Strong Convergence of an Iterative Method for Generalized Mixed Equilibrium Problems and Fixed Point Problems

In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of nonexpansive mappings. Furthermore, we show a strong convergence theorem under some mild conditions.

A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators

An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method.

PROXIMAL POINT ALGORITHM WITH ERRORS FOR GENERALIZED STRONGLY NONLINEARQUASIVARIATIONAL INCLUSIONS

In this paper, a class of generalized strongly nonlinear quasivariational inclusions are studied. By using the properties of the resolvent operator associated with a maximal monotone; mapping in Hilbert space, an existence theorem of solutions for generalized strongly nonlinear quasivariational inclusion is established and a new proximal point algorithm with errors is suggested for finding approximate solutions which strongly converge to the exact solution of the generalized strongly, nonlinear quasivariational inclusion. As special cases, some known results in this field are also discussed.

Generalized Strongly Nonlinear Quasi-Complementarity Problems

Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem.

Classification of Single Traveling Wave Solutions to the Generalized Strong Nonlinear Boussinesq Equation without Dissipation Terms in <i>P</i>= 1

By the complete discrimination system for polynomial method, we obtained the classification of single traveling wave solutions to the generalized strong nonlinear Boussinesq equation without dissipation terms in p=1.

Global Attractors of Strong Solution for the Generalized Kuramoto-Sivashinsky Equation

Using a new method developed in [5], we prove the existence of global attractors for the Generalized Kuramoto-Sivashinsky equation in H^3per（Ω） and H^4per（Ω）.

Strongly Generalized Convex Fuzzy-Valued Function and Its Application in Fuzzy Optimization

Based on the ordering of fuzzy numbers proposed by Goetschel and Voxman,the representations and some properties of strongly preinvex fuzzy-valued function are defined and obtained, several new concepts of strongly monotonicities fuzzy functions are introduced, the relationship among the strongly preinvex, strongly invex and monotonicities under some suitable and appropriate conditions is established and a necessary condition for strongly pseudoinvex functions is given. As an application, the conditions of local optimal solution and global optimal solution in the mathematical programming problem are discussed.

Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces

A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.

Continuity of the Solution Mappings for Parametric Generalized Strong Vector Equilibrium Problems

The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for a parametric generalized strong vector equilibrium problem. By virtue of a nonlinear scalarization technique, a new density result of the solution mapping is obtained. Based on the density result, we give sufficient conditions for the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mapping to the parametric generalized strong vector equilibrium problem. In addition, some examples were given to illustrate that our results improve ones in the literature.

Invariant Subspaces and Exact Solutions to the Generalized Strongly Dispersive DGH Equation

In this paper, the invariant subspaces of the generalized strongly dispersive DGH equation are given, and the exact solutions of the strongly dispersive DGH equation are obtained. Firstly, transform nonlinear partial differential Equation (PDE) into ordinary differential Equation (ODE) systems by using the invariant subspace method. Secondly, combining with the dynamical system method, we use the invariant subspaces which have been obtained to construct the exact solutions of the equation. In the end, the figures of the exact solutions are given.

Homotopy Analysis Method for Large-Amplitude Free Vibrations of Strongly Nonlinear Generalized Duffing Oscillators

In this study, the homotopy analysis method (HAM) is used to solve the generalized Duffing equation. Both the frequencies and periodic solutions of the nonlinear Duffing equation can be explicitly and analytically formulated. Accuracy and validity of the proposed techniques are then verified by comparing the numerical results obtained based on the HAM and numerical integration method. Numerical simulations are extended for even very strong nonlinearities and very good correlations which achieved between the results. Besides, the optimal HAM approach is introduced to accelerate the convergence of solutions.

教育家精神的生成逻辑、价值意蕴与弘扬路径

教育家精神是强国建设的重要思想资源和精神动能,大力弘扬教育家精神是新时代教师队伍建设的根本所在。中国特有的教育家精神的生成有其必然性,马克思主义教育理论是其生成的理论逻辑、中华优秀教育传统是其生成的历史逻辑、中国共产党百年奋斗教育成就和经验是其生成的实践逻辑。新时代大力弘扬教育家精神,是建设教育强国的题中之义,有助于办好人民满意的教育,为锻造强国之师提供精神动能,是落实立德树人根本任务的根本保障。新征程弘扬和践行教育家精神,要强化思想引领,筑牢教师队伍建设的思想根基;坚持目标导向,健全中国特色高质量教师教育体系;完善制度保障,构建弘扬教育家精神的长效机制;营造尊师重教良好风尚,真正让教师成为令人羡慕的职业。

基于强乘积运算下图的广义和连通度指标上下界

对于图G,令E(G)表示G的边集,令V(G)表示G的点集,d_(G)(v)表示v的度。对于边e=uv,定义广义和连通度指标χ_(α)(e)=(d_(G)(u)+d_(G)(v))^(α),其中α为任一实数。本文先介绍了图的S,R,Q,T四种运算,然后给出了四种运算下的强乘积,并利用最大度最小度确定了其四种图的广义和连通度指标的上下界。

Banach空间中可数算子族的不动点集和广义混合均衡问题的公共解的强收敛性

在自反Banach空间框架中,提出一类新的收缩投影算法,来逼近一闭Bregman拟渐近非扩张可数算子族的不动点集和广义混合均衡问题的公共解,建立了一闭Bregman拟渐近非扩张可数算子族的不动点集和广义混合均衡问题的公共解的强收敛性结果,并用一数值例子来支撑文中所得的结果.无论算子族从有限个到可数个,还是算子从Bregman相对非扩张到Bregman拟渐近非扩张等方面,均对Jantakarn K和Kaewcharoen A(2021)的结果进行了的拓展和补充.

