COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES

In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized （ψ, Ф）-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.

Unique Common Fixed Points for Two Weakly C~*-contractive Mappings on Partially Ordered 2-metric Spaces

In this paper, we give existence theorems of common fixed points for two mappings with a weakly C*-contractive condition on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point.

Determination of Weak Points Based on Risk Theory and Application to Transmission Network Planning

In the traditional power transmission network planning,deterministic analysis methods are widely used.In such methods,all contingencies are deemed to have the same occurrence probability,which is not reasonable.In this paper,risk assessment is introduced to the process of transmission network planning considering the probabilistic characteristics of contingencies.Risk indices are given to determine the weak points of the transmission network based on local information,such as bus risk,line overload risk,contingency severity.The indices are calculated by the optimal cost control method based on risk theory,which can help planners to quickly determine weak points in the planning and find solution to them.For simplification,only line overload violation is considered.Finally,the proposed method is validated by an IEEE-RTS test system and a real power system in China from two aspects.In the first case,the original system is evaluated by the proposed method to find the weak points,and then four planning schemes are established,among which the best scheme is selected.In the second case,four initial planning schemes are established by combining the experiences of planners,and after the evaluation by using the proposed method,the best planning scheme is improved based on the information of weak points in the initial schemes,and the risk of improved scheme is reduced from 42 531.86 MW·h per year to 4 431.26 MW·h per year.

Spaces with σ-point-discrete N_0-weak bases

It is discussed in this paper the spaces with σ-point-discrete N_0-weak bases. The main results are： （1） A space X has a σ-compact-finite N_0-weak base if and only if X is a k-space with a σ-point-discrete N_0-weak base; （2） Under （CH）, every separable space with a σ-point-discrete N_0-weak base has a countable N_0-weak base.

Fixed Point Theory for 1-Set Weakly Contractive Operators in Banach Spaces

In this work, using an analogue of Sadovskii＇s fixed point result and several important inequalities we investigate and give new existence theorems for the nonlinear operator equation F（x） =μx, （μ≥1） for some weakly sequentially continuous, weakly condensing and weakly 1-set weakly contractive operators with different boundary conditions. Correspondingly, we can obtain some applicable fixed point theorems of Leray-Schauder, Altman and Furi-Pera types in the weak topology setting which generalize and improve the corresponding results of [3,15,16].

Four-Step Iteration Scheme to Approximate Fixed Point for Weak Contractions

Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems.It is known that many problems in applied sciences and engineering can be formulated as functional equations.Such equations can be transferred to fixed point theorems in an easy manner.Moreover,we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations.Let X be a non-empty set.A fixed point for a self-mapping T on X is a point𝑒𝑒∈𝑋𝑋that satisfying T e=e.One of the most challenging problems in mathematics is to construct some iterations to faster the calculation or approximation of the fixed point of such problems.Some mathematicians constructed and generated some new iteration schemes to calculate or approximate the fixed point of such problems such as Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Berinde(2004b);Agarwal,O’Regan and Sahu(2007)].The main purpose of the present paper is to introduce and construct a new iteration scheme to calculate or approximate the fixed point within a fewer number of steps as much as we can.We prove that our iteration scheme is faster than the iteration schemes given by Sintunavarat et al.[Sintunavarat and Pitea(2016);Agarwal,O’Regan and Sahu(2007);Mann(1953);Ishikawa(1974)].We give some numerical examples by using MATLAB to compare the efficiency and effectiveness of our iterations scheme with the efficiency of Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Abbas and Nazir(2014);Agarwal,O’Regan and Sahu(2007)]schemes.Moreover,we introduce a problem raised from Newton’s law of cooling as an application of our new iteration scheme.Also,we support our application with a numerical example and figures to illustrate the validity of our iterative scheme.

FIXED POINTS FOR WEAKLY INWARD MAPPINGS IN BANACH SPACES (Ⅱ)

S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i（A, Ω, p） is equal to nonzero, where i（A, Ω, p） is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2].

FIXED POINT INDEX THEORY FOR WEAKLY INWARD MAPPINGS

In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imposed. This makes ns to deal with these kinds of mappings more easily. As obvious applications, some results in [3],[5],[7],[9],[10] are deepened and extended.

Common Fixed Point Results for Occasionally Weakly Compatible Maps in G-Symmetric Spaces

The notion of a G-symmetric space is introduced and the common fixed points for some pairs of occasionally weakly compatible maps satisfying some contractive conditions in a G-symmetric space are proved. The results extend and improve some results in literature.

Coincidence and Common Fixed Point of Weakly Compatible Maps in Fuzzy Metric Space

The aim of this paper is to establish some new common fixed point theorems for generalized contractive maps in fuzzy metric space by using property (E.A.), common property (E.A.), JCLRST property and CLRS property. Our results improve and extend the results of Chauhan et al. [1] and Sedghi et al. [2] besides several known results. We also furnish an illustrative example in support of our results.

Endpoints of Multi-Valued Weak Contractions on the Metric Space of Partially Ordered Groups

The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).

A Common Fixed Point Theorem for Weakly Compatible Mappingsin Fuzzy Semi-Metric Space

In this paper, we establish a common fixed pointtheorem for three pairs of self-mappings in fuzzy semi-metric space which improves and extends similar known results in the literature.

