Abstract:
Out of thermal equilibrium state, the vacuum is unstable and evolves in time. Consequently, the annihilation operators associated with the unstable vacuum depend on time. This dissipative time-evolution of quantum systems can be systematically treated, within the canonical operator formalism referred to as non-equilibrium thermo-field dynamics. Given is an alternative route to derive the time-dependent annihilation operators within the formalism. As an example, time-dependent annihilation operators for the systems of bosonic and fermionic semi-free fields are derived.

Abstract:
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first introduced, and next a new regularization scheme is presented. It is shown that the renormalization of an action functional in the generating functional leads to an anomalous diffusion exponent in full order of the perturbation series with respect to a nonlinearity.

Abstract:
The relation between the uniformizing equation of the complex hyperbolic structure on the moduli space of marked cubic surfaces and an Appell-Lauricella hypergeometric system in nine variables is clarified.

Abstract:
This paper is concerned with asymptotic theory for penalized spline estimator in bivariate additive model. The focus of this paper is put upon the penalized spline estimator obtained by the backfitting algorithm. The convergence of the algorithm as well as the uniqueness of its solution are shown. The asymptotic bias and variance of penalized spline estimator are derived by an efficient use of the asymptotic results for the penalized spline estimator in marginal univariate model. Asymptotic normality of estimator is also developed, by which an approximate confidence interval can be obtained. Some numerical experiments confirming theoretical results are provided.

Abstract:
. In the paper a nonlinear version of an identity known in the literature as the Picone's formula is derived and then it is used to extend the classical Sturmian comparison theory to forced superlinear equations of the second order.

Abstract:
The Greenhouse gases Observing SATellite (GOSAT) was launched on 23 January 2009 to monitor global distributions of carbon dioxide and methane. The Thermal And Near-infrared Sensor for carbon Observation-Fourier Transform Spectrometer (TANSO-FTS) onboard GOSAT measures the short-wavelength infrared (SWIR) spectra. Radiometric accuracy directly influences the accuracy of the retrieved greenhouse gas concentrations. From a 2.5-yr retrieval analysis of GOSAT data, we found that the minimum of the mean-squared value of the residuals (the difference between observed and fitted spectra) and the radiance adjustment factor (one of the ancillary parameters to be retrieved with the gas concentrations for adjusting the radiance level between the bands) changed with time, possibly due to inaccurate degradation correction. In this study, the radiometric degradation of TANSO-FTS was evaluated from the on-orbit solar calibration data and modeled as a function of time and wavenumber for each spectral band. The radiometric degradation of TANSO-FTS Band 1 (centered at 0.76 μm) after the launch was found to be about 4 to 6%, varying with wavenumber, whereas the other two bands (Band 2: 1.6 μm and Band 3: 2.0 μm) showed about 1% degradation and small wavenumber dependency. When we applied the new degradation model in the retrieval analysis, the above-mentioned issues disappeared.

Abstract:
The Greenhouse gases Observing SATellite (GOSAT) was launched on 23 January 2009 to monitor global distributions of carbon dioxide and methane. The Thermal And Near-infrared Sensor for carbon Observation-Fourier Transform Spectrometer (TANSO-FTS) onboard GOSAT measures short-wavelength infrared (SWIR) spectrum, and its radiometric accuracy directly influences the accuracy of the retrieved greenhouse gas concentrations. From a 2.5-yr retrieval analysis of GOSAT data, we found that the minimum of the mean-squared value of the residuals (the difference between observed and fitted spectra) and the radiance adjustment factor (one of the ancillary parameter to be retrieved with the gas concentrations for adjusting the radiance level between the bands) changed with time, possibly due to inaccurate degradation correction. In this study, the radiometric degradation of TANSO-FTS was evaluated from the on-orbit solar calibration data and modeled as a function of time and wavenumber for each spectral band. The radiometric degradation of TANSO-FTS Band 1 (centered at 0.76 μm) after the launch was evaluated to be about 4 to 6%, varying with wavenumber, whereas the other two bands (Band 2: 1.6 μm and Band 3: 2.0 μm) showed about 1% degradation and small wavenumber dependency. When we applied the new degradation model in the retrieval analysis, the above-mentioned issues disappeared.

Abstract:
Numerical simulations of two-dimensional granular flows under uniform shear and external body torque were performed in order to extract the constitutive equations for the system. The outcome of the numerical simulations is analyzed on the basis of the micropolar fluid model. Uniform mean shear field and mean spin field, which is not subordinate to the vorticity field, are realized in the simulations. The estimates of stresses based on kinetic theory by Lun [Lun, J. Fluid Mech., 1991, vol. 233, 539] are in good agreement with the simulation results for a low area fraction ν=0.1 but the agreement becomes weaker as the area fraction gets higher. However, the estimates in the kinetic theory can be fitted to the simulation results up to ν=0.7 by renormalizing the coefficient of roughness. For a relatively dense granular flow (ν=0.8), the simulation results are also compared with Kanatani's theory [Kanatani, Int. J. Eng. Sci., 1979, vol. 17, 419]. It is found that the dissipation function and its decomposition into the constitutive equations in Kanatani's theory are not consistent with the simulation results.