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Vibration Diagnosis and Optimization of Industrial Robot Based on TPA and EMD Methods
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作者 xiaoping xie Shijie Cheng Xuyang Li 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第6期2425-2448,共24页
This paper proposedmethod that combined transmission path analysis(TPA)and empirical mode decomposition(EMD)envelope analysis to solve the vibration problemof an industrial robot.Firstly,the deconvolution filter timed... This paper proposedmethod that combined transmission path analysis(TPA)and empirical mode decomposition(EMD)envelope analysis to solve the vibration problemof an industrial robot.Firstly,the deconvolution filter timedomain TPA method is proposed to trace the source along with the time variation.Secondly,the TPA method positioned themain source of robotic vibration under typically different working conditions.Thirdly,independent vibration testing of the Rotate Vector(RV)reducer is conducted under different loads and speeds,which are key components of an industrial robot.The method of EMD and Hilbert envelope was used to extract the fault feature of the RV reducer.Finally,the structural problems of the RV reducer were summarized.The vibration performance of industrial robots was improved through the RV reducer optimization.From the whole industrial robot to the local RV Reducer and then to the internal microstructure of the reducer,the source of defect information is traced accurately.Experimental results showed that the TPA and EMD hybrid methods were more accurate and efficient than traditional time-frequency analysis methods to solve industrial robot vibration problems. 展开更多
关键词 Industrial robots RV reducer vibration deconvolution filter time-domain TPA method EMD fault diagnosis
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High glucose promotes macrophage M1 polarization through miR-32/Mef2d/cAMP signaling pathway
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作者 Cong Chen Jingsong Cao +6 位作者 Yan Gao xiaoping xie Zhibo Zhao Qing Yuan Yuqi He Xuyu Zu Jianghua Liu 《Genes & Diseases》 SCIE CSCD 2024年第2期539-541,共3页
Chronic inflammation is a crucial inducerof diabetesvascular complications.Onereason is that high glucose easily induces macrophage activation.1 Macrophages are the principal participants in innate immunity and exist ... Chronic inflammation is a crucial inducerof diabetesvascular complications.Onereason is that high glucose easily induces macrophage activation.1 Macrophages are the principal participants in innate immunity and exist in all human tissues.In pathological vascular,infiltrated macrophages secrete inflammatory factors leading to an increase in plaque stability.?In macrophage polarization,autophagy plays an important role.Enhancement of macrophage autophagy could induce macrophage polarization from the M1 phenotype to M2 phenotype and inhibit inflammatory reactions.3 Our previous research found that high glucose condition promotes miR-32 expression and macrophage M1 polarization,4 but the mechanism of miR-32 promoting macrophage M1 polarization is unclear.In this study,we found that,under a high-glucose condition,miR-32/Mef2d/cAMP signaling promoted M1 macrophage polarization via inhibited autophagy.These results provide a theoretical and experimental basis for the prevention and treatment of T2D vascular inflammation. 展开更多
关键词 MACROPHAGE MIR prevention
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Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model
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作者 Jihong Xiao Zimo Zhu xiaoping xie 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2023年第1期79-110,共32页
This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for t... This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for the stress approximation,degree k+1 for the velocity approximation,and degree k for the numerical trace of velocity on the inter-element boundaries.The temporal discretization in the fully discrete method adopts a backward Euler difference scheme.We show the existence and uniqueness of the semi-discrete and fully discrete solutions,and derive optimal a priori error estimates.Numerical examples are provided to support the theoretical analysis. 展开更多
