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The Inverse Mean Curvature Flow in Rotationally Symmetric Spaces

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Chinese Annals of Mathematics,Series B 2011年第1期32卷 27-44页

作者： qi DING School of Mathematical Sciences Fudan University Shanghai 200433 China

In this paper,the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally symmetric spaces is *** is proved that the flow converges to a unique geodesic spher... 详细信息

关键词： Asymptotic behavior Inverse mean curvature flow Hyperbolic space

Quenching Phenomenon for a Parabolic MEMS Equation

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Chinese Annals of Mathematics,Series B 2018年第1期39卷 129-144页

作者： qi WANG College of Science University of Shanghai for Science and Technology

This paper deals with the electrostatic MEMS-device parabolic equation u_t-?u =λf(x)/(1-u)~p in a bounded domain ? of R^N,with Dirichlet boundary condition,an initial condition u0(x) ∈ [0,1) and a nonnegative profile f,where λ > 0,p > *** study is motivated by a simplified micro-electromechanical system(MEMS for short) device *** this paper,the author first gives an asymptotic behavior of the quenching time T*for the solution u to the parabolic problem with zero initial ***,the author investigates when the solution u will quench,with general λ,u0(x).Finally,a global existence in the MEMS modeling is shown.

关键词： MEMS equation Quenching time Global existence

Numerical Solutions of Fractional Boussinesq Equation

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Communications in Theoretical Physics 2007年第3期47卷 413-420页

作者： WANG qi School of Mathematical Sciences Fudan University Shanghai 200433 China Key Laboratory of Mathematics Mechanizations the Chinese Academy of Sciences Beijing 100080 China

Based upon the Adomian decomposition method, a scheme is developed to obtain numerical solutions of a fractional Boussinesq equation with initial condition, which is introduced by replacing some order time and space derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the traditional Adomian decomposition method for differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional differential equations. The solutions of our model equation are calculated in the form of convergent series with easily computable components.

关键词： fractional Boussinesq equation Adomian decomposition method

Mean Spherical Approximation-Based Partitioned Density Functional Theory

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Communications in Theoretical Physics 2003年第6X期40卷 721-726页

作者： ZHOUShi-qi InstituteofModernStatisticalMechanicsandDepartmentofPackagingEngineering ZhuzhouInstituteofTechnologyZhuzhou412008China

Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =ζ∫ dr4a(r4 - r1)a(r4 - r2)a(r4 - r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ζ and the short range of the a kernel *** over the previous theories is proposed and tested.

关键词：球形近似密度函数理论直接相关函数 FPEA 流体力学函数扰动扩张近似

A Global Investigation About Hard Core Attractive Yukawa Approximation and Adhesive Hard Sphere Approximation for Structure of Colloidal Dispersion Systems

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Communications in Theoretical Physics 2005年第3期43卷 567-576页

作者： ZHOUShi-qi InstituteofModernStatisticalMechanics ZhuzhouInstituteofTechnologyZhuzhou412008China

The accuracy of hard core attractive Yukawa (HCAY) potential and adhesivehard sphere (AH) potential in representing the structure factor of short range square well potentialand Asakura and Oosawa (AO) depletion potential is examined by comparing theoretical predictionswith the existing simulation data and the present numerical results from the non-linear optimizedrandom phase approximation closure for Ornstein—Zernike equation. For the case of square-well (SW)potential, it is shown that the structure factor of HCAY potential based on a recently proposedsemi-analytical expression for the radial distribution function can describe the structure factor ofSW potential with reduced well width λ ≤ 2 only if the reduced contact potential βε_(sw) ≤0.25, while the analytical expression for the structure factor of AH potential under Percus-Yevick(PY) approximation completely fails for the case of λ > 1.2. For the case of AO depletionpotential, the domain of validity of both HCAY potential and AH potential is complementary. With theabove analysis and considering the solid-liquid transition of the AH potential with an adhesiveparameter τ below 1.31 cannot be predicted by modified weighted density approximation, the roleplayed by the HCAY potential about the mapping manipulation should not be ignored.

关键词： colloidal dispersion structure factor

Adaptive sampling for corrugated plate digitization using a laser displacement sensor

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Science China(Technological Sciences) 2024年第5期67卷 1510-1523页

作者： WU ChengXing qi qi CHEN BaiJin YANG JiXiang DING Han State Key Laboratory of Intelligent Manufacturing Equipment and Technology School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhan430074China State Key Laboratory of Intelligent Manufacturing Equipment and Technology School of Materials Science and EngineeringHuazhong University of Science and TechnologyWuhan430074China

The surface quality of a corrugated plate directly determines the heat transfer property of the thermal power mechanical *** detection methods are impractical for real-world production,being slow and *** contrast,the point laser displacement sensor,employing the optical triangle method,emerges as a promising device for assessing parts with variable curvature and highly reflective *** its benefits,high-density sampling by an innate frequency introduces challenges such as data redundancy and a poor signal-to-noise ratio,potentially affecting the efficiency and precision of subsequent data *** address these challenges,adjustable frequency data sampling has been developed for this sensor,allowing adaptive sampling for corrugated plate *** process begins with surface digitization to extract discrete points,which are transformed into intersection curves using the B-spline fitting ***,dominant points are identified,considering multigeometric constraints for curvature and arch ***,the sampling signal is adjusted based on the distribution information of dominant *** results indicate that the proposed method effectively minimizes redundant sampling without compromising the accurate capture of essential geometric features.

