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Multi-fan is an analogous notion of fan in toric theory. Fan is a combina-torial object associated to a toric variety. Multi-fan is associated to an orbifold with an action of half the dimension of the orbifold. In this paper the equivariant elliptic genus and the equivariant orbifold elliptic genus of multi-fans are defined and their character formulas are(More)
We introduce the notion of a multi-fan. It is a generalization of that of a fan in the theory of toric varieties in algebraic geometry. Roughly speaking a toric variety is an algebraic variety with an action of an algebraic torus of the same dimension as that of the variety, and a fan is a combinatorial object associated with the toric variety.(More)
The recent financial crisis has prompted academia, country authorities, and international bodies to study quantitative tools to monitor the financial system, especially systemic risk measures. This paper aims to outline these measures and apply them to Japan's financial system. The paper demonstrates that they are effective tools for monitoring the(More)
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