Topological degree for 1-set-contractive fields in M-PN spaces and its applications

In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.

Vertex degree autocorrelation topological index and its application in QSAR study of organic chemicals

Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as A t, B t, C t and D t was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Autocorrelation function f(i) was calculated from the square root of the vertex degree, revised vertex degree and their combination, and they are (δ i) 1/2 , (δ V i) 1/2 ,(δ V i+δ i) 1/2  and (δ E i-δ i) 1/2 / N. With the matrix description method achieved, and the unit input in matrix of unsaturated bond and heteroatoms revised based on the adjacency matrix and distance matrix of organic molecular graph, the corresponding computer software has also been designed and developed. Better results have been obtained for the application of these indexes in QSAR study of organic chemicals.

TOPOLOGICAL DEGREE THEORY AND FIXED POINT THEOREMS IN PROBABILISTIC METRIC SPACES

The Leray-Schauder topological degree theory is established in the probabilistic linearnormed spaces.Based.on this theory,some fixed point theorems for mappings in theprobabilistic linear normed spaces are shown.

Degree of Compactness in I-fuzzy Topological Spaces

In this paper, the concept of degree of compactness is introduced in the general framework of I-fuzzy topological spaces, and its property is discussed. All good compactness are generalized to I-fuzzy topological spaces accordingly.

Remarks on computation of topological degree

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Degree and connectivity of the Internet's scale-free topology

This paper theoretically and empirically studies the degree and connectivity of the Internet＇s scale-free topology at an autonomous system （AS） level. The basic features of scale-free networks influence the normalization constant of degree distribution p（k）. It develops a new mathematic model for describing the power-law relationships of Internet topology. From this model we theoretically obtain formulas to calculate the average degree, the ratios of the kmin-degree （minimum degree） nodes and the kmax-degree （maximum degree） nodes, and the fraction of the degrees （or links） in the hands of the richer （top best-connected） nodes. It finds that the average degree is larger for a smaller power-law exponent A and a larger minimum or maximum degree. The ratio of the kmin-degree nodes is larger for larger λ and smaller kmin or kmax. The ratio of the kmax-degree ones is larger for smaller λ and kmax or larger kmin. The richer nodes hold most of the total degrees of Internet AS-level topology. In addition, it is revealed that the increased rate of the average degree or the ratio of the kmin-degree nodes has power-law decay with the increase of kmin. The ratio of the kmax-degree nodes has a power-law decay with the increase of kmax, and the fraction of the degrees in the hands of the richer 27% nodes is about 73% （the 73/27 rule＇）. Finally, empirically calculations are made, based on the empirical data extracted from the Border Gateway Protocol, of the average degree, ratio and fraction using this method and other methods, and find that this method is rigorous and effective for Internet AS-level topology.

Leray-Schauder度的一种推广及不动点和固有值

设Χ是实Banach空间,dimΧ=∞,Ω(?)Χ是有界开集,F:(?)→Χ全连续,f=I-F,p∈Χ\kf((?)Ω),k∈R且k>O.我们定义d_L(kf,Ω,p)=d_(LS)(f,Ω,(1/k)p).于是d_L具有Leray-Schauder度的基本性质.应用这个拓扑度可以推广Schauder不动点定理和Rothe不动点定理.并且我们得到固有值存在定理:设F:(?)→Χ全连续,O∈(?),F(0)=0.假设S(?)(?)是非空闭集,使得inf{||x-y|| |x∈X\S,y∈(?)F(S)}>0,则F有无穷多个固有值.

Lower bounds of the topological entropy for nonautonomous dynamical systems

In this paper, lower bounds of the topological entropy for nonautonomous dynamical systems are given via the growths of topological complexity in fundamental group and in degree.

