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Bubbling solutions of fourth order mean field equations on S^(4)

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Science China Mathematics 2023年第6期66卷 1217-1236页

作者： changfeng gui Yeyao Hu Weihong Xie Department of Mathematics The University of Texas at San AntonioSan AntonioTX 78249USA School of Mathematics and Statistics Hunan Key Laboratory of Analytical Mathematics and ApplicationsCentral South UniversityChangsha 410083China

In this paper,we first establish the existence of blow-up solutions with two antipodal points of the fourth order mean field equations on S^(4).Moreover,we construct non-axially symmetric solutions with blow-up points at the vertices of regular configurations,i.e.,equilateral triangles on a great circle,regular tetrahedrons,cubes,octahedrons,icosahedrons and dodecahedrons.The bubbling rates of these blow-up solutions rely on various bubbling configurations.

关键词： Paneitz operator bubbling solution axially symmetric solution non-axially symmetric solution regularpolyhedra

Completion of R^(2)with a Conformal Metric as a Closed Surface

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Analysis in Theory and Applications 2021年第1期37卷 59-73页

作者： changfeng gui Qinfeng Li Department of Mathematics The University of Texas at San AntonioSan AntonioTexas 78249USA School of Mathematics Hunan UniversityChangshaHunan 410082China

In this paper,we obtain some asy mptotic behav ior results for solutions to the prescribed Gaussian curvature equation.Moreover,we prove that under a con-formal metric in R^(2),if the total Gaussian curvature is 4π,the conformal area of R^(2)is finite and the Gaussian curvature is bounded,then R^(2)is a compact C^(l,α)surface after completion at∞,for anya∈(0,1).If the Gaussian curvature has a Holder decay at in-finity,then the completed surface is C^(2).For radial solutions,the same regularity holds if the Gaussian curvature has a limit at infinity.

关键词： Gaussian curvature conformal geometry semilinear equations entire solutions

Multiple Non-Axially Solutions to a Mean Field Equation on S^2

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Analysis in Theory and Applications 2020年第1期36卷 19-32页

作者： Zhuoran Du changfeng gui Jiaming Jin Yuan Li School of Mathematics Hunan UniversityChangshaHunan 410082China Department of Mathematics University of Texas at San AntonioTX78249USA

We study the following mean field equation■,whereρis a real parameter.We obtain the existence of multiple non-axially symmetric solutions bifurcating from u=0 at the valuesρ=4 n(n+1)πfor any odd integer n≥3.

关键词： Mean field equation non-axially solutions bifurcation

Phase Transition,Minimal Surface and De Giorgi Conjecture

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Phase Transition,Minimal Surface and De Giorgi Conjecture

Allen-Cahn方程的行波解速度的渐近公式

Nanjing Workshop on Geometry and Analysis 2005

作者： changfeng gui

In 1979 De Giorgi conjectured that some entire solutions to the stationary Allen-Cahn equation, which is a well-known model in phase transition, must only depend on one direction if the dimension is less than 9. The conjecture is closed related to the Bernstein problem in geometry on the complete minimal graph surfaces in the entire space. The conjecture is completely proven for dimensions 2 and 3. Recently there are significant progress in higher dimensions. In this talk, I will explain the connection of the conjecture with phase transition and minimal surfaces, discuss the recent progresses.

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中国科学：数学 2016年第5期46卷 549-562页

作者：桂长峰赵铭锋湖南大学数学与计量经济学院长沙410082 Department of Mathematics The University of Texas at San Antonio Department of Mathematics The University of British Columbia

本文研究通常Laplacian和分数次Laplacian的Allen-Cahn方程的行波解,以及方程在线性扰动情形下的行波速度的渐近公式,通过用非线性函数对行波解速度的估计,可以得到行波解的一致估计和解的导数在无穷远处的一致衰减估计,从而得到行波速... 详细信息

本文研究通常Laplacian和分数次Laplacian的Allen-Cahn方程的行波解,以及方程在线性扰动情形下的行波速度的渐近公式,通过用非线性函数对行波解速度的估计,可以得到行波解的一致估计和解的导数在无穷远处的一致衰减估计,从而得到行波速度的渐近公式.

