We review the results of very early phase optical follow-up observations of recent gamma-ray bursts (GRBs) with the multi-color optical telescopes “MITSuME”. The MITSuME telescopes were designed to perform “real time” and “automatic” follow-up observations prompted by the GCN alerts via the Internet. The rapidly slewing equatorial mounts allow MITSuME to start photometric observations within 100 seconds after the trigger for several GRBs. In particular, we detected a brightening just after the trigger for two GRBs. These phenomena could be interpreted as the “on-set” of afterglow. In this paper we summarize these optical observations with a brief interpretation.

Nanostructural characterizations of liquid metal–organic precursors-derived cobalt-doped amorphous silica (Si–Co–O) membranes supported on a mesoporous anodic alumina capillary (MAAC) tube were performed to study their unique high-temperature hydrogen gas permeation properties. Cross-sectional scanning transmission electron microscopy images and selected-area electron diffraction patterns indicated that the metal cobalt and the different oxidation states of cobalt oxides (CoO and Co3O4) nanocrystallites having a size range of 5–20 nm were in situ formed in the mesopore channels of the MAAC tube. In addition, high-resolution transmission electron microscopy micrographs and electron energy loss spectroscopy elemental mapping images indicated that the highly dense Co-doped amorphous Si–O formed within the mesopore channels of the MAAC tube. These nanostructural features could contribute to the hydrogen-selective permeation properties observed for the membranes.

The Voronoi tessellation generated by a Gibbs point process is considered. Using the algebraic formalism of polymer expansion, the limit theorem and the large deviation principle for the number of Voronoi vertices are proved.