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.

GNN Representation Learning and Multi-Objective Variable Neighborhood Search Algorithm for Wind Farm Layout Optimization

With the increasing demand for electrical services,wind farm layout optimization has been one of the biggest challenges that we have to deal with.Despite the promising performance of the heuristic algorithm on the route network design problem,the expressive capability and search performance of the algorithm on multi-objective problems remain unexplored.In this paper,the wind farm layout optimization problem is defined.Then,a multi-objective algorithm based on Graph Neural Network(GNN)and Variable Neighborhood Search(VNS)algorithm is proposed.GNN provides the basis representations for the following search algorithm so that the expressiveness and search accuracy of the algorithm can be improved.The multi-objective VNS algorithm is put forward by combining it with the multi-objective optimization algorithm to solve the problem with multiple objectives.The proposed algorithm is applied to the 18-node simulation example to evaluate the feasibility and practicality of the developed optimization strategy.The experiment on the simulation example shows that the proposed algorithm yields a reduction of 6.1% in Point of Common Coupling(PCC)over the current state-of-the-art algorithm,which means that the proposed algorithm designs a layout that improves the quality of the power supply by 6.1%at the same cost.The ablation experiments show that the proposed algorithm improves the power quality by more than 8.6% and 7.8% compared to both the original VNS algorithm and the multi-objective VNS algorithm.

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].

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).

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.

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.

Application of Rollout Strategy to Test Points Selection for Integer-Coded Fault Wise Table

Test points selection for integer-coded fault wise table is a discrete optimization problem. The global minimum set of test points can only be guaranteed by an exhaustive search which is eompurationally expensive. In this paper, this problem is formulated as a heuristic depth-first graph search problem at first. The graph node expanding method and rules are given. Then, rollout strategies are applied, which can be combined with the heuristic graph search algorithms, in a computationally more efficient manner than the optimal strategies, to obtain solutions superior to those using the greedy heuristic algorithms. The proposed rollout-based test points selection algorithm is illustrated and tested using an analog circuit and a set of simulated integer-coded fault wise tables. Computa- tional results are shown, which suggest that the rollout strategy policies are significantly better than other strategies.

AUTOMATIC SEARCHING OF CONTROL POINT IN NOAA AVHRR IMAGE

This paper discusses the approaches for automatical searching of control points in the NOAA AVHRR image on the basis of data rearrangement in the form of latitude and longitude grid. The vegetation index transformation and multi-level matching strategies have been proven effective and successful as the experiments show while the control point database is established.

ON THE EXISTENCE OF COMMON FIXED POINTS FOR A PAIR OF LIPSCHITZIAN MAPPINGS IN BANACH SPACES

The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0.

An Adaptive Steganographic Algorithm for Point Geometry Based on Nearest Neighbors Search

In this study, we extend our previous adaptive steganographic algorithm to support point geometry. For the purpose of the vertex decimation process presented in the previous work, the neighboring information between points is necessary. Therefore, a nearest neighbors search scheme, considering the local complexity of the processing point, is used to determinate the neighbors for each point in a point geometry. With the constructed virtual connectivity, the secret message can be embedded successfully after the vertex decimation and data embedding processes. The experimental results show that the proposed algorithm can preserve the advantages of previous work, including higher estimation accuracy, high embedding capacity, acceptable model distortion, and robustness against similarity transformation attacks. Most importantly, this work is the first 3D steganographic algorithm for point geometry with adaptation.

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.

Approximation of Common Fixed Points of Pointwise Asymptotic Nonexpansive Maps in a Hadamard Space

We establish weak and strong convergence of Ishikawa type iterates of two pointwise asymptotic nonexpansive maps in a Hadamard space. For weak and strong convergence results, we drop “rate of convergence condition”, namely (Cn(x)-1)< to answer in the affirma-tive to the open question posed by Tan and Xu [1] even in a general setup.

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 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.

