Shingo Takeuchi

J-GLOBAL         Last updated: Aug 25, 2019 at 11:33
 
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Name
Shingo Takeuchi
URL
http://www.sic.shibaura-it.ac.jp/~shingo/english/index.html
Affiliation
Shibaura Institute of Technology
Section
Department of Mathematical Sciences, College of Systems Engineering and Science
Job title
Professor
Degree
Ph.D.(Waseda University)
Research funding number
00333021

Profile

I moved to Shibaura Institute of Technology in April 2011. In the northern half of the Omiya campus there is an original forest left, which is a very pleasant environment for me, who is living in a city. Among them, the building of the department of mathematical sciences is located in the closest place to the primeval forest, and it is very exciting to me, who love insects. I am healed by the sound of cicadas that can be heard especially at dusk of the summer. My hobbies include fishing, swimming, history walks, caring for turtles. The portrait was written by a student at Gakushuin University.

I study the p-Laplacian, which generalizes Laplacian. The p-Laplacian is a typical nonlinear operator with degeneracy-singularity and has been studied mathematically since ancient times. I had previously dreamed of building a dynamical system theory of parabolic partial differential equations with degeneracy-singularty and was studying a reaction-diffusion equation with the p-Laplacian as its model case. While studying the influence of degeneracy-singularity on the shape of solution from the viewpoint of free boundary problem and infinite dimensional dynamical system, I came to the idea that the p-Laplacian's eigenvalue problem is essential. Therefore, recently, I am doing something like classical analysis to investigate the properties and applications of generalized trigonometric functions, which are eigenfunctions of the p-Laplacian, and elliptic integrals and Jacobi elliptic functions generalized by using them. Unexpectedly, Ramanujan formulas of hypergeometric function are useful and relationships with number theory are getting visible, and I am feeling that I wandered into "mathematical" primeval forest.

Research Areas

 
 

Academic & Professional Experience

 
Apr 2016
 - 
Today
Professor, College of Systems Engineering and Science, Shibaura Institute of Technology
 
Apr 2011
 - 
Mar 2016
Associate Professor, College of Systems Engineering and Science, Shibaura Institute of Technology
 
Apr 2007
 - 
Mar 2011
Associate Professor, Faculty of Engineering, Kogakuin University
 
Apr 2003
 - 
Mar 2007
Lecturer, Faculty of Engineering, Kogakuin University
 
Oct 2000
 - 
Mar 2003
Assistant Professor, Faculty of Science, Gakushuin University
 
Apr 2000
 - 
Sep 2000
Research Fellowship for Young Scientists (PD), JSPS
 
Jan 1999
 - 
Mar 2000
Research Fellowship for Young Scientists (DC2), JSPS
 

Education

 
Apr 1997
 - 
Mar 2000
Doctoral Course in Mathematical Sciences, Graduate School of Science and Engineering, Waseda University
 
Apr 1995
 - 
Mar 1997
Master's Course in Mathematical Sciences, Graduate School of Science and Engineering, Waseda University
 
Apr 1991
 - 
Mar 1995
Bachelor's Course in Mathematics, Department of Science, School of Education, Waseda University
 

Committee Memberships

 
Sep 2010
 - 
Today
American Mathematical Society  Reviewer for Mathematical Reviews
 

Awards & Honors

 
Apr 2017
Teaching Award, Shibaura Institute of Technology
 

Published Papers

 
Shingo Takeuchi
arXiv preprint, arXiv:1904.01827, to appear in Differential Equations & Applications      2020   [Refereed]
Hiroyuki Kobayashi, Shingo Takeuchi
Communications on Pure and Applied Analysis   18(3) 1509-1521   May 2019   [Refereed]
Shingo Takeuchi
The Ramanujan Journal   46(6) 309-321   Jun 2018   [Refereed]
Toshiki Kamiya, Shingo Takeuchi
Journal of Classical Analysis   10(1) 15-25   Jan 2017   [Refereed]
Shingo Takeuchi
Journal of Mathematical Analysis and Applications   444(2) 1000-1014   Dec 2016   [Refereed]

Misc

 
Double-angle formulas of generalized trigonometric functions related to the trefoil
Shingo Takeuchi
in preparation      May 2019
Shota Sato, Shingo Takeuchi
arXiv preprint, arXiv:1904.09880      Apr 2019
Shingo Takeuchi
RIMS Kôkyûroku   2032 76-100   Jun 2017   [Invited]
Shingo Takeuchi
RIMS Kôkyûroku   1838 71-101   Jun 2013   [Invited]
Shingo Takeuchi
RIMS Kôkyûroku   1640 85-103   Apr 2009   [Invited]

Conference Activities & Talks

 
Integral formulas of generalized trigonometric functions with two parameters [Invited]
Hiroyuki Kobayashi, Shingo Takeuchi
The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications (AIMS2018), National Taiwan University, Taipei, Taiwan   7 Jul 2018   
Applications of generalized trigonometric functions to nonlocal boundary value problems [Invited]
Shingo Takeuchi
The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications (AIMS2018), National Taiwan University, Taipei, Taiwan   6 Jul 2018   
Generalization of the trigonometric functions
Shingo Takeuchi
The 2nd SIT-UOG workshop on pure/applied mathematics and computer science, Shibaura Institute of Technology, Saitama, Japan   9 Jun 2018   
Legendre's relation for incomplete elliptic integrals and its generalization [Invited]
Shingo Takeuchi
Workshop on Geometric Function Theory and Special Functions II, Tohoku University, Sendai, Japan   4 Aug 2017   
Arithmetic properties of eigenfunctions of the one-dimensional Tex-Laplacian [Invited]
Shingo Takeuchi
International Workshop on Nonlinear PDEs 2016 in Osaka, Osaka Prefecture University, Osaka, Japan   9 Dec 2016   

Research Grants & Projects

 
Study on eigenvalue problems of p-Laplacian and related elliptic integrals
JSPS: Grant-in-Aid for Scientific Research (C)
Project Year: Apr 2017 - Mar 2022    Investigator(s): Shingo Takeuchi
Free boundary problems of PDEs with degeneracy-singularity
JSPS: Grant-in-Aid for Scientific Research (C)
Project Year: Apr 2012 - Mar 2017    Investigator(s): Shingo Takeuchi
Free boundary problems of PDEs with degeneracy-singularity and their applications
JSPS: Grant-in-Aid for Young Scientists (B)
Project Year: Apr 2008 - Mar 2012    Investigator(s): Shingo Takeuchi
Dynamical systems theory of degenerate parabolic equations
JSPS: Grant-in-Aid for Young Scientists (B)
Project Year: Apr 2003 - Mar 2006    Investigator(s): Shingo Takeuchi
Dynamical systems theory of degenerate parabolic equations
JSPS: Grant-in-Aid for Young Scientists (B)
Project Year: Apr 2001 - Mar 2003    Investigator(s): Shingo Takeuchi