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ITER第一壁出水管焊接变形数值模拟
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作者 朱小波 缑俊 +7 位作者 胡丹 周毅 邱嵘 李佳霖 吴晶 范小平 谌继明 王平怀 《核聚变与等离子体物理》 北大核心 2026年第1期15-21,共7页
国际热核聚变实验堆(ITER)第一壁进、出水管的内孔焊缝处在结构支点薄弱位置,焊接会造成结构整体严重变形,造成现场安装时第一壁水管接口与预留管口错位,无法完成安装焊接。基于热弹塑性理论,借鉴机器人学中的位姿概念,采用SYSWELD软件... 国际热核聚变实验堆(ITER)第一壁进、出水管的内孔焊缝处在结构支点薄弱位置,焊接会造成结构整体严重变形,造成现场安装时第一壁水管接口与预留管口错位,无法完成安装焊接。基于热弹塑性理论,借鉴机器人学中的位姿概念,采用SYSWELD软件对出水管内孔焊接变形进行模拟,获得弯管安装接口位置的变化,实现了复杂姿态变化的定量比较。计算结果表明,焊接起弧位置显著影响焊后的安装端位置与姿态,以及现场安装时矫正位置与姿态所需的装配力与力矩。而造成这种差异的直接原因是起弧位置影响轴向焊接收缩量的分布。对比不同条件下的计算结果,认为合理选择焊接起弧位置、预留焊接变形尺寸余量,可以减少焊接变形、减少现场安装时所需的装配力与力矩。 展开更多
关键词 iter 焊接变形 第一壁 管焊接 数值模拟
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The analysis of drill string dynamics for extra-deep wells based on successive over-relaxation node iteration method
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作者 Wen-Chang Wang He-Yuan Yang +4 位作者 Da-Kun Luo Ming-Ming You Xing Zhou Feng Chen Qin-Feng Di 《Petroleum Science》 2025年第8期3293-3303,共11页
The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of dril... The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string.Due to the super slenderness ratio of drill string,strong nonlinearity implied in dynamic analysis and the complex load environment,dynamic simulation of drill string faces great challenges.At present,many simulation methods have been developed to analyze drill string dynamics,and node iteration method is one of them.The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall,but its drawback is that the calculation consumes a considerable amount of time.This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method(SOR node iteration method).Through theoretical analysis and numerical examples,the correctness and validity of this method were verified,and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed.The results demonstrate that,in contrast to the conventional node iteration method,the SOR node iteration method can increase the computational efficiency by 48.2%while achieving comparable results.And the whirl trajectory of the extra-deep well drill string is extremely complicated,the maximum rotational speed downhole is approximately twice the rotational speed on the ground.The dynamic torque increases rapidly at the position of the bottom stabilizer,and the lateral vibration in the middle and lower parts of drill string is relatively intense. 展开更多
关键词 Extra-deep well Drill string dynamics Calculation speed-up method SOR iteration method
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Effect of Tooth Geometry on Multi-cycle Meshing Temperature of POM Worm Gears:Parametric Study via an Adaptive Iteration Algorithm
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作者 Kaixing Li Wujiao Xu +1 位作者 Yonggang Liu Datong Qin 《Chinese Journal of Mechanical Engineering》 2025年第2期427-439,共13页
Meshing temperature analyses of polymer gears reported in the literature mainly concern the effects of various material combinations and loading conditions,as their impacts could be seen in the first few meshing cycle... Meshing temperature analyses of polymer gears reported in the literature mainly concern the effects of various material combinations and loading conditions,as their impacts could be seen in the first few meshing cycles.However,the effects of tooth geometry parameters could manifest as the meshing cycles increase.This study investigated the effects of tooth geometry parameters on the multi-cycle meshing temperature of polyoxymethylene(POM)worm gears,aiming to control the meshing temperature elevation by tuning the tooth geometry.Firstly,a finite element(FE)model capable of separately calculating the heat generation and simulating the heat propagation was established.Moreover,an adaptive iteration algorithm was proposed within the FE framework to capture the influence of the heat generation variation from cycle to cycle.This algorithm proved to be feasible and highly efficient compared with experimental results from the literature and simulated results via the full-iteration algorithm.Multi-cycle meshing temperature analyses were conducted on a series of POM worm gears with different tooth geometry parameters.The results reveal that,within the range of 14.5°to 25°,a pressure angle of 25°is favorable for reducing the peak surface temperature and overall body temperature of POM worm gears,which influence flank wear and load-carrying capability,respectively.However,addendum modification should be weighed because it helps with load bearing but increases the risk of severe flank wear.This paper proposes an efficient iteration algorithm for multi-cycle meshing temperature analysis of polymer gears and proves the feasibility of controlling the meshing temperature elevation during multiple cycles by tuning tooth geometry. 展开更多
关键词 POM worm gears Multi-cycle meshing temperature Adaptive iteration algorithm Tooth geometry parameters Parametric study
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A Homotopy Method for Continuous-Time Model-Free LQR Control Based on Policy Iteration
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作者 Wenwu Fan Junlin Xiong 《IEEE/CAA Journal of Automatica Sinica》 2025年第8期1673-1682,共10页
