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Acta Mathematica Sinica,English Series 2005年第3期21卷 631-642页

作者： yi bing SHEN Xiao Hua ZHU Department of Mathematics Zhejiang University Hangzhou 310028 P. R. China School of Mathematical Sciences Peking University Beijing 100871 P. R. China

By using curvature estimates, we prove that a complete non-compact hypersurface M with constant mean curvature and finite l^n-norm curvature in R^1＋1 must be minimal, so that M is a hyperplane if it is strongly stable. This is a generalization of the result on stable complete minimal hypersurfaces of R^n＋1. Moreover, complete strongly stable hypersurfaces with constant mean curvature and finite l^1-norm curvature in R^1＋1 are considered.

关键词： Constant mean curvature Strong stability l^p-norm curvature

A Smoothing Method for Solving Bilevel Multiobjective Programming Problems

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Journal of the Operations Research Society of China 2014年第4期2卷 511-525页

作者： yi-bing lü Zhong-Ping Wan School of information and Mathematics Yangtze UniversityJingzhou 434023HubeiChina School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

in this paper,a bilevel multiobjective programming problem,where the lower level is a convex parameter multiobjective program,is *** the KKT optimality conditions of the lower level problem,this kind of problem is transformed into an equivalent one-level nonsmooth multiobjective optimization ***,a sequence of smooth multiobjective problems that progressively approximate the nonsmooth multiobjective problem is *** is shown that the Pareto optimal solutions(stationary points)of the approximate problems converge to a Pareto optimal solution(stationary point)of the original bilevel multiobjective programming *** results showing the viability of the smoothing approach are reported.

关键词： Bilevel multiobjective programming Stationary point Constraint qualification Smoothing method

Effectiveness and longevity of amendments to a cadmium-contaminated soil

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Journal of integrative Agriculture 2020年第4期19卷 1097-1104页

作者： ZHAO Rui lv yi-zhong MA yi-bing li Ju-mei College of Resources and Environmental Sciences China Agricultural UniversityBeijing 100193P.R.China institute of Agricultural Resources and Regional Planning Chinese Academy of Agricultural SciencesBeijing 100081P.R.China

The effectiveness and longevity of amendments will influence the reduction in cadmium(Cd) bioavailability by in situ remediation techniques. Different amendments, including red mud(RM), corn straw(CS), rape straw(RS), and their combinations with zinc(Zn) fertilizer, were evaluated based on a long-term field experiment. it was found that all amendments decreased the concentration of available-Cd(EDTA-Cd and Exch-Cd) in soil and also reduced the Cd content(%) in plants. The amendments were still effective after eight years, although the effect did decline over time. The reduction of plant Cd content was 83.5% for red mud plus rape straw(RMRS), 65.3% for red mud plus corn straw(RMCS), 50.9% for RS, 54.0% for RM, and 37.3% for CS in the first few years. The reduction in plant Cd content was still 17.2% for RMRS after eight years, and RMRS was found to be the most effective treatment for decreasing Cd bioavailability. This study also explained that why the reduction in plant Cd content declined over time is the change of available Cd content in soil over time, which is important for guiding agricultural practice. it was concluded that RM, CS, RS, and their combinations with Zn fertilizer as effective amendments can have a profound and lasting positive impact on Cd-contaminated soils.

关键词： cadmium(Cd) amendment bioavailability Cd reduction

Microsatellite DNA Variation of the Gametophyte Clones isolated from introduced laminaria japonica (Phaeophyta) and l. longissima of China and Varieties Derived from them

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Journal of integrative Plant Biology 2008年第3期50卷 352-359页

作者： bing-Jun li Yuan-Yuan Shi Guan-Pin Yang Shi Che Xiao-Jie li yi-Zhou Cong College of Marine life Sciences Ocean University of China Qingdao 266003 China Shandong Oriental Ocean Sci-tech Co. ltd. Yantai 264005 China College of Oceanography Yantai University Yantai 264005 China

The variation of 90 laminaria gametophyte clones representing the introduced laminaria japonica （Group 1） and laminaria iongissima （Group 2）, the varieties of l. japonica （Group 3） and the varieties derived from interspecific hybrids （Group 4） was determined with 18 microsatellite markers. The allelic diversity and Nei＇s gene diversity of Group 1 were significantly higher than those of Group 2 （2.9 vs. 1.8 and 0.414 vs. 0.161, respectively）, demonstrating that the variation of the introduced l. japonica is richer than that of l. iongissima. Both allelic diversity and Nei＇s gene diversity of Group 3 were lower than those of Group 1, indicating that only a portion of variation of l. japonica was incorporated into the varieties of l. japonica. Significant genetic differentiation was detected between four groups and between female （Population 1 ） and male （Population 2） gametophyte clones in each group. The variation among groups accounted for 39.95%, while that among populations accounted for 21.65% of the total. The genetic distance between Group 1 and Group 4 was obviously longer than that between Group 2 and Group 4 （0.686 vs. 0.291）, indicating that maternal gametophyte clone contributed more variation to the hybrids than the paternal gametophyte clone did.

