A priori bounds and multiplicity for fully nonlinear equations with quadratic growth in the gradient

We consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient, such as

$?F(x,u,Du,D^{2}u)=\lambda c(x)u+〈M(x)Du,Du〉+h(x)$

in a bounded domain with a Dirichlet boundary condition; here $\lambda \in \mathbb{R}$, $c,h\in L^p(\mathrm{\Omega })$, $p>n\ge 1$, $c?0$ and the matrix M satisfies $0<{\mu }_{1}I\le M\le {\mu }_{2}I$. Recently this problem was studied in the “coercive” case $\lambda c\le 0$, where uniqueness of solutions can be expected; and it was conjectured that the solution set is more complex for noncoercive equations. This conjecture was verified in 2015 by Arcoya, de Coster, Jeanjean and Tanaka for equations in divergence form, by exploiting the integral formulation of the problem. Here we show that similar phenomena occur for general, even fully nonlinear, equations in nondivergence form. We use different techniques based on the maximum principle.We develop a new method to obtain the crucial uniform a priori bounds, which permit to us to use degree theory. This method is based on basic regularity estimates such as half-Harnack inequalities, and on a Vázquez type strong maximum principle for our kind of equations.     

CoFe2O4/CuO活化过氧乙酸高效降解磺胺甲恶唑(英文)

利用化学沉淀法和溶胶凝胶法,通过两步法成功制备出含有尖晶石钴铁氧体和氧化铜的复合催化剂CoFe₂O₄/CuO,通过扫描电子显微镜(SEM)、X射线光电子能谱(XPS)和X射线衍射(XRD)对制备出的CoFe₂O₄/CuO进行表征,探究不同高级氧化体系对磺胺甲恶唑(SMX)去除能力,考察过氧乙酸(PAA)浓度、催化剂投加量、水体中常见干扰物质(Cl^-,HCO-3,SO₄^2-,HA)和不同自由基捕获剂对SMX去除的影响。分析结果表明CoFe₂O₄/CuO同时具有CoFe₂O₄与CuO的特征,对比单独CoFe₂O₄与CuO,CoFe₂O₄/CuO对PAA展现出极高的活化性能,在最佳反应条件下(催化剂投加量=20mg·L^-1,c(PAA)=200μ...     

Anisotropy resolved multidimensional emission spectroscopy (ARMES): A new tool for protein analysis

Structural analysis of proteins using the emission of intrinsic fluorophores is complicated by spectral overlap. Anisotropy resolved multidimensional emission spectroscopy (ARMES) overcame the overlap problem by the use of anisotropy, with chemometric analysis, to better resolve emission from different fluorophores. Total synchronous fluorescence scan (TSFS) provided information about all the fluorophores that contributed to emission while anisotropy provided information about the environment of each fluorophore. Here the utility of ARMES was demonstrated via study of the chemical and thermal denaturation of human serum albumin (HSA).     

Performance monitoring of a mammalian cell based bioprocess using Raman spectroscopy

Being able to predict the final product yield at all stages in long-running, industrial, mammalian cell culture processes is vital for both operational efficiency, process consistency, and the implementation of quality by design (QbD) practices. Here we used Raman spectroscopy to monitor (in terms of glycoprotein yield prediction) a fed-batch fermentation from start to finish. Raman data were collected from 12 different time points in a Chinese hamster ovary (CHO) based manufacturing process and across 37 separate production runs. The samples comprised of clarified bioprocess broths extracted from the CHO cell based process with varying amounts of fresh and spent cell culture media. Competitive adaptive reweighted sampling (CoAdReS) and ant colony optimization (ACO) variable selection methods were used to enhance the predictive ability of the chemometric models by removing unnecessary spectral information. Using CoAdReS accurate prediction models (relative error of predictions between 2.1% and 3.3%) were built for the final glycoprotein yield at every stage of the bioprocess from small scale up to the final 5000 L bioreactor. This result reinforces our previous studies which indicate that media quality is one of the most significant factors determining the efficiency of industrial CHO-cell processes. This Raman based approach could thus be used to manage production in terms of selecting which small scale batches are progressed to large-scale manufacture, thus improving process efficiency significantly.     

Principal eigenvalues and the Dirichlet problem for fully nonlinear elliptic operators

We study uniformly elliptic fully nonlinear equations of the type F(D²u,Du,u,x)=f(x). We show that convex positively 1-homogeneous operators possess two principal eigenvalues and eigenfunctions, and study these objects; we obtain existence and uniqueness results for nonproper operators whose principal eigenvalues (in some cases, only one of them) are positive; finally, we obtain an existence result for nonproper Isaac's equations.     

光谱相关色谱及其在中药色谱指纹图谱分析中的应用

基于相同的化学物质具有相同的光谱，在大多数情况下，同一样本的化学成分在同种类型的色谱柱上虽然保留时间不可能完全相同，但是洗脱的顺序应基本一致，提出光谱相关色谱的新概念。利用联用色谱的光谱信息与色谱信息，判断复杂中药色谱指纹图谱中的组分相关性和表征不同实验条件下所得的中药色谱指纹图谱，从而实现仪器的系统误差的化学计量学校准。