关键词： corrugated plate laser displacement sensor adaptive sampling dominant point curvature arch height

掺杂单层MoS_(2)电子结构与光催化性质的第一性原理计算

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原子与分子物理学报 2025年第1期42卷 35-40页

作者：徐启远高朋刘正堂九江学院机械与智能制造学院九江332005 西北工业大学材料学院西安710072

为了提高MoS_(2)的光催化能力,本研究基于第一性原理平面波赝势方法,对Cr、W、Fe、Co、Ni替换单层MoS_(2)晶格中的Mo进行研究.结果表明:W的替换能为正值,Cr、Fe、Co、Ni的替换能为负值.Cr、W掺杂晶格产生畸变主要是杂质原子的共价半径... 详细信息

为了提高MoS_(2)的光催化能力,本研究基于第一性原理平面波赝势方法,对Cr、W、Fe、Co、Ni替换单层MoS_(2)晶格中的Mo进行研究.结果表明:W的替换能为正值,Cr、Fe、Co、Ni的替换能为负值.Cr、W掺杂晶格产生畸变主要是杂质原子的共价半径引起的;Fe、Co、Ni掺杂晶格产生畸变主要是掺杂原子的自旋导致的.Cr、W、Fe、Co、Ni掺杂单层MoS_(2)带隙类型没有发生改变,仍然为直接带隙,但禁带宽度变小,吸收带红移,尤其Fe、Co、Ni掺杂,导带下方有杂质能级使费米能级向高能方向移动,可以作为捕获电子陷阱,增加电子密度,减少光激发电子-空穴对的复合,有利于提升光催化能力.

关键词：掺杂单层二硫化钼光催化电子结构

不同干细胞来源外泌体及其携非编码RNA诊疗骨性关节炎

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中国组织工程研究 2025年第19期29卷 4122-4131页

作者：王喆齐岩松徐永胜内蒙古自治区人民医院骨科中心(运动医学中心) 内蒙古自治区呼和浩特市010017

背景:外泌体可在骨性关节炎患者滑液和血浆中检测出来,其水平随着骨性关节炎的进展而不断变化,并且可以对骨性关节炎的局部炎症、软骨钙化和关节退化起缓解作用。目的:旨在全面了解不同干细胞来源外泌体在骨性关节炎诊疗中的作用和机制... 详细信息

背景:外泌体可在骨性关节炎患者滑液和血浆中检测出来,其水平随着骨性关节炎的进展而不断变化,并且可以对骨性关节炎的局部炎症、软骨钙化和关节退化起缓解作用。目的:旨在全面了解不同干细胞来源外泌体在骨性关节炎诊疗中的作用和机制,并提出了外泌体治疗骨性关节炎的前景和挑战。方法:检索PubMed及中国知网数据库,英文检索词为“exosomes,osteoarthritis,mesenchymal stem cells,stem cells”,中文检索词为“外泌体,骨性关节炎,间充质干细胞,干细胞”,对2003年10月至2023年10月发表的文献进行检索,最终纳入99篇文献进行综述。结果与结论:外泌体的出现给骨性关节炎的诊断和治疗带来了希望。外泌体内含RNA、蛋白质及脂类的差异能够作为骨性关节炎的生物标志物用于诊断。同时,来自不同干细胞的外泌体均能够有效保护软骨细胞、缓解炎症、维持软骨基质代谢以及调节血管生成和软骨下骨重塑,表现出治疗骨性关节炎的优秀潜力。工程化外泌体则突破传统局限,通过调节特定非编码RNA表达增强治疗特异性与效率,为骨性关节炎的治疗提供新策略。

关键词：外泌体骨性关节炎间充质干细胞干细胞软骨修复软骨再生软骨细胞 RNA 工程化外泌体

Bang-Bang Principle of Time Optimal Controls and Null Controllability of Fractional Order Parabolic Equations

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Acta Mathematica Sinica,English Series 2010年第12期26卷 2377-2386页

作者： qi LU School of Mathematics Sichuan University Chengdu 610064 P. R. China

In this paper, we establish a bang-bang principle of time optimal controls for a controlled parabolic equation of fractional order evolved in a bounded domain Ω of R^n, with a controller w to be any given nonempty open subset of Ω. The problem is reduced to a new controllability property for this equation, i.e. the null controllability of the system at any given time T 〉 0 when the control is restricted to be active in ω× E, where E is any given subset of [0, T] with positive （Legesgue） measure. The desired controllability result is established by means of a sharp observability estimate on the eigenfunctions of the Dirichlet Laplacian due to Lebeau and Robbiano, and a delicate result in the measure theory due to Lions.

关键词： Bang-bang principle time optimal control null controllability fractional order parabolicequation