RECENT PROGRESSES ON GENUS ONE EXTENSIONS OF MIXED TATE MOTIVES OVER Z (Various aspects of multiple zeta values)

In this survey article, we give an overview of recent progress of construction of genus one extension of the category of mixed Tate motives over ℤ by Brown [6] and Hain-Matsumoto [18]

On a non-abelian generalization of the Bloch–Kato exponential map

The present paper establishes a non-abelian generalization of the Bloch–Kato exponential map. Then, we relate p-adic polylogarithms introduced by Coleman to `-adic polylogarithms introduced by Wojtkowiak. This formula is another analog of the Coleman–Ihara formula obtained by Nakamura, Wojtkowiak, and the author

Polylogarithmic analogue of the Coleman-Ihara formula, II (Algebraic Number Theory and Related Topics 2014)

"Algebraic Number Theory and Related Topics 2014". December 1～5, 2014. edited by Takeshi Tsuji, Hiroki Takahashi and Yuichiro Hoshi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.In this paper, generalizing our result in Part I, we show a formula that expresses a certain linear sum of Galois polylogarithms as a corresponding sum of the Coates-Wiles homomorphisms multiplied by Coleman's p-adic polylogarithms. These linear sums are characterized by tensor conditions of Zagier's conjecture on Bloch groups

On a non-abelian generalization of the Bloch–Kato exponential map

The present paper establishes a non-abelian generalization of the Bloch–Kato exponential map. Then, we relate p-adic polylogarithms introduced by Coleman to `-adic polylogarithms introduced by Wojtkowiak. This formula is another analog of the Coleman–Ihara formula obtained by Nakamura, Wojtkowiak, and the author

Ti-bridged silsesquioxanes as precursors of silica-supported titanium oxide catalysts for the epoxidation of cyclooctene

Silica-supported titanium oxide catalysts were prepared by the controlled calcination of Ti-bridged polyhedral oligomeric silsesquioxanes (POSS) bearing four Si–O–Ti bonds, Ti[(c-C5H9)7Si7O11(OSiMe2R)]2 (1a; R = vinyl, 1b; R = methyl) and Ti[(c-C5H9)8Si8O13)]2 (2), supported on various silicas, and these catalysts showed excellent activities for the epoxidation of cyclooctene by tBuOOH as an oxidant to selectively give cyclooctene oxide in high yields. On the other hand, catalysts prepared using a corner-capped-type Ti-containing POSS, CpTi[(c-C5H9)7Si7O12] (3, Cp = cyclopentadienyl), or tetraisopropoxytitanium (4) showed lower activities. The catalysts prepared from Ti-bridged POSS can be easily separated from the reaction mixture and reused without a significant loss of activity. These catalysts were also applicable for the epoxidation of limonene. A spectroscopic study revealed that calcination of Ti-bridged POSS supported on silica gave isolated tetrahedral Ti(IV) species, which would be responsible for the high activity, while calcination of silica-supported 3 or 4 gave aggregated surface titanium oxide species