关键词 Quasistatic Maxwell viscoelastic model weak Galerkin method semi-discrete scheme fully discrete scheme error estimate
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Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field
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作者 Yongke Wu xiaoping xie 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2023年第2期489-510,共22页
Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field.The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navi... Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field.The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navier-Stokes equations.By skillfully introducing some new variables,the model is rewritten as several decoupled subsystems that can be solved independently.Mixed finite element formulations are given to discretize the decoupled systems with proper finite element spaces.Existence and uniqueness of the mixed finite element solutions are shown,and optimal order error estimates are obtained under some reasonable assumptions.Numerical experiments confirm the theoretical results. 展开更多
关键词 Ferrofluid flow decoupled system mixed finite element method error estimate
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A Linearized Adaptive Dynamic Diffusion Finite Element Method for Convection-Diffusion-Reaction Equations
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作者 Shaohong Du Qianqian Hou xiaoping xie 《Annals of Applied Mathematics》 2023年第3期323-351,共29页
In this paper,we consider a modified nonlinear dynamic diffusion(DD)method for convection-diffusion-reaction equations.This method is free of stabilization parameters and capable of precluding spurious oscillations.We... In this paper,we consider a modified nonlinear dynamic diffusion(DD)method for convection-diffusion-reaction equations.This method is free of stabilization parameters and capable of precluding spurious oscillations.We develop a reliable and efficient residual-type a posteriori error estimator,which is robust with respect to the diffusivity parameter.Furthermore,we propose a linearized adaptive DD algorithm based on the a posteriori estimator.Finally,we perform numerical experiments to verify the theoretical analysis and the performance of the adaptive algorithm. 展开更多
关键词 Convection-diffusion-reaction equation dynamical diffusion method residualtype a posteriori error estimator adaptive algorithm
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UNIFORMLY-STABLE FINITE ELEMENT METHODS FOR DARCY-STOKES-BRINKMAN MODELS 被引量:19
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作者 xiaoping xie Jinchao Xu Guangri Xue 《Journal of Computational Mathematics》 SCIE EI CSCD 2008年第3期437-455,共19页
在这篇论文,我们认为 2D 和 3D Darcy 司烧连接问题。这些方程与 Brinkman 模型有关震颤两个 Darcy 是法律并且司烧在 PDE,但是与强烈不连续的粘性系数和 zeroth 顺序的一种单个形式的方程称为系数。我们在场构造一致地稳定的有限元... 在这篇论文,我们认为 2D 和 3D Darcy 司烧连接问题。这些方程与 Brinkman 模型有关震颤两个 Darcy 是法律并且司烧在 PDE,但是与强烈不连续的粘性系数和 zeroth 顺序的一种单个形式的方程称为系数。我们在场构造一致地稳定的有限元素近似的三个不同方法。开始的二个方法基于 Darcy-Stokes-Brinkman 方程的原来的弱明确的表达。在我们考虑存在的第一个方法司烧元素。我们证明一个马厩司烧如果并且仅当分离地没有分叉的速度暗示几乎到处没有分叉的,元素关于系数和 Darcy-Stokes-Brinkman 方程的 jumps 也是一致地稳定的。在第二个方法,我们由修改遵守元素的一些著名 H (div ) 构造一致地稳定的元素。我们以一个统一方法给一些新 2D 和 3D 元素。在最后方法,我们与一个稳定术语修改 Darcy-Stokes-Brinkman 方程的原来的弱明确的表达。我们证明所有传统的马厩司烧元素在这新明确的表达下面关于系数和他们的 jumps 是一致地稳定的。 展开更多
关键词 有限元分析 稳定性 斯托克斯方程 计算方法
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ROBUST GLOBALLY DIVERGENCE-FREE WEAK GALERKIN METHODS FOR STOKES EQUATIONS 被引量:11
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作者 Gang Chen Minfu Feng xiaoping xie 《Journal of Computational Mathematics》 SCIE CSCD 2016年第5期549-572,共24页
这份报纸建议并且分析柔韧的全球性没有分叉的弱 Galerkin (WG ) 的一个班有限元素方法为司烧方程。新方法使用 Pk/Pk-1 (k 1 ) 为在元素的内部的速度和压力的不连续的有限元素联合,和 piecewise Pl/Pk (l = k - 1, k ) 为内部元素的... 这份报纸建议并且分析柔韧的全球性没有分叉的弱 Galerkin (WG ) 的一个班有限元素方法为司烧方程。新方法使用 Pk/Pk-1 (k 1 ) 为在元素的内部的速度和压力的不连续的有限元素联合,和 piecewise Pl/Pk (l = k - 1, k ) 为内部元素的边界上的速度和压力的踪迹近似。我们的方法不仅产出全球性没有分叉的速度答案,而且关于雷纳兹数字有一致错误估计。数字实验被提供显示出建议方法的坚韧性。[从作者抽象] 展开更多
