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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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Behavior of Theta-series under Modular Substitutions

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Acta Mathematica Sinica,English Series 2011年第9期27卷 1705-1716页

作者： bing Yong xie LMAM School of Mathematical Science Peking University Beijing 10087'1 P. R. China

In this article we provide a transformation formula of certain theta series, and apply it to obtain non-holomorphic vector-valued modular forms.

关键词： Theta series nonholomorphic vector-valued modular forms

Extraction of vanadium from high calcium vanadium slag using direct roasting and soda leaching

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International Journal of Minerals,Metallurgy and Materials 2012年第7期19卷 595-601页

作者： Xin-sheng Li bing xie College of Materials Science and Engineering Chongqing University Chongqing 400044 China

The extraction of vanadium from high calcium vanadium slag was attempted by direct roasting and soda leaching. The oxidation process of the vanadium slag at different temperatures was investigated by X-ray diffraction （XRD）, scanning electron microscopy （SEM）, and energy dispersive spectroscopy （EDS）. The effects of roasting temperature, roasting time, Na2CO3 concentration, leaching tem- perature, leaching time, and liquid to solid ratio on the extraction of vanadium were studied. The results showed that olivine phases and spinel phases in the vanadium slag were completely decomposed at 500 and 800℃, respectively. Vanadium-rich phases were formed at above 850℃. The leaching rate of vanadium reached above 90% under the optimum conditions： roasting temperature of 850℃, roasting time of 60 min, Na2CO3 concentration of 160 g/L, leaching temperature of 95℃, leaching time of 150 min, and liquid to solid ratio of 10：1 mL/g. The main impurities were Si and P in the leach liquor.

关键词： vanadium metallurgy extraction slag roasting leaching

Surface properties of bacteria from activated sludge in relation to bioflocculation

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Journal of Environmental Sciences 2010年第12期22卷 1840-1845页

作者： bing xie Jidong Gu Jun Lu Key Laboratory of Urbanization and Ecological Restoration of Shanghai Department of Environmental Science & Technology East China Normal University Shanghai 200062 China Laboratory of Environmental Toxicology Department of Ecology & Biodiversity The University of Hong Kong Pokfulam Road Hong Kong SAR China Department of Interdisciplinary Studies Faculty of Health & Environmental Sciences Auckland University of Technology Auckland 1142 New Zealand School of Biological Sciences Faculty of Science University of Auckland Auckland 1142 New Zealand

Two bacterial stains were isolated from the activated sludge and identified as Leucobacter sp. and Alcaligenesfaecalis by 16S rDNA sequencing. Pure cultures of these two strains, representing well or poorly settled bacteria, were used to investigate the mechanism of bioflocculation in activated sludge. Based on the analyses of the characteristics of cells hydrophobicity, ζ-potential, flocculation ability and extracellular polymeric substance （EPS） composition under different growth stages, it was found that the ratio of cell EPS protein had the highly influence on ζ-potential and hydrophobicity, which were important factors to bioflocculation. Cellulase and Proteinase K could destroy the extracellular biopolymer and resulted in a decrease in the hydrophobicity and ζ-potential. However, in our study, the flocculation characteristics exhibited differently in relation to cellulase and Proteinase K. Flocculation of cells treated with cellulase and Proteinase K decreased sharply, and then recovered quickly in cellulase treatment, while cells treated with Proteinase K showed no sign of recovery. This reveals that the presence of protein in extracellular biopolymer plays an important role to the bioflocculation of cells.

关键词： activated sludge hydrophobicity ζ-potential bioflocculation pure culture

Analysis of Crystallization Behavior of Mold Fluxes Containing TiO_2 Using Single Hot Thermocouple Technique

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Journal of Iron and Steel Research International 2016年第4期23卷 322-328页

作者： Yun LEI bing xie Wen-hui MA State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization Kunming University of Science and Technology College of Materials Science and Engineering Chongqing University

The crystallization behavior of mold fluxes containing 0-8 mass% TiO2 was investigated using the single hot therrnocouple technique （SHTT） and X ray diffraction （XRD） to study the possible effects on the coordination of heat transfer control and strand lubrication for casting crack sensitive peritectic steels. Time-temperature-transforma tion （TTT） and continuous-cooling transformation （CCT） curves were plotted using the data obtained from SHTT to characterize the crystallization of the mold fluxes. The results showed that crystallization of the mold fluxes during isothermal and non-isothermal processes was suppressed with TiO2 addition. From the TTT curves, it could be seen that the incubation and growth time of crystallization increased significantly with TiO2 addition. The CCT curves showed that the crystallization temperature initially decreased, and then suddenly increased with increasing the TiO2 content. XRD analysis suggested the presence of cuspidine in the mold fluxes with lower TiO2 content （〈4 mass%） , while both perovskite and cuspidine were detected in the mold fluxes when the TiO2 content was increased to 8 mass%. In addition, the growth mechanisms of the crystals changed during the isothermal crystallization process from interface controlled growth to diffusion-controlled growth with increasing the TiO2 content.

