Noncommutative Spectral Decomposition with Quasideterminant

We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative Cayley-Hamilton's theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it has noncommutative entries. As examples, the noncommutative spectral decomposition and the exponential matrices of a quaternionic matrix and of a matrix with entries being harmonic oscillators are given.Comment: 18 pages, no figure

Some Formulas for Invariant Phases of Unitary Matrices by Jarlskog

We describe calculations of Jarlskog's determinant in the case of n=3,4 in detail. Next, we investigate some formulas for invariant phases of unitary matrices and derive some explicit relations of them.Comment: 14pages, no figure

An Approximate Solution of the Jaynes-Cummings Model with Dissipation

In this paper we treat the Jaynes-Cummings model with dissipation and give an approximate solution to the master equation for the density operator {\bf under the general setting} by making use of the Zassenhaus expansion.Comment: Latex ; 18 pages ; no figure. This is a paper based on hard calculatio

Aging, Saving, and Public Pensions in Japan

We analyze the impact of population aging on Japan's household saving rate and on its public pension system and the impact of that system on Japan's household saving rate and obtain the following results: first, the age structure of Japan's population can explain the level of, and past and future trends in, its household saving rate; second, the rapid aging of Japan's population is causing Japan's household saving rate to decline and this decline can be expected to continue; third, the pay-as-you-go nature of the public pension system, combined with rapid population aging, created considerable intergenerational inequities and increased the saving rates of cohorts born after 1965, which in turn slowed the decline in Japan's household saving rate; and fourth, the 2004 public pension reform alleviated the intergenerational inequities of Japan's public pension system somewhat but will in the long run exacerbate the downward trend in Japan's household saving rate.

Aging, Saving, and Public Pensions in Japan

We analyze the impact of population aging on Japan's household saving rate and on its public pension system and the impact of that system on Japan's household saving rate and obtain the following results: first, the age structure of Japan's population can explain the level of, and past and future trends in, its household saving rate; second, the rapid aging of Japan's population is causing Japan's household saving rate to decline and this decline can be expected to continue; third, the pay-as-you-go nature of the public pension system, combined with rapid population aging, created considerable intergenerational inequities and increased the saving rates of cohorts born after 1965, which in turn slowed the decline in Japan's household saving rate; and fourth, the 2004 public pension reform alleviated the intergenerational inequities of Japan's public pension system somewhat but will in the long run exacerbate the downward trend in Japan's household saving rate.