关键词： genetic diversity genetic differentiation laminaria japonica laminaria iongissima microsatellite DNA marker

Representations and Fusion Rules for the Orbifold Vertex Operator Algebras l_(sl_(2))(k,0)^(Z_(3))

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Algebra Colloquium 2022年第2期29卷 241-264页

作者： bing Wang School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 200240China Shanghai lixin University of Accounting and Finance Shanghai 201209 China

For the cyclic group Z_(3)and a positive integer k,we study the representations of the orbifold vertex operator algebra l_(sl_(2))(k,0)^(Z_(3)).All the irreducible modules for l_(sl_(2))(k,0)^(Z_(3))are classified and... 详细信息

关键词： orbifold vertex operator algebras irreducible modules fusion rules

l^(p)-Estimate for linear Forward-Backward Stochastic Differential Equations

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Acta Mathematica Sinica,English Series 2023年第5期39卷 827-845页

作者： bing XiE Zhi Yong YU School of Mathematics Shandong UniversityJinan 250100P.R.China

This paper is concerned with coupled linear forward-backward stochastic differential equations(FBSDEs,for short).When the homogeneous coefficients are deterministic(the non-homogeneous coefficients can be random),we obtain an l^(P)-result(p>2),including the existence and uniqueness of the p-th power integrable solution,a p-th power estimate,and a related continuous dependence property of the solution on the coefficients,for coupled linear FBSDEs in the monotonicity framework over large time *** order to get rid of the stubborn constraint commonly existing in the literature,i.e.,the lipschitz constant of σ with respect to z is very small,we introduce a linear transformation to overcome the difficulty on small intervals,and then"splice"the l^(P)-results obtained on many small intervals to yield the desired one on a large interval.

关键词： Forward-backward stochastic differential equation l^(P)-estimate monotonicity condition large interval

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isothermal reduction kinetics of Panzhihua ilmenite concentrate under 30vol% CO–70vol% N2 atmosphere

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international Journal of Minerals,Metallurgy and Materials 2017年第3期24卷 240-248页

作者： ying-yi Zhang Wei lü Xue-wei lü Sheng-ping li Chen-guang Bai bing Song Ke-xi Han College of Materials Science and Engineering Chongqing University Chongqing 400044 China Panzhihua iron and Steel Research institute Panzhihua 617000 China

The reduction of ilmenite concentrate in 30vol% CO–70vol% N_2 atmosphere was characterized by thermogravimetric and differential thermogravimetric(TG–DTG) analysis methods at temperatures from 1073 to 1223 *** isothermal reduction results show that the reduction process comprised two stages;the corresponding apparent activation energy was obtained by the iso-conversional and model-fitting *** the first stage,the effect of temperature on the conversion degree was not obvious,the phase boundary chemical reaction was the controlling step,with an apparent activation energy of 15.55–40.71 k J·mol^(–1).For the second stage,when the temperatures was greater than 1123 K,the reaction rate and the conversion degree increased sharply with increasing temperature,and random nucleation and subsequent growth were the controlling steps,with an apparent activation energy ranging from 182.33 to 195.95 k J·mol^(–1).For the whole reduction process,the average activation energy and pre-exponential factor were 98.94^(–1)18.33 k J·mol^(–1) and 1.820^(–1).816 min^(–1),respectively.

关键词： ilmenite isothermal reduction kinetics carbon monoxide

A generalized l_2-discrepancy for cubature and uncertainty quantification of nonlinear structures

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Science China(Technological Sciences) 2016年第6期59卷 941-952页

作者： CHEN Jian bing SONG Peng Yan State Key laboratory of Disaster Reduction in Civil Engineering & School of Civil Engineering Tongji University College of Civil Engineering and Architecture Hebei University

The numerical method for multi-dimensional integrals is of great importance, particularly in the uncertainty quantification of engineering structures. The key is to generate representative points as few as possible but of acceptable accuracy. A generalized l2（Gl2）-discrepancy is studied by taking unequal weights for the point set. The extended Koksma-Hlawka inequality is discussed. Thereby, a worst-case error estimate is provided by such defined Gl2-discrepancy, whose dosed-form expression is available. The characteristic values of Gl2-discrepancy are investigated. An optimal strategy for the selection of the representative point sets with a prescribed cardinal number is proposed by minimizing the Gl2-discrepancy. The three typical examples of the multi-dimensional integrals are investigated. The stochastic dynamic response analysis of a nonlinear structure is then studied by incorporating the proposed method into the probability density evolution method. it is shown that the proposed method is advantageous in achieving tradeoffs between the efficiency and accuracy of the exemplified problems. Problems to be further studied are discussed.

关键词： Koksma-Hlawka inequality cubature l2-discrepancy nonlinear structure stochastic dynamics

Spatial and historical distribution of organic phosphorus driven by environment conditions in lake sediments

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Journal of Environmental Sciences 2018年第2期30卷 32-41页

作者： Changwei lü Jiang He bing Wang School of Ecology and Environment Inner Mongolia University institute of Environmental Geology Inner Mongolia University Forestry College Inner Mongolia Agricultural University

The chemistry of sedimentary organic phosphorus（OP） and its fraction distribution in sediments are greatly influenced by environmental conditions such as terrestrial inputs and runoffs. The linkage of OP with environmental conditions was analyzed on the basis of OP spatial and historical distributions in lake sediments. The redundancy analysis and OP spatial distribution results suggested that both Na OH-OP（OP extracted by Na OH） and Re-OP（residual OP） in surface sediments from the selected 13 lakes reflected the gradient effects of environmental conditions and the autochthonous and/or allochthonous inputs driven by latitude zonality in China. The lake level and salinity of lake Hulun and the runoff and precipitation of its drainage basin were reconstructed on the basis of the geochemistry index. This work showed that a gradient in weather conditions presented by the latitude zonality in China impacts the OP accumulation through multiple drivers and in many *** drivers are mainly precipitation and temperature, governing organic matter（OM）production, degradation rate and transportation in the watershed. Over a long temporal dimension（4000 years）, the vertical distributions of Re-OP and Na OH-OP based on a dated sediment profile from HlH were largely regulated by the autochthonous and/or allochthonous inputs, which depended on the environmental and climate conditions and anthropogenic activities in the drainage basin. This work provides useful environmental geochemistry information to understand the inherent linkage of OP fractionation with environmental conditions and lake evolution.

关键词： Organic phosphorus Spatial and historical distribution Environmental conditions Sediment lake