Language：English   Publishing type：Research paper (scientific journal)   Publisher：Nonlinearity  

In this paper, we provide a systematic methodology for calculating multi-order asymptotic expansion of blow-up solutions near blow-up for autonomous ordinary differential equations. Under the specific form of the principal term of blow-up solutions for a class of vector fields, we extract algebraic objects determining all possible orders in the asymptotic expansions. Examples for calculating concrete multi-order asymptotic expansions of blow-up solutions are finally collected.

DOI： 10.1088/1361-6544/adb52d

Web of Science

Scopus

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Nonlinearity  

In this paper, we provide a natural correspondence of eigenstructures of Jacobian matrices associated with equilibria for appropriately transformed two systems describing finite-time blow-ups for ODEs with quasi-homogeneity in an asymptotic sense. As a corollary, we see that asymptotic expansions of blow-ups proposed in Part I themselves provide a criterion of the existence of blow-ups with an intrinsic gap structure of stability information among two systems. Examples provided in Part I are revisited to show the above correspondence.

DOI： 10.1088/1361-6544/adb52e

Web of Science

Scopus

Language：Japanese   Publisher：Japan Society for Science Education  

<p>Demands and expectations for data science education have been increasing in recent years. Data science education requires not just acquiring knowledge and skills, but also the ability to use them to solve real-world problems. To achieve this, it is recommended that project-based learning be conducted using realistic data. In this paper we reported on a PBL-type teaching practice carried out in collaboration among three universities. The classes were structured to allow communication between students with different knowledge and experience in data science education and between students with different fields of expertise. In addition, we provided opportunities for graduate students to answer questions from undergraduate students in order to develop consulting skills within the class. By analyzing real data, the students became more interested in data science and actively engaged in problem solving. Regarding consulting, the questioner was asked to confirm the knowledge he or she lacked in solving the problem, while the respondent made an effort to explain things in a way that suited the questioner. This paper provides an overview of the classes conducted collaboratively by the three universities and discusses the effects of these collaborative classes on student learning.</p>

DOI： 10.14935/jssej.49.135

CiNii Research

Language：English   Publishing type：Research paper (scientific journal)   Publisher：International Mathematics Research Notices  

Based on the analogies between mapping class groups and absolute Galois groups, we introduce an arithmetic pro-ℓ analogue of Orr invariants for a Galois element associated with Galois action on étale fundamental groups of punctured projective lines. At the same time, we also introduce pro-ℓ Orr space as an arithmetic analogue of Orr space whose third homotopy group is a target group of Orr invariant. We then determine its rank as ℤℓ-module following Igusa-Orr's computation. Moreover, we investigate its relation with Ellenberg's obstruction to π1-sections associated with lower central series filtration in the context of Grothendieck's section conjecture.

DOI： 10.1093/imrn/rnac138

Scopus

Language：English   Publishing type：Research paper (scientific journal)  

We reconfigure the Milnor invariant of links in terms of central group extensions and unipotent Magnus embeddings. We also develop a diagrammatic computation of the invariant and compute the first non-vanishing invariants of Milnor link and of several other links. Moreover, we refine the original Milnor invariants of higher degree.

DOI： 10.1016/j.topol.2019.106991

Type：Academic society, research group, etc. 

Type：Peer review 

Audience：Infants,　Schoolchildren,　Junior students,　High school students