Multidimensional Dynamical Systems Accepting the Normal Shift

The dynamical systems of the form \ddot\bold r=\bold F (\bold r,\dot\bold r) in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force field \bold F(\bold r,\dot\bold r) of the dynamical systems with weak and complete normality are derived.Comment: AMS-TeX, ver. 2.1, IBM AT-386, size 16K (ASCII), short versio

Penalized flexible Bayesian quantile regression

Copyright © 2012 SciResThis article has been made available through the Brunel Open Access Publishing Fund.The selection of predictors plays a crucial role in building a multiple regression model. Indeed, the choice of a suitable subset of predictors can help to improve prediction accuracy and interpretation. In this paper, we propose a flexible Bayesian Lasso and adaptive Lasso quantile regression by introducing a hierarchical model framework approach to en- able exact inference and shrinkage of an unimportant coefficient to zero. The error distribution is assumed to be an infi- nite mixture of Gaussian densities. We have theoretically investigated and numerically compared our proposed methods with Flexible Bayesian quantile regression (FBQR), Lasso quantile regression (LQR) and quantile regression (QR) methods. Simulations and real data studies are conducted under different settings to assess the performance of the pro- posed methods. The proposed methods perform well in comparison to the other methods in terms of median mean squared error, mean and variance of the absolute correlation criterions. We believe that the proposed methods are useful practically

Solitons on a finite-gap background in Bullough-Dodd-Jiber-Shabat model

The determinant formula for N-soliton solutions of the Bullough-Dodd-Jiber-Shabat equation on a finite-gap background is obtained. Nonsingularity conditions for them and their asymptotics are investigated.Comment: AmSTeX, 7 pages, amsppt style, 1 figur

Instability of some divalent rare earth ions and photochromic effect

It was shown that the divalent rare earth ions (La, Ce, Gd, Tb, Lu, and Y) in cubic sites in alkaline earth fluorides are unstable with respect to electron autodetachment since its d1(eg) ground state is located in the conduction band which is consistent with the general tendency of these ions in various compounds. The localization of doubly degenerate d1(eg) level in the conduction band creates a configuration instability around the divalent rare earth ion that leading to the formation of anion vacancy in the nearest neighborhood, as was reported in the previous paper [Journal of Physics and Chemistry of Solids 74 (2013) 530-534]. Thus, the formation of the stable divalent ions as La, Ce, Gd, Tb, Lu, and Y (PC+ centers) in CaF2 and SrF2 crystals during x-ray irradiation occurs via the formation of charged anion vacancies near divalent ions (Re2+va), which lower the ground state of the divalent ion relative to the conductivity band. Photochromic effect occurs under thermally or optically stimulated electron transition from the divalent rare earth ion to the neighboring anion vacancy and reverse under ultraviolet light irradiation.Comment: 22 pages, 9 figure