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Classification of Positive Solutions to a Divergent Equation on the Upper Half Space

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Acta Mathematica Sinica,English Series 2022年第3期38卷 499-509页

作者： Jin Ge YAO jing Bo dou School of Mathematics and Statistics Shaanxi Normal UniversityXi’an710119P.R.China

In this paper we classify the positive solutions of the divergent equation with Neumann boundary on the upper half space{-div(t^(α)∇u)=t^(β)f(u),(y,t)∈R^(n+1)_(+),lim t→0^(+)t^(α)■u/■t=0 by the method of moving spheres and Kelvin transformations,where n≥1,α>0,β>−1,n−1/n+1β≤α<β+2,and f:(0,∞)→(0,∞)is non-negative continuous function satisfying some *** equation arises from a weighed Sobolev inequality involving divergent operator div(t^(α)∇u)on the upper half space.

关键词： Divergent operator Liouville theorem Neumann boundary method of moving spheres Kelvin transformation

Improved Hardy–Littlewood–Sobolev Inequality on S^(n)under Constraints

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Acta Mathematica Sinica,English Series 2023年第11期39卷 2149-2163页

作者： Yun Yun HU jing Bo dou School of Mathematics and Statistics Shaanxi Normal UniversityXi’an 710119P.R.China

In this paper,we establish an improved Hardy–Littlewood–Sobolev inequality on Snunder higher-order moments ***,by constructing precise test functions,using improved Hardy–Littlewood–Sobolev inequality on S^(n),we show such inequality is almost optimal in critical *** an application,we give a simpler proof of the existence of the maximizer for conformal Hardy–Littlewood–Sobolev inequality.

关键词： Hardy–Littlewood–Sobolev inequality higher-order moments constraint concentration compactness principle almost optimal

Liouville Type Theorems for a System of Integral Equations on Upper Half Space

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Acta Mathematica Sinica,English Series 2014年第2期30卷 261-276页

作者： Su Fang TANG jing Bo dou School of Statistics Xi’an University of Finance and Economics

In this paper,we consider the following system of integral equations on upper half space {u（x） = ∫Rn ＋（1/｜x-y｜n-α-1/｜-y｜n-α） λ1up1（y）＋ μ1vp2（y）＋ β1up3（y）vp4（y） dy;v（x） = ∫Rn ＋（1/｜x-y｜n-α-1/｜-y｜n-α）（λ2uq1（y）＋ μ2vq2（y）＋ β2uq3（y）vq4（y） dy,where Rn ＋ = {x =（x1,x2,...,xn） ∈ Rn｜xn〉 0}, =（x1,x2,...,xn-1,-xn） is the reflection of the point x about the hyperplane xn= 0,0 〈 α 〈 n,λi,μi,βi≥ 0（i = 1,2） are constants,pi≥ 0 and qi≥ 0（i = 1,2,3,4）.We prove the nonexistence of positive solutions to the above system with critical and subcritical exponents via moving sphere method.

关键词： System of integral equations Liouville type theorem moving spheres method regularity

Highly permeable reverse osmosis membranes incorporated with hydrophilic polymers of intrinsic microporosity via interfacial polymerization

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Chinese Journal of Chemical Engineering 2022年第5期35卷 194-202页

作者： jing dou Shuo Han Saisai Lin Zhikan Yao Lian Hou Lin Zhang Engineering Research Center of Membrane and Water Treatment of MOE College of Chemical&Biological EngineeringZhejiang UniversityHangzhou 310027China Research Institute of Ningbo Zhejiang UniversityNingbo 315100China Xi’an High-Tech Institute Xi’an 710025China

Enhancing the water permeation while maintaining high salt rejection of existing reverse osmosis(RO)membranes remains a considerable ***,we proposed to introduce polymer of intrinsic microporosity,PIM-1,into the selective layer of reverse osmosis membranes to break the trade-off effect between permeability and selectivity.A water-soluble a-LPIM-1 of low-molecular-weight and hydroxyl terminals was *** designed characteristics endowed it with high solubility and *** it was mixed with m-phenylenediamine and together served as aqueous monomer to react with organic monomer of trimesoyl chloride via interfacial *** characterization results exhibited that more“nodule”rather than“leaf”structure formed on RO membrane surface,which indicated that the introduction of the high free-volume of a-LPIM-1 with three dimensional twisted and folded structure into the selective layer effectively caused the frustrated packing between polymer *** virtue of this effect,even with reduced surface roughness and unchanged layer thickness,the water permeability of prepared reverse osmosis membranes increased 2.1 times to 62.8 L·m^(-2)·h^(-1) with acceptable Na Cl rejection of 97.6%.This attempt developed a new strategy to break the trade-off effect faced by traditional polyamide reverse osmosis membranes.

关键词： PIM-1 Intrinsic microporosity Reverse osmosis Interfacial polymerization Trade-off

New C(21) steroidal glycoside from Cynanchum paniculatum

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Chinese Chemical Letters 2007年第3期18卷 300-302页

作者： jing dou Ping Li Zhi Ming Bi Jian Liang Zhou Ministry of Education Key Laboratory of Modern Chinese Medicines Department of Pharmacognosy China Pharmaceutical University Nanjing 210038 China

A new C21 steroidal glycoside, neocynapanogenin F 3-O-β-D-thevetoside 1, as well as its known aglycone neocynapanogenin F 2, which have an aberrant 13, 14：14, 15-disecopregnane-type skeleton were isolated from the root of Cynanchum paniculatum. Their structures were elucidated on the basis of spectroscopic data analysis. These compounds showed certain cytotoxic activities in vitro.

