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.     

Fem for Schrödinger equation with Rashba effect

A finite element method for treating two-dimensional electron systems with Rashba spin–orbit interaction is developed. The Rashba spin–orbit interaction removes spin degeneracy, so that each spin contributes to the conductance differently. By accounting for the connection between a system and leads, this method yields the conductance of a nanoscale quantum device for each spin state. As an example, this calculation method is applied to a model of a quantum point contact. The results of this calculation indicate conductance quantization and a large spin polarization. We discuss the estimated accuracies of this calculation.     

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.     

Rotational and vibrational states of excitonic molecules in CuBr studied by the two-photon-resonant Raman scattering

Excited states of excitonic molecules are found in the study of the two-photon-resonant Raman scattering. These states consist of four levels and have binding energies of 1.0–1.8 meV, which are very small compared with those of the ground states. They are considered to be the rotational and vibrational states of excitonic molecules.     

A model calculation in a new approach to the three-body problem

A method to calculate the binding energy of a system of three identical particles is proposed. The kernel of a previously derived integral equation in two variables is replaced by an approximation of finite rank. It turns out that a one term approximation is already sufficient to determine the binding energy very well.