关键词 全球性没有分叉 本地消除 一致错误估计 Galerkin
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LOW ORDER NONCONFORMING RECTANGULAR FINITE ELEMENT METHODS FOR DARCY-STOKES PROBLEMS 被引量:7
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作者 Shiquan Zhang xiaoping xie Yumei Chen 《Journal of Computational Mathematics》 SCIE CSCD 2009年第2期400-424,共25页
In this paper,we consider lower order rectangular finite element methods for the sin-gularly perturbed Stokes problem.The model problem reduces to a linear Stokes problemwhen the perturbation parameter is large and de... In this paper,we consider lower order rectangular finite element methods for the sin-gularly perturbed Stokes problem.The model problem reduces to a linear Stokes problemwhen the perturbation parameter is large and degenerates to a mixed formulation of Pois-son's equation as the perturbation parameter tends to zero.We propose two 2D andtwo 3D nonconforming rectangular finite elements,and derive robust discretization errorestimates.Numerical experiments are carried out to verify the theoretical results. 展开更多
关键词 矩形有限元 有限元方法 斯托克斯问题 STOKES问题 非协调 低阶 摄动参数 奇异摄动
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ERROR REDUCTION,CONVERGENCE AND OPTIMALITY OF AN ADAPTIVE MIXED FINITE ELEMENT METHOD 被引量:2
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作者 Shaohong DU xiaoping xie 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2012年第1期195-208,共14页
这份报纸证明错误减小为泊松方程的一个适应混合有限元素方法(AMFEM ) 的性质(浸透性质) ,集中和 optimality。在 AMFEM 的每个步骤,本地精炼被执行基于简单也面向边的剩余或面向边的数据摆动,仅仅取决于标记的策略,在精炼的某限制... 这份报纸证明错误减小为泊松方程的一个适应混合有限元素方法(AMFEM ) 的性质(浸透性质) ,集中和 optimality。在 AMFEM 的每个步骤,本地精炼被执行基于简单也面向边的剩余或面向边的数据摆动,仅仅取决于标记的策略,在精炼的某限制下面。这里使用的主要工具是 Carstensen 和 Hoppe (2006 ) 给的严格的分离本地效率性质, quasi-orthogonality 估计由陈, Holst,和徐(2009 ) 证明。数字实验充分证实理论分析。 展开更多
关键词 混合有限元法 自适应 收敛性 泊松方程 面向数据 数值试验 财产 证明
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ON RESIDUAL-BASED A POSTERIORI ERROR ESTIMATORS FOR LOWEST-ORDER RAVIART-THOMAS ELEMENT APPROXIMATION TO CONVECTION-DIFFUSION-REACTION EQUATIONS 被引量:2
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作者 Shaohong Du xiaoping xie 《Journal of Computational Mathematics》 SCIE CSCD 2014年第5期522-546,共25页
剩余类型的一种新技术 posteriori 错误分析被开发因为低顺序的 Raviart-Thomas 混合了 convection-diffusion-reaction 方程的有限元素 discretizations 在二尺寸或三尺寸。集中的混合计划和迎风加权的混合计划被考虑。一个 posteriori... 剩余类型的一种新技术 posteriori 错误分析被开发因为低顺序的 Raviart-Thomas 混合了 convection-diffusion-reaction 方程的有限元素 discretizations 在二尺寸或三尺寸。集中的混合计划和迎风加权的混合计划被考虑。一个 posteriori 错误评估者,在 L2 标准加分级的排水量错误为压力变量错误发源,没有任何另外的费用,能直接与混合计划的答案被计算,并且被证明可靠。没有任何浸透假设,依赖于在系数的本地变化的本地效率被获得,并且从传送对流或反应不是到传送对流主导或反应主导的问题的现在的案例成立。分析的主要工具是修改奥斯瓦尔多插值的分级的排水量,抽象错误估计,和性质的 postprocessed 近似。数字实验被执行支持我们的理论结果并且显示出建议 posteriori 错误估计的竞争行为。[从作者抽象] 展开更多
关键词 后验误差估计 扩散反应方程 混合对流 托马斯 低阶 残余 逼近 有限元离散化
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Coordinative Optimization of Hydro-photovoltaic-wind-battery Complementary Power Stations 被引量:2
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作者 Yuan An Zehaohan Zhao +2 位作者 Songkai Wang Qiang Huang xiaoping xie 《CSEE Journal of Power and Energy Systems》 SCIE CSCD 2020年第2期410-418,共9页
The depletion of fossil energy and the deterioration of the ecological environment have severely restricted the development of the power industry.Therefore,it is extremely urgent to transform energy production methods... The depletion of fossil energy and the deterioration of the ecological environment have severely restricted the development of the power industry.Therefore,it is extremely urgent to transform energy production methods and vigorously develop renewable energy sources.It is therefore important to ensure the stability and operation of a large multi-energy complementary system,and provide theoretical support for the world’s largest single complementary demonstration project with hydro-wind-PV power-battery storage in Qinghai Province.Considering all the multiple power supply constraints,an optimization scheduling model is established with the objective of