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.

Integral formulas of generalized trigonometric functions with two parameters[Invited]

Hiroyuki Kobayashi, 〇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]

TAKEUCHI Shingo

Workshop on Geometric Function Theory and Special Functions II, Tohoku University, Sendai, Japan 4 Aug 2017

Arithmetic properties of eigenfunctions of the one-dimensional p-Laplacian[Invited]

TAKEUCHI Shingo

International Workshop on Nonlinear PDEs 2016 in Osaka, Osaka Prefecture University, Osaka, Japan 9 Dec 2016