In recent years,reinforcement learning control theory has been well developed.However,model-free value iteration needs many iterations to achieve the desired precision,and modelfree policy iteration requires an initia... In recent years,reinforcement learning control theory has been well developed.However,model-free value iteration needs many iterations to achieve the desired precision,and modelfree policy iteration requires an initial stabilizing control policy.It is significant to propose a fast model-free algorithm to solve the continuous-time linear quadratic control problem without an initial stabilizing control policy.In this paper,we construct a homotopy path on which each point corresponds to an linear quadratic regulator problem.Based on policy iteration,model-based and model-free homotopy algorithms are proposed to solve the optimal control problem of continuous-time linear systems along the homotopy path.Our algorithms are speeded up using first-order differential information and do not require an initial stabilizing control policy.Finally,several practical examples are used to illustrate our results. 展开更多
关键词 Homotopy path initial stabilizing control policy linear quadratic control policy iteration reinforcement learning
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Value Iteration-Based Distributed Adaptive Dynamic Programming for Multi-Player Differential Game With Incomplete Information
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作者 Yun Zhang Yuqi Wang Yunze Cai 《IEEE/CAA Journal of Automatica Sinica》 2025年第2期436-447,共12页
In this paper,a distributed adaptive dynamic programming(ADP)framework based on value iteration is proposed for multi-player differential games.In the game setting,players have no access to the information of others&#... In this paper,a distributed adaptive dynamic programming(ADP)framework based on value iteration is proposed for multi-player differential games.In the game setting,players have no access to the information of others'system parameters or control laws.Each player adopts an on-policy value iteration algorithm as the basic learning framework.To deal with the incomplete information structure,players collect a period of system trajectory data to compensate for the lack of information.The policy updating step is implemented by a nonlinear optimization problem aiming to search for the proximal admissible policy.Theoretical analysis shows that by adopting proximal policy searching rules,the approximated policies can converge to a neighborhood of equilibrium policies.The efficacy of our method is illustrated by three examples,which also demonstrate that the proposed method can accelerate the learning process compared with the centralized learning framework. 展开更多
关键词 Distributed adaptive dynamic programming incomplete information multi-player differential game(MPDG) value iteration
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A New Inversion-free Iterative Method for Solving the Nonlinear Matrix Equation and Its Application in Optimal Control
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作者 GAO Xiangyu XIE Weiwei ZHANG Lina 《应用数学》 北大核心 2026年第1期143-150,共8页
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ... In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method. 展开更多
关键词 Nonlinear matrix equation Maximal positive definite solution Inversion-free iterative method Optimal control
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A Kind of Fast Iterative Methods With the Application Based on Diagonal Matrix Splitting
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作者 XU Qiuyan 《宁夏大学学报(自然科学版中英文)》 2026年第1期1-13,共13页
The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix sp... The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are analyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experiments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically. 展开更多
关键词 iteration matrix splitting diffusion equation CONVERGENCE optimal relaxation factor
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Dual-Mode Data-Driven Iterative Learning Control:Applications in Precision Manufacturing and Intelligent Transportation Systems
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作者 Lei Wang Menghan Wei +3 位作者 Ziwei Huangfu Shunjie Zhu Xuejian Ge Zhengquan Li 《Computers, Materials & Continua》 2026年第2期153-184,共32页
Iterative Learning Control(ILC)provides an effective framework for optimizing repetitive tasks,making it particularly suitable for high-precision applications in both precision manufacturing and intelligent transporta... Iterative Learning Control(ILC)provides an effective framework for optimizing repetitive tasks,making it particularly suitable for high-precision applications in both precision manufacturing and intelligent transportation systems(ITS).This paper presents a systematic review of ILC's developmental progress,current methodologies,and practical implementations across these two critical domains.The review first analyzes the key technical challenges encountered when integrating ILC into precision manufacturing workflows.Through case studies,it evaluates demonstrated improvements in positioning accuracy,surface finish quality,and production throughput.Furthermore,the study examines ILC’s applications in ITS,with particular focus on vehicular motion control applications including autonomous vehicle trajectory tracking,platoon coordination,and traffic signal timing optimization,where its data-driven characteristics enhance adaptability to dynamic environments.Finally,the paper proposes targeted future research directions that are essential for fully realizing ILC’s potential in advancing these interconnected yet distinct fields. 展开更多
