双线性Fourier乘子交换子的有界性与紧性

假定T_σ是关于乘子σ的双线性Fourier乘子算子,其中σ满足如下Sobolev正则条件:对某个s∈(n,2n],有sup_(κ∈Z)‖σ_k‖W~s(R~(2m))∞.对于p_1,p_2,p∈(1,∞)且满足1/p=1/p_1+1/p_2和ω=(ω_1,ω_2)∈A_(p/t)(R~(2n)),建立了T_σ及其与函数b=(b_1,b_2)∈(BMO(R~n))~2生成的交换子T_(σ,b)由L~(p_1,λ)(ω_1)×L~(p_2,λ)(ω_2)到L~(p,λ)(v_w)的有界性;同时,在b_1,b_2∈CMO(R~n)(C_c~∞(R~n)在BMO拓扑下的闭包)的条件下,证明交换子T_(σ,b)是L~(p_1,λ)(ω_1)×L~(p_2,λ)(ω_2)到L~(p,λ)(v_w)的紧算子.为了得到主要结果,我们先后建立了几个双(次)线性极大函数在加多权Morrey空间上的有界性以及该空间中准紧集的判定.     

On the Ambrosetti‐Prodi problem for a system involving p‐Laplacian operator

In this work we study an Ambrosetti‐Prodi type problem for an elliptic system involving p‐Laplacian operator. The sub and supersolution method and the Leray‐Schauder Degree Theory are used in order to prove our result.     

A critical assessment of hidden markov model sub‐optimal sampling strategies applied to the generation of peptide 3D models

Hidden Markov Model derived structural alphabets are a probabilistic framework in which the complete conformational space of a peptidic chain is described in terms of probability distributions that can be sampled to identify conformations of largest probabilities. Here, we assess how three strategies to sample sub‐optimal conformations—Viterbi k‐best, forward backtrack and a taboo sampling approach—can lead to the efficient generation of peptide conformations. We show that the diversity of sampling is essential to compensate biases introduced in the estimates of the probabilities, and we find that only the forward backtrack and a taboo sampling strategies can efficiently generate native or near‐native models. Finally, we also find such approaches are as efficient as former protocols, while being one order of magnitude faster, opening the door to the large scale de novo modeling of peptides and mini‐proteins. © 2016 Wiley Periodicals, Inc.     

Influence of Heat Treatment Time on Cathode Material Cr8O21 for Lithium Battery北大核心CSCD

Chromium oxide (Cr8O21) cathode material for lithium batteries was synthesized by thermal decomposition of chromium trioxide (CrO3) at high temperature. The electrochemical properties of chromium oxide depended on the time and temperature during the heat treatment. Pure phase chromium oxide was prepared, and the effects of heat treatment time on the structures and electrochemical properties of Cr8O21 were systematically studied. The first discharge mechanism of chromium oxide in lithium batteries was explored, and the results were similar to that in lithium-sulfur batteries. The crystal phases and electrochemical properties of the prepared chromium oxide were analyzed by TGA, XRD, SEM, EDS, ICP, EIS techniques and constant current discharge measurement. The results show that heat treatment time had an important impact. Extending the heat treatment time was beneficial to improve the electrochemical properties of the material. The less the amount of residual CrO3, the better the electrochemical performance. The severe oxidation reaction between CrO3 and the electrolyte caused the electrode to be corroded. The material obtained in 48 h exhibited excellent performance, complete crystallization, good morphology, and low electrochemical impedance. At a constant discharge current of 0.05 mA, the specific capacity of the material reached 383.26 mAh窑g-1 with the specific energy of 1153.83 mWh窑g-1 and the average discharge voltage of 3.01 V. This study provides an effective way to prepare pure phase chromium oxide and proves its potential application in the field of lithium batteries. © 2021 Authors. All rights reserved.     

