ON EXISTENCE， UNIQUENESS AND REGULARITY OF STEADY STATE SOLUTIONS TO THE BASIC SEMICONDUCTOR EQUATIONS

ＯＮＥＸＩＳＴＥＮＣＥ，ＵＮＩＱＵＥＮＥＳＳＡＮＤＲＥＧＵＬＡＲＩＴＹＯＦＳＴＥＡＤＹＳＴＡＴＥＳＯＬＵＴＩＯＮＳＴＯＴＨＥＢＡＳＩＣＳＥＭＩＣＯＮＤＵＣＴＯＲＥＱＵＡＴＩＯＮＳＷａｎｇＹｕａｎｍｉｎｇ（王元明）ＦａｎＪｉｓｈａｎ（樊继山）（Ｄｅｐｔ...     

Stability of weak solutions to equations of magnetohydrodynamics with Lebesgue initial data

We prove the existence, the uniqueness and the Lipschitz continuous dependence on the initial data of global weak solutions to equations of magnetohydrodynamics (MHD) with the initial data in the Lebesgue spaces.     

Local well‐posedness for the Cauchy problem of the MHD equations with mass diffusion

This paper studies the Cauchy problem of the MHD equations with mass diffusion. We use the Tikhonov fixed point theorem to prove a local‐in‐time well‐posedness theorem. Copyright © 2010 John Wiley & Sons, Ltd.     

Low Mach number limit of the compressible magnetohydrodynamic equations with zero thermal conductivity coefficient

The low Mach number limit for classical solutions of the compressible magnetohydrodynamic equations without thermal conductivity is, here, studied. A uniform existence result for the Cauchy problem in is proved under the assumption that the initial data are uniformly bounded with respect to the Mach number in and are well‐prepared in . Copyright © 2011 John Wiley & Sons, Ltd.     

Doubly and triply linked porphyrin-perylene monoimides as near IR dyes with large dipole moments and high photostability

Doubly and triply linked porphyrin-perylene monoimides 3 and 4, with extraordinary stability, large dipole moments, and strong near IR absorption, were prepared by means of one-pot oxidative cyclodehydrogenation promoted by FeCl(3).     

Regularity Criterion for a Nonhomogeneous Incompressible Ginzburg-Landau-Navier-Stokes System

Applications of Mathematics - We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in ?3. It is proved that if the...     

Random sampling-high dimensional model representation (RS-HDMR) and orthogonality of its different order component functions

High dimensional model representation is under active development as a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior based on a hierarchy of functions of increasing dimensions. The HDMR component functions are optimally constructed from zeroth order to higher orders step-by-step. This paper extends the definitions of HDMR component functions to systems whose input variables may not be independent. The orthogonality of the higher order terms with respect to the lower order ones guarantees the best improvement in accuracy for the higher order approximations. Therefore, the HDMR component functions are constructed to be mutually orthogonal. The RS-HDMR component functions are efficiently constructed from randomly sampled input-output data. The previous introduction of polynomial approximations for the component functions violates the strictly desirable orthogonality properties. In this paper, new orthonormal polynomial approximation formulas for the RS-HDMR component functions are presented that preserve the orthogonality property. An integrated exposure and dose model as well as ionospheric electron density determined from measured ionosonde data are used as test cases, which show that the new method has better accuracy than the prior one.     

A water-soluble hexa-peri-hexabenzocoronene: synthesis, self-assembly and role as template for porous silica with aligned nanochannels

A water-soluble hexa-peri-hexabenzocoronene was prepared and shown to undergo ordered columnar self-assembly either in water solution or bulk and therefore served as template for the fabrication of porous silica with aligned nanochannels.     

Hexa-peri-hexabenzocoronenes by efficient oxidative cyclodehydrogenation: the role of the oligophenylene precursors

[reaction: see text] Oligophenylene precursors based on 1,3,5-tris-(2'-biphenyl)ylbenzene (4a) and 1,4-bis-(2'-biphenyl)yl-2,5-diphenylbenzene (5a) were prepared and utilized for efficient hexabenzocoronene (HBC) synthesis by cyclodehydrogenations. Parent HBC 6a was efficiently synthesized from the 1,3,5-tris-(2'-biphenyl)ylbenzene precursor, and novel D(3)(h)() symmetrical HBCs were prepared from 1,3,5-tris-(2'-biphenyl)ylbenzenes with various substitution types. For the preparation of a tert-butyl containing HBC 7 with D(2)(h)() symmetry, a two-step cyclodehydrogenation was required because of changes in the spin density distribution.