关键词 iterative learning control systematic review precisionmanufacturing intelligent transportation systems
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Unpacking the Role of Grammarly in Iterative Continuation Tasks to Develop L2 Grammar Learning Strategies,Grit,and Competence
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作者 Jianling Zhan Chuyi Zhou 《Chinese Journal of Applied Linguistics》 2026年第1期112-132,161,共22页
The iterative continuation task(ICT)requires English as a foreign language(EFL)learners to read a segment and write a continuation that aligns with the preceding segment of an English novel with successive turns,offer... The iterative continuation task(ICT)requires English as a foreign language(EFL)learners to read a segment and write a continuation that aligns with the preceding segment of an English novel with successive turns,offering exposure to diverse grammatical structures and opportunities for contextualized usage.Given the importance of integrating technology into second language(L2)writing and the critical role that grammar plays in L2 writing development,automated written corrective feedback provided by Grammarly has gained significant attention.This study investigates the impact of Grammarly on grammar learning strategies,grammar grit,and grammar competence among EFL college students engaged in ICT.This study employed a mixed-methods sequential exploratory design;56 participants were divided into an experimental group(n=28),receiving Grammarly feedback for ICT,and a control group(n=28),completing ICT without Grammarly feedback.Quantitative results revealed that both groups showed improvements in L2 grammar learning strategies,grit and competence.For the experimental group,significant differences were observed across all variables of L2 grammar learning strategies,grit,and competence between pre-and post-tests.For the control group,significant differences were only observed in the affective dimension of grammar learning strategies,Consistency of Interest(COI)of grammar grit,and grammar competence.However,the control group presented a significantly higher improvement in grammar competence.Qualitative analysis showed both positive and negative perceptions of Grammarly.The pedagogical implications of integrating Grammarly and ICT for L2 grammar development are discussed. 展开更多
关键词 grammar learning strategies grammar grit grammar competence iterative continuation tasks Grammarly
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CAPGen: An MLLM-Based Framework Integrated with Iterative Optimization Mechanism for Cultural Artifacts Poster Generation
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作者 Qianqian Hu Chuhan Li +1 位作者 Mohan Zhang Fang Liu 《Computers, Materials & Continua》 2026年第1期494-510,共17页
Due to the digital transformation tendency among cultural institutions and the substantial influence of the social media platform,the demands of visual communication keep increasing for promoting traditional cultural ... Due to the digital transformation tendency among cultural institutions and the substantial influence of the social media platform,the demands of visual communication keep increasing for promoting traditional cultural artifacts online.As an effective medium,posters serve to attract public attention and facilitate broader engagement with cultural artifacts.However,existing poster generation methods mainly rely on fixed templates and manual design,which limits their scalability and adaptability to the diverse visual and semantic features of the artifacts.Therefore,we propose CAPGen,an automated aesthetic Cultural Artifacts Poster Generation framework built on a Multimodal Large Language Model(MLLM)with integrated iterative optimization.During our research,we collaborated with designers to define principles of graphic design for cultural artifact posters,to guide the MLLM in generating layout parameters.Later,we generated these parameters into posters.Finally,we refined the posters using an MLLM integrated with a multi-round iterative optimization mechanism.Qualitative results show that CAPGen consistently outperforms baseline methods in both visual quality and aesthetic performance.Furthermore,ablation studies indicate that the prompt,iterative optimization mechanism,and design principles significantly enhance the effectiveness of poster generation. 展开更多
关键词 Aesthetic poster generation prompt engineering multimodal large language models iterative optimization design principles
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Global context-aware multi-scale feature iterative refinement for aviation-road traffic semantic segmentation
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作者 Mengyue ZHANG Shichun YANG +1 位作者 Xinjie FENG Yaoguang CAO 《Chinese Journal of Aeronautics》 2026年第2期429-441,共13页
