Phase Distribution Measurement of Light Wave by Adaptive Control of Pupil Function with Local Algorithm

In developing a new method to measure the phase distribution of a light wave utilizing the adaptive control of the pupil function with a liquid crystal panel, the optimization procedure for the adaptive control is shown to improve when a local algorithm is adopted. The feasibility of the proposed system is confirmed by computer simulation as well as by some basic experiments.     

Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems

We consider initial value/boundary value problems for fractional diffusion-wave equation: , where 0<α?2, where L is a symmetric uniformly elliptic operator with t-independent smooth coefficients. First we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to ∞ and the proofs are based on the eigenfunction expansions. Second for α∈(0,1), we apply the eigenfunction expansions and prove (i) stability in the backward problem in time, (ii) the uniqueness in determining an initial value and (iii) the uniqueness of solution by the decay rate as t→∞, (iv) stability in an inverse source problem of determining t-dependent factor in the source by observation at one point over (0,T).     

Approximate controllability for fractional diffusion equations by interior control

We consider the approximate controllability by interior control of a partial differential equation with time derivatives of non-integer order. First, we prove the well-posedness of the inhomogeneous problem for the controlled system. Next, we study the dual system and show a weak type of unique continuation property. Finally, we prove the approximate controllability.     

Stability of Inverse Problems for Ultrahyperbolic Equations

In this paper, the authors consider inverse problems of determining a coefficient or a source term in an ultrahyperbolic equation by some lateral boundary data. The authors prove Hlder estimates which are global and local and the key tool is Carleman estimate.     

A self-organized mesh generator using pattern formation in a reaction–diffusion system

A new type of mesh generator is developed by using a self-organized pattern in a reaction–diffusion system. The system is the Gray–Scott model, which creates a spot pattern in a specific parameter region. The spots correspond to nodes of a mesh. The mesh generator has several advantages: the algorithm is simple and processes to improve the mesh, such as smoothing, (locally) addition, and removal of nodes, are automatically performed by the system.     

Bandwidth selection for a data sharpening estimator in nonparametric regression

This paper is concerned with data-based selection of the bandwidth for a data sharpening estimator in nonparametric regression. Two kinds of bandwidths are considered: a bandwidth vector which has a different bandwidth for each covariate, and a scalar bandwidth that is common for all covariates. A plug-in method is developed and its theoretical performance is fully investigated. The proposed plug-in method works efficiently in our simulation study.     

Application of Protonic Acid-Doped Silica Gels to Electric Double-Layer Capacitors

Silica gels doped with several protonic acids such as HClO₄, H₂SO₄ and H₃PO₄ have been prepared by the sol-gel method and totally solid electric double-layer capacitors have been successfully fabricated using the highly proton-conductive silica gels as an electrolyte and activated carbon powder (ACP) hybridized with the silica gels as a polarizable electrode. It was found that the addition of HClO₄, which had the highest value of acid dissociation constant among these three acids, most effectively increased the proton conductivity of the resultant acid-doped silica gels. Tablets of the HClO₄-doped silica gels exhibited conductivities as high as 10^–5–10^–2 S cm^–1 at room temperature in dry N₂ atmosphere. One of the capacitors fabricated using the protonic acid-doped silica gels had a capacitance of 44 F/(gram of total ACP in the capacitor), which was comparable to those of conventional capacitors using liquid electrolytes.     

Molecular origin of the hydrophobic effect: analysis using the angle-dependent integral equation theory

The molecular origin of the hydrophobic effect is investigated using the angle-dependent integral equation theory combined with the multipolar water model. The thermodynamic quantities of solvation (excess quantities) of a nonpolar solute are decomposed into the translational and orientational contributions. The translational contributions are substantially larger with the result that the temperature dependence of the solute solubility, for example, can well be reproduced by a model simple fluid where the particles interact through strongly attractive potential such as water and the particle size is as small as that of water. The thermodynamic quantities of solvation for carbon tetrachloride, whose molecular size is approximately 1.9 times larger than that of water, are roughly an order of magnitude smaller than those for water and extremely insensitive to the strength of solvent-solvent attractive interaction and the temperature. The orientational contributions to the solvation energy and entropy are further decomposed into the solute-water pair correlation terms and the solute-water-water triplet and higher-order correlation terms. It is argued that the formation of highly ordered structure arising from the enhanced hydrogen bonding does not occur in the vicinity of the solute. Our proposition is that the hydrophobic effect is ascribed to the interplay of the exceptionally small molecular size and the strongly attractive interaction of water, and not necessarily to its hydrogen-bonding properties.     

Synthesis of 3‐Acyl‐4‐alkenylpyrrolidines by Platinum‐Catalyzed Hydrative Cyclization of Allenynes

A series of nitrogen‐tethered allenynes (‘5‐aza‐1,2‐dien‐7‐ynes’) 1 were transformed to the corresponding 3‐acyl‐4‐alkenylpyrrolidines 3 when treated with a catalytic amount of PtCl₂ in MeOH at 70°. Initial Pt‐promoted cyclization forms a nonclassical carbocationic intermediate. In contrast to the cycloisomerization in toluene, which produced the bicyclic cyclobutenes 2 , the intermediate is intercepted by addition of an oxygen nucleophile to achieve the formal hydrative cyclization.