A novel three-step implicit iteration process for threeΦ-hemicontractive mapping in the intermediate sense

In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.

Fast and Accurate Predictor-Corrector Methods Using Feedback-Accelerated Picard Iteration for Strongly Nonlinear Problems

Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A novel class of correctors based on feedback-accelerated Picard iteration(FAPI)is proposed to further enhance computational performance.With optimal feedback terms that do not require inversion of matrices,significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts;however,the computational complexities are comparably low.These advantages enable nonlinear engineering problems to be solved quickly and accurately,even with rough initial guesses from elementary predictors.The proposed method offers flexibility,enabling the use of the generated correctors for either bulk processing of collocation nodes in a domain or successive corrections of a single node in a finite difference approach.In our method,the functional formulas of FAPI are discretized into numerical forms using the collocation approach.These collocated iteration formulas can directly solve nonlinear problems,but they may require significant computational resources because of the manipulation of high-dimensionalmatrices.To address this,the collocated iteration formulas are further converted into finite difference forms,enabling the design of lightweight predictor-corrector algorithms for real-time computation.The generality of the proposed method is illustrated by deriving new correctors for three commonly employed finite-difference approaches:the modified Euler approach,the Adams-Bashforth-Moulton approach,and the implicit Runge-Kutta approach.Subsequently,the updated approaches are tested in solving strongly nonlinear problems,including the Matthieu equation,the Duffing equation,and the low-earth-orbit tracking problem.The numerical findings confirm the computational accuracy and efficiency of the derived predictor-corrector algorithms.

Calculation of Mass Concrete Temperature Containing Cooling Water Pipe Based on Substructure and Iteration Algorithm

Mathematical physics equations are often utilized to describe physical phenomena in various fields of science and engineering.One such equation is the Fourier equation,which is a commonly used and effective method for evaluating the effectiveness of temperature control measures for mass concrete.One important measure for temperature control in mass concrete is the use of cooling water pipes.However,the mismatch of grids between large-scale concrete models and small-scale cooling pipe models can result in a significant waste of calculation time when using the finite element method.Moreover,the temperature of the water in the cooling pipe needs to be iteratively calculated during the thermal transfer process.The substructure method can effectively solve this problem,and it has been validated by scholars.The Abaqus/Python secondary development technology provides engineers with enough flexibility to combine the substructure method with an iteration algorithm,which enables the creation of a parametric modeling calculation for cooling water pipes.This paper proposes such a method,which involves iterating the water pipe boundary and establishing the water pipe unit substructure to numerically simulate the concrete temperature field that contains a cooling water pipe.To verify the feasibility and accuracy of the proposed method,two classic numerical examples were analyzed.The results showed that this method has good applicability in cooling pipe calculations.When the value of the iteration parameterαis 0.4,the boundary temperature of the cooling water pipes can meet the accuracy requirements after 4∼5 iterations,effectively improving the computational efficiency.Overall,this approach provides a useful tool for engineers to analyze the temperature control measures accurately and efficiently for mass concrete,such as cooling water pipes,using Abaqus/Python secondary development.

Value Iteration-Based Cooperative Adaptive Optimal Control for Multi-Player Differential Games With Incomplete Information

This paper presents a novel cooperative value iteration(VI)-based adaptive dynamic programming method for multi-player differential game models with a convergence proof.The players are divided into two groups in the learning process and adapt their policies sequentially.Our method removes the dependence of admissible initial policies,which is one of the main drawbacks of the PI-based frameworks.Furthermore,this algorithm enables the players to adapt their control policies without full knowledge of others’ system parameters or control laws.The efficacy of our method is illustrated by three examples.

Another SSOR Iteration Method

Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.