关键词： Neocynapanogenin F 3-O-β-D-thevetoside Neocynapanogenin F Cynanchum paniculatum

Crystal Form Transition during Heating of Solvent-induced Crystalline Syndiotactic Polystyrene

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Chinese Chemical Letters 2000年第10期11卷 931-932页

作者： Cheng Shen ZHU Hong jing dou Su Qin HE Zhi Shen MO Material Engineering Department Zhengzhou UniversityZhengzhou 450052 Changchun Institute of Applied Chemistry Chinese Academy of SciencesChangchun 130022

The phase transition of two kinds of solvent-induced crystalline syndiotactic polystyrene (sPS). gamma-sPS and delta(c)-sPS, has been studied via WAXD and DSC. gamma-sPS transform to a-sPS at 195-225 degrees C before melt during heating, whereas delta(e)-sPS transform to first gamma-sPS and then a-sPS at 100-200 degrees C and 200-215 degrees C, respectively. The transition of delta(e)-gamma and gamma-a occurs for below melting point of sPS indicates they are all solid-solid transition.

关键词： crystal form transition gamma-sPS delta(e)-sPS alpha-sPS

Modification of Mn on corrosion and mechanical behavior of biodegradable Mg(88)Y4Zn2Li5 alloy with long-period stacking ordered structure

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Journal of Materials Science & Technology 2020年第7期42卷 130-142页

作者： Jiaxin Zhang Jinshan Zhang Fuyin Han Wei Liu Longlong Zhang Rui Zhao Chunxiang Xu jing dou College of Materials Science and Engineering Taiyuan University of TechnologyTaiyuan030024China Shanxi Key Laboratory of Advanced Magnesium-based Materials Taiyuan030024China

The biological corrosion behavior and mechanical properties of Mg(89-x)Y4 Zn2 Li5 Mnx(x=0,0.5,1,1.5 and2 at.%) alloy with long-period stacking ordered(LPSO) structure were investigated in this *** magnesium matrix and the eutectic phase of Mg(88)Y4 Zn2 Li5 Mn1 alloy are effectively refined by the grain boundary segregation of Mn,and the average size of matrix and the eutectic phase decreased by 66%and 74%,*** ultimate tensile strength(UTS) and elongation enhanced by 36% and 55%,*** corrosion rates obtained by weight loss and hydrogen evolution of Mg(88)Y4 Zn2 Li5 Mn1 alloy were 79% and 84% lower than that of Mg(88)Y4 Zn2 Li5 ***,Mg(88)Y4 Zn2 Li5 Mn1 alloy also presents superior corrosion behavior in electrochemical *** is verified that Mn plays a positive role in both corrosion and mechanical properties of the Mg(88)Y4 Zn2 Li5 Mn1 alloy,which provides a reference for further experimental work.

关键词： Magnesium alloy LPSO Corrosion Mechanical behavior EIS

Vacancy healing for stable perovskite solar cells via bifunctional potassium tartrate

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Journal of Energy Chemistry 2024年第1期88卷 64-70,I0002页

作者： jing dou Yue Ma Xiuxiu Niu Wentao Zhou Xueyuan Wei Jie dou Zhenhua Cui Qizhen Song Tinglu Song Huanping Zhou Cheng Zhu Yang Bai Qi Chen Experimental Centre for Advanced Materials School of Materials Science and EngineeringBeijing Institute of TechnologyBeijing 100081China Beijing Key Laboratory for Theory and Technology of Advanced Battery Materials Key Laboratory of Polymer Chemistry and Physics of Ministry of EducationBIC-ESATSchool of Materials Science and EngineeringPeking UniversityBeijing 100871China

Perovskite solar cell has gained widespread attention as a promising technology for renewable ***, their commercial viability has been hampered by their long-term stability and potential Pb leakage. Herein, we demonstrate a bifunctional passivator of the potassium tartrate(PT) to address both challenges. PT minimizes the Pb leakage in perovskites and also heals cationic vacancy defects, resulting in improved device performance and stability. Benefiting from PT modification, the power conversion efficiency(PCE) is improved to 23.26% and the Pb leakage in unencapsulated films is significantly reduced to 9.79 ppm. Furthermore, the corresponding device exhibits no significant decay in PCE after tracking at the maximum power point(MPP) for 2000 h under illumination(LED source, 100 mW cm^(-2)).

关键词： Perovskite Potassium tartrate Lead leakage Long-term stability

Existence of Normalized Ground State Solutions for Quasilinear Elliptic Problems in RN

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Acta Mathematica Sinica,English Series 2024年

作者： Yuan Yuan LI jing Bo dou School of Mathematics and Statistics North China University of Water Resources and Electric Power School of Mathematics and Statistics Shaanxi Normal University

In this paper, we investigate the existence of normalized solutions for a quasilinear elliptic problem as follows ■ where-?pis the p-Laplace operator, 10 andλ> 0. f is a continuous function and satisfies some suitable conditions. Based on a Nehari-Pohozaev manifold, we show the existence of positive normalized solutions by using the minimization method.

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