关键词：行波解行波速度 Allen-Cahn方程分数次Laplacian

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球面上的平均场方程

数学理论与应用 2021年第3期41卷 13-37页

作者：桂长峰胡烨耀谢维洪得克萨斯大学圣安东尼奥分校圣安东尼奥78249 中南大学数学与统计学院长沙410075

本文介绍球面上平均场类方程的新进展及公开问题.特别地,我们引入一些新的Aubin-Onofri型不等式,同时讨论这些不等式与平均场类方程之间的紧密联系.

关键词：平均场方程 Paneitz算子共形度量 Szeg?极限定理 Moser-Trudinger不等式

Removal of dust from flue gas in magnetically stabilized fluidized bed

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Particuology 2008年第2期6卷 116-119页

作者： Yinghui Wang Keting gui Mingheng Shi changfeng Li School of Energy and Power Engineering Jiangsu University Zhenjiang 212013 Jiangsu China Key Laboratory of Clean Coal Power Generation and Combustion Technology of Ministry of Education Southeast University Nanjing 210096 Jiangsu China

A magnetically stabilized fluidized bed （MSFB,Ф 500mm×2100mm） was designed to study dust removal from flue gas. Based on the mechanism of dust removal in a fixed bed, the effects on collection efficiency of magnetic field intensity, ratio of flue gas velocity to minimum fluidization velocity, bed height, and particle average diameter, were investigated. Then feasible methods for MSFB to better remove dust were proposed. Over 95 % of dust removal with MSFB can be achieved, when stable fluidization is maintained and when magnetic particles are frequently renewed.

关键词： Magnetically stabilized fluidized bed （MSFB） Stable fluidization Dust removal Magnetic particles renewal

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响应面法优化制备污泥生物炭负载纳米零价铁

环境科学与技术 2022年第7期45卷 152-160页

作者：韩涛戴亮王刚蒙凯陶玲马贵贾怀宏吴长峰兰州交通大学环境与市政工程学院甘肃兰州730070 宁夏师范学院宁夏固原756000 兰州城市供水(集团)有限公司甘肃兰州730060

为了确定污泥生物炭(SBC)负载纳米零价铁(nZVI@SBC)的最优制备条件,文章以市政污泥、七水合硫酸亚铁为原料,采用限氧高温热解、酸洗改性和液相还原法制备nZVI@SBC材料。以水中Cd(Ⅱ)的去除率为吸附指标,利用Plackett-Burman实验设计筛... 详细信息

为了确定污泥生物炭(SBC)负载纳米零价铁(nZVI@SBC)的最优制备条件,文章以市政污泥、七水合硫酸亚铁为原料,采用限氧高温热解、酸洗改性和液相还原法制备nZVI@SBC材料。以水中Cd(Ⅱ)的去除率为吸附指标,利用Plackett-Burman实验设计筛选显著因素,并采用Box-Behnken响应面法对制备条件进行优化,进一步通过扫描电镜、X射线能谱和傅里叶变换红外光谱等手段对nZVI@SBC进行表征分析。结果表明,二次多项式模型拟合显著(P0.05),模型决定系数(R^(2))为0.9813,模型拟合良好。在SBC热解温度为691℃,铁土质量比(M_(Fe)/M_(SBC))为1.90,酸洗HCl浓度为3.75 mol/L,混合搅拌时间150 min,无水乙醇添加量50 mL的最优条件下,nZVI@SBC对200 mg/L Cd(Ⅱ)的实际去除率为74.77%,与模型理论预测值74.95%接近,证明采用响应面法优化n ZVI@SBC制备条件可靠。

关键词：污泥生物炭纳米零价铁响应面法 Plackett-Burman实验 Cd(Ⅱ)

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五轴水泥土搅拌桩止水帷幕关键施工技术研究

江西建材 2022年第8期 232-235页

作者：宋珪江西省地质工程(集团)公司江西南昌330029

文中以上海长风10号南地块项目基坑工程五轴水泥土搅拌桩止水帷幕为例,通过试验桩研究确定了五轴水泥土搅拌桩施工技术参数,并对五轴水泥土搅拌桩止水帷幕施工过程中常见孔内事故原因和预防处理措施进行了分析,为类似工程提供了借鉴和... 详细信息

文中以上海长风10号南地块项目基坑工程五轴水泥土搅拌桩止水帷幕为例,通过试验桩研究确定了五轴水泥土搅拌桩施工技术参数,并对五轴水泥土搅拌桩止水帷幕施工过程中常见孔内事故原因和预防处理措施进行了分析,为类似工程提供了借鉴和参考。

关键词：五轴水泥土搅拌桩止水帷幕施工技术