A torus subgroup of the isotropy group of a bounded homogeneous domain

We show that the isotropy group of a bounded homogeneous domain always has a non-trivial torus subgroup, which gives an answer to the problem posed by Hundemer.     

Reversible control of light reflection of a colloidal crystal film fabricated from monodisperse mesoporous silica spheres

In this letter, we report a novel method for controlling the light reflection of a colloidal crystal. Highly monodisperse mesoporous silica spheres have been successfully organized into a hexagonally close-packed colloidal crystal film. Just by introducing water vapor into the fabricated colloidal film, the structural color and reflection spectra were changed dramatically because of water vapor adsorption occurring in the mesoporous channels. This phenomenon can be observed reversibly over five cycles. We are convinced that this is the first report on controlling the light reflection of a colloidal crystal film dynamically by taking advantage of adsorption properties inherent to mesoporous silica spheres.     

On symplectic representations of normal j-algebras and their application to Xu's realizations of Siegel domains

We present a canonical construction of an injective normal symplectic representation of a given normal j-algebra. On the other hand, the image of the holomorphic map corresponding to any normal symplectic representation is described as a subset of the Siegel upper half plane by using vector spaces of matrices satisfying certain axioms. Combining these results, we naturally obtain Xu's realization of homogeneous Siegel domains [Y.C. Xu, Automorphism groups of homogeneous bounded domains, Acta Math. Sinica 19 (1976) 161-191; Y.C. Xu, On the isomorphism of homogeneous bounded domains, Acta Math. Sinica 20 (1977) 248-266].     

Wavelet Transforms for Semidirect Product Groups with Not Necessarily Commutative Normal Subgroups

Let G be the semidirect product group of a separable locally compact unimodular group N of type I with a closed subgroup H of Aut(N). The group N is not necessarily commutative. We consider irreducible subrepresentations of the unitary representation of G realized naturally on L²(N), and investigate the wavelet transforms associated to them. Furthermore, the irreducible subspaces are characterized by certain singular integrals on N analogous to the Cauchy-Szegö integral.     

Synthetic aperture digital holography with cross-correlation of reconstruction images

We propose a new nonoverlapping synthetic aperture digital holography without additional instruments. The relative distance between adjacent subholograms is estimated from the cross-correlation of reconstruction images from each subhologram. From the cross-correlation, the shift amount of the reconstruction object is estimated. Then, the relationship between the position of the subhologram and the reconstruction object from it enables the relative distance between adjacent subholograms to be calculated. The nonoverlapping synthetic aperture experiments with two subholograms are presented in two ways by changing the object. In the experiments, we show that the resolution of the reconstruction object increased twofold, thanks to the nonoverlapping.