The present author proposed 'Origami Technology', and envisages the formation of a new discipline; mathematical analysis of Origami and its development in academic applications especially in engineering use. Origami structures consisting of zigzagged faces have foldable/deployable functions as well as solidification characters. Models presented in this paper include typical foldable/deployable thin cylinders, conical-shaped membranes, circular sheets which may be folded or wrapped. These shape-changeable origami models are analytically designed by folding or creasing a flat sheet or a thin plate into a 3-dimentional shape. New types of ultra-light 3-D honeycomb core models and a newly developed core panel named "dia-core" (consisting of 2 periodically dimpled panel pieces) are also presented for use in building such as aerospace structures. The former models are designed by analyzing the helical patterns or structures often found in living organisms, because such helical structures are easily deployed due to the presence of fewer dynamic restraints. The latter are developed on purely geometrical basis. As for academic applications of Origami modeling, two examples are shown; the phyllotaxis of leaves or flowers showing helical patterns, and axial buckling and torsional buckling of cylindrical tubes and conical shells are explained by using origami modeling.

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微生物や昆虫は自分の体(の一部)を運動させることで水や空気のような流体の中を動き回ることができる.このような推進や飛翔の機構は流れの性質により異なる.ここでは最初に微生物の推進運動について議論し,次に蝶の飛翔を取り上げ,その違いについて数理的視点から述べる.最後に蝶の飛翔の理論解析に関する話題を述べる.

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We study the scattering problem for the pseudo-conformally invariant nonlinear Schrodinger equation in space-time R^<n+1>. In Section 1, we give a brief survey on nonlinear Schrodinger equations with various critical powers. In Section 2, the scattering problem is formulated. In Section 3, we introduce a recent joint work with R. Carles on new identities of wave operators and associated Poisson formulas.

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暗号方式の安全性を議論するとき,証明が容易なランダムオラクルモデルで安全性を確認した後に,標準モデルでの証明を試みるランダムオラクル方法論がある.この解説では,この方法論は必ずしも正しくないことの反例を構成する.ランダムオラクル方法論が成立するための必要十分条件として「強識別不可能性(Indifferentiability)」という新しい概念を導入して,その理論について概説する.強識別不可能性理論によれば,ランダムオラクルをプログラムや回路として実装できないという否定的結論を証明できる.一方,この理論は種々の暗号システムの設計に役立ち,例えば安全性証明可能な「ハッシュ関数の設計論」の基礎となることを示す.

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