Complete Asymptotic Expansions of Solutions of the System of Elastostatics in the Presence of an Inclusion of Small Diameter and Detection of an Inclusion

We consider the system of elastostatics for an elastic medium consisting of an imperfection of small diameter, embedded in a homogeneous reference medium. The Lamé constants of the imperfection are different from those of the background medium. We establish a complete asymptotic formula for the displacement vector in terms of the reference Lamé constants, the location of the imperfection and its geometry. Our derivation is rigorous, and based on layer potential techniques. The asymptotic expansions in this paper are valid for an elastic imperfection with Lipschitz boundaries. In the course of derivation of the asymptotic formula, we introduce the concept of (generalized) elastic moment tensors (Pólya–Szegö tensor) and prove that the first order elastic moment tensor is symmetric and positive (negative)-definite. We also obtain estimation of its eigenvalue. We then apply these asymptotic formulas for the purpose of identifying with high precision the order of magnitude of the diameter of the elastic inclusion, its location, and its elastic moment tensors.     

Time dependent Ginzburg-Landau equations for strong coupling superconductors

We derive time dependent Ginzburg-Landau equations for strong coupling superconductors. It is shown that due to a certain separability of the order parameter the equation for it’s time dependent fluctuations is again of diffusion type. Strong coupling effects show up only in the numerical coefficients of the diffusion equation. We apply our findings to the problem of electrical resistivity in strong coupling superconducting materials above the transition temperatureT _c.     

An Alumanylyttrium Complex with an Absorption due to a Transition from the Al−Y Bond to an Unoccupied d-Orbital

The reaction between a dialkyl-substituted alumanyl anion and [Y(CH₂SiMe₃)₂(thf)₃][BPh₄] resulted in the formation of (dialkylalumanyl)yttrium complex 2 , which exhibits the first 2-center–2-electron (2 c-2 e) Al−Y bond. The ¹H and ¹³C NMR spectra of 2 together with an X-ray crystallographic analysis indicated a C_2v symmetrical structure. DFT calculations on 2 revealed that its LUMO consists of overlapping 3 p- and 4 d-orbitals of the Al and Y atoms, respectively, and that the HOMO–LUMO gap is narrow. The UV/Vis spectrum of 2 exhibited a visible absorption at 432 nm, which suggests that the strong σ-donating and π-accepting character of the three-coordinate dialkylalumanyl ligand generates a colored d⁰-complex that does not contain any π-electrons.     

Role of cyclic dithiocarbonate as a promoter in the reaction of epoxide and imine in the presence of water

It was demonstrated that the reaction of epoxide and imine as a latent initiator under highly humid conditions was accelerated by addition of 5‐phenoxymethyl‐1,3‐oxathiolane‐2‐thione ( 1 ). When 1 was added to a mixture of glycidyl phenyl ether and an imine, the reaction of the epoxide with an amine released from the imine became faster than was the case without 1 , that is, 1 worked as a promoter of the reaction. The curing rate and initial adhesive strength of epoxy resin increased compared with that without 1 . © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4276–4283, 2004     

Periodic-orbit bifurcation and shell structure at exotic deformation

We have investigated the semiclassical origin of superdeformed shell structure and also of reflection-asymmetric deformed shapes by means of the periodic orbit theory and the deformed cavity model. Systematic analysis of the quantum-classical correspondence reveals that bifurcation of equatorial orbits into three-dimensional ones play predominant role in the formation of these shell structures. Presented by K. Matsuyanagi at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

Use of naphthalene as a solvent for selective formation of the 1:1 diels-alder adduct of C60 with anthracene

A reaction of C₆₀ with an equimolar amount of anthracene in refluxing naphtlhalene gives the 1:1 Diels-Alder adduct in 67% yield based on consumed C₆₀: the adduct was fully characterized by IR, UV-vis, ¹H and ¹³C NMR, and MS spectroscopy, and exhibited reversible reduction waves at the potential 0.11 to 0.19 V more negative and an irreversible oxidation peak at the potential 0.11 V less positive than those of C₆₀ itself.     

Adaptive regularizations in an iterative regularized pseudoinverse method

Adaptive regularizations in the implementation of the iterative regularized pseudoinverse method are described. Three different ways of increasing the regularizing parameter are investigated through computer simulations. It is shown that the optimum type of adaptive regularization is identical with the one we have proposed in the previous works.     

Theoretical Study on Intra-Cavity Distributed-Bragg-Reflection Quasi-Phase-Matched Second-Harmonic Lasers

The characteristics of intra-cavity distributed Bragg reflector (DBR) quasi-phase-matched (IDQPM) second-harmonic-generation (SHG) lasers are theoretically studied. In the IDQPM-SHG laser, a QPM device and a DBR for feedback are separately fabricated on the same substrate with the QPM device placed between the DBR and a semiconductor laser. The threshold current of the IDQPM-SHG laser depends on the coupling efficiency between the laser diode and the QPM waveguide and the reflectivity of the DBR. The SH output of the IDQPM-SHG laser is strongly dependent on the generalized SHG conversion efficiency, x. This laser has the potential to attain an SH output over a 30-mW using a currently available 50-mW semiconductor laser for the fundamental light source, when highly efficient QPM device (x=2.2 W⁻¹) is used. Its tolerance for various deviations from the initial design and the problems to develop a commercially available IDQPM-SHG laser are also discussed.     

Measurement of Focusing Properties of Axially Asymmetric Lenses Using Moire Technique

Most lenses composed of spherical or aspherical surfaces have symmetrical focusing properties about an optical axis. On the other hand, unconventional optical systems such as cylindrical lenses, astigmatic or progressive power glasses have axially asymmetrical focusing properties. In this study, the method of measuring focusing properties by the moire technique is extended to asymmetrical lenses. Some unconventional lenses were experimentally tested, and the focusing power in the interesting region and azimuthal direction of the aperture was evaluated.