A general method for construction of (<Emphasis Type="Italic">t</Emphasis>, <Emphasis Type="Italic">n</Emphasis>)-threshold visual secret sharing schemes for color images

This paper is concerned with the construction of basis matrices of visual secret sharing schemes for color images under the (t, n)-threshold access structure, where n ≥ t ≥ 2 are arbitrary integers. We treat colors as elements of a bounded semilattice and regard stacking two colors as the join of the two corresponding elements. We generate n shares from a secret image with K colors by using K matrices called basis matrices. The basis matrices considered in this paper belong to a class of matrices each element of which is represented by a homogeneous polynomial of degree n. We first clarify a condition such that the K matrices corresponding to K homogeneous polynomials become basis matrices. Next, we give an algebraic scheme for the construction of basis matrices. It is shown that under the (t, n)-threshold access structure we can obtain K basis matrices from appropriately chosen K − 1 homogeneous polynomials of degree n by using simple algebraic operations. In particular, we give basis matrices that are unknown so far for the cases of t = 2, 3 and n − 1.     

Water-dispersible ultrathin Au nanowires prepared using a lamellar template of a long-chain amidoamine derivative

Straight ultrathin Au nanowires (NWs) with diameters less than 2 nm were synthesized using the lamellar structure of C18AA in an organogel and its selective adsorption for specific gold surfaces. In addition, the potential to form a bilayer structure with interdigitated hydrocarbon chains enabled the production of water-dispersible Au NWs without morphological change.     

Formation and dielectric properties of anodic oxide films on Zr–Al alloys

Zr–Al alloys containing up to 26 at.% aluminum, prepared by magnetron sputtering, have been anodized in 0.1 mol dm⁻³ ammonium pentaborate electrolyte, and the structure and dielectric properties of the resultant anodic oxide films have been examined by grazing incidence X-ray diffraction, transmission electron microscopy, Rutherford backscattering spectroscopy, and AC impedance spectroscopy. The anodic oxide film formed on zirconium consists of monoclinic and tetragonal ZrO₂ with the former being a major phase. Two-layered anodic oxide films, comprising an outer thin amorphous layer and an inner main layer of crystalline tetragonal ZrO₂ phase, are formed on the Zr–Al alloys containing 5 to 16 at.% aluminum. Further increase in the aluminum content to 26 at.% results in the formation of amorphous oxide layer throughout the thickness. The anodic oxide films become thin with increasing aluminum content, while the relative permittivity of anodic oxide shows a maximum at the aluminum content of 11 at.%. Due to major contribution of permittivity enhancement, the maximum capacitance of the anodic oxide films is obtained on the Zr–11 at.% Al alloy, being 1.7 times than on zirconium at the formation voltage of 100 V.     

The role of intermolecular hydrogen bond on dielectric properties in hydrogen-bonded material 5-bromo-9-hydroxyphenalenone: theoretical investigation

Dielectric properties of the hydrogen-bonded material, 5-bromo-9-hydroxyphenalenone (C(13)H(7)O(2)Br; BrHPLN), are investigated theoretically by means of electronic structure calculations and Monte Carlo simulations. The density functional calculations of BrHPLN crystals have revealed that the polarization per one molecule can be about 1.7 times larger than that of the isolated monomer. It is also found that there exists significant electron density (0.01 e bohr(-3)) in an intermolecular C-H···O region, which, together with the interatomic distances of 2.39 ? for H···O and 3.34 ? for C···O, suggests the existence of intermolecular weak hydrogen bonding that may enhance the molecular polarization. The induced polarization effects in various intermolecular configurations are evaluated with the Fragment Molecular Orbital method. In addition to the π-π stacking interactions, two types of "in plane" intermolecular weak hydrogen-bonding configurations are found to affect the molecular dipole moment most significantly. These effects are efficiently included in a Monte Carlo simulation method in terms of "dipole corrections" as functions of both the intermolecular arrangements and the intramolecular proton configurations. The application to the dielectric phase transition of a BrHPLN crystal shows that the dipole corrections almost double the transition temperature, toward better agreement with experiments, and qualitatively affect the temperature dependence of the dielectric constant. Discussions are given to support that the results will remain adequate and consistent even after explicit inclusion of the quantum tunneling effects.     

Effects of sub-millimeter-bubble injection on transition to turbulence in natural convection boundary layer along a vertical plate in water

Temperature and velocity measurements are performed to clarify the effects of sub-millimeter-bubble injection on the transition to turbulence in the natural convection boundary layer along a vertical plate in water. In particular, we focus on the relationship between the bubble injection position L and the transition to turbulence in the natural convection boundary layer. The bubble injection positions used in our experiments are L = 1.6 and 3.6 mm. Bubble injection at L = 1.6 mm delays the transition to turbulence in the natural convection boundary layer, while that at L = 3.6 mm accelerates the transition to turbulence in the boundary layer. In the case of L = 1.6 mm, the appearance region of the liquid velocity fluctuation in the bubble-induced upward flow in the upstream unheated section is restricted to near the wall, although the peak of the liquid velocity fluctuation is high. In contrast, in the case of L = 3.6 mm, the relatively large liquid velocity fluctuation is distributed widely over the laminar boundary layer width. These results suggest that the effect of the liquid velocity fluctuation on the laminar boundary layer is quite different between L = 1.6 and 3.6 mm. It is therefore expected that the transition to turbulence in the natural convection boundary layer for the case with bubble injection is dependent on the magnitude and appearance region of the liquid velocity fluctuation in the bubble-induced upward flow in the upstream unheated section.     

Fractional maximal operators with weighted Hausdorff content

Positivity - Let $$n\ge 2$$ be the spatial dimension. The purpose of this note is to obtain some weighted estimates for the fractional maximal operator $${{\mathfrak {M}}}_{\alpha }$$ of order...     

Data driven time scale in Gaussian quasi-likelihood inference

We study parametric estimation of ergodic diffusions observed at high frequency. Different from the previous studies, we suppose that sampling stepsize is unknown, thereby making the conventional Gaussian quasi-likelihood not directly applicable. In this situation, we construct estimators of both model parameters and sampling stepsize in a fully explicit way, and prove that they are jointly asymptotically normally distributed. High order uniform integrability of the obtained estimator is also derived. Further, we propose the Schwarz (BIC) type statistics for model selection and show its model-selection consistency. We conducted some numerical experiments and found that the observed finite-sample performance well supports our theoretical findings.