minimizing the volatility of output power.As particle swarm optimization(PSO)has a problem of premature convergence and slow convergence in the latter half,combined with niche technology in evolution,a niche particle swarm optimization(NPSO)is proposed to determine the optimal solution of the model.Finally,the multiple stations’coordinated operation is analyzed taking the example of 10 million kilowatt complementary power stations with hydropower,wind power,PV power,and battery storage in the Yellow River Company Hainan prefecture.The case verifies the rationality and feasibility of the model.It shows that complementary operations can improve the utilization rate of renewable energy and reduce the impact of wind and PV power’s volatility on the power grid. 展开更多
关键词 Complementary system coordinative optimization multi-energy new energy power generation NPSO
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ERROR REDUCTION, CONVERGENCE AND OPTIMALITY FOR ADAPTIVE MIXED FINITE ELEMENT METHODS FOR DIFFUSION EQUATIONS 被引量:1
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作者 Shaohong Du xiaoping xie 《Journal of Computational Mathematics》 SCIE CSCD 2012年第5期483-503,共21页
没有标记数据的摆动,错误减小,集中和 optimality 为散开方程为适应混合有限元素方法(AMFEM ) 被分析。第一,伪错误,即应力变量误差的和和放大误差评估者,与在二个连续的适应的环之间的一个固定因素被显示出到还原剂,直到摆动。... 没有标记数据的摆动,错误减小,集中和 optimality 为散开方程为适应混合有限元素方法(AMFEM ) 被分析。第一,伪错误,即应力变量误差的和和放大误差评估者,与在二个连续的适应的环之间的一个固定因素被显示出到还原剂,直到摆动。第二, AMFEM 的集中加流动错误的分叉关于伪错误被获得。最后,伪最佳的集中率为全部的错误被建立,即加数据摆动的压力变量错误。 展开更多
关键词 混合有限元方法 扩散方程 收敛性 自适应 最优性 误差估计 最优收敛速度 振荡
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Extended finite element methods for optimal control problems governed by Poisson equation in non-convex domains 被引量:1
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作者 Tao Wang Chaochao Yang xiaoping xie 《Science China Mathematics》 SCIE CSCD 2021年第8期1917-1934,共18页
This paper analyzes two extended finite element methods(XFEMs)for linear quadratic optimal control problems governed by Poisson equation in non-convex domains.We follow the variational discretization concept to discre... This paper analyzes two extended finite element methods(XFEMs)for linear quadratic optimal control problems governed by Poisson equation in non-convex domains.We follow the variational discretization concept to discretize the continuous problems,and apply an XFEM with a cut-off function and a classic XFEM with a fixed enrichment area to discretize the state and co-state equations.Optimal error estimates are derived for the state,co-state and control.Numerical results confirm our theoretical results. 展开更多
关键词 extended finite element method optimal control non-convex domain variational discretization concept
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Lymphatic endothelial cells regulate B-cell homing to lymph nodes via a NIK-dependent mechanism 被引量:1
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作者 Jie Yang Siya Zhang +7 位作者 Lingyun Zhang xiaoping xie Hui Wang Zuliang Jie Meidi Gu Jin-Young Yang Xuhong Cheng Shao-Cong Sun 《Cellular & Molecular Immunology》 SCIE CAS CSCD 2019年第2期165-177,共13页
B cells home to the lymph nodes(LNs)via high endothelial venules(HEVs)under the guidance of chemokines,particularly CXCL13.However,as CXCL13 is not directly made in HEVs,the molecular mechanism mediating B-cell homing... B cells home to the lymph nodes(LNs)via high endothelial venules(HEVs)under the guidance of chemokines,particularly CXCL13.However,as CXCL13 is not directly made in HEVs,the molecular mechanism mediating B-cell homing to LNs has remained unclear.We show here that nuclear factor(NF)-κB-inducing kinase(NIK),a kinase mediating activation of the noncanonical NF-κB pathway,functions in lymphatic endothelial cells(LECs)to regulate B-cell homing to LNs.LEC-conditional deletion of NIK in mice did not affect the integrity or global function of lymphatic vessels but caused a severe reduction in the frequency of B cells in LNs.The LEC-specific NIK deficiency did not affect the survival of B cells or the frequency of B cells in the spleen.B-cell adoptive transfer studies revealed that the LEC-specific NIK deletion impairs the ability of LNs to recruit B cells.We further show that NIK mediates expression of the chemokines CXCL13 and CCL19 in LECs.Although CCL19 is also expressed in blood endothelial cells(BECs),CXCL13 is not produced in BECs.These results suggest that NIK regulates naive B-cell homing to LNs via mediating production of the B-cell homing chemokine CXCL13 in LECs. 展开更多