Iteration and evaluation of shale oil development technology for continental rift lake basins

By benchmarking with the iteration of drilling technology,fracturing technology and well placement mode for shale oil and gas development in the United States and considering the geological characteristics and development difficulties of shale oil in the Jiyang continental rift lake basin,East China,the development technology system suitable for the geological characteristics of shale oil in continental rift lake basins has been primarily formed through innovation and iteration of the development,drilling and fracturing technologies.The technology system supports the rapid growth of shale oil production and reduces the development investment cost.By comparing it with the shale oil development technology in the United States,the prospect of the shale oil development technology iteration in continental rift lake basins is proposed.It is suggested to continuously strengthen the overall three-dimensional development,improve the precision level of engineering technology,upgrade the engineering technical indicator system,accelerate the intelligent optimization of engineering equipment,explore the application of complex structure wells,form a whole-process integrated quality management system from design to implementation,and constantly innovate the concept and technology of shale oil development,so as to promote the realization of extensive,beneficial and high-quality development of shale oil in continental rift lake basins.

Strong Convergence of an Implicit Iteration Process for a Finite Family of Asymptotically Ф-pseudocontractive Mappings

Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new composite implicit iteration scheme with errors. The results presented in this paper extend and improve the main results of Sun, Gu and Osilike published on J. Math. Anal. Appl.

A Modified Averaging Composite Implicit Iteration Process for Common Fixed Points of a Finite Family of k-Strictly Asymptotically Pseudocontractive Mappings

The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process.

BRUCK FORMULA FOR A PERTURBED LIPSCHITZIAN ITERATION OF LIPSCHITZ PSEUDOCONTRACTIVE MAPS

The solution to evolution equations has developed an independent theory within nonlinear analysis dealing with the existence and approximation of such solution （ fixed point） of pseudocontractive operators and its variants. The object is to introduce a perturbed iteration method for proving the convergence of sequence of Lipschitzian pseudocontractive mapping using approximate fixed point technique. This iteration can be ued for nonlinear operators which are more general than Lipschitzian pseudocontractive operator and Bruck iteration fails for proving their convergence. Our results generalize the results of Chidume and Zegeye.

A fixed point theorem for Proinov mappings with a contractive iterate

In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces.We consider examples to illustrate the validity of the obtained result.

Variational Iteration Method for Solving Time Fractional Burgers Equation Using Maple

The Time Fractional Burger equation was solved in this study using the Mabel software and the Variational Iteration approach. where a number of instances of the Time Fractional Burger Equation were handled using this technique. Tables and images were used to present the collected numerical results. The difference between the exact and numerical solutions demonstrates the effectiveness of the Mabel program’s solution, as well as the accuracy and closeness of the results this method produced. It also demonstrates the Mabel program’s ability to quickly and effectively produce the numerical solution.

Policy Iteration for Optimal Control of Discrete-Time Time-Varying Nonlinear Systems

Aimed at infinite horizon optimal control problems of discrete time-varying nonlinear systems,in this paper,a new iterative adaptive dynamic programming algorithm,which is the discrete-time time-varying policy iteration(DTTV)algorithm,is developed.The iterative control law is designed to update the iterative value function which approximates the index function of optimal performance.The admissibility of the iterative control law is analyzed.The results show that the iterative value function is non-increasingly convergent to the Bellman-equation optimal solution.To implement the algorithm,neural networks are employed and a new implementation structure is established,which avoids solving the generalized Bellman equation in each iteration.Finally,the optimal control laws for torsional pendulum and inverted pendulum systems are obtained by using the DTTV policy iteration algorithm,where the mass and pendulum bar length are permitted to be time-varying parameters.The effectiveness of the developed method is illustrated by numerical results and comparisons.

