MINIMAL AND MAXIMAL FIXED POINT THEOREMS AND ITERATIVE TECHNIQUE FOR NONLINEAR OPERATORS IN PRODUCT SPACES

In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikantham[21 and the results obtained by Lan in [4], and [6].

ON THE SPACES OF THE MAXIMAL POINTS

For a continuous domain D, some characterization that the convex powerdomain CD is adomain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it isproved that the set of the maximal points Max(CD) of CD with the relative Scott topology ishomeomorphic to the set of all Scott compact subsets of Max(D) with the topology induced bythe Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable.

MODIFIED APPROXIMATE PROXIMAL POINT ALGORITHMS FOR FINDING ROOTS OF MAXIMAL MONOTONE OPERATORS

In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0￥ ( hk - 1 ) < + ￥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.

Boundary Points,Minimal L^(2)Integrals and Concavity PropertyⅢ—Linearity on Riemann Surfaces and Fibrations over Open Riemann Surfaces

In this article,we consider a modified version of minimal L^(2) integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points,and obtain a concavity property of the modified version.As applications,we give characterizations for the concavity degenerating to linearity on open Riemann surfaces and on fibrations over open Riemann surfaces.

Boundary points, minimal L^(2) integrals and concavity property Ⅱ: Weakly pseudoconvex Kähler manifolds

In this paper, we consider minimal L^(2) integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K?hler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal L^(2) integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a concavity property related to modules at inner points of the sublevel sets, an optimal support function related to modules, a strong openness property of modules and a twisted version, and an effectiveness result of the strong openness property of modules.

Algorithms of common solutions to quasi variational inclusion and fixed point problems

The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space.Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich（Ekonomika i Matematicheskie Metody,1976,12（4）：747-756）,but also extend and replenish the corresponding results obtained by Iiduka and Takahashi（Nonlinear Anal TMA,2005,61（3）：341-350）,Takahashi and Toyoda（J Optim Theory Appl,2003, 118（2）：417-428）,Nadezhkina and Takahashi（J Optim Theory Appl,2006,128（1）：191- 201）,and Zeng and Yao（Taiwan Residents Journal of Mathematics,2006,10（5）：1293-1303）.

Viscosity method for hierarchical fixed point and variational inequalities with applications

A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.

A New Fixed Point Theorem in L-Convex Spaces with Applications

In this paper, we present a new fixed point theorem in L-convex spaces and apply it to obtain a maximal element theorem, a variational inequality and a saddle point theorem in L-convex spaces.

Discrete Conley index and bifurcation points

In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition for determining whether they may have the similar bifurcation points is given.

Fan-Browder Type Fixed Point Theorems and Its Applications on Generalized Convex Product Spaces

Fan-Browder type fixed point theorems are obtained for non-selfmaps on non-compact generalized convex product spaces and new existence problems of(partially) maxi-mal element and equilibrium point are discussed as applications of above results.

Quadratic minimization for equilibrium problem variational inclusion and fixed point problem

The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating a solution of the above min- imization problem. The results presented in the paper extend and improve some recent results.

含电动汽车的主动配电网多目标分层优化调度

为了协调电动汽车车主和主动配电网2个不同主体之间的利益关系,针对电动汽车接入后主动配电网的优化调度问题,文中提出一种考虑电动汽车充电综合满意度和主动配电网运行效益的多目标分层优化方法。上层模型注重最大化电动汽车车主的充电利益,采用归一化法向约束法求解电动汽车的最优充放电计划,并将其输入下层优化模型。下层模型旨在最大化主动配电网的运行效益,根据电动汽车的充放电计划调整可控分布式电源的输出功率,采用二阶锥松弛转换法和带权极小模理想点法求解该非线性多目标问题。仿真结果表明,所提含电动汽车的主动配电网多目标分层优化方法能够在促使电动汽车充电综合满意度超过0.9的同时,减少有功网损约94.12%、运行成本约30.90%,实现电动汽车车主和主动配电网的双赢。

基于不动点深度学习的IRS辅助毫米波移动通信系统全信道估计

将智能反射面(IRS)与大规模MIMO结合能够保证和提高毫米波通信系统性能。针对基站(BS)-用户直连信道与用户-IRS-BS反射信道混叠场景,该文提出一种自适应的全信道估计方法。首先,引入辅助变量,采用原子范数将直连信道与反射信道的稀疏角度域子空间进行关联;然后,利用原子范数最小化将全信道估计问题建模为连续角度域稀疏矩阵重建规划;最后,基于不动点深度学习网络设计低复杂度的问题求解算法。该算法不仅能够克服传统基于模型解法中非线性估计算子对先验知识的依赖还可根据移动场景变化自适应调节算法复杂度。仿真结果表明,所提算法能够避免传统时分估计策略引起的差错传播效应,具有更高的估计精度和更低的复杂度。

