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図式による結び目、絡み目及び空間グラフの研究

结、链接和空间图的图解研究

基本信息

批准号：
10J07723
负责人：
清水理佳
金额：
$ 0.9万
依托单位：
Osaka City University
依托单位国家：
日本
项目类别：
Grant-in-Aid for JSPS Fellows
财政年份：
2010
资助国家：
日本
起止时间：
2010 至 2011
项目状态：
已结题

项目摘要

研究の主題であるひずみ度を用いて,新しい多項式ひずみ多項式を定義しその性質を調べる等,独創的な研究を進めた.また受入研究者である河内明夫教授との共同研究によりひずみ交差多項式を定義して,結び目射影図の研究にもつなげることができ,大変有意義な結果を得ることができた.今年度は当初の計画通り,結び目の射影図についても深く考察し,結び目射影図における局所変形に関する結果も発表した.さらに,結び目図式の領域交差交換に関する研究代表者の結果を応用して,河内明夫教授,岸本健吾氏と研究代表者の共同発明でゲームを発明し特許出願した.研究代表者はアルゴリズム作成,およびコンピュータを用いた実際のゲーム作成等の役割を務めた.平成23年12月にはこのゲームがAndroidスマートフォン用のアプリとなり,世界同時公開され国内外から注目を集めた.日本数学会およびアメリカ数学会の学会を初め,国内外の研究集会や学会での発表も精力的に行った.平成23年度の講演回数は19回(内2回はポスター発表)であり,本予算を出張旅費に多く費やしたがどれも大変有意義な出張であった.出張先での議論や研究打ち合わせにより新しい研究テーマおよび新しい結果を得ることができた.

The main topic of the study is the use of information technology, the definition of the new multi-item model, the definition of the multi-item model, and so on, and the independent research is improved. Professor Hanoi joined the researcher, Professor Mingfu Hanoi, to jointly study the definition of the intersection of multiple items, the visual effect of the study, the accuracy of the study, the accuracy of the study, the results of the study, and the results of the study. At the beginning of this year, the project was reviewed, and the results were shown in the table of the results of the program. The results show that the research representatives of the field traffic and transportation industry, Professor Akio Hanoi and Kishimoto Kishimoto, have jointly demonstrated that they have been invited to participate in the field of communication. The representative of the research team is responsible for the production of such service cutting operations as well as the use of international equipment. In December 23, Pingcheng announced that the Android market was in full swing. At the same time, the world made public the collection of attention at home and abroad. The Japanese Mathematical Society said that it was the beginning of the mathematics society, and that it was the first time for the Japanese Mathematical Society to learn how to do it. In Pingcheng 23, the number of performances back to 19 times (within 2 times), it was calculated that there was a lot of trouble in the travel industry. In the first part of the discussion, there was a combination of research and development. The results showed that the results were satisfactory.