Abstract. The matrix sign function is a matrix function that can be used to solve the Sylvester equation, and algorithms such as the Schur method and the Newton method have been considered as numerical methods for it. In this paper, we propose a method to compute matrix sign functions numerically with Double Exponential (DE) formula, and evaluate its performance theoretically. The proposed method can be applied to large matrices which are difficult to compute by conventional methods by using parallel computation.

Abstract. We extend Odagaki’s SIQR model to simulate or predict the time evolution of successive epidemic waves of the COVID-19. In order to investigate the time evolution of the epidemic wave after the 3rd wave in Japan, we perform simulation of the epidemic spread in primary cities using our model. Additionally, we extend our model to include the effects of the vaccination. Finally, we evaluate the effects of the vaccination on the basis of data in UK, which starts vaccinations, and investigate the effects of the vaccination, quantitatively.

Abstract. This paper proposes new design and manufacturing methods of the oblique honeycomb cores by using the origami production techniques. The oblique honeycombs have inclined hexagonal-prism cells and cause various visual effects including change in transparency depending to the view angle and multiple shadows. It is possible to develop attractive translucent building materials with various visual effects without impairing the excellent mechanical properties of the honeycomb cores. We developed a prototype of a new transparent panel by combining highly transparent film, and verified special visual effects such as the blind effect that changes depending on the viewing angle.

Abstract. The max-plus algebra is a semiring with addition “max” and multiplication “+”. The study of the max-plus algebra originated from manufacturing and has been developed independently in various elds of theory and application. In the present paper, we focus on the eigenvalue problem over the max-plus algebra and explain the fundamental facts including computational algorithms. We also introduce recent theoretical developments in the eigenvalue problem. Further, we describe applications of the eigenvalue problem to discrete event systems and integrable systems.