A class of differential equations of PI-type with the quasi-Painlevé property

We present a certain class of second order nonlinear differential equations containing the first Painlevé equation (PI). Each equation in it admits the quasi-Painlevé property, namely every movable singularity of a general solution is at most an algebraic branch point. For these equations we show some basic properties.     

Optical fiber coupler array for multi-point sound field measurements

A pressure-sensitive device using an optical fiber coupler is proposed, and is integrated into an array system to measure sound field distributions. The optical coupling between two optical fibers is modulated by the applied sound field with the use of a membrane mechanically connected to the coupler. In the array system, a large number of the optical coupler sensors are connected two-dimensionally, and sound pressure at each sensor can be read out by switching the input light sources in turn. A prototype of the basic array system based on this principle was made, and its performance was demonstrated. The signal discrimination between each element was confirmed in a 2x2 array; then, using a four-element linear array, we demonstrated the steering of beam based on the phased array method.     

Recurrent dimensions of quasi-periodic solutions for nonlinear evolution equations

In this paper we introduce recurrent dimensions of discrete dynamical systems and we give upper and lower bounds of the recurrent dimensions of the quasi-periodic orbits. We show that these bounds have different values according to the algebraic properties of the frequency and we investigate these dimensions of quasi-periodic trajectories given by solutions of a nonlinear PDE.

     

Energetics and structural stability of Cs3C60

Using the ab initio pseudopotential total-energy method and the density-functional theory, we study the energetics of face-centered-cubic Cs₃C₆₀ which is a material of great interest as a possible high transition-temperature superconductor. At the optimized lattice constant the volume per C₆₀ is found to be smaller than the the most-stable hexagon-coordination A15 phase, while the total energy of the fcc phase is about 0.9 eV higher than the A15 phase. These results indicate that a low-temperature and high-pressure synthesis method might be a possible way to produce the fcc Cs₃C₆₀ phase. In addition, it is also found that the A15 Cs₃C₆₀ should show a phase transformation from a hexagon-coordination phase to a pentagon-coordination phase under hydrostatic pressure.     

Development of ion transportation, extraction and neutralization systems for atomic beam resonance method

A device that produces a low-energy and largely spin polarized RI beam based on the atomic beam resonance method (RIABR) has been developed. We have performed measurements of stopping and drifting an incoming RI ion beam in a gas chamber, extraction of the ions into a vacuum region, and neutralization of the extracted low-energy ion beam. The drift efficiency of RI ions in a gas and the extraction efficiency at a Laval-type glass nozzle were found to be 0.72±0.04 and 0.033, respectively. The result of the experiment for the neutralization is also discussed.     

Reproducing Kernels for Iterated Parabolic Operators on the Upper Half Space with Application to Polyharmonic Bergman Spaces

We consider parabolic operators of fractional order and their iterates on the upper half space of the euclidean space. We deal with Hilbert spaces of solutions of those parabolic equations. We shall show, in this note, the existence of reproducing kernels and give a formula by using their fundamental solutions. As an application, we also discuss the polyharmonic Bergman spaces and give their reproducing kernels by using the Poisson kernel on the upper half space.     

Phase structure change and ER effect in liquid crystalline polymer/dimethylsiloxane blends

The mechanism of the electrorheological (ER) effect in two types of liquid crystalline polymer (LCP)/dimethylsiloxane (DMS) blends was investigated by rheological measurements and by structure observation under electric field and shear flow. The results show that the phase structures of these immiscible blends can be categorized into slipping (low viscosity) and non-slipping (high viscosity) states. In the non-slipping state, higher viscosity LCP domains connect the electrodes. In the slipping state, on the other hand, LCP domains do not connect the electrodes and the shear is mainly confined in the lower viscosity DMS domains. The ER effect (electrically induced viscosity increase) originates from the electrically induced slipping to non-slipping transition. In one of the blends, the ER effect occurs only at high shear rate, since this blend is in non-slipping state even under no field if the shear rate is low. Received: 29 April 1997 Accepted: 3 November 1997     

Formal [6+4] cycloaddition of a dicobalt acetylene complex with furan derivatives

An efficient method for constructing a 10-membered carbocycle with an oxygen bridge has been developed on the basis of a formal [6+4] cycloaddition reaction. Under the influence of EtAlCl₂, a dicobalt hexacarbonyl acetylene complex possessing a benzoyloxy group and an allylsilane moiety reacted with furan to give a 11-oxabicyclo[6.2.1]undec-9-ene derivative. On treatment with iodine, the cycloadduct underwent decomplexation followed by rearrangement of the oxygen bridge to afford a 11-oxabicyclo[5.3.1]undeca-1,5-diene derivative.