关键词： mold flux single hot thermocouple technique kinetics crystallization TTT curve CCT curve

Monogamy and polygamy for the generalized W-class states using unified-(q,s)entropy

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Science China(Physics,Mechanics & Astronomy) 2024年第1期67卷 10-22页

作者： Bo Li bing xie Zhanjun Zhang Heng Fan School of Computer and Computing Science Hangzhou City UniversityHangzhou 310015China Department of Mathematics East China University of TechnologyNanchang 330013China School of Information&Electronic Engineering(Sussex Artificial Intelligence Institute) Zhejiang Gongshang UniversityHangzhou 310018China Institute of Physics Chinese Academy of SciencesBeijing 100190China

We describe the entanglement distribution and restricted shareability of the multipartite generalized W-class states and their reduced density matrix under arbitrary partitions by using monogamy and polygamy relation based on the unified-(q,s)***,we provide an analytical formula of unified-(q,s)entanglement(UE)and an analytical lower bound of unified-(q,s)entanglement of assistance(UEo A)for a reduced density matrix of a generalized W-class ***,we use these two analytical formulas to derive the monogamy and polygamy inequalities for a reduced density matrix of a qudit generalized W-class(GW)*** establish two partition-dependent residual entanglements based on the new monogamy relation,which is helpful to obtain a comprehensive analysis of entanglement dynamics of generalized W-class ***,we investigate tighter monogamy and polygamy relations based on the power ofαth(α≥0)for UE andβth(β≥0)for UEo A,*** results show that the entanglement distribution characteristics of generalized W-class states satisfying stronger constraints can be described more accurately.

关键词： monogamy polygamy multiqudit unified entropy

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Slag formation path during dephosphorization process in a converter

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International Journal of Minerals,Metallurgy and Materials 2015年第12期22卷 1260-1265页

作者： Jiang Diao Yong Qiao Xuan Liu xie Zhang Xin Qiu bing xie College of Materials Science and Engineering Chongqing University

The slag formation path is important for efficient dephosphorization in steelmaking processes. The phosphorus capacity and the melting properties of the slag are critical parameters for optimizing the slag formation path. Regarding these two factors, the phosphorus partition ratio was calculated using the regular solution model （RSM）, whereas the liquidus diagrams of the slag systems were estimated using the FactSage thermodynamic package. A slag formation path that satisfies the different requirements of dephosphorization at different stages of dephosphorization in a converter was thus established through a combination of these two aspects. The composition of the initial slag was considered to be approximately 15wt%CaO-44wt% SiOz-41wt%FeO. During the dephosphorization process, a slag formation path that follows a high-iron route would facilitate efficient dephosphorization. The composition of the final dephosphorization slag should be approximately 53wt%***% SiO2-21.5wt%FeO. The composition of the final solid slag after dephosphorization is approximately 63.6wt%CaO-30.3wt%SiO2-6. 1wt%FeO.

关键词： steelmaking dephosphorization slag composition optimization

Mass transfer of phosphorus in high-phosphorus hot-metal refining

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International Journal of Minerals,Metallurgy and Materials 2015年第3期22卷 249-253页

作者： Jiang Diao Xuan Liu Tao Zhang bing xie College of Materials Science and Engineering Chongqing University

Mass transfer of phosphorus in high-phosphorus hot-metal refining was investigated using CaO-FetO-SiO2 slags at 1623 K. Based on a two-film theory kinetic model and experimental results, it was found that the overall mass transfer coefficient, which includes the effects of mass transfer in both the slag phase and metal phase, is in the range of 0.0047 to 0.0240 cm/s. With the addition of a small amount of fluxing agents A1203 or Na20 into the slag, the overall mass transfer coefficient has an obvious increase. Silicon content in the hot metal also influences the overall mass transfer coefficient. The overall mass transfer coefficient in the lower [Si] heat is much higher than that in the higher [Si] heat. It is concluded that both fluxing agents and lower [Si] hot metal facilitate mass transfer of phosphorus in liquid phases. Fur- thermore, the addition of Na20 could also prevent rephosphorization at the end of the experiment.

关键词： steelmaking refining dephosphorization mass transfer coefficients kinetics

An assessment method of annual climatic status in China using extreme climate indices:2021 as an example

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Advances in Climate Change Research 2022年第6期13卷 868-874页

作者： Zeng-Yuan GUO Li-Juan CHEN bing xie Climate Studies Key Laboratory National Climate CenterChina Meteorological AdministrationBeijing 100081China Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters(CIC-FEMD) Nanjing University of Information Science&TechnologyNanjing 210044China

A proper assessment of annual climatic status(ACS)is conducive to rationally formulating disaster prevention and mitigation *** former definition of ACS lacks either information on extreme climate or an intuitive grade feature service to the *** ACS defined in the National Standard of the People's Republic of China(GBACS)only considers the accumulated climate effects of each weighted 10-d temperature/precipitation anomaly in a *** global warming,the losses caused by extreme climate events often have a significant impact on the grades of ACS,but this impact cannot be reasonably reflected by *** study proposed the assessment of ACS using extreme climate indices(extreme climate-based ACS(ECACS))and compared it with *** results indicated that GBACS and ECACS can be used to evaluate the ACS from different *** ECACS is an important supplement to the GBACS,especially considering the years with frequently occurring extreme climate *** sum of GBACS and ECACS is a reasonable and comprehensive way to evaluate the *** empirical orthogonal function(EOF)analysis indicated a uniform mode(EOF1)and a dipole mode(EOF2)in GBACS and ECACS in *** interannual variation characteristics of ECACS in northern and southern China(EOF2 pattern)are consistent with real climate features,which is conducive to providing better and more detailed regional information in the ACS forecast *** results have essential instructive and application value for ACS assessment and government decision making.

关键词： Extreme climate indices Annual climatic status Temperature Precipitation