关键词 B-cell homing lymphatic vessel NIK noncanonical NF-κB
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Accurate 8-Node Hybrid Hexahedral Elements with Energy-Compatible Stress Modes 被引量:1
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作者 Shiquan Zhang xiaoping xie 《Advances in Applied Mathematics and Mechanics》 SCIE 2010年第3期333-354,共22页
In this paper,an energy-compatibility condition is used for stress optimization in the derivation of new accurate 8-node hexahedral elements for threedimensional elasticity.Equivalence of the proposed hybrid method to... In this paper,an energy-compatibility condition is used for stress optimization in the derivation of new accurate 8-node hexahedral elements for threedimensional elasticity.Equivalence of the proposed hybrid method to an enhanced strains method is established,which makes it easy to extend the method to general nonlinear problems.Numerical tests show that the resultant elements possess high accuracy at coarse meshes,are insensitive to mesh distortions and free from volume locking in the analysis of beams,plates and shells. 展开更多
关键词 Finite element hybrid stress method Hellinger-Reissner principle LOCKING
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AN ADAPTIVE HYBRID STRESS TRANSITION QUADRILATERAL FINITE ELEMENT METHOD FOR LINEAR ELASTICITY
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作者 Feiteng Huang xiaoping xie Chensong Zhang 《Journal of Computational Mathematics》 SCIE CSCD 2016年第4期339-364,共26页
在这份报纸,我们讨论一个适应混合压力为线性弹性问题的四边的网孔上的有限元素方法。处理在适应网孔精炼产生的挂的节点,我们建议混合应力的新转变类型有 5 ~ 7 个节点的四边的元素。特别地,我们导出一个 priori 错误评价让 5- 节... 在这份报纸,我们讨论一个适应混合压力为线性弹性问题的四边的网孔上的有限元素方法。处理在适应网孔精炼产生的挂的节点,我们建议混合应力的新转变类型有 5 ~ 7 个节点的四边的元素。特别地,我们导出一个 priori 错误评价让 5- 节点转变混血儿压力元素证明它是免费的从锁泊松,在错误跳了在的意义 priori 估计独立于瘸的常数。我们介绍,为四边的网孔, refinement/coarsening 算法,不要求明确地存储精炼树,并且给一个适应算法。最后,我们提供一些数字结果。[从作者抽象] 展开更多
关键词 杂交应力元 自适应算法 四边形网格 有限元法 混合 线弹性 先验误差估计 网格细化
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TRAF2 regulates T cell immunity by maintaining a Tpl2-ERK survival signaling axis in effector and memory CD8 T cells
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作者 xiaoping xie Lele Zhu +8 位作者 Zuliang Jie Yanchuan Li Meidi Gu Xiaofei Zhou Hui Wang Jae-Hoon Chang Chun-Jung Ko Xuhong Cheng Shao-Cong Sun 《Cellular & Molecular Immunology》 SCIE CAS CSCD 2021年第9期2262-2274,共13页
Generation and maintenance of antigen-specific effector and memory T cells are central events in immune responses against infections.We show that TNF receptor-associated factor 2(TRAF2)maintains a survival signaling a... Generation and maintenance of antigen-specific effector and memory T cells are central events in immune responses against infections.We show that TNF receptor-associated factor 2(TRAF2)maintains a survival signaling axis in effector and memory CD8 T cells required for immune responses against infections.This signaling axis involves activation of Tpl2 and its downstream kinase ERK by NF-κB-inducing kinase(NIK)and degradation of the proapoptotic factor Bim.NIK mediates Tpl2 activation by stimulating the phosphorylation and degradation of the Tpl2 inhibitor p105.Interestingly,while NIK is required for Tpl2-ERK signaling under normal conditions,uncontrolled NIK activation due to loss of its negative regulator,TRAF2,causes constitutive degradation of p105 and Tpl2,leading to severe defects in ERK activation and effector/memory CD8 T cell survival.Thus,TRAF2 controls a previously unappreciated signaling axis mediating effector/memory CD8 T cell survival and protective immunity. 展开更多
关键词 T cell survival Effector and memory CD8 T cells Protective immunity Bacterial infection TRAF2 NIK Tpl2