Automated registration of wide-baseline point clouds in forests using discrete overlap search

Forest is one of the most challenging environments to be recorded in a three-dimensional(3D)digitized geometrical representation,because of the size and the complexity of the environment and the data-acquisition constraints brought by on-site conditions.Previous studies have indicated that the data-acquisition pattern can have more influence on the registration results than other factors.In practice,the ideal short-baseline observations,i.e.,the dense collection mode,is rarely feasible,considering the low accessibility in forest environments and the commonly limited labor and time resources.The wide-baseline observations that cover a forest site using a few folds less observations than short-baseline observations,are therefore more preferable and commonly applied.Nevertheless,the wide-baseline approach is more challenging for data registration since it typically lacks the required sufficient overlaps between datasets.Until now,a robust automated registration solution that is independent of special hardware requirements has still been missing.That is,the registration accuracy is still far from the required level,and the information extractable from the merged point cloud using automated registration could not match that from the merged point cloud using manual registration.This paper proposes a discrete overlap search(DOS)method to find correspondences in the point clouds to solve the low-overlap problem in the wide-baseline point clouds.The proposed automatic method uses potential correspondences from both original data and selected feature points to reconstruct rough observation geometries without external knowledge and to retrieve precise registration parameters at data-level.An extensive experiment was carried out with 24 forest datasets of different conditions categorized in three difficulty levels.The performance of the proposed method was evaluated using various accuracy criteria,as well as based on data acquired from different hardware,platforms,viewing perspectives,and at different points of time.The proposed method achieved a 3D registration accuracy at a 0.50-cm level in all difficulty categories using static terrestrial acquisitions.In the terrestrial-aerial registration,data sets were collected from different sensors and at different points of time with scene changes,and a registration accuracy at the raw data geometric accuracy level was achieved.These results represent the highest automated registration accuracy and the strictest evaluation so far.The proposed method is applicable in multiple scenarios,such as 1)the global positioning of individual under-canopy observations,which is one of the main challenges in applying terrestrial observations lacking a global context,2)the fusion of point clouds acquired from terrestrial and aerial perspectives,which is required in order to achieve a complete forest observation,3)mobile mapping using a new stop-and-go approach,which solves the problems of lacking mobility and slow data collection in static terrestrial measurements as well as the data-quality issue in the continuous mobile approach.Furthermore,this work proposes a new error estimate that units all parameter-level errors into a single quantity and compensates for the downsides of the widely used parameter-and object-level error estimates;it also proposes a new deterministic point sets registration method as an alternative to the popular sampling methods.

Research on the MPPT of Photovoltaic Power Generation Based on the CSA-INC Algorithm

The existing Maximum Power Point Tracking(MPPT)method has low tracking efficiency and poor stability.It is easy to fall into the Local Maximum Power Point(LMPP)in Partial Shading Condition(PSC),resulting in the degradation of output power quality and efficiency.It was found that various bio-inspired MPPT based optimization algorithms employ different mechanisms,and their performance in tracking the Global Maximum Power Point(GMPP)varies.Thus,a Cuckoo search algorithm(CSA)combined with the Incremental conductance Algorithm(INC)is proposed(CSA-INC)is put forward for the MPPT method of photovoltaic power generation.The method can improve the tracking speed by more than 52%compared with the traditional Cuckoo Search Algorithm(CSA),and the results of the study using this algorithm are compared with the popular Particle Swarm Optimization(PSO)and the Gravitational Search Algorithm(GSA).CSA-INC has an average tracking efficiency of 99.99%and an average tracking time of 0.19 s when tracking the GMPP,which improves PV power generation’s efficiency and power quality.

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 Points and Almost-like Coincidence Points on Generalized ConvexSpaces with Applications

We introduce the concept of a weakly G-quasiconvex map with respect to a map on generalized convex spaces and use the concept to prove coincidence point theorems and almost-like coincidence point theorems. As applications of the above results, we derive almost fixed point theorems and fixed point theorem. These main results generalize and improve some known results in the literature.