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The approximating character on nonlinearities of solutions of Cauchy problem for a singular diffusion equation
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特集「大学におけるeラーニングプラットフォーム : システムの概要、将来展望と導入例
Equations in p-curvature and intertwiners
The equations in p-curvatures, which is a key to prove a stable equivalence of Jacobian problem and Dixmier conjecture in the author’s previous paper, is provided an easier proof, related to the existence of ‘intertwining operator’. In an appendix, we show that every symplectic morphism between nonsingular symplectic varieties are of Jacobian 1, regardless of the characteristics
The formation of the efficient market in Tokugawa Japan
* Revised: [06-28, 2006]The ¯rst modern futures market is said to date back to the Chicago Board of Tradeestablished in 1848. However, there existed an older precedent; the Dojima Rice Marketestablished in 1730 in Osaka. The past literature on Dojima has made it clear thatDojima had well-established trading systems. However, a important question remainsunanswered: whether the ¯rst well-established futures market e±cient or not? Thispaper ¯rst constructs the daily price index from the original historical document, andapplies the test of unbiasedness hypothesis and the classic measure of market e±ciency;\weak-form e±ciency" to Dojima Rice Market, and shows that there existed these typesof e±ciency
The tail estimation of the quadratic variation of a quasi left continuous local martingale
We discuss some estimates of the tail distributions of the supremum and the quadratic variation of a local martingale. The assumption made so far in the literature on exponential moments involving a quasi left continuous local martingale is improved