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Multiplicity of solutions for the semilinear subelliptic Dirichlet problem

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Science China Mathematics 2024年第3期67卷 475-504页

作者： Hua Chen Hong-Ge Chen Jin-Ning Li Xin liao School of Mathematics and Statistics Wuhan UniversityWuhan 430072China Wuhan Institute of Physics and Mathematics Innovation Academy for Precision Measurement Science and TechnologyChinese Academy of SciencesWuhan 430071China

In this paper,we study the semilinear subelliptic equation{−△Xu=f(x,u)+g(x,u)inΩ,u=0 on∂Ω,where△X=−∑m i=1 Xi∗Xi is the self-adjoint Hormander operator associated with the vector fields X=(X_(1),X_(2),...,X_(m))satisfying the Hormander's condition,f(x,u)∈C(Ω×R),g(x,u)is a Carathéodory function onΩ×R,andΩis an open bounded domain in R~n with smooth *** the perturbation from the symmetry method with the approaches involving the eigenvalue estimate and the Morse index in estimating the minimax values,we obtain two kinds of existence results for multiple weak solutions to the problem ***,we discuss the difference between the eigenvalue estimate approach and the Morse index approach in degenerate *** with the classical elliptic cases,both approaches here have their own strengths in the degenerate *** new phenomenon implies that the results in general degenerate cases would be quite different from the situations in classical elliptic cases.

关键词： degenerate elliptic equations Hormander operators perturbation method Morse index

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Applications of M/N/C analogue catalysts in PEM fuel cells and metal-air/oxygen batteries: Status quo, challenges and perspectives

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Progress in Natural Science:Materials International 2020年第6期30卷 807-814页

作者： Bin Chi Xiaorong Zhang Mingrui Liu Shijie Jiang Shijun liao The Key Laboratory of Fuel Cell Technology of Guangdong Province & The Key Laboratory of New Energy Technology of Guangdong Universities School of Chemistry and Chemical Engineering South China University of Technology

To meet the sharp increase in demand for clean and renewable energy, it is necessary to develop new energyconversion and storage technologies, such as proton exchange membrane fuel cells(PEMFCs) and metal-air/oxygen batteries(MABs). Due to the sluggish reaction kinetics of the oxygen reduction reaction(ORR) and the oxygen evolution reaction(OER) in the cathodes of PEMFCs and MABs, significant amounts of precious metal catalysts need to be used, driving up the cost of fuel cells and MABs and thereby hindering their commercialization on a large scale. Transition metal and nitrogen co-doped carbonaceous catalysts(M/N/C) have high catalytic activity towards the ORR and OER once the catalysts are modified with certain promoters/additives. In addition, M/N/C catalysts can be prepared from abundant, inexpensive materials, making their cost negligible compared with precious metal catalysts, a development that would efficiently decrease the cost of PEMFCs and MABs. In last decade, numerous researchers have attempted to realize these applications of M/N/C catalysts, and some exciting results have been achieved, making these promising replacements for precious metal ***, some serious problems and significant challenges remain. In this paper, we review the research on the application of M/N/C analogue catalysts in PEMFCs and MABs in the last 10 years, indicate the remaining challenges, and suggest the future research directions.

关键词： PEM fuel cell MABs M/N/C catalysts Oxygen reaction

Temporal alterations in pericytes at the acute phase of ischemia/reperfusion in the mouse brain

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Neural Regeneration Research 2022年第10期17卷 2247-2252页

作者： Shuang Zhang Xue-Jing liao Jia Wang Yi Shen Han-Fen Shi Yan Zou Chong-Yang Ma Xue-Qian Wang Qing-Guo Wang Xu Wang Ming-Yang Xu Fa-feng Cheng Wan-Zhu Bai Beijing Key Laboratory School of Basic Medical SciencesBeijing University of Chinese MedicineBeijingChina Institute of Acupuncture and Moxibustion China Academy of Chinese Medical SciencesBeijingChina Shineway Pharmaceutical Group Ltd. ShijiazhuangHebei ProvinceChina School of Traditional Chinese Medicine Capital Medical UniversityBeijingChina

