The Equivalence between the Mann and Ishikawa Iterations for Generalized Contraction Mappings in a Cone

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.

Generalized Kannan-type contraction and fixed point theorems

In this paper,the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced.The fixed point theorems satisfying generalized contractive conditions are obtained,without appealing to completeness of X or normality of the cone.The continuity of the mapping is relaxed.Furthermore,we prove that the completeness in cone metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X.These results greatly generalize several well-known comparable results in the literature.

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

A New Generalized FB Complementarity Function for Symmetric Cone Complementarity Problems

We establish that the generalized Fischer-Burmeister（FB） function and penalized Generalized Fischer-Burmeister （FB） function defined on symmetric cones are complementarity functions （C-functions）, in terms of Euclidean Jordan algebras, and the Generalized Fischer-Burmeister complementarity function for the symmetric cone complementarity problem （SCCP）. It provides an affirmative answer to the open question by Kum and Lim （Kum S H, Lim Y. Penalized complementarity functions on symmetric cones. J. Glob. Optim.. 2010, 46： 475-485） for any positive integer.

A Note on the Paper “Generalized -Contraction for a Pair of Mappings on Cone Metric Spaces”

We note that Theorem 2.3 [1] is a consequence of the same theorem for one map.

Generalized cone-subconvexlike set-valued maps and applications to vector optimization

The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.

GENERALIZATIONS OF THE SUZUKI AND KANNAN FIXED POINT THEOREMS IN G-CONE METRIC SPACES

In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces.

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.

Multiplicity Results for Second-order Generalized Sturm-Liouville Boundary Value Problems with Dependence on the First Order Derivative

By using fixed point theorems,we consider multiplicity of positive solutions for second-order generalized Sturm-Liouville boundary value problem,where the first order derivative is involved in the nonlinear term explicitly.We show the existence of multiple positive solutions for the problems.Example is given to illustrate the main results of the article.

基于改进灰狼优化算法的含光伏配电网动态无功优化

针对光伏并网对配电网造成的电压波动、线损增加,以及光伏和负荷出力的不确定性等问题,本文构建基于二阶锥规划的线性凸优化模型,通过控制有载调压变压器和电容器组动作,以及光伏逆变器和静止无功发生器无功补偿能力约束,对日前日内双时间尺度无功优化模型进行动态分析,在简化求解过程的同时加大找到全局最优解的可能性。提出一种基于混沌学习初始化、非线性收敛因子、最优粒子柯西扰动结合蜘蛛猴算法位置更新方式的改进灰狼优化算法,防止算法陷入局部最优并增强其全局搜索能力。最后,运用改进的灰狼优化算法对含光伏的IEEE 33节点系统进行建模仿真,结果表明该算法具有寻优效率高、收敛速度快的优点,验证了算法的可行性和高效性。

考虑电力负荷需求和分布式电源不确定性的配电网重构

随着可再生能源和可变负荷在配电系统中比例的逐步提高,配电网中电力流向的不确定性对最优网络拓扑结构的影响越来越显著。由于分布式发电和需求响应受时间因素影响,按单时段建模所得到的拓扑结构在一天中的不同时段难以达到最优。为解决这种不确定因素的影响,文章提出了一种基于二阶锥优化的配电网重构模型,进行计及需求响应的多时段潮流分析。基于实际配网系统所存在的“源-储-荷”结构,建立了以网络运行成本和开关运行成本为目标的约束条件,利用二阶锥松弛将非凸形式搜索空间转化为凸可行域,从而进行快速求解。在改进的IEEE 33节点配电网上进行测试分析,结果表明,文章提出的方法比传统方法具有更高的准确性和更快的求解速度。

基于多目标双层规划的分布式电源选址定容

针对高比例分布式电源(distributed generators, DGs)并网位置与容量大小优化问题,提出一种解决多DGs选址定容问题的多目标双层优化模型。该模型中上层模型结合损耗灵敏度和电压稳定指数挑选并网位置,下层模型获得并网位置后以有功损耗、电压偏移指数、电压稳定指数为优化目标函数调整DGs容量。其次,由于下层模型中含有非凸的DistFlow潮流方程,通过二阶锥凸松弛技术将下层模型转化为混合整数二阶锥规划模型,并运用多权重法将多目标优化模型转化为易于处理的单目标优化模型。最后在PG&E69节点系统中测试,结果表明,DGs在最佳位置接入特定容量,可显著降低配电网有功损耗,改善电压分布、提高电网电压稳定性。与现有文献中优化算法对比分析,验证了所提模型的有效性,此外,还分析了测试系统接入DGs的最佳数目和渗透水平。

