Abstract. A magnetic pulse welding is a technology which joins two metal sheets with an electromagnetic force. In this paper, we have the numerical expression which describe the deformation. The numerical expression satis es the initial boundary value problem of the wave equation. From the solution of the wave equation, we investigate deformation phenomena of the metal sheet using numerical simulation. We put a graph of the deformation and have the moving velocity and collision angle of collision point.

Abstract. Sakajo and Yokoyama have shown that any streamline topology for a 2D Hamiltonian vector field is uniquely represented by a sequence of letters. Although a conversion algorithm has been provided conceptually in these papers, its real implementation is difficult, since we need to identify a component of streamline topologies visually. In this paper, we realize a new procedure implementable to the conversion algorithm on computers through Reeb graph representations of Hamiltonian functions and extraction of specific streamline topologies using persistent homology.

Abstract. This paper presents a new numerical algorithm for solving systems of nonlinear equations. The objective is to nd a solution near the initial approximate solution. In order to realize this, we apply an idea similar to Hirano's method for algebraic equations and Armijo's rule for nonlinear optimization. The effectiveness of the proposed method is demonstrated by numerical experiments on various systems of algebraic and nonlinear equations.