Semantic segmentation for mixed scenes of aerial remote sensing and road traffic is one of the key technologies for visual perception of flying cars.The State-of-the-Art(SOTA)semantic segmentation methods have made re... Semantic segmentation for mixed scenes of aerial remote sensing and road traffic is one of the key technologies for visual perception of flying cars.The State-of-the-Art(SOTA)semantic segmentation methods have made remarkable achievements in both fine-grained segmentation and real-time performance.However,when faced with the huge differences in scale and semantic categories brought about by the mixed scenes of aerial remote sensing and road traffic,they still face great challenges and there is little related research.Addressing the above issue,this paper proposes a semantic segmentation model specifically for mixed datasets of aerial remote sensing and road traffic scenes.First,a novel decoding-recoding multi-scale feature iterative refinement structure is proposed,which utilizes the re-integration and continuous enhancement of multi-scale information to effectively deal with the huge scale differences between cross-domain scenes,while using a fully convolutional structure to ensure the lightweight and real-time requirements.Second,a welldesigned cross-window attention mechanism combined with a global information integration decoding block forms an enhanced global context perception,which can effectively capture the long-range dependencies and multi-scale global context information of different scenes,thereby achieving fine-grained semantic segmentation.The proposed method is tested on a large-scale mixed dataset of aerial remote sensing and road traffic scenes.The results confirm that it can effectively deal with the problem of large-scale differences in cross-domain scenes.Its segmentation accuracy surpasses that of the SOTA methods,which meets the real-time requirements. 展开更多
关键词 Aviation-road traffic Flying cars Global context-aware Multi-scale feature iterative refinement Semantic segmentation
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Complex seismic wavefi eld interpolation based on the Bregman iteration method in the sparse transform domain 被引量:2
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作者 勾福岩 刘财 +2 位作者 刘洋 冯晅 崔芳姿 《Applied Geophysics》 SCIE CSCD 2014年第3期277-288,350,351,共14页
In seismic prospecting, fi eld conditions and other factors hamper the recording of the complete seismic wavefi eld; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, ... In seismic prospecting, fi eld conditions and other factors hamper the recording of the complete seismic wavefi eld; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, prestack missing data affect the subsequent highprecision data processing workfl ow. Compressive sensing is an effective strategy for seismic data interpolation by optimally representing the complex seismic wavefi eld and using fast and accurate iterative algorithms. The seislet transform is a sparse multiscale transform well suited for representing the seismic wavefield, as it can effectively compress seismic events. Furthermore, the Bregman iterative algorithm is an efficient algorithm for sparse representation in compressive sensing. Seismic data interpolation methods can be developed by combining seismic dynamic prediction, image transform, and compressive sensing. In this study, we link seismic data interpolation and constrained optimization. We selected the OC-seislet sparse transform to represent complex wavefields and used the Bregman iteration method to solve the hybrid norm inverse problem under the compressed sensing framework. In addition, we used an H-curve method to choose the threshold parameter in the Bregman iteration method. Thus, we achieved fast and accurate reconstruction of the seismic wavefi eld. Model and fi eld data tests demonstrate that the Bregman iteration method based on the H-curve norm in the sparse transform domain can effectively reconstruct missing complex wavefi eld data. 展开更多
关键词 Bregman iteration OC-seislet transform seismic data interpolation compressive sensing H-curve norm
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Variational iteration method for solving the mechanism of the Equatorial Eastern Pacific El Nino-Southern Oscillation 被引量:35
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作者 莫嘉祺 王辉 +1 位作者 林万涛 林一骅 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第4期671-675,共5页
A class of coupled system for the E1 Nifio-Southern Oscillation (ENSO) mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO mode... A class of coupled system for the E1 Nifio-Southern Oscillation (ENSO) mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered. 展开更多
关键词 nonlinear method of variational iteration perturbation theory El Nino- Southern Oscillation model
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Variational iteration solving method for El Nio phenomenon atmospheric physics of nonlinear model 被引量:14
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作者 MO Jiaqi WANG Hui +1 位作者 LIN Wantao LIN Yihua 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2005年第5期35-38,共4页
A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conce... A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method. 展开更多
关键词 NONLINEAR variational iteration method E1 Niйo phenomenon
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ON THE MONOTONE CONVERGENCE OF THE PROJECTED ITERATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS 被引量:5
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作者 白中治 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1996年第2期228-233,共6页
Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate o... Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated. 展开更多
关键词 LINEAR complementarity PROBLEM projected iteration method MONOTONE convergence.
