy (XPS) measurements under bias can observe low density interface states for metal-oxide-semiconductor (MOS) diodes with low densities. This method can give energy distribution of interface states for ultrathin insulating layers for which electrical measurements cannot be performed due to a high density leakage current. During the XPS measurements, a bias voltage is applied to the rear semiconductor surface with respect to the ∼3 nm-thick front platinum layer connected to the ground, and the bias voltage changes the occupation of interface states. Charges accumulated in the interface states shift semiconductor core levels at the interface, and thus the analysis of the bias-induced shifts of the semiconductor core levels measured as a function of the bias voltage gives energy distribution of interface states. In the case of Si-based MOS diodes, the energy distribution and density of interface states strongly depend on the atomic density of silicon dioxide (SiO₂) layers and the interfacial roughness, respectively. All the observed interface state spectra possess peaked-structures, indicating that they are due to defect states. An interface state peak near the Si midgap is attributable to isolated Si dangling bonds at the interface, while those above and below the midgap to Si dangling bonds interacting weakly with Si or oxygen atoms in the SiO₂ layers. A method of the elimination of interface states and defect states in Si using cyanide solutions has been developed. The cyanide method simply involves the immersion of Si in KCN solutions. Due to the high Si-CN bond energy of ∼4.5 eV, the bonds are not ruptured at 800 °C and upon irradiation. The cyanide treatment results in the improvement of the electrical characteristics of MOS diodes and solar cells.     

Spectroscopy on very neutron-rich nuclei beyond N = 20

Recent studies on nuclear structure by using radioactive isotope beams available at the RIKEN projectile-fragment separator (RIPS) are introduced. Special emphasis is given to two selected experiments from recent programs that highlight studies on the magicity loss observed for very neutron-rich nuclei beyond N = 20 in the “island-of-inversion” region; the particle stability of ³¹F, and the low-lying excited states of ³⁴Mg. Received: 1 May 2001 / Accepted: 4 December 2001