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Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations
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作者 Dongdong Liang Wei Gong xiaoping xie 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2022年第1期165-199,共35页
In this paper,we consider parabolic distributed control problems with cost functional of pointwise observation type either in space or in time.First,we show the well-posedness of the optimization problems and derive t... In this paper,we consider parabolic distributed control problems with cost functional of pointwise observation type either in space or in time.First,we show the well-posedness of the optimization problems and derive the first order optimality systems,where the adjoint state can be expressed as the linear combination of solutions to two backward parabolic equations that involve the Dirac delta distribution as source either in space or in time.Second,we use a space-time finite element method to discretize the control problems,where the state variable is approximated by piecewise constant functions in time and continuous piecewise linear polynomials in space,and the control variable is discretized by following the variational discretization concept.We obtain a priori error estimates for the control and state variables with order O(k 12+h)up to a logarithmic factor under the L 2-norm.Finally,we perform several numerical experiments to support our theoretical results. 展开更多
关键词 Parabolic optimal control problem pointwise observation space-time finite element method parabolic PDE with Dirac measure error estimate
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Semi-Discrete and Fully Discrete Mixed Finite Element Methods for Maxwell Viscoelastic Model of Wave Propagation
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作者 Hao Yuan xiaoping xie 《Advances in Applied Mathematics and Mechanics》 SCIE 2022年第2期344-364,共21页
Semi-discrete and fully discrete mixedfinite element methods are consid-ered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid.This mixedfinite element framework allows the use of a large... Semi-discrete and fully discrete mixedfinite element methods are consid-ered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid.This mixedfinite element framework allows the use of a large class of exist-ing mixed conformingfinite elements for elasticity in the spatial discretization.In the fully discrete scheme,a Crank-Nicolson scheme is adopted for the approximation of the temporal derivatives of stress and velocity variables.Error estimates of the semi-discrete and fully discrete schemes,as well as an unconditional stability result for the fully discrete scheme,are derived.Numerical experiments are provided to verify the theoretical results. 展开更多
关键词 Maxwell viscoelastic model mixedfinite element semi-discrete and fully discrete error estimate stability.
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High Order Mixed Finite Elements with Mass Lumping for Elasticity on Triangular Grids
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作者 Yan Yang xiaoping xie 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2022年第1期227-250,共24页
A family of conforming mixed finite elements with mass lumping on triangular grids are presented for linear elasticity.The stress field is approximated by symmetric H(div)−Pk(k≥3)polynomial tensors enriched with high... A family of conforming mixed finite elements with mass lumping on triangular grids are presented for linear elasticity.The stress field is approximated by symmetric H(div)−Pk(k≥3)polynomial tensors enriched with higher order bubbles so as to allow mass lumping,and the displacement field is approximated by C−1−Pk−1 polynomial vectors enriched with higher order terms.For both the proposed mixed elements and their mass lumping schemes,optimal error estimates are derived for the stress and displacement in H(div)norm and L 2 norm,respectively.Numerical results confirm the theoretical analysis. 展开更多
关键词 Linear elasticity mixed finite element mass lumping error estimate
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