1,165 research outputs found
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.
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