Valley City State University assistant professor of mathematics, Dr. Takayuki Yamauchi, gave an invited talk at the Sixth International Conference on Dynamic Systems and Applications held in Atlanta, GA on May 27, 2011, hosted by International Federation of Nonlinear Analysts.
The conference was held from May 25 to May 28, 2011. His last invited presentation was at The Fifth World Congress of Nonlinear Analysts held in Orlando, FL, July 2008 (The World Congress of Nonlinear Analysts is the olympiad of nonlinear analysis that is held every four years in Olympic years).
Nonlinear analysis is a branch of mathematics for rigorously analyzing problems that arise in all branches of science including physics, chemistry, biology, medical science, computer science, earth science, electrical engineering, mechanical engineering, chemical engineering, civil engineering, biomedical engineering, material science, computer engineering, statistics, resource management, public health, business administration, and economics.
Dr. Yamauchi Presentation was titled "Regularity Properties of a State of Equilibrium of a Plasma Flow in a Nuclear Fusion Reactor." This presentation is a continuation of the paper published in the Dec. 2007 issue of The International Journal of Evolution Equations. The original problem was proposed in 1958 by three pioneers of nuclear fusion: physicists at Courant Institute of Mathematics at New York University. Mathematical analysis of the problem had been challenged unsuccessfully by many famous mathematicians around the world including 1994 Fields Medalist P.L. Lions. In the paper mentioned above, he obtained a sufficient condition under which a smooth equilibrium solution is obtained, which had been considered unattainable. Based on this result, he was invited to give a talk at The Fifth World Congress of Nonlinear Analysts in July 2008. At that time, however, no rigorous concept of smooth re-arrangement of a given smooth function was available. The concept of one kind of continuous re-arrangement of a given smooth function had been developed by F. Brock in 2000, but no concept of general continuous re-arrangement had been developed. Since Dec 2007, he developed a heuristic concept of not only continuous but also smooth (no zig-zag path or corner is allowed) re-arrangement. In this talk, he presented a heuristic idea of smooth re-arrangement of a given smooth function.
The full schedule of the conference is available HERE