We study the effect of inflation on gaugino condensation in supergravity. Unless the Hubble scale H is significantly below the gaugino condensation scale, the gaugino condensate is a dynamical variable which cannot be integrated out. For a sufficiently high H, the gaugino condensate evolves to zero which in turn leads to dilaton/moduli destabilization. In practice, this often occurs at the Hubb...

We study the boundedness of the Hausdorff measure of the singular set of any solution for a semi-linear elliptic equation in general dimensional Euclidean space Rn. In our previous paper, we have clarified the structures of the nodal set and singular set of a solution for the semi-linear elliptic equation. In particular, we showed that the singular set is (n − 2)-rectifiable. In this paper, we ...

BACKGROUND AND OBJECTIVE Our previous histological studies indicated that near-infrared (NIR) irradiation stimulates collagen proliferation in rat and human skin for 3 months. High collagen density in the dermis and smoothing of the epidermis were observed in irradiated rat skin, and appeared to last up to 6 months. Epidermal smoothness in irradiated rat skin seems to resemble scarring. Here, w...

In this paper we propose a method for the estimation of time-varying autoregressive processes. The approach is essentially to regularize the heavily underdetermined unconstrained prediction equations with a smoothness priors type side constraint. The implementation of nonhomogenous smoothness properties is straightforward. The method is compared to the usual determistic regression approach (TVA...

In this paper severely ill-posed problems are studied which are represented in the form of linear operator equations with innnitely smoothing operators but with solutions having only a nite smoothness. It is well known, that the combination of Morozov's discrepancy principle and a nite dimensional version of the ordinary Tikhonov regularization is not always optimal because of its saturation pr...

In the present paper, we prove a global direct theorem for the modified Baskakov type operators in terms of so called DitzianTotik modulus of smoothness.

Density regression provides a flexible strategy for modeling the distribution of a response variable Y given predictors X = (X1, . . . ,Xp) by letting that the conditional density of Y given X as a completely unknown function and allowing its shape to change with the value of X. The number of predictors p may be very large, possibly much larger than the number of observations n, but the conditi...

This paper deals with estimation of the spectral density f(x) = |1− eix|−2df∗(x), of a stationary fractional Gaussian process, where −1/2 < d < 1/2 and f∗ is positive. The optimal rate of convergence of an estimate of f is shown not to depend on d but only on the smoothness of f∗, and thus is the same for a long range (d > 0) and a short range dependent (d = 0) process. When the Fourier coeffic...