基于区域判别生成对抗网络的宫颈癌放射治疗锥形束CT影像质量提升研究

目的:提出基于区域判别生成对抗网络(GAN)的改善宫颈癌放射治疗锥形束CT(CBCT)图像质量模型,以满足自适应放疗图像质量的需求。方法:采用基于区域判别的策略与生成对抗网络思想,构建一种能够关注宫颈癌放疗影像局部细节的CBCT图像质量提升模型,其判别器可提高图像局部细节的生成质量。将该图像质量模型应用于宫颈癌放疗中的CBCT图像,通过量化指标和可视化评价图像处理效果。结果:CBCT图像质量提升后其纹理清晰度与对比度皆得到明显提升。图像峰值信噪比提高47.2%,结构相似性指标提升至0.838以上。相对于其他模型,在可视化和指标角度皆表现出更好的模型效能,结构相似性与U-Net网络和CycleGAN网络比较分别提高11.88%和19.54%;峰值信噪比分别提高19.75%和25.99%。结论:基于区域判别的GAN可有效提升宫颈癌放疗CBCT图像整体与细节上的生成质量,能够为提升低剂量CBCT图像质量提供新的技术路径,为提高放疗安全性和有效性发挥重要作用,并对制定和执行放疗计划具有重要临床价值。

Common Fixed Point Theorems in Non-normal Cone Metric Spaces with Banach Algebras

In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generalize some results in the literature. Moreover,we give an example to support the main assertions.

Connectedness of Cone-efficient Solution Set for Cone-quasiconvex Multiobjective Programming in Hausdorff Topological Vector Spaces

这份报纸在局部地凸的 Hausdorff 拓扑的向量空格为向量优化处理锥有效的解决方案集合的 connectedness。锥有效的答案集合的 connectedness 为在选择的一个紧缩的凸的集合上印射的连续一对一的 cone-quasiconvex 定义的 multiobjective 编程被证明。在证明期间，概括僵绳定理起一个关键作用。

Generation characteristics of a metal ion plasma jet in vacuum discharge

To improve the performance of a metal ion plasma jet in vacuum discharge, an anode-insulated cone-cylinder electrode with insulating sleeve is proposed in this paper. Discharge characteristics and generation characteristics of plasma of the electrode are investigated, effects of diameter of insulating sleeve, variety of cathode material and length of the insulating sleeve on characteristics of metal ion plasma jet are discussed. Results indicate that a directional and steady plasma jet is formed by using the novel electrode with insulating sleeve under high vacuum conditions. Moreover, the properties of metal ion plasma jet are improved by using the aluminum cathode and thin and long insulating sleeve. The study provides strong support for research of vacuum metal ion plasma thruster and ion implantation technology.

EXISTENCE OF AREA MINIMIZING TANGENT CONES OF INTEGRAL CURRENTS WITH PRESCRIBED MEAN CURVATURE

Given an integral M-currrent To in Rm+k and a tensor H of type(m.l)on Rn+k with values orthogonal to each of its arguments we proved in a previous peper[3]the sxistence of anintegral m-current T =γ(M,θ.ζ)with boundary T0 and mean curvature vector H by minimizing an appropriate functional on suitable subclasses of the set of all integral currents.In thes paperwe discuss the existence and structure of oriented tangent cones C of T at points x∈spt(T) spt(T),especially we show that C is locally mass minimizing.

Some Random Coincidence Point and Common Fixed Point Results in Cone Metric Spaces Over Banach Algebras

In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.

基于广义线性多面体的有源配电网仿射可调鲁棒优化方法

针对传统的多面体集合对分布式光伏出力相关性缺乏考虑,提出了基于广义线性多面体集合的有源配电网仿射可调鲁棒优化方法,以量化相关性对优化结果的影响。首先,采用多面体集合来描述分布式光伏出力的不确定性,利用分布式光伏出力的历史数据得到不确定性出力相关性的分布包络图;然后,结合相关性分布包络图重构了多面体集合的边界,并针对重构后的相关性多面体集合存在的保守性偏大的问题,进一步建立了描述分布式光伏出力相关性的广义多面体集合;最后,通过算例对比分析了广义多面体集合对有源配电网仿射可调鲁棒优化结果的影响。

基于数据驱动与物理模型的主动配电网双时间尺度协调优化

高比例间歇性分布式电源与电动汽车接入配电网时,容易导致功率与电压频繁、快速、剧烈波动。文中结合数据驱动与物理建模方法,提出了一种配电网双时间尺度有功无功协调优化策略。针对短时间尺度(分钟级或秒级)的功率波动,以静止无功补偿器、分布式电源无功功率为决策变量,以网损最小为目标函数,计及物理约束,针对平衡与不平衡配电网分别构建了二阶锥与二次规划模型。针对长时间尺度(小时级)的优化,以有载调压变压器分接头变比、可投切电容电抗器挡位、储能系统充放电功率为动作,以网损为代价,计及节点电压越限惩罚,构建了马尔可夫决策过程。为克服连续-离散动作空间维数灾,采用一种基于松弛-预报-校正的深度确定性策略梯度强化学习求解算法。通过IEEE 33节点与IEEE 123节点配电系统验证了所提方法的有效性。