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Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem 被引量:5
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作者 SUN Yong-ping 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第4期413-419,共7页
The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″(t) + q(t)f(t,u(t),u′(t)) = 0, 0 〈 t 〈 1, u(0) = u″(0) = u′(1) = 0 is studied.... The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″(t) + q(t)f(t,u(t),u′(t)) = 0, 0 〈 t 〈 1, u(0) = u″(0) = u′(1) = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method. 展开更多
关键词 third-order two-point boundary value problem monotone iterative method positive solution existence iterative scheme
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Three-dimensional gravity inversion based on sparse recovery iteration using approximate zero norm 被引量:7
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作者 Meng Zhao-Hai Xu Xue-Chun Huang Da-Nian 《Applied Geophysics》 SCIE CSCD 2018年第3期524-535,共12页
This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zer... This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated. 展开更多
关键词 THREE-DIMENSIONAL gravity inversion sparse recovery APPROXIMATE ZERO NORM iterative method density constraint PENALTY function
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Generalized Variational Iteration Solution of Soliton for Disturbed KdV Equation 被引量:24
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作者 莫嘉琪 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第3期440-442,共3页
The corresponding solution for a class of disturbed KdV equation is considered using the analytic method. From the generalized variational iteration theory, the problem of solving soliton for the corresponding equatio... The corresponding solution for a class of disturbed KdV equation is considered using the analytic method. From the generalized variational iteration theory, the problem of solving soliton for the corresponding equation translates into the problem of variational iteration. And then the approximate solution of the soliton for the equation is obtained. 展开更多
关键词 SOLITON disturbed variational iteration
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Higher Order Aitken Extrapolation with Application to Converging and Diverging Gauss-Seidel Iterations 被引量:4
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作者 Ababu Teklemariam Tiruneh 《Journal of Applied Mathematics and Physics》 2013年第5期128-143,共16页
In this paper, Aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduce... In this paper, Aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduced that enables successive decomposition of high Eigen values of the iteration matrix to enable convergence. While extrapolation of a convergent fixed point iteration using a geometric series sum is a known form of Aitken acceleration, it is shown that in this paper, the same formula can be used to estimate the solution of sets of linear equations from diverging Gauss-Seidel iterations. In both convergent and divergent iterations, the ratios of differences among the consecutive values of iteration eventually form a convergent (divergent) series with a factor equal to the largest Eigen value of the iteration matrix. Higher order Aitken extrapolation is shown to eliminate the influence of dominant Eigen values of the iteration matrix in successive order until the iteration is determined by the lowest possible Eigen values. For the convergent part of the Gauss-Seidel iteration, further acceleration is made possible by coupling of the extrapolation technique with the successive over relaxation (SOR) method. Application examples from both convergent and divergent iterations have been provided. Coupling of the extrapolation with the SOR technique is also illustrated for a steady state two dimensional heat flow problem which was solved using MATLAB programming. 展开更多
关键词 Linear EQUATIONS GAUSS-SEIDEL iteration Aitken EXTRAPOLATION ACCELERATION Technique iteration Matrix Fixed Point iteration
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The Equivalence between the Mann and Ishikawa Iterations for Generalized Contraction Mappings in a Cone 被引量:3
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作者 L. Jones Tarcius Doss T. Esakkiappan 《Applied Mathematics》 2011年第11期1369-1371,共3页
In this paper, equivalence between the Mann and Ishikawa iterations for a generalized contraction mapping in cone subset of a real Banach space is discussed.
关键词 MANN iteration ISHIKAWA iterationS Generalized CONTRACTION CONE
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