Positive Definite Solutions of the Nonlinear Matrix Equation X+AHXˉ−1A=IX+A^{\mathrm{H}}\bar{X}^{-1}A=I

This paper is concerned with the positive definite solutions to the matrix equation $X+A^{\mathrm{H}}\bar{X}^{-1}A=I$ where $X$ is the unknown and $A$ is a given complex matrix. By introducing and studying a matrix operator on complex matrices, it is shown that the existence of positive definite solutions of this class of nonlinear matrix equations is equivalent to the existence of positive definite solutions of the nonlinear matrix equation $W+B^{\mathrm{T}}W^{-1}B=I$ which has been extensively studied in the literature, where $B$ is a real matrix and is uniquely determined by $A.$ It is also shown that if the considered nonlinear matrix equation has a positive definite solution, then it has the maximal and minimal solutions. Bounds of the positive definite solutions are also established in terms of matrix $A$. Finally some sufficient conditions and necessary conditions for the existence of positive definite solutions of the equations are also proposed

Atomistic Simulations of Flash Memory Materials Based on Chalcogenide Glasses

In this chapter, by using ab-initio molecular dynamics, we introduce the latest simulation results on two materials for flash memory devices: Ge2Sb2Te5 and Ge-Se-Cu-Ag. This chapter is a review of our previous work including some of our published figures and text in Cai et al. (2010) and Prasai & Drabold (2011) and also includes several new results.Comment: 24 pages, 20 figures. This is a chapter submitted for the book under the working title "Flash Memory" (to be published by Intech ISBN 978-953-307-272-2

ENANTIOSELECTIVE DEMETHYLATION: THE KEY TO THE NORNICOTINE ENANTIOMERIC COMPOSITION IN TOBACCO LEAF

Nicotine and nornicotine are the two main alkaloids that accumulate in Nicotiana tabacum L. (tobacco), and nornicotine is the N-demethylation metabolite of nicotine. Nicotine is synthesized in the root, and probably primarily in the root tip. Both nicotine and nornicotine exist as two isomers that differ from each other by the orientation of H atom at the C-2\u27 position on the pyrrolidine ring. (S)-nicotine is the dominant form in tobacco leaf and the enantiomer fraction of nicotine (EFnic), the fraction of (R)-enantiomer over the total nicotine, is approximately 0.002. Despite considerable efforts to elucidate nicotine and nornicotine related metabolism, a comprehensive understanding of the factors responsible for regulating the variable EF for nornicotine (0.04 to 0.75 ) relative to nicotine has been lacking. The objectives of these investigations were to understand the mechanisms behind the discrepancy. There are three nicotine demethylases reported to be active in tobacco. In vitro recombinant CYP82E4, CYP82E5v2 and CYP82E10 demethylated (R)-nicotine three, ten and ten-fold faster than (S)-nicotine, respectively, and no racemization was observed in either nicotine or nornicotine during demethylation. To confirm these in vitro results, the accumulation and demethylation of nicotine enantiomers throughout the growth cycle and curing process were investigated. Scion stock grafts were used to separate the contributions of roots (source) from leaves (sink) to the final accumulation of nicotine and nornicotine in leaf. The results indicate that nicotine consists of 4% of the R enantiomer (0.04 EFnic) when synthesized. However, (R)-nicotine is selectively demethylated by CYP82E4, CYP82E5 and CYP82E10, resulting in an approximate 0.01 EFnic and 0.60 EFnnic in the root. After most of (R)-nicotine is demethylated in root, nicotine and nornicotine are translocated to leaf, where nicotine is further demethylated. Depending on the CYP82E4 activity, an EFnnic of 0.04 to 0.60 is produced and only 0.2% of the remaining nicotine in the leaf is (R)-configuration