Finiteness of Crystalline Cohomology of Higher Level

We prove the finiteness of crystalline cohomology of higher level. An important ingredient is a "higher de Rham complex" and a kind of Poincar\'e lemma for it.Comment: 24 pages; to appear in Annales de l'Institut Fourie

Euler characteristic reciprocity for chromatic, flow and order polynomials

The Euler characteristic of a semialgebraic set can be considered as a generalization of the cardinality of a finite set. An advantage of semialgebraic sets is that we can define "negative sets" to be the sets with negative Euler characteristics. Applying this idea to posets, we introduce the notion of semialgebraic posets. Using "negative posets", we establish Stanley's reciprocity theorems for order polynomials at the level of Euler characteristics. We also formulate the Euler characteristic reciprocities for chromatic and flow polynomials.Comment: 16 pages; flow polynomial reciprocity added; title change

アナログメモリ素子応用に向けたタンタル酸化物におけるフォーミングおよび抵抗変化現象に関する研究

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」京都大学新制・課程博士博士(工学)甲第24622号工博第5128号新制||工||1980(附属図書館)京都大学大学院工学研究科電子工学専攻(主査)教授 木本 恒暢, 教授 白石 誠司, 准教授 小林 圭学位規則第4条第1項該当Doctor of Philosophy (Engineering)Kyoto UniversityDFA