Modeling of Dark Solitons for Nonlinear Longitudinal Wave Equation in a Magneto-Electro-Elastic Circular Rod

In this paper, sub equation and expansion methods are proposed to construct exact solutions of a nonlinear longitudinal wave equation (LWE) in a magneto-electro-elastic circular rod. The proposed methods have been used to construct hyperbolic, rational, dark soliton and trigonometric solutions of the LWE in the magneto-electro-elastic circular rod. Arbitrary values are given to the parameters in the solutions obtained. 3D, 2D and contour graphs are presented with the help of a computer package program. Solutions attained by symbolic calculations revealed that these methods are effective, reliable and simple mathematical tool for finding solutions of nonlinear evolution equations arising in physics and nonlinear dynamics.     

H2气氛下褐煤快速热解过程中CH4逸出规律的分析

在带有输送煤样的管式反应器上进行了霍林河褐煤加压快速氢解实验,分析了H<sub>2sub>对煤/半焦的化学键断裂和对CH<sub>4sub>生成规律的影响。在加压快速氢解条件下,CH<sub>4sub>产率随着热解温度升高、压力的增大而增大;在50% H<sub>2sub>气氛下,操作压力为1.0 MPa、温度为900 ℃时,CH<sub>4sub>产率为8.08%,达到最大,较N<sub>2sub>气氛下的提高了72.5%。H<sub>2sub>或H·自由基诱发了芳环的开裂、侧链、脂肪链和醚键的断裂,促进了煤热解。CH<sub>4sub>产率的增加主要是由于外部供H的结果;热解温度低于700 ℃时,H<sub>2sub>对煤结构中活性基团的作用促进了煤热解,导致了CH<sub>4sub>产率的增加;而热解温度高于700 ℃后,煤/半焦加氢气化促进了CH<sub>4sub>产率的增加。     

基于图像处理的莫尔条纹测量的CCD亚像素标定

 Talbot-Moiré技术是目前长焦距测量研究的热点。利用Talbot-Moiré技术测量长焦距时,很多都需要测量莫尔条纹的宽度或斜率,而CCD的标定精度直接影响测量精度,因此需要对CCD精确标定。文中提出采用光栅作为系统的自基准进行标定,再用图像处理的方法标定CCD。为了检验该方法的精度,在MATLAB中生成一个标准条纹图案,用图像处理和灰度拟合对其进行亚像素定位。经过对标准条纹的标定,验证了采用该文的定位方法条纹中心定位误差小于0.1个像素。最后用光栅为自基准标定了CCD,并与量块的标定结果进行了对比,证明该文的标定方法不但简单可行,而且精度较高。     

Critical higher order Sturm–Liouville difference operators

We investigate the so-called critical 2nth-order Sturm–Liouville difference operators and associated symmetric banded matrices. We show that arbitrarily small (in a certain sense) negative perturbation of a non-negative critical operator leads to an operator which is no longer non-negative.     

不同前驱体相对摩尔量对气相爆燃制备纳米SiO2的影响

 以SiCl<sub>4sub>为前驱体,以空气和氢气的混合气体为爆源,通过改变前驱体的相对摩尔量,考察前驱体的相对摩尔量对产物的影响。通过X射线荧光谱（XRF）、透射电子显微镜（TEM）和X射线衍射（XRD）等测试手段对纳米SiO<sub>2sub>粉体进行表征及分析。通过XRF对产物进行成分分析,测得实验所得产物主要由SiO<sub>2sub>组成,且纯度达到99.9%以上;由XRD分析得知,生成的SiO<sub>2sub>产物属于典型的非晶态结构;由TEM图像可以看出,随着前驱体相对摩尔量的增加,所得到的产物粒子逐渐出现粘结,分散性下降,前驱体相对摩尔比应该控制在1.5以内。     

Stability of planar waves in the buffered bistable system

This paper is concerned with the asymptotic stability of planar waves in the buffered bistable system on , where n ≥ 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar waves as t → ∞ . The convergence is uniform in . Copyright © 2012 John Wiley & Sons, Ltd.