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.     

Small and high-density GeSiC dots stacked on buried Ge hut-clusters in Si

Self-assembled GeSiC dots stacked on a Ge hut-cluster layer buried in Si have been investigated. The critical thickness for formation of GeSiC dots is reduced owing to the strain fields from the buried hut-clusters. By utilizing the stacked structure, the dot size is decreased and the uniformity is improved. The highest density of the GeSiC dots with stacked structures is 7.4×10¹⁰ cm⁻², which is six times larger than that of single GeSiC dots. The formation of the self-assembled GeSiC dots is strongly influenced by being stacked with buried Ge dots as well as C incorporation.     

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.     

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     

Structural and electrical properties of crystalline (1−x)Ta2O5−xTiO2 thin films fabricated by metalorganic decomposition

Polycrystalline (1−x)Ta₂O₅−xTiO₂ thin films were formed on Si by metalorganic decomposition (MOD) and annealed at various temperatures. As-deposited films were in the amorphous state and were completely transformed to crystalline after annealing above 600 °C. During crystallization, a thin interfacial SiO₂ layer was formed at the (1−x)Ta₂O₅−xTiO₂/Si interface. Thin films with 0.92Ta₂O₅–0.08TiO₂ composition exhibited superior insulating properties. The measured dielectric constant and dissipation factor at 1 MHz were 9 and 0.015, respectively, for films annealed at 900 °C. The interface trap density was 2.5×10¹¹ cm⁻² eV⁻¹, and flatband voltage was −0.38 V. A charge storage density of 22.8 fC/μm² was obtained at an applied electric field of 3 MV/cm. The leakage current density was lower than 4×10⁻⁹ A/cm² up to an applied electric field of 6 MV/cm.     

Self-aligned imaging system using phase conjugate readout from elementary holographic grating

We propose a self-aligned imaging system (SAIS) using phase conjugate readout from an elementary holographic grating. The SAIS provides a huge amount of interconnections between a lot of points on two corresponding imaging planes without troublesome mechanical alignment. In the SAIS, a hologram for one-to-one interconnection is used for many-to-many interconnections. In addition, the SAIS has the capability of correcting aberration. Preliminary experiments verify the principle and the capability of the SAIS.     

Development and application of high strength ternary boride base cermets

Reaction boronizing sintering is a novel strategy to form a ternary boride coexisting with a metal matrix in a cermet during liquid phase sintering. This new sintering technique has successfully developed world first ternary boride base cermets with excellent mechanical properties such as Mo₂FeB₂, Mo₂NiB₂ and WCoB base ones.In these cermets Mo₂FeB₂ and Mo₂NiB₂ base ones consist of a tetragonal M₃B₂ (M: metal)-type complex boride as a hard phase and a transition metal base matrix. The cermets have already been applied to wear resistant applications such as injection molding machine parts, can making tools, and hot copper extruding dies, etc.This paper focuses on the characteristics, effects of the additional elements on the mechanical properties and structure, and practical applications of the ternary boride base cermets.     

Host-guest complexation effect of 2,3,6-tri-O-methyl-β-cyclodextrin on a C60-porphyrin light-to-photocurrent conversion system

In a light-to-photocurrent conversion system based on a C₆₀-porphyrin bilayer prepared by electrostatic alternate adsorption, porphyrin units in a porphyrin polymer have been isolated by cyclodextrin utilizing the host-guest interaction. In this system, a high quantum yield was achieved by suppression of self-quenching of porphyrin units.