A new matrix method based on rigid elements and its application to plane problems

A new matrix is proposed here which is based on rigid elements. The efficiency and usefulness of this method has been demonstrated for plane problems. The purpose of this paper is to formulate the method and to indicate its validity.     

Estimates for Hyperbolic Equations of Space Dimension 3

We discuss the problem of boundedness fromL^p(Rⁿ) toL^p′(Rⁿ) (1/p+1/p′=1, 1?p?2) of operators of the typeM=F⁻¹e^i?(ξ)a(ξ) F, which is related to the study of hyperbolic equations with constant coefficients. The boundedness is dependent on a geometrical property ofΣ=?⁻¹(1), and its dependence has been exactly determined in the casesn=2, 1?p?2 andn?3,p=1, 2 (M. Sugimoto,Math. Z.215(1994), 519–531;222(1996), 521–531). This paper is devoted to the unsolved case 1<p<2, and a strange phenomenon is exhibited in the simplest casen=3.     

Weighted Sobolev L2 estimates for a class of Fourier integral operators

In this paper we develop elements of the global calculus of Fourier integral operators in ${{\mathbb R}^n}$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L² estimates for a class of Fourier integral operators that appears in the analysis of global smoothing problems for dispersive partial differential equations. As an application, we exhibit a new type of weighted estimates for hyperbolic equations, where the decay of data in space is quantitatively translated into the time decay of solutions.     

Localized solutions to the nonlinear wave equation for flexural motions of an elastic beam traveling in an air-filled tube

Steady-progressive-wave solutions are sought to the nonlinear wave equation derived previously [J. Fluids Struct. 16 (2002) 597] for flexural motions of an elastic beam traveling in an air-filled tube along its center axis at a subsonic speed. Fluid-structure interactions are taken into account through aerodynamic loading on the lateral surface of the beam subjected to small but finite deflection but end effects and viscous effects are neglected. Linear dispersion characteristics are first examined by exploiting the small ratio of the induced mass to the mass of the beam per unit length. Centered around the traveling speed of the beam, there exists such a narrow range of propagation velocity that the linear steady propagation is prohibited. In this range, it is revealed that some interesting nonlinear solutions exist. The periodic wavetrain is found to exist as the exact solution. Asymptotic analysis is then made by applying the method of multiple scales and the stationary nonlinear Schrödinger equation is derived for a complex amplitude. A monochromatic solution to this equation corresponds to the exact periodic solution. Imposing undisturbed boundary conditions at infinity, it is revealed that the localized solution exists as a result of balance between the linear instability and the nonlinearity. This solution is checked by solving the nonlinear equation numerically. It is further revealed that the amplitude-modulated wavetrain exists not only in the range of the velocity mentioned above but also outside of it.     

Purcell effect of GaAs quantum dots by photonic crystal microcavities

We fabricate photonic crystal slab microcavities embedded with GaAs quantum dots by electron beam lithography and droplet epitaxy. The Purcell effect of exciton emission of the quantum dots is confirmed by the micro photoluminescence measurement. The resonance wavelengths, widths, and polarization are consistent with numerical simulation results.     

Quenching treatment for improvement of nonlinear optical response time in high-χ CuCl-doped glasses

Quenching treatments were performed on CuCl microcrystallite-doped glasses prepared by a melting method. Radiative decay time measurement and χ⁽³⁾ measurement for the quenched glasses were performed using ps and ns laser. The glasses showed that the radiative decay time were shortened by one order of magnitude without a decrease of third-order nonlinear susceptibility χ⁽³⁾ after the quenching treatment from above 300°C. The distorted structure of CuCl microcrystallites quenched from high temperature was considered to be most effective for the shortening of the lifetime of Z₃ exciton.     

Structural effect of synthetic zwitterionic cosolutes on the stability of DNA duplexes

The molecular design of useful cosolutes for polymerase chain reaction (PCR), which is one of the most important techniques in molecular biology, plays a significant role in amplification of highly stable genome sequences because during PCR, strand dissociation sometimes fails due to high melting temperature. Here, we designed and synthesized eight new zwitterionic cosolutes derived from glycine betaine, a destabilizing reagent for GC-rich DNA duplexes, and systematically compared their ability to destabilize DNA duplexes and to amplify genome DNA by PCR. We found that introduction of n-butyl groups rather than methyl groups into the ammonium group reduced the melting temperature of DNA duplexes 11-fold more than what was observed for the scaffold cosolute, glycine betaine, and furthermore, the cosolute can amplify the stable genome sequence by PCR.