Fraunhofer Diffraction Pattern by a Slit Aperture between a Knife Edge and a Metal Cylinder

The Fraunhofer diffraction pattern of an aperture formed between a knife edge and a smooth surface of a turned metal cylinder or half cylinder is different from the diffraction pattern of an ideal slit aperture. The diffraction pattern is simulated by adding the light reflected by the cylinder surface to the pattern formed by a slit, and is measured using a cylinder that has been partly cut away so that it can represent either a full or half cylinder. The theoretical and measured patterns agree well with each other.     

O2/n2-separation by polymer-bound cobalt complexes

Facilitated or complexation-mediated transport of oxygen in the solid membrane containing a fixed carrier was described, by using the polymer-bound cobalt Schiff's base chelate (CoS) and cobaltporphyrin (CoP). α³ β-Substituted cobaltporphyrin derivatives were synthesized: The oxygen-binding reaction to cobalt was affected by the cavity structure on porphyrin, i.e., unbulky amido-substituted groups such as acetylamido- and acrylamido-substituents enhanced oxygen-binding and -dissociation rate constant or provided an oxygen-binding pathway. Oxygen transport through the membranes of these polymer-bound CoP derivatives was selectively augmented due to the rapid and reversible oxygen-binding. Diffusion constants via the fixed CoPs correlated to the characteristics of oxygen-binding reaction.     

Three-dimensional visualization of columnar vortices in rotating Rayleigh–Bénard convection

Journal of Visualization -  To enrich the three-dimensional experimental details of vortex structures in rotating Rayleigh–Bénard convection, we established a technique...     

Epitaxial strain effects on the metal-insulator transition in V2O3 thin films

Effects of epitaxial stress on the metal-insulator transition of V₂O₃ have been studied for in the form of epitaxial thin films grown on α-Al₂O₃ (0001) and LiTaO₃ (0001) substrates. A metallic phase is stabilized down to 2 K in the V₂O₃ thin film on α-Al₂O₃ (0001), where the a-axis is compressed by 4% owing to large epitaxial stress. On the other hand, the transition temperature T_MI is raised by 20 K from the value of 170 K in bulk samples in the film on LiTaO₃ (0001), where the a-axis is expanded. These results suggest an intimate relationship between the a-axis length and T_MI in V₂O₃. The conductivity of the metallic ultrathin films shows logarithmic temperature dependence below 20 K, probably due to the Anderson localization in two-dimensional systems.     

Constructing finitely presented monoids which have no finite complete presentation

Squier (1987) showed that if a monoid is defined by a finite complete rewriting system, then it satisfies the homological finiteness condition FP₃, and using this fact he gave monoids (groups) which have solvable word problems but cannot be presented by finite complete systems. In the present paper we show that a monoid cannot have a finite complete presentation if it contains certain special elements. This observation enables us to construct monoids without finite complete presentation in a direct and elementary way. We give a finitely presented monoid which has (1) a word problem solvable in linear time and (2) linear growth but (3) no finite complete presentation. We also give a finitely presented monoid which has (1) a word problem solvable in linear time, (2) finite derivation type in the sense of Squier and (3) the property FP_∞, but (4) no finite complete presentation.     

Direct Monitoring of Thickness and Refractive Index of Optical Thin Film Deposited on Fiber End-face

We propose a system for depositing thin films on waveguides which enables low-temperature deposition and precise control of the refractive index and film thickness. It is composed of a conventional ion-beam sputtering (IBS) system and a new system for directly monitoring film characteristics during deposition. We controlled refractive indices over a wide range from 1.52 to 1.97 by moving the sputtering targets (SiO₂ and Si₃N₄) in the IBS system. The refractive index or film thickness was in-situ monitored by observing the optical power reflected from the end-face of a monitoring fiber set in the deposition chamber. Antireflection coating films were successfully deposited on a fiber end-face and a laser diode chip facet with low reflectivity from 0.05 to 0.07%. This deposition system is attractive for constructing highly functional optical devices for future photonic networks.     

Limit theorems for trimmed sums

This paper studies the heavily trimmed sums (*) _{[ns] + 1} ^[nt] X _j ⁽ⁿ⁾ , where {X _j ⁽ⁿ⁾ } _{j = 1} ⁿ are the order statistics from independent random variables {X ₁,...,X _n } having a common distributionF. The main theorem gives the limiting process of (*) as a process oft. More smoothly trimmed sums like _{j = 1} ^[nt] J(j/n)X _j ⁽ⁿ⁾ are also discussed.     

Perturbations of Solitons and Solitary Waves

A direct perturbation method is developed to investigate the evolution of solitary waves in the presence of small perturbations. A uniformly valid first order solution is constructed. The method is applied to several nonlinear evolution equations which support solitons or solitary waves. Finally, the method is compared with other approaches in the literature.