Pericytes,as the mural cells surrounding the microvasculature,play a critical role in the regulation of microcirculation;however,how these cells respond to ischemic stroke remains *** determine the temporal alterations in pericytes after ischemia/reperfusion,we used the 1-hour middle cerebral artery occlusion model,which was examined at 2,12,and 24 hours after *** results showed that in the reperfused regions,the cerebral blood flow decreased and the infarct volume increased with ***,the pericytes in the infarct regions contracted and acted on the vascular endothelial cells within 24 hours after *** effects may result in incomplete microcirculation reperfusion and a gradual worsening trend with time in the acute *** findings provide strong evidence for explaining the“no-reflow”phenomenon that occurs after recanalization in clinical practice.

关键词： acute ischemic stroke alpha-smooth muscle cerebral blood flow microcirculation no-reflow phenomenon pericytes platelet endothelial cell adhesion molecule-1 platelet-derived growth factor receptor beta vascular endothelial cells

基于Bayes准则的STAP协方差矩阵估计算法

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西安电子科技大学学报 2008年第2期35卷 223-227页

作者：刘聪锋廖桂生西安电子科技大学雷达信号处理重点实验室陕西西安710071

针对杂波功率随距离缓变的非均匀环境,提出了一种新的基于Bayes准则的加权最大似然估计(WMLE)算法,以改善空时自适应处理(STAP)中的协方差矩阵估计.通过对训练数据进行事件定义,利用Bayes准则给出了加权系数的准确计算方法,解决了WMLE... 详细信息

针对杂波功率随距离缓变的非均匀环境,提出了一种新的基于Bayes准则的加权最大似然估计(WMLE)算法,以改善空时自适应处理(STAP)中的协方差矩阵估计.通过对训练数据进行事件定义,利用Bayes准则给出了加权系数的准确计算方法,解决了WMLE中加权系数的求解难题.仿真分析验证了所提出算法的正确性和有效性.

关键词：空时自适应处理非均匀环境协方差矩阵估计数据加权 Bayes准则

Estimation of Lateral Correlation Length: a stochastic approach for deep reflection seismic interpretation

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Estimation of Lateral Correlation Length: a stochastic appro...

Analysis of maximum traffic intensity for guaranteed handover and channel complete sharing scheme under pre-set QoS requirements in LEO-MSS

2020年中国地球科学联合学术年会

作者： yong Fan feng Jie Institute of Geophysical and Geochemical Exploration China University of Geosciences in Beijing

1. Introduction The fractal nature of crustal seismic velocity heterogeneity makes the interpretation of deep seismic reflection data difficult by conventional methods developed in shallow sedimentary. Statistical approaches were thought to be a valuable powerful tool for interpretation. Crustal exposures and deep borehole well log indicate that some stochastic models could be used to describe the heterogeneity of crustal rocks (Goff and Levander 1996, Holliger and Levander 1992, Leary 1991).

关键词： Estimation of Lateral Correlation Length a stochastic approach for deep reflection seismic interpretation

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The Journal of China Universities of Posts and Telecommunications 2015年第4期22卷 56-65页

作者： liao Mingxia Liu Yuan'an Yuan Dongming Hu Heifei Ran Jing School of Electronic Engineering Beijing University of Posts and Telecommunications

The maximum traffic intensity supported by a low earth orbit（LEO） mobile satellite system（MSS）（LEO-MSS） is important in practical application for providing satisfactory service. An analytical approach is proposed for determining the maximum traffic intensity of guaranteed handover（GH） scheme and channel complete sharing（CCS） scheme in LEO-MSS under quality of service（Qo S） constraints. By evaluating performance of these two schemes, the relationship between the traffic intensity and the Qo S constraints is established. The expressions of maximum traffic intensity of GH scheme and CCS scheme are deduced. Compared with the traditional method, the proposed analytical approach is more computationally efficient owing to the needlessness of the repeated iteration calculation. It also avoids the complex choice of the initial value of new call traffic intensity and its increment. Lastly, the accuracy and validity of the analysis approach have been verified by computer simulations.

