We study central hyperplane arrangements with integral coefficients modulo positive integers q. We prove that the cardinality of the complement of the hyperplanes is a quasi-polynomial in two ways,… (More)

A response in movement of a two-layered water body in Lake Nakaumi to a strong wind, which suddenly rose and continued for 15 h with nearly constant speed and direction, was observed using the… (More)

Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. We generalize elliptically contoured… (More)

An active filter (AF) is required to have a high current control capability of tracking a time-varying current reference. However, a steady-state current error always exists because the current… (More)

Let q be a positive integer. In [8], we proved that the cardinality of the complement of an integral arrangement, after the modulo q reduction, is a quasi-polynomial of q, which we call the… (More)

An integral coefficient matrix determines an integral arrangement of hyperplanes in Rm. After modulo q reduction (q ∈ Z>0), the same matrix determines an arrangement Aq of “hyperplanes” in Zq . In… (More)

For an irreducible root system R, consider a coefficient matrix S of the positive roots with respect to the associated simple roots. Then S defines an arrangement of “hyperplanes” modulo a positive… (More)

We consider the same problem as in Kamiya and Takemura (1997), but for discriminant analysis on (n−1) -dimensional unit sphere Sn−1. That is, we regard pairwise discriminant analysis of m populations… (More)

We study properties of global cross sections and characterize the class of all global cross sections. Then generalizing the cross-sectionally contoured distributions of Takemura and Kuriki (1996), we… (More)

We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of… (More)