We review the development trends and state-of-the-art technologies of large-port-count optical switches over the past decade. Practical implementation of optical switch fabrics is discussed in terms… (More)

X iv :0 80 3. 40 62 v1 [ nl in .C D ] 28 M ar 2 00 8 Ultradiscretization of solvable one-dimensional chaotic maps Kenji Kajiwara1, Atsushi Nobe2 and Teruhisa Tsuda1 1 Faculty of Mathematics, Kyushu… (More)

We present a solvable two-dimensional piecewise linear cha otic map which arises from the duplication map of a certain tropical cubic curve. Its gener al solution is constructed by means of the… (More)

We study theq-difference analogue of the sixth Painlev é equation ( q-PVI ) by means of tau functions associated with a ffine Weyl group of typeD5. We prove that a solution of q-PVI coincides with a… (More)

We prove that a certain sequence of tau functions of the Garnier system satisfies Toda equation. We construct a class of algebraic solutions of the system by the use of Toda equation; then show that… (More)

The universal character is a polynomial attached to a pair of partitions and is a generalization of the Schur polynomial. In this paper, we introduce an integ rable system ofq-difference lattice… (More)

Optical communication system is moving from WDM pipe to photonic network, where optical switching is requested as key functionality. This presentation reviews the current trend of photonic network,… (More)

The UC hierarchy is an extension of the KP hierarchy, which possesses not only an infinite set of positive time evolutions but also that of negative ones. Through a similarity reduction we derive… (More)

The universal character is a generalization of the Schur fun ctio attached to a pair of partitions. We study an integrable system of q-difference equations satisfied by the universal characters,… (More)