关键词： LEO-MSS maximum traffic intensity QoS guaranteed handover channel complete sharing

A comparative study using state-of-the-art electronic structure theories on solid hydrogen phases under high pressures

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npj Computational Materials 2019年第1期5卷 172-177页

作者： Ke liao Xin-Zheng Li Ali Alavi Andreas Grüneis Max Planck Institute for Solid State Research Heisenbergstrasse 170569 StuttgartGermany School of Physics State Key Laboratory for Artificial Microstructure and Mesoscopic PhysicsPeking University100871 BeijingP.R.China Collaborative Innovation Centre of Quantum Matter Peking University100871 BeijingP.R.China Department of Chemistry University of CambridgeLensfield RoadCambridge CB21EWUK Institute for Theoretical Physics Vienna University of TechnologyWiedner Hauptstrasse 8-101040 ViennaAustria

Identifying the atomic structure and properties of solid hydrogen under high pressures is a long-standing problem of high-pressure physics with far-reaching significance in planetary and materials *** the pressure-temperature phase diagram of hydrogen is challenging for experiment and theory due to the extreme conditions and the required accuracy in the quantum mechanical treatment of the constituent electrons and nuclei,***,we demonstrate explicitly that coupled cluster theory can serve as a computationally efficient theoretical tool to predict solid hydrogen phases with high *** present a first principles study of solid hydrogen phases at pressures ranging from 100 to 450 *** computed static lattice enthalpies are compared to state-of-the-art diffusion Monte Carlo results and density functional theory *** coupled cluster theory results for the most stable phases including C2/c-24 and P2_(1)/c-24 are in good agreement with those obtained using diffusion Monte Carlo,with the exception of Cmca-4,which is predicted to be significantly less *** discuss the scope of the employed methods and how they can contribute as efficient and complementary theoretical tools to solve the long-standing puzzle of understanding solid hydrogen phases at high pressures.

关键词： solid high structure

Production of titanium powder by metallothermic reduction of TiO2 in cold pressed pellets

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Journal of Central South University 2021年第1期28卷 48-57页

作者： ZHENG Hai-yan GUO yong-chun SHEN feng-man Key Laboratory for Ecological Metallurgy of Multimetallic Mineral(Ministry of Education) Northeastern UniversityShenyang 110819China School of Metallurgy Northeastern UniversityShenyang 110819China

In order to produce low-cost titanium(Ti)with high productivity,fundamental studies on producing metallic Ti from titanium dioxide(TiO2)in the cold pressed pellets were conducted by metallothermic reduction with an indirect contact *** paper focuses on discussing the mechanism of the reduction process and the relationships of RM(a revised reduction index)with reduction temperature,reduction time,and mole ratio of TiO2 to CaCl2(nTiO2/nCaCl2)in the *** results show that metallic Ti was obtained from the reduction of TiO2 in the pellets by calcium(Ca)vapor;pellets were reduced homogenously and Ca vapor diffused into the porous pellets by Knudsen diffusion or the mixing diffusion of molecular diffusion and Knudsen diffusion at 1273 K;RM increased with the increases of temperature and reduction time and was 96.34%when TRedu=1273 K,tRedu=6 h,and nTiO2/nCaCl2=4;the reasonable nTiO2/nCaCl2 value is 3−5 for the pellets with enough strength and high RM.

关键词： titanium dioxide titanium powder metellothermic reduction cold pressed pellet reduction index

Dynamic consequences of mutating the typical HPGG motif of apocytochrome b_5 revealed by computer simulation

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Chinese Chemical Letters 2009年第5期20卷 631-634页

作者： Ying Wu Lin Tian Lei Ying Li Fu liao School of Chemistry and Chemical Engineering University of South China Hengyang 421001 China Department of Chemistry University of Illinois at Urbana-Champaign Urbana IL 61801 USA Chemical Biology Lab Department of Chemistry Fudan University Shanghai 200433 China

Apocytochrome b5 with a typical heme-binding motif of HPGG, and its variants with mutated motifs, GPGG, GPGH, HVGG, and HPGP, have been subjected to molecular dynamics simulation. Comparison of the dynamic consequences has revealed the crucial role of HPGG in assembling the heine group of cytochrome b5 and in modulating protein structure, property and function.

关键词： Apocytochrome b5 Heme-binding motif HPGG Molecular dynamics simulation