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大域構造の空間を基軸とする低次元トポロジーの研究とその応用

基于全局结构空间的低维拓扑研究及其应用

基本信息

批准号：
22K03313
负责人：
小林毅
金额：
$ 2.08万
依托单位：
Nara Women's University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2022
资助国家：
日本
起止时间：
2022-04-01 至 2026-03-31
项目状态：
未结题

项目摘要

本研究は二つの観点を持っている. それぞれについて実績の概要を述べる.観点1では「大域的構造のなす空間」という視点から三次元多様体，結び目・絡み目等に関係した研究を推し進める, としているがこれに関して三次元多様体内の絡み目の（strongly）keen bridge 分解と呼ばれる概念を定義し, そのような bridge splittingが豊富に存在することを証明した. また3次元球面内の結び目・絡み目に関しては, 橋分解と呼ばれる概念には二つの解釈が存在することを注意しそれらを, bridge splitting と bridge decomposition と呼称しその違いを調べる研究を実施した. これはこの分野の研究の進展にとって重要な事実の指摘になっていると考える. また waterbomb tube と呼ばれる剛体折り紙の剛体変形について研究を行い対称性の仮定の下でcylinder solutionが存在するための必要十分条件を考察した．基本形を横に並べる個数をnとすると，「cylinder solutionが存在する」為の必要十分条件は「nが5以上」であることを明らかにしたが, これはwaterbomb tubeの興味深い変形が実現できることを明らかにしたものである.観点2では機械学習の研究にトポロジーの観点を取り入れデータ解析等に新しい研究のフレームワークを提案し応用トポロジーの発展に寄与する,としているが, 対話のテキスト文からその感情の動きを組み紐として可視化する方法について研究を行なった. また, Gabrielsson-Carlsson による畳み込み層の中のフィルターの集合に適切な距離を入れその距離のもと, その層に含まれるフィルター全体の形に関する研究について情報を収集したがこれは観点２の研究を進めるために有益であると考える.

In this study, there are two points in this study. Please tell me how to describe the summary. In this paper, we discuss the development of three-dimensional multi-dimensional multiplets, such as the analysis of the three-dimensional multi-dimensional multi-body, the development of the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional space, the three-dimensional multi-dimensional space, the three-dimensional multi-dimensional space, the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional space, the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional multi-dimensional space, the three-dimensional multi-dimensional space The purpose of this paper is to analyze the concept of the three-dimensional spherical surface, to analyze the concept, to solve the problem, to pay attention to the problem, and to study the problem in the third dimension, the bridge splitting bridge decomposition is called the research tool. There are many important issues in the field of research, such as criticism, criticism, examination and examination. The waterbomb tube calls for the study of the shape of the body, the shape of the body, the shape of The word "cylinder solution" means that it is necessary to make sure that the information is more than five percent, and that the information is clear, and that the waterbomb tube has a strong message. At point 2, the study of mechanical mechanics, the acquisition of information points, and other new information, such as the analysis of information, and so on, the proposal was sent to the audience in an exhibition, and was sent to the audience in an exhibition. In the middle of the Gabrielsson-Carlsson, we need to know that the collection is far away from each other, and that the whole body is required to study the situation. The collection of information is not available.