基于h-BN的方向依赖高次谐波产生(特邀)

利用紧束缚电子能带结构并结合求解两能带半导体Bloch方程的方法,研究了单层h-BN的高次谐波产生过程。结果显示平行于驱动光偏振方向的谐波分量在截止区表现出异常的晶格取向依赖关系,当光子能量超过7.31 eV时,奇次谐波的取向依赖相对于较低级次的奇次谐波取向依赖表现出明显的30°角度偏移。确定了能够发生偏移的那些谐波光子能量与布里渊区M点处的载流子动力学相关。进一步的时频分析表明,当驱动光偏振沿zigzag方向时,截止区谐波仅在特定极性的激光半周期内产生,这导致了zigzag方向谐波的急剧减弱,从而造成了截止区晶格取向分布的偏移。这一现象对利用高次谐波光谱重建电子能带结构具有重要意义。

基于电流位置关系的DSEG整流器开路故障诊断算法

整流器作为电励磁双凸极发电机(DSEG)的重要组件,其承受频繁的高压和大电流,容易产生故障。然而由于DSEG相电流的不对称性和非正弦性,传统的故障诊断算法在变工况的暂态极易出现误检测。为了诊断DSEG整流单元的开路故障,提出了一种基于相电流大小位置关系的强鲁棒性诊断策略。理论推导和试验验证表明,所提出的强鲁棒性开路故障诊断策略在变负载、变励磁和变转速的暂态不会出现误诊断,并且可以在一个基波周期内检测出所有类型的单管和双管开路故障,计算量小,占用空间小。

生成式AI嵌入数字政府的价值审思与路径展望

随着数字技术的不断迭代,以生成式人工智能为代表的强人工智能为数字政府建设提供了一个新的契机。相较于传统弱人工智能,将生成式人工智能嵌入数字政府有助于推动数字政府科学精准决策,促进国家公共治理体系革新,实现公共政务服务亲民和善。但在享受强赋能效果的同时,生成式人工智能的嵌入也存在技术滥用、资本侵蚀以及安全隐患等多重风险,稍不留意就会影响数字政府建设的健康有序发展。有鉴于此,为实现技术赋能与风险防范的逻辑统一,今后必须以全链条审查实现数字技术价值理性,以全方位监督框定技术资本运行边界,以全周期信息维护公共政务服务安全,从而最终将数字政府建设融入法治轨道。

强干扰下的SVG微弱谐波信号传感检测方法

静止无功发生器(Static Var Generator,SVG)微弱谐波信号处于强干扰区域的中心频带时,会影响谐波信号检测有效性。为提升谐波信号检测性能,提出强干扰下的SVG微弱谐波信号传感检测方法。在强干扰下提取出SVG信号,并采用修正投影阻塞法消除SVG信号中存在的干扰。选取振动传感器作为SVG微弱谐波信号检测仪器,由于振动传感器中的仪表放大器会对放大后的SVG信号叠加较多高频噪声,所以在强干扰抑制的基础上进一步滤除噪声。将振动传感器放置在振动台上,并检测处理后的SVG信号。通过数字示波器观测SVG微弱谐波信号在放大电路中的输出波形,判断信号在输送期间是否出现失真问题,从而实现SVG微弱谐波信号传感检测。实验结果表明,所提方法的信噪比高于23.51 dB,幅值检测误差低于0.63 Hz,频率检测误差低于7.1 Hz。

强人工智能刑事责任主体资格的否定

在是否应当赋予强人工智能刑事责任主体资格的论战中,否定论具有逻辑严密性与结论正当性。首先,从实证角度出发,在强人工智能的发展进路中,存在大量科技、哲学难题,强人工智能时代难以来临。其次,假设强人工智能存在,其所具备的辨认与控制能力也并无刑法意义,因此无法被认定为刑事责任主体。再次,对强人工智能施加刑罚,难以实现报应目的与预防目的。最后,基于刑法人类中心主义,理应排除强人工智能的刑事责任主体地位。

习近平关于体育工作重要论述生成逻辑的五维向度探赜

全面建设社会主义现代化强国,需要在各方面都协同推进.体育事业事关国家强盛、民族振兴,是国家强盛的题中应有之义.进入新时代,习近平总书记高度重视体育工作,从实现中华民族伟大复兴的战略出发,发表了系列关于体育事业发展的重要论述,为新时代建设体育强国指明了方向.没有先进的理论,就没有先进的运动,从时代视域下我国体育行业日益复杂的改革与重塑之困所构建的问题向度,主体之历、管理之思与发展之结的“三轮”驱使所构建的实践向度,中华体育文明的当代传承与奥林匹克精神的中国观照所构建的文化向度,站起来、富起来、强起来的初心使命情怀之时代彰显与推崇所构建的价值向度,马克思主义的体育思维与方法论之动力性表达所构建的思维方法向度等五维向度,探索新时代习近平关于体育工作重要论述生成的发展逻辑与时代价值对推进健康中国建设提供思想引领和实践指导,对2035年实现“建成体育强国”的总体目标具有重大意义.