Abstract. Fireflies in Papua New Guinea, Pteroptyx effulgens, form a traveling wave pattern in their synchronous flashing. In this paper, we propose a novel model with pulse-coupled oscillators based on the flash-induced experiments by Hanson et al. The numerical analysis reveals that there exists a precise condition which fully characterizes the formation of the traveling waves. We prove that the condition is necessary and sufficient for the formation of the traveling waves from the initial states in a global synchronization.
Abstract. We consider 2-point boundary value problem (BVP) for 4-th order ordinary differential equation with Periodic, Dirichlet, Dirichlet-Neumann and Neumann boundary conditions. A solution of BVP represents bending of a beam on an elastic foundation under a tension. BVP has an unique solution which is described using Green function. As its application, we obtain the best constant of the corresponding Sobolev inequality is equal to the maximum of diagonal value of Green function. The engineering meaning of Sobolev inequality is that the maximum displacement of bending can be estimated by the constant multiple of its potential energy.
Abstract. Additional Tier1 (AT1) bond is a defaultable fixed income security with some pre-specified triggers for mandatory principal reduction. In this paper, we improve a structural AT1 bond pricing model so as to consider not only default but such principalreduction trigger events such as Point Of Non-Viability trigger” as well as accounting trigger under both complete and incomplete information. We use some market price data of AT 1 bonds issued in Japan and Europe to discuss practical usefulness of our proposed model.