The Euler multiplicity and addition-deletion theorems for multiarrangements

The addition–deletion theorems for hyperplane arrangements,which were originally shown by Terao [J. Fac. Sci. Univ. TokyoSect. IA Math. 27 (1980) 293–320.], provide useful waysto construct examples of free arrangements. In this article,we prove addition–deletion theorems for multiarrangements.A key to the generalization is the definition of a new multiplicity,called the Euler multiplicity, of a restricted multiarrangement.We compute the Euler multiplicities in many cases. Then we applythe addition–deletion theorems to various arrangements,including supersolvable arrangements and the Coxeter arrangementof type A₃, to construct free and non-free multiarrangements.     

The Virtual Class of the Moduli Stack of Stable r-Spin Curves

We recall the outline of the Seely-Singer-Witten construction of the virtual class on the moduli of stable r-spin curves. We prove that the obtained classes satisfy the axioms of Jarvis-Kimura-Vaintrob.     

Controlled-release system mediated by a retro Diels-Alder reaction induced by the photothermal effect of gold nanorods

Controlled-release systems that respond to external stimuli have received great interest for use in medical treatments such as for drug delivery to specific sites. Gold nanorods have an absorption band at the near-infrared region and convert the absorbed light energy into heat, which is known as a "photothermal effect". Therefore, gold nanorods are expected to act not only as an on-demand thermal converter for photothermal therapy but also as a controller of a drug-release system capable of responding to the near-infrared light irradiation. In this study, to construct a controlled-release system that responds to near-infrared light irradiation, we modified gold nanorods with polyethylene glycol (PEG) through Diels-Alder cycloadducts. When the modified gold nanorods were irradiated by near-infrared light, the PEG chains were released from the gold nanorods because of the retro Diels-Alder reaction induced by the photothermal effect. As a result of the PEG release, the gold nanorods formed aggregates. This type of controlled-release system coupled with the aggregate formation of the gold nanorods triggered by near-infrared light could be expanded to applications of gold nanorods in medical fields such as drug and photothermal therapy.     

Iridium-catalyzed direct tetraborylation of perylene bisimides

Treatment of perylene bisimides (PBIs) with bis(pinacolato)diboron in the presence of an iridium catalyst provides tetraborylated PBIs at 2,5,8,11-positions in good yields with perfect regioselectivity. The planar structure of the perylene core has been confirmed by X-ray diffraction analysis. Oxidation of tetraborylated PBI with hydroxylamine hydrochloride affords tetrahydroxy PBI in excellent yield, which exhibits a substantially blue-shifted absorption spectrum due to an intramolecular hydrogenbonding interaction between carbonyl and hydroxy groups.     

Nickel(II) oxide surface-modified titanium(IV) dioxide as a visible-light-active photocatalyst

The electronic modification of TiO(2) with highly dispersed NiO particles smaller than ca. 2 nm by the chemisorption-calcination-cycle technique has given rise to a high level of visible-light-activity exceeding that of iron oxide-surface modified TiO(2) simultaneously with the UV-light-activity being significantly increased.     

Laser Light and X-Ray Diffraction Studies of Oriented Isotactic Polypropylene (iPP) Prepared by Temperature Slope Crystallization

Isotactic polypropylene (iPP) film was melt-crystallized in a temperature gradient. The iPP film showed well oriented α- and β-crystalline textures along the gradient. The crystalline structure, phase transition boundary and lamellar twisting were examined by X-ray diffraction and laser light diffraction (LLD). On the α-β boundary, LLD shows a sharp streak perpendicular to the boundary, where the a-axis of the β-crystal is oriented perpendicular to the temperature gradient. Apart from the boundary, the a-axis of the β-crystal becomes parallel to the gradient. The β-crystal shows lamellar twisting with a pitch of 200 μm at room temperature. When heated the β-crystal, the lamellar distance of 295Å at room temperature decreases to 285Å at 80–100°C and then increases to more than 300Å above 120°C. During the heating, the value of the twist period increases from 200 to 210 μm at 90–100°C, and then to above 224 μm at 140°C. The increase of the twist period is related to the increasing crystalline thickness of the β-lamellae.