Iteration dependent interval based open‐closed‐loop iterative learning control for time varying systems with vector relative degree

For linear time varying(LTV)multiple input multiple output(MIMO)systems with vector relative degree,an open‐closed‐loop iterative learning control(ILC)strategy is developed in this article,where the time interval of operation is iteration dependent.To compensate the missing tracking signal caused by iteration dependent interval,the feedback control is introduced in ILC design.As the tracking signal of many continuous iterations is lost in a certain interval,the feedback control part can employ the tracking signal of current iteration for compensation.Under the assumption that the initial state vibrates around the desired initial state uniformly in mathematical expectation sense,the expectation of ILC tracking error can converge to zero as the number of iteration tends to infinity.Under the circumstance that the initial state varies around the desired initial state with a bound,as the number of iteration tends to infinity,the expectation of ILC tracking error can be driven to a bounded range,whose upper bound is proportional to the fluctuation.It is revealed that the convergence condition is dependent on the feed-forward control gains,while the feedback control can accelerate convergence speed by selecting appropriate feedback control gains.As a special case,the controlled system with integrated high relative degree is also addressed by proposing a simplified iteration dependent interval based open‐closed‐loop ILC method.Finally,the effectiveness of the developed iteration dependent interval based open‐closed‐loop ILC is illustrated by a simulation example with two cases on initial state.

A Novel Method to Enhance the Inversion Speed and Precision of the NMR T_(2) Spectrum by the TSVD Based Linearized Bregman Iteration

The low-field nuclear magnetic resonance(NMR)technique has been used to probe the pore size distribution and the fluid composition in geophysical prospecting and related fields.However,the speed and accuracy of the existing numerical inversion methods are still challenging due to the ill-posed nature of the first kind Fredholm integral equation and the contamination of the noises.This paper proposes a novel inversion algorithmto accelerate the convergence and enhance the precision using empirical truncated singular value decompositions(TSVD)and the linearized Bregman iteration.The L1 penalty term is applied to construct the objective function,and then the linearized Bregman iteration is utilized to obtain fast convergence.To reduce the complexity of the computation,empirical TSVD is proposed to compress the kernel matrix and determine the appropriate truncated position.This novel inversion method is validated using numerical simulations.The results indicate that the proposed novel method is significantly efficient and can achieve quick and effective data solutions with low signal-to-noise ratios.

非理性偏好下动力电池再制造供应链最优决策与协调研究

考虑动力电池剩余容量不确定特征,构建由电池供应商和汽车制造商组成的再制造供应链,分别探讨决策双方完全理性、单向非理性偏好和双向非理性偏好等5种决策情形下的均衡解。研究发现:动力电池再制造容量起始点对回收量具有正向作用。在双向非理性偏好情形下,供应商的利他(公平)偏好程度增加导致制造商和系统总利润提高(降低),而自身利润总是降低;制造商的非理性偏好对供应链成员及系统利润的影响与供应商的非理性偏好程度有关。在单向非理性情形下,供应链成员的利他(公平)偏好程度增加导致自身利润下降(上升)而对方利润上升(下降)。两部定价契约和收益共享契约能够实现双向非理性偏好情形下再制造供应链的协调。

供给与需求不确定情形下的供应链回购契约与补偿契约比较

在供应链存在不确定性的情况下,企业之间通过签订有效的契约(如补偿契约或回购契约)对供应链成员的行为进行约束。研究了需求和生产不确定同时存在时,一个两级供应链中的制造商和零售商在一个定价-订购-生产-销售周期内进行斯坦伯格博弈的模型,各成员的目标均为实现自身利润最大化。从理论上证明了使利润最大化的最优投入产量和最优订购量均衡存在且唯一,揭示了生产成本、批发价格、生产与需求的不确定性等因素对均衡的影响。最后,从制造商和零售商角度比较了其在不同契约机制下的利润水平。对于制造商,当零售商补偿单价相对于制造商生产成本较高时,多数情况下补偿契约优于回购契约;当零售商补偿单价相对于制造商生产成本较小时则恰好相反。对于零售商,多数情况下回购契约优于补偿契约,唯一的特殊情况是制造商产品盈利空间相对较小、生产不确定较大以及需求不确定较小。