一类耦合代数Riccati方程的解

耦合代数Riccati方程在控制论中具有广泛的应用,文章研究了一类耦合代数Riccati方程的解。基于M-矩阵和非负矩阵的理论,在一定假设条件下,证明了这类耦合代数Riccati方程存在最小非负解。最后通过数值算例,验证了所得结果的有效性。

多点射频微创治疗三叉神经痛的临床分析

目的探讨多点射频微创治疗对三叉神经痛患者疼痛及复发的影响。方法选取2021年1月至2023年1月焦作市第五人民医院收治的150例三叉神经痛患者,采用随机数字表法将其两组,每组各75例,对照组:药物治疗,观察组:多点射频微创治疗,比较两组患者的疼痛度、复发率、术后并发症、氧化应激指标水平及炎症因子水平。结果两组患者治疗前疼痛度评分、氧化应激指标水平、炎症因子水平无明显差异(P>0.05),经治疗后,两组患者疼痛度评分、炎性因子水平、NO水平均较治疗前降低,且观察组患者更低,GSH-Px、SOD水平均升高,且观察组患者更高(P<0.05);组间复发率和并发症无差异(P>0.05)。结论多点射频微创治疗三叉神经痛,可有效减轻其疼痛度,且具有较高的安全性,值得推广。

智能反射面辅助的非正交多址系统协作多点传输方案研究

智能反射面(Intelligent Reflection Surface,IRS)和非正交多址接入(Non-Orthogonal Multiple Access,NOMA)被认为是6G的关键创新型技术,将两者融合可以大幅提高通信系统的频谱效率与能量效率。文中针对IRS辅助的双小区协作多点与非正交多址接入融合系统展开研究,具体地,将IRS部署于两小区中间的小区边缘附近,用来提升边缘用户的信号质量。在考虑用户服务质量(Quality of Service,QoS)与基站发射功率限制的条件下,建立了最大化小区边缘用户可达速率的优化问题。由于该问题是非凸的,很难直接求解,将此问题分解为两个子优化问题,采用交替优化算法进行求解。具体地,采用二分法解决功率分配系数优化问题;采用均方误差(Mean-Square Error,MSE)方法将优化问题转化为等效形式,再通过最大最小化(Majorization-Minimization,MM)算法进一步解决相移优化问题。仿真结果显示,所提出的解决方案使得边缘用户可达速率明显高于其他基准方案。

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.

MAXIMAL ELEMENTS OF A FAMILY OF G_B-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS

A new family of GB-majorized mappings from a topological space into a finite continuous topological spaces （in short, FC-space） involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of GB-majorized mappings are proved under noncompact setting of product FCspaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.

New iterative schemes for strongly relatively nonexpansive mappings and maximal monotone operators

In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.

根据心肺最佳点构建反向传播神经网络最大摄氧量预测模型

背景:研究证明最大摄氧量被认为是评价有氧运动能力的“金标准”,但测试其所需运动强度较大且存在指标再现性低、测试者主观影响效应等限制因素。目的:通过反向传播神经网络采用新型次最大运动评估指标“心肺最佳点”构建最大摄氧量预测模型。方法:试验经国家体育总局体育科学研究所伦理委员会批准,招募80名健康大学生受试者(男40名,女40名),了解试验流程、目的并自愿签署知情同意书配合完整试验过程。受试者进行递增负荷心肺运动试验,采集最大摄氧量与心肺最佳点等相关指标,进行相关性分析获得具有统计学意义的指标,并构建最大摄氧量预测模型。结果与结论:①最大摄氧量与心肺最佳点、体质量指数、性别、心肺最佳点对应的摄氧量和功率均存在显著相关性(P<0.01);②运用反向传播神经网络构建经典3层拓扑结构最大摄氧量预测模型(包含5个输入层、10个隐藏层和1个输出层),该模型预测值与实测值绝对误差均值为0.227 L/min、相对误差均值为12%,提示基于心肺最佳点构建的反向传播神经网络可准确且有效预测最大摄氧量;③反向传播神经网络模型最大摄氧量预测值与多元线性回归预测值相比差异无显著性意义(P>0.05),但依据心肺最佳点构建的反向传播神经网络模型预测精度要优于多元线性回归模型。