Doubly nonlinear evolution equations with non-monotone perturbations in reflexive Banach spaces

Let V and V* be a real reflexive Banach space and its dual space, respectively. This paper is devoted to the abstract Cauchy problem for doubly nonlinear evolution equations governed by subdifferential operators with non-monotone perturbations of the form: ?_V y^t (u￠(t)) + ?_V j(u(t)) + B(t, u(t)) ' f(t){\partial_V \psi^t (u{^\prime}(t)) + \partial_V \varphi(u(t)) + B(t, u(t)) \ni f(t)} in V*, 0 < t < T, u(0) = u ₀, where ?_V y^t, ?_V j: V ? 2^V*{\partial_V \psi^t, \partial_V \varphi : V \to 2^{V^*}} denote the subdifferential operators of proper, lower semicontinuous and convex functions y^t, j: V ? (-￥, +￥]{\psi^t, \varphi : V \to (-\infty, +\infty]}, respectively, for each t ? [0,T]{t \in [0,T]}, and f : (0, T) → V* and u₀ ? V{u_0 \in V} are given data. Moreover, let B be a (possibly) multi-valued operator from (0, T) × V into V*. We present sufficient conditions for the local (in time) existence of strong solutions to the Cauchy problem as well as for the global existence. Our framework can cover evolution equations whose solutions might blow up in finite time and whose unperturbed equations (i.e., B o 0{B \equiv 0}) might not be uniquely solved in a doubly nonlinear setting. Our proof relies on a couple of approximations for the equation and a fixed point argument with a multi-valued mapping. Moreover, the preceding abstract theory is applied to doubly nonlinear parabolic equations.     

Sharp photonic Crystal Defect Modes and Their Response to Ultrashort Optical Pulses

Single photonic crystal defects based on an air-bridge structure were fabricated. We obtained sharp defect modes with quality factors higher than 600 and observed their response to ultrashort optical pulses by utilizing two-photon absorption.     

Synthesis of a pyrrole‐based methine bridge type liquid‐crystalline conjugated polymer

Conjugated polymers consisting of pyrrole or an N‐substituted pyrrole bridged by methine with a mesogenic group were synthesized. Chemical structures of the products were confirmed with IR, NMR, UV–visible (UV–vis) spectroscopy, and gel permeation chromatography analysis. Liquid crystallinity was examined with differential scanning calorimetry measurements and polarizing optical microscopy observations. Liquid crystal domains of the polymer were macroscopically oriented in one direction by an external magnetic force (10 Tesla). The polymer orientation was confirmed by optical microscopy and X‐ray analysis. One of the polymers exhibited a striated fan‐shaped texture when observed with a polarizing optical microscope. This is attributed to the formation of a chiral smectic C (SmC^*) phase, which is a property of ferroelectricity. Spontaneous polarization of the polymer occurred at 110 nC/cm². © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 616–629, 2005     

Optical Storage Media with Dye-Doped Minute Spheres on Polymer Films

We have fabricated a new optical storage media using minute spheres arranged on a surface relief grating (SRG). Using minute spheres as recording bits, we can limit recordable regions by sphere size, and can realize high resolution reproduction in the plane direction. Surface relief structures were made on a polymer thin film on which we performed diffusion arrangement and adsorptive fixation of minute spheres. The stability of the arranged spheres was confirmed for heating and washing. Furthermore, we used a dipping method for a more simple arrangement of minute spheres on a large area of the substrate and made a monolayer sample of the spheres. We were able to realize a highly sensitive reconstruction of the medium using a confocal optical system as a record and readout system.     

Selection of spectral lines and transition probability data in plasma temperature measurements by photoelectric scanning spectrometry

A strict, comparative investigation of published transition probabilities for thermometric lines and an experimental study of determinations of plasma temperatures were made for improving the accuracy in temperature measurements by the well-known slope method. Four sets of FeI lines which satisfy the requirements for the thermometric lines were selected in the wavelength region of 200–400 nm. A statistical method was used to evaluate degrees of agreement among different sets of transition probabilities. In the experimental study, excitation temperatures of a stabilized arc plasma were determined from relative line-intensities recorded by photoelectric scanning spectrometry. In conclusion, two recommended combinations of lines and transition probability data are presented for the slope temperature measurement. Line pairs used in combination of selected transition probabilities suitable for the two-line method are also given.     

Molecular rotation and lattice dynamical properties for cyclodextrin-ferrocene and some its ring-substituted derivative clathrates

This paper reports the unusual relaxation effect in the⁵⁷Fe Mössbauer spectra of -cyclodextrin(-cyclopentadienyl)(-ethylcyclopentadienyl)iron(II) clathrate. At low temperatures it consists of a simple quadrupole doublet. However, the Mössbauer spectrum collapses to a broad peak at 320 K. This behavior is interpreted in terms of a model that a ferrocene molecule in the cavity of clathrate lattices rotates as temperature is raised. The relaxation reaches a critical rate, a lifetime of the excited nuclear state. The relaxation time for the reorientation of (-cyclopentadienyl)(-ethylcyclopentadienyl)iron(II) in a cavity was 1.2×10^–7 s at 320 K and a barrier to rotation of about 8.8 KJ/mol was estimated.     

A novel synthesis of alkyl phenylsulfinates

Alkyl phenylsulfinates (Ph-SO-OR) were prepared from thiophenol (or diphenyldisulfide) by electrolysis in acetic acid with alcohols and sodium acetate in satisfactory yields.     

Further studies on palytoxin. II. structure of palytoxin

The full structure of palytoxin, a potent coelenterate toxin, is reported.     

Remarks on “theory of scattering in a superconducting state”

Recently the author showed that in a superconductor the existence of scatterers like non-magnetic impurities or phonons in their long wavelength limit never limits the infinite ‘Ohmic’ conductivity which could be expected in the absence of those scatterers. In this paper we discuss the relation of such an infinite conductivity with the freely acceleratable current which is described by the second London equation. Then the results of the former paper are reproduced here by virtue of the canonical transformation technique. It is also suggested that due to the infinite ‘Ohmic’ conductivity giant voltage noises would occur as the temperature approached zero, since then the conductivity is determined by the vanishing density of current carriers (Bogolons) multiplied by an infinite (effective) momentum relaxation time.