Abstract. A novel framework of generating iterative solvers for symmetric positive definite linear systems is proposed. In the framework, iterative solvers are generated by applying the discrete gradient method to initial value problems whose equilibrium coincides with the exact solution of the linear systems. The framework can generate potentially a large number of linear solvers with unconditional convergence property. As a simple example, we show that the framework includes the SOR method.

Abstract. The circulatory lane of a roundabout is divided into a finite number of cells and a difference equation is derived in order to descr ibe the time-evolution of the probability that each cell is occupied by a vehicle. The steady state solution of the equation proves stable under a mild condition. In addition, a roundabout under regular operation is shown to be sensitive to the irregular interruption in the case where the circulatory lane is crowded.

Abstract. Adams’ method of apportionment has burst into the spotlight in the recentelectoral reforms in Japan. The media tells that it can give the distribution of seats in a legislature, based proportionally on the population of electoral districts, in addition, reducing the disparity of one vote value. As a matter of fact, the method is not well known in our country. Under the Adams method, therefore, we allocate legislative seats in several countries, specifically, in Japan, France and Canada, and then we examine the results of seat allocations carefully.