基于全国新生儿复苏培训平台分析医务人员新生儿复苏理论知识薄弱点现状

目的 分析我国医务人员新生儿复苏理论知识的薄弱点,为开展针对性培训、提高培训效果提供支持。方法 利用全国新生儿复苏培训平台2020年7月1日至2022年8月25日的培训考核数据,分析医护人员首次考核通过率、总通过率和知识点回答正确率,比较不同职业医务人员知识掌握情况的差异。结果 38 780名医护人员8个课程的首次考核通过率均低于80%,其中气管插管、正压通气、早产儿复苏、特殊情况和初步复苏首次考核通过率均低于60%。42个知识点的回答正确率为44.48%~78.75%,其中12个知识点的正确率低于60%,主要分布在正压通气、复苏概论、初步复苏、气管插管和药物使用方面,胸外按压和早产儿复苏课程知识点掌握情况较好。不同职业医务人员的比较结果显示,医生组知识点掌握情况较好,有30个知识点的回答正确率高于护士/助产士组,6个知识点的回答正确率低于护士/助产士组,差异均有统计学意义(均P<0.05)。结论 医护人员新生儿复苏知识的首次考核通过率不高,存在明显的知识薄弱点,且医生和护士/助产士的掌握情况存在差异。需要设计有针对性的培训计划,持续提高医护人员新生儿复苏技能水平,保障新生儿安全。

中药穴位贴敷联合耳穴压豆对阴虚阳亢型老年高血压合并衰弱的临床观察

目的探讨中药穴位贴敷联合耳穴压豆对阴虚阳亢型老年高血压合并衰弱的临床效果,为老年高血压合并衰弱患者的防治提供借鉴。方法选取2023年3—11月医院收治的60例阴虚阳亢型老年高血压合并衰弱患者作为研究对象,按照组间基线资料具有可比性的原则分为对照组和观察组,各30例。对照组给予常规降血压护理和健康教育,宣教2周,每周1次,共宣教2次;观察组在对照组基础上采用中药穴位贴敷联合耳穴压豆治疗,每天1次,1周为1疗程,共干预2周。2周结束后,比较两组患者干预后的临床效果。干预前、干预2周后采用电子血压计、中医证候积分量表、老年人衰弱评估量表评估两组患者的收缩压(SBP)、舒张压(DBP)、中医证候积分及老年衰弱评分的改善程度。结果干预前,两组患者血压、中医证候积分、老年衰弱评分比较,差异无统计学意义(P>0.05);干预后,观察组患者在血压、中医证候积分、老年衰弱评分均低于对照组,差异具有统计学意义(P<0.05)。干预后,观察组降压效果优于对照组,两组间比较差异有统计学意义(P<0.05)。结论对阴虚阳亢型老年高血压合并衰弱患者进行中药穴位贴敷和耳穴压豆,根据其证型选穴贴压肝、肾、交感、神门、降压沟、皮质下、胆、心八大穴位,其效果良好,操作简便,无不良反应发生,可有效改善患者血压、中医证候及衰弱症状,促进患者康复。

地震速报新媒体平台的应用创新与发展策略

融媒体背景下,地震速报新媒体平台以其突出的技术优势和传播优势,在信息发布、震后应急、地震科普等方面发挥了重要的作用。本文基于地震速报新媒体平台的基本功能,深入探讨地震速报新媒体平台的创新点和薄弱点。该平台开拓了“人工+自动”的新媒体运维模式,实现了政府、公众的双向服务,具备一定创新性,但在联动能力、内容生产能力上仍存在发展空间。结合当下发展,提出了进一步提升地震速报新媒体平台影响力的发展策略。

深地万米井测井电缆强度分析

中国超深层油气资源潜力巨大,推进超深层油气勘探、实现新层系突破是开拓油气新领域的重点方向。针对深地某科探井万米电缆遇卡等问题,采用截面法,建立电缆在井下、天滑轮、地滑轮、滚筒等位置处的有限元模型,研究拉力棒、滚筒直径、上提速度对万米测井电缆强度的影响。计算结果表明:为保证在电缆不断的情况下使设置的弱点先断,并为电缆保留一定安全系数,可以选用5000lbf^(*)拉力棒;选用大直径的滚筒来减小电缆张力,优先选用直径700mm的滚筒;测井电缆正常上提工作速度取6000m/h,此时电缆张力可达61.4kN,满足强度要求。研究成果为深地万米井测井作业电缆、滚筒、拉力棒的选取提供了基础数据。

新能源电力系统振荡薄弱点定位方法研究

为减轻振荡对新能源电力系统的冲击,有必要在线评估系统稳定状态并定位系统振荡薄弱点,提前采取措施。为此,分别从端口频域特性和时域响应角度提出两种新能源电力系统振荡薄弱点定位方法。频域方法基于新能源场站端口阻抗特性评估系统稳定状态,并根据各新能源场站端口阻抗实部的大小定位薄弱场站。时域方法通过主动注入宽频小扰动信号,利用HHT(希尔伯特-黄变换)分析各新能源场站端口电流响应,提取薄弱模态的阻尼比,根据阻尼比大小定位薄弱场站。以三个风电场构成的小型新能源系统为例,对上述两种定位方法的有效性进行验证,结果表明两种方法均能准确定位系统振荡的薄弱点。

THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.

基于点阵激光的弱纹理对象三维建模研究

针对弱纹理对象表面信息要素少,机器视觉三维建模困难的问题,提出一种使用双目视觉技术配合点阵激光重建目标对象的方法。采用点阵激光赋予目标对象表面纹理,提出相应的特征点识别及匹配算法。根据相邻视角中相机间的空间位姿关系拼接多视角的点云三维图。实验结果表明,重建的三维模型直径平均误差为2.05%,三维模型边缘和实物边缘的重合度为87.4%,点云坐标与实际点的三维坐标偏差较小,能满足针对弱纹理对象的三维建模需求。

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.