A generalization of the weighted Strichartz estimates for wave equations and an application to self‐similar solutions

Weighted Strichartz estimates with homogeneous weights with critical exponents are proved for the wave equation without a support restriction on the forcing term. The method of proof is based on expansion by spherical harmonics and on the Sobolev space over the unit sphere, by which the required estimates are reduced to the radial case. As an application of the weighted Strichartz estimates, the existence and uniqueness of self‐similar solutions to nonlinear wave equations are proved on up to five space dimensions. © 2006 Wiley Periodicals, Inc.     

Temperature sensitivity of Ge-B-SiO(2) waveguide Bragg gratings on a crystallized glass substrate

Waveguide Bragg gratings were fabricated by plasma-enhanced chemical-vapor deposition followed by irradiation with KrF excimer laser light through a phase mask. The period of the Bragg grating was 0.53 mum, and the Bragg wavelength was ~1.53 mum . The temperature dependence of the Bragg wavelength was 11 pm/ degrees C for a 10GeO(2) -90SiO(2)(mol.%) core waveguide on a Si substrate, and the Bragg wavelength shift was successfully reduced to 5.0pm/ degrees C by use of a 14GeO(2)-12B(2)O(3)-74SiO(2) (mol.%) core and a crystallized glass substrate with a thermal-expansion coefficient of -2.0x10(-6)(/ degrees C) .     

On the sampling conditions for reconstruction of an acoustic field from a finite sound source

A simple and accurate method for the estimation of ultrasonic transducer fields is developed. In the method, the angular spectrum is employed to evaluate the three-dimensional propagation from a measured plane to an arbitrary parallel plane. The implementation uses a discrete convolution that is described in detail. Relative to conventional spatial-frequency representations, the implementation of the angular spectrum method in this paper has the advantage of being free from artifacts, enabling sample spacing to be greater than one half wavelength, using memory efficiently, and interpolating the measured data. The loosened sampling requirement and natural interpolation of the method permit efficient reconstruction of the full three-dimensional acoustic field from a coarse sound pressure measurement on single plane.     

A fully linear-time approximation algorithm for grammar-based compression

A linear-time approximation algorithm for the grammar-based compression is presented. This is an optimization problem to minimize the size of a context-free grammar deriving a given string. For each string of length n, the algorithm guarantees approximation ratio without suffix tree construction.     

Congruence classes of Frenet curves in complex quadrics

Congruent classes of Frenet curves of order 2 in the complex quadric are studied, obtaining that each congruence class is a level set of a family of certain smooth functions, that are generalizations of isoparametric functions on the unit sphere in the tangent space of the complex quadric.     

On planar hypohamiltonian graphs

We present a planar hypohamiltonian graph on 42 vertices and (as a corollary) a planar hypotraceable graph on 162 vertices, improving the bounds of Zamfirescu and Zamfirescu and show some other consequences. We also settle the open problem whether there exists a positive integer N, such that for every integer n≥N there exists a planar hypohamiltonian/hypotraceable graph on n vertices. © 2010 Wiley Periodicals, Inc. J Graph Theory 67: 55‐68, 2011     

Femtosecond laser-induced stimulation of a single neuron in a neuronal network

We demonstrated the stimulation of neurons at a single-cell level in cultured neuronal network by a focused femtosecond laser. When the femtosecond laser was focused on a neuron loaded with a fluorescent calcium indicator, the fluorescence intensity immediately increased at the laser spot, suggesting that intracellular Ca²⁺ increases in the neuronal cell due to the femtosecond laser irradiation. The probability of Ca²⁺ elevation at the laser spot depended on the average laser power, irradiation time, and position of the focal point along the optical axis, indicating that the femtosecond laser activates neurons because of multiphoton absorption. Moreover, after laser irradiation of a single neuron cultured on multielectrode arrays, the evoked electrical activity of the neurons was demonstrated by electrophysiological systems, which concluded that the focused femtosecond laser could achieve stimulating a single neuron in a neuronal network with high spatial and temporal resolution.     

Nanophotonic droplet: a nanometric optical device consisting of size- and number-selective coupled quantum dots

Although recent advances in fabrication technologies have allowed the realization of highly accurate nanometric devices and systems, most approaches still lack uniformity and mass-production capability sufficient for practical use. We have previously demonstrated a novel technique for autonomously coupling heterogeneous quantum dots to induce particular optical responses based on a simple phonon-assisted photocuring method in which a mixture of quantum dots and photocurable polymer is irradiated with light. The cured polymer sequentially encapsulates coupled quantum dots, forming what we call a nanophotonic droplet. Recently, we found that each quantum dot in the mixture is preferably coupled with other quantum dots of similar size due to a size resonance effect of the optical near-field interactions between them. Moreover, every nanophotonic droplet is likely to contain the same number of coupled quantum dots. In this paper, we describe the basic mechanisms of autonomously fabricating nanophotonic droplets, and we examine the size- and number-selectivity of the quantum dots during their coupling process. The results from experiments show the uniformity of the optical properties of mass-produced nanophotonic droplets, revealed by emission from the contained coupled quantum dots, due to the fundamental characteristics of our method.