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预拓扑与网族的预收敛类 被引量:11
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作者 钟晓静 李生刚 苏华飞 《山东大学学报(理学版)》 CAS CSCD 北大核心 2007年第8期62-66,共5页
引入了网族及预收敛类的概念,给出了从T(X)(即X上的预拓扑的全体)到S(X)(即X上的预收敛类的全体)的单射,证明了当X是有限集时该映射是双射.
关键词 拓扑 预收敛 完备格同构 网族
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关于“预拓扑与网族的预收敛类”的注 被引量:1
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作者 杨小飞 伏文清 李生刚 《数学杂志》 CSCD 北大核心 2012年第3期506-510,共5页
本文研究了预拓扑空间中的收敛问题.利用完备格同构的方法,获得了预拓扑与预收敛类可以相互确定的结果,推广了拓扑与收敛类可以相互确定的结果,同时推广了文献[1]的结果.
关键词 拓扑 预收敛 完备格同构 网族
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用网族的预收敛类刻画预拓扑空间的可数性公理 被引量:1
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作者 钟晓静 《山东大学学报(理学版)》 CAS CSCD 北大核心 2009年第6期25-28,共4页
给出了预拓扑空间中第一、二可数性公理的定义,并利用网族的预收敛类的理论具体刻划满足第一、二可数性公理的预拓扑空间。
关键词 拓扑空间 预收敛 网族 第一可数性公理 第二可数性公理
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Hamilton算子的广义弱预解收敛性
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作者 彭正卿 侯国林 《内蒙古大学学报(自然科学版)》 CAS 北大核心 2022年第1期1-5,共5页
引入线性算子广义弱预解收敛的定义。进而,讨论了稠定闭线性算子弱预解收敛与广义弱预解收敛之间的关系,并给出了辛自伴无穷维Hamilton算子广义强弱预解收敛等价性的证明。
关键词 HAMILTON算子 辛自伴 解式 广义强收敛 广义弱收敛
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大断面隧道地层超前预加固及开挖支护过程稳定性的数值模拟 被引量:20
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作者 周捷 漆泰岳 +1 位作者 旷文涛 李斌 《隧道建设》 2009年第2期185-188,201,共5页
在低黏聚力的软弱地层、大断面隧道开挖中,掌子面稳定是施工中面临的很大问题。采用超前预加固工法,对浏阳河隧道开挖过程进行数值模拟,通过分析超前预加固法对隧道位移、受力的影响,并研究各加固参数的敏感性,得到掌子面的超前锚杆加... 在低黏聚力的软弱地层、大断面隧道开挖中,掌子面稳定是施工中面临的很大问题。采用超前预加固工法,对浏阳河隧道开挖过程进行数值模拟,通过分析超前预加固法对隧道位移、受力的影响,并研究各加固参数的敏感性,得到掌子面的超前锚杆加固长度对掌子面的稳定性影响最大,掌子面外超前预加固对改善超前核心土受力也有较大影响。 展开更多
关键词 大断面隧道 超前加固 开挖支护 挤出变形 超前核心土 预收敛 稳定性 数值模拟
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一类变分不等式组迭代解的收敛性
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作者 严慧文 《汕头大学学报(自然科学版)》 2013年第4期15-18,共4页
本文研究了一类变分不等式组逼近解的收敛性问题.利用预解算子的技术注明,在一定的松弛强度,连续条件下,逼近解是收敛的.该结果大大减弱了文献(Applied Mathematics and Computation 214(2009)26-30)中的条件,而且明显地改进了该文中的... 本文研究了一类变分不等式组逼近解的收敛性问题.利用预解算子的技术注明,在一定的松弛强度,连续条件下,逼近解是收敛的.该结果大大减弱了文献(Applied Mathematics and Computation 214(2009)26-30)中的条件,而且明显地改进了该文中的迭代计算方法. 展开更多
关键词 解算子 变分不等式组 解方法的收敛
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新意法隧道设计施工概述 被引量:30
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作者 翟进营 杨会军 王莉莉 《隧道建设》 2008年第1期46-50,55,共6页
20世纪70年代中期,意大利的Pietro Lunardi教授开始研究并逐步创立了岩土控制变形分析法(ADECO-RS法),该方法用中文解释为"新意法"。介绍新意法的理论基础、新意法隧道设计施工的基本步骤以及新意法与新奥法的不同之处,为新... 20世纪70年代中期,意大利的Pietro Lunardi教授开始研究并逐步创立了岩土控制变形分析法(ADECO-RS法),该方法用中文解释为"新意法"。介绍新意法的理论基础、新意法隧道设计施工的基本步骤以及新意法与新奥法的不同之处,为新意法在我国的推广应用提供参考。 展开更多
关键词 岩土控制变形分析法(ADECO-RS法) 超前核心土 挤出变形 预收敛 收敛 约束作用 超前约束作用
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基于预设时间收敛的分布式优化算法
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作者 杨涛 常怡然 +1 位作者 张坤朋 徐磊 《控制与决策》 EI CSCD 北大核心 2023年第8期2364-2374,共11页
考虑一类分布式优化问题,其目标是通过局部信息交互,使得局部成本函数之和构成的全局成本函数最小.针对该类问题,通过引入时基发生器(TBG),提出两种基于预设时间收敛的分布式比例积分(PI)优化算法.与现有的基于有限/固定时间收敛的分布... 考虑一类分布式优化问题,其目标是通过局部信息交互,使得局部成本函数之和构成的全局成本函数最小.针对该类问题,通过引入时基发生器(TBG),提出两种基于预设时间收敛的分布式比例积分(PI)优化算法.与现有的基于有限/固定时间收敛的分布式优化算法相比,所提出算法的收敛时间不依赖于系统的初值和参数,且可以任意预先设计.此外,在全局成本函数关于最优值点有限强凸,局部成本函数为可微的凸函数,且具有局部Lipschitz梯度的条件下,通过Lyapunov理论证明了所提算法都能实现预设时间收敛.最后,通过数值仿真验证了所提出算法的有效性. 展开更多
关键词 分布式优化 设时间收敛 比例积分算法 有限强凸 时基发生器
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地铁隧道施工引起地层位移空间特征研究 被引量:2
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作者 李奎 高波 夏志强 《路基工程》 北大核心 2008年第4期5-7,共3页
运用数值分析方法研究浅埋地铁隧道暗挖施工引起地层变形的空间特征,特别是隧道变形的空间特征。研究表明只有正确认识了隧道收敛变形、预收敛变形和掌子面挤压变形之间相互关联,才能够正确认识到引起隧道整个变形过程的真正诱因。
关键词 浅埋隧道 收敛变形 挤压变形 预收敛变形 核心土体
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新意法概述及其应用建议 被引量:3
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作者 李开庆 唐天龙 《山西建筑》 2013年第28期170-172,共3页
介绍了新意法的核心思想和工作流程,对比了其与新奥法在力学分析模式、变形反馈和响应等方面的区别,并总结了新意法的优点,最后对新意法在国内的应用前景做了分析并提出几点建议,旨在为新意法探索中国化发展道路提供参考。
关键词 隧道施工 新意法 超前核心土 预收敛 控制变形
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复合支护方法在高地应力区破碎软岩巷道中的应用
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作者 周永鸿 《煤》 2006年第1期28-30,共3页
阐述了在高地压区破碎带软岩巷道施工中应用复合支护的方法,主要指出围岩变形是绝对的,巷道设计时应预留一定收敛空间,以释放部分地应力能。初期支护后,通过工程监测为二次支护提供较准确的时间依据,尽量减小巷道变形,减少巷道维修工程量。
关键词 支护 预收敛 工程监测 二次支护
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Energy-absorption forecast of thin-walled structure by GA-BP hybrid algorithm 被引量:7
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作者 谢素超 周辉 +1 位作者 赵俊杰 章易程 《Journal of Central South University》 SCIE EI CAS 2013年第4期1122-1128,共7页
