We demonstrate the close relationship between Chern-Simons gauge theory with gauge group Osp(1|2) and N = 1 induced supergravity in two dimensions. More precisely, the inner product of the physicalâ€¦ (More)

Employing profits data of Japanese companies in 2002 and 2003, we identify the non-Gibrat's law which holds in the middle profits region. From the law of detailed balance in all regions, Gibrat's lawâ€¦ (More)

The wave function of the universe is evaluated by using the Euclidean path integral approach. As is well known, the real Euclidean path integral diverges because the Einstein-Hilbert action is notâ€¦ (More)

Employing data on the assessed value of land in 1983 â€“ 2005 Japan, we investigate the dynamical behavior in the high scale region of non-equilibrium systems. From the detailed quasi-balance andâ€¦ (More)

We report the proof that the extension of Gibratâ€™s law in the middle scale region is unique and the probability distribution function (pdf) is also uniquely derived from the extended Gibratâ€™s law andâ€¦ (More)

We propose a new method for estimating the power-law exponent of a firm size variable, such as annual sales. Our focus is on how to empirically identify a range in which a firm size variable followsâ€¦ (More)

We study distributions which have both fractal and non-fractal scale regions by introducing a typical scale into a scale invariant system. As one of models in which distributions follow power law inâ€¦ (More)

In order to describe fractal and non-fractal distributions in a unified framework analytically , we introduce 2-dimensional quantum gravity with R 2 term. This model is obtained by adding anâ€¦ (More)

We study disk amplitudes whose boundaries have heterogeneous matter states in a system of (4, 5) conformal matter coupled to 2-dim gravity. They are analysed by using the 3-matrix chain model in theâ€¦ (More)

In order to understand characteristics common to distributions which have both fractal and non-fractal scale regions in a unified framework, we introduce a concept of typical scale. We employ a modelâ€¦ (More)