批准生效合同责任承担的体系构造——《民法典合同编通则解释》第12条评释

《民法典合同编通则解释》第12条仅涉及法律、行政法规这一层级法源设立的直接影响债权合同生效的报批手续,属于法律规定的特别生效要件。合同已成立未生效时产生形式拘束力,包括不得擅自变更或解除的消极义务以及履行报批义务等积极义务。法定报批义务以及围绕报批义务的约定独立生效,属于依据诚实信用原则产生的附随义务,相对方有权采取请求继续履行报批义务的救济方式。第12条第1款在第一阶段新创设了一种法定解除权,“违反报批义务的赔偿责任”应仅限于固有利益的直接损失,而不应参照违反预约合同的赔偿范围。第2款在第二阶段的解除权符合《民法典》第563条要件,赔偿范围参照违约责任时需考察通过批准的难易度、报批义务人拒不报批的主观恶性程度以及整个交易的完成度和成熟度。第4款在第三阶段批准机关决定不予批准时无须规定解除权,报批义务人承担过错责任,依据《民法典》第157条考虑适用财产返还和折价补偿制度的替代效果。

政府合同概念的体系化重构

现有政府合同管理规范对政府合同的内涵和外延进行了界定,但学理意义上的概念构造尚未完成,“政府合同=行政协议+缔结主体一方为行政机关的民事合同”之结论存在缺陷。通过把合同还原为通用于各部门法的中性工具,将政府合同的研究视角从救济前移至行政过程,政府合同的识别标准被调整为“行政机关与任何主体订立的合同均为政府合同”。以行政任务为出发点,可将政府合同区分为公务型政府合同和管理型政府合同,公务型政府合同可被进一步区分为内部公务型政府合同与外部公务型政府合同。以救济途径为落脚点,可以将政府合同区分为行政协定与非行政协定,非行政协定可被进一步区分为行政协议、民事合同、磋商性文件和劳动人事协议,其中,民事合同和行政协议属于狭义政府合同。将两条基于不同场景的体系化路径进行对接与融合,有助于形成对政府合同概念相对立体的认知,动态还原政府合同概念的全貌。

基于整车路面谱的副车架开裂台架试验及仿真

针对前悬架稳定杆与副车架连接处在整车试验场耐久测试过程中出现的疲劳破坏问题,通过对稳定杆进行贴片标定,获得了试验场环境下稳定杆的连杆力和稳定杆扭转相对位移的强化耐久路谱,设计搭建了稳定杆副车架系统的物理台架,并按照耐久性规范进行了台架试验。试验结果表明:该台架试验装置能良好地再现整车耐久路试下的断裂位置,疲劳寿命相对于整车耐久路试的疲劳寿命偏差仅为2.5%。在此基础上,建立了稳定杆与副车架多体的仿真模型,设定了与系统试验台架相同的约束边界,通过虚拟迭代的方法及准静态有限元疲劳寿命分析法对系统进行了仿真分析。仿真得到稳定杆连杆力和稳定杆扭转相对位移信号,与测试结果进行对比分析可以看出,时域下相位和幅值重合度良好,频域下的PSD谱重合度较高,穿级计数载荷统计基本一致,载荷相对损伤均在1附近,相关风险位置处的仿真疲劳寿命与整车耐久试验寿命偏差比为6.25%,获得了较高精度的风险位置载荷,实现了耐久风险位置的复现。最后,基于仿真模型对副车架风险位置处进行了结构优化设计,改进后的方案顺利通过了后续的台架试验和整车耐久路试。

构建全球教师发展与职业变革的社会契约--基于对联合国教科文组织《全球教师报告》的解读

全球中小学教师不仅在生师比上面临绝对性数量短缺,而且在学科、性别、高质量教师、地区分配等方面也存在结构性短缺。全球教师短缺归因于教师社会地位不高,学生从教意愿低,教师招聘与管理体制不畅,教师流失率高。基于此,不少国家的政府部门重视加强规划与调控,强化教师行业投资水平,提高教师社会地位与职业吸引力,以期建设更加稳定与高质量的教师队伍。