In order to analyze the influence rule of experimental parameters on the energy-absorption characteristics and effectively forecast energy-absorption characteristic of thin-walled structure, the forecast model of GA-B... In order to analyze the influence rule of experimental parameters on the energy-absorption characteristics and effectively forecast energy-absorption characteristic of thin-walled structure, the forecast model of GA-BP hybrid algorithm was presented by uniting respective applicability of back-propagation artificial neural network (BP-ANN) and genetic algorithm (GA). The detailed process was as follows. Firstly, the GA trained the best weights and thresholds as the initial values of BP-ANN to initialize the neural network. Then, the BP-ANN after initialization was trained until the errors converged to the required precision. Finally, the network model, which met the requirements after being examined by the test samples, was applied to energy-absorption forecast of thin-walled cylindrical structure impacting. After example analysis, the GA-BP network model was trained until getting the desired network error only by 46 steps, while the single BP-ANN model achieved the same network error by 992 steps, which obviously shows that the GA-BP hybrid algorithm has faster convergence rate. The average relative forecast error (ARE) of the SEA predictive results obtained by GA-BP hybrid algorithm is 1.543%, while the ARE of the SEA predictive results obtained by BP-ANN is 2.950%, which clearly indicates that the forecast precision of the GA-BP hybrid algorithm is higher than that of the BP-ANN. 展开更多
关键词 thin-walled structure GA-BP hybrid algorithm IMPACT energy-absorption characteristic FORECAST
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New Estimates for the Rate of Convergence of the Method of Subspace Corrections 被引量:1
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作者 Durkbin Cho Jinchao Xu Ludmil Zikatanov 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2008年第1期44-56,共13页
We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a ... We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a special case,a lower bound for preconditioners defined via the method of successive subspace corrections. 展开更多
关键词 Method of subspace corrections preconditioning convergence rate of linear iterative method
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Studies on quasi-Newton methods in timedomain multiscale full waveform inversion
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作者 Dai Meng-Xue Zhang Hua Tian Xiao 《Applied Geophysics》 SCIE CSCD 2022年第2期221-231,307,308,共13页
The time-domain multiscale full waveform inversion(FWI)mitigates the influence of the local minima problem in nonlinear inversion via sequential inversion using different frequency components of seismic data.The quasi... The time-domain multiscale full waveform inversion(FWI)mitigates the influence of the local minima problem in nonlinear inversion via sequential inversion using different frequency components of seismic data.The quasi-Newton methods avoid direct computation of the inverse Hessian matrix,which reduces the amount of computation and storage requirement.A combination of the two methods can improve inversion accuracy and efficiency.However,the quasi-Newton methods in time-domain multiscale FWI still cannot completely solve the problem where the inversion is trapped in local minima.We first analyze the reasons why the quasi-Newton Davidon–Fletcher–Powell and Broyden–Fletcher–Goldfarb–Shanno methods likely fall into the local minima using numerical experiments.During seismic-wave propagation,the amplitude decreases with the geometric diffusion,resulting in the concentration of the gradient of the velocity model in the shallow part,and the deep velocity cannot be corrected.Thus,the inversion falls into the local minima.To solve this problem,we introduce a virtual-source precondition to remove the influence of geometric diffusion.Thus,the model velocities in the deep and shallow parts can be simultaneously completely corrected,and the inversion can more stably converge to the global minimum.After the virtual-source precondition is implemented,the problem in which the quasi-Newton methods likely fall into the local minima is solved.However,problems remain,such as incorrect search direction after a certain number of iterations and failure of the objective function to further decrease.Therefore,we further modify the process of timedomain multiscale FWI based on virtual-source preconditioned quasi-Newton methods by resetting the inverse of the approximate Hessian matrix.Thus,the validity of the search direction of the quasi-Newton methods is guaranteed.Numerical tests show that the modified quasi-Newton methods can obtain more reasonable inversion results,and they converge faster and entail lesser computational resources than the gradient method. 展开更多
关键词 Full waveform inversion Multiscale QUASI-NEWTON Virtual-source precondition Convergence rate
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Preconditioning Schur Complement Systems of Highly-Indefinite Linear Systems for a Parallel Hybrid Solver
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作者 I.Yamazaki E.G.Ng 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2010年第3期352-366,共15页
A parallel hybrid linear solver based on the Schur complement method has the potential to balance the robustness of direct solvers with the efficiency of preconditioned iterative solvers.However,when solving large-sca... A parallel hybrid linear solver based on the Schur complement method has the potential to balance the robustness of direct solvers with the efficiency of preconditioned iterative solvers.However,when solving large-scale highly-indefinite linear systems,this hybrid solver often suffers from either slow convergence or large memory requirements to solve the Schur complement systems.To overcome this challenge,we in this paper discuss techniques to preprocess the Schur complement systems in parallel. Numerical results of solving large-scale highly-indefinite linear systems from various applications demonstrate that these techniques improve the reliability and performance of the hybrid solver and enable efficient solutions of these linear systems on hundreds of processors,which was previously infeasible using existing state-of-the-art solvers. 展开更多
关键词 Schur complement method PRECONDITIONING matrix preprocessing.
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Prediction of plastic zone size around circular tunnels in non-hydrostatic stress field 被引量:6
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作者 Behnam Bagheri Fazlollah Soltani Hamid Mohammadi 《International Journal of Mining Science and Technology》 SCIE EI 2014年第1期81-85,共5页
This paper discusses the calculation of plastic zone properties around circular tunnels to rock-masses that satisfy the Hoek–Brown failure criterion in non-hydrostatic condition,and reviews the calculation of plastic... This paper discusses the calculation of plastic zone properties around circular tunnels to rock-masses that satisfy the Hoek–Brown failure criterion in non-hydrostatic condition,and reviews the calculation of plastic zone and displacement,and the basis of the convergence–confinement method in hydrostatic condition.A two-dimensional numerical simulation model was developed to gain understanding of the plastic zone shape.Plastic zone radius in any angles around the tunnel is analyzed and measured,using different values of overburden(four states)and stress ratio(nine states).Plastic zone radius equations were obtained from fitting curve to data which are dependent on the values of stress ratio,angle and plastic zone radius in hydrostatic condition.Finally validation of this equation indicate that results predict the real plastic zone radius appropriately. 展开更多
关键词 Plastic zone radius Convergence-confinement method Non-hydrostatic condition Stress ratio
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Implicit Variational Inclusions and Algorithms Involving (A, η)-monotone Operators in 2-uniformly Smooth Banach Spaces
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作者 N. K. Sahu 《Journal of Mathematics and System Science》 2015年第6期269-278,共10页
This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used t... This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the (A, η)-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also investigated for variational inclusion problems involving (H, η)-monotone mappings. 展开更多
关键词 Semi-inner product space Generalized resolvent operator Variational inclusion 2-uniformly smooth Banach space.
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Partial functional linear quantile regression 被引量:4
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作者 TANG QingGuo CHENG LongSheng 《Science China Mathematics》 SCIE 2014年第12期2589-2608,共20页
This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables.... This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology. 展开更多
关键词 partial functional linear quantile regression quantile estimator functional principal coraponent analysis convergence rate
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