A Study of Cellular Neural Networks with Vertex-Edge Topological Descriptors

The CellularNeuralNetwork(CNN)has various parallel processing applications,image processing,non-linear processing,geometric maps,highspeed computations.It is an analog paradigm,consists of an array of cells that are interconnected locally.Cells can be arranged in different configurations.Each cell has an input,a state,and an output.The cellular neural network allows cells to communicate with the neighbor cells only.It can be represented graphically;cells will represent by vertices and their interconnections will represent by edges.In chemical graph theory,topological descriptors are used to study graph structure and their biological activities.It is a single value that characterizes the whole graph.In this article,the vertex-edge topological descriptors have been calculated for cellular neural network.Results can be used for cellular neural network of any size.This will enhance the applications of cellular neural network in image processing,solving partial differential equations,analyzing 3D surfaces,sensory-motor organs,and modeling biological vision.

Topological Configuration and Rotation Analysis of the Three⁃Order Rubik􀆳s Cube

The mechanism of three⁃order Rubik􀆳s Cube(RC)has the characteristics of recombination and variable degree of freedom,and it is difficult to accurately describe the degree of its freedom.This paper takes RC as the research object,and the adjacency matrix is constructed based on topology and graph theory in order to describe the variation rule of topological configuration in the single layer rotation of RC.In this paper,the degree of freedom of the RC in any shape can be described by defining the concept of entanglement degree of freedom,establishing a set of adjacency matrix,and determining the degree of freedom of the RC which is attributed to the number of non⁃zero elements in the set of adjacent matrix.The prime number is proposed to describe the rotation of the RC combined with the rotation recognition of RC,which is simple and convenient for computer processing.The research contents in this paper are beneficial to the study of RC from the perspective of mechanism science.Meanwhile,it is of great significance to the study of other complex mechanisms with variable degrees of freedom.

The Degree Theory of a New Operator

This paper defines a concept of a semi k set contract operator and establishes a degree theory for it.

Existence of Weak Solution for p(x)-Kirchhoff Type Problem Involving the p(x)-Laplacian-like Operator by Topological Degree

In this paper,we study the existence of"weak solution"for a class of p(x)-Kirchhoff type problem involving the p(x)-Laplacian-like operator depending on two real parameters with Neumann boundary condition.Using a topological degree for a class of demicontinuous operator of generalized(S_(+))type and the theory of the variable exponent Sobolev space,we establish the existence of"weak solution"of this problem.

基于ANSYS的工业机械臂结构分析与拓扑优化设计

机械臂的刚度和固有频率对其可靠性有重要影响,需对其进行深入研究。文章对某型六自由度工业机械臂进行建模设计,在ANSYS软件采用有限元分析方法对机械臂在力矩最大的工况下进行静态结构分析和模态分析,验证其刚度和固有频率是否符合要求。进一步采用拓扑优化方法对大臂进行优化,然后对大臂进行模型重构,导入到整个机械臂中进行结构分析与模态分析,比较优化前后机械臂的性能差异,验证了改良后机械臂的可靠性,实现轻量化目标,为后续生产提供参考依据。

一种变自由度单回路机构的变拓扑结构设计及拓扑分析

特殊单回路机构通过一些特殊位置后会发生自由度变化,从而使其拓扑学、运动学/动力学性能发生变化,并适用于不同的应用背景。研究设计了一种由8个转动副(R)组成的单回路并联机构,它有3种运动模式,分别为2自由度、4自由度以及3自由度驱动,对应3个机构;然后,分析计算了3种运动模式下机构的方位特征集、自由度、耦合度3个主要拓扑特性,并分析了3种机构变拓扑结构的稳定性及可转变性;同时,对运动模式1、模式3下机构的位置正反解进行了分析。为基于这种变自由度单回路机构单元的可重构并联机构的研究提供了基础。

一类非局部临界椭圆方程组高能量解的多重性

利用变分方法,结合拓扑度理论,该文证明了一类带有Hardy-Littlewood-Sobolev临界指标的椭圆方程组至少存在两个正的高能量解.

基于节点交互度的社会网络链路预测

链路预测是通过已知的网络拓扑和节点属性挖掘未来时刻节点潜在关系的重要手段,是预测缺失链路和识别虚假链路的有效方法,在研究社会网络结构演化中具有现实意义.传统的链路预测方法基于节点信息或路径信息相似性进行预测,然而,前者考虑指标单一导致预测精度受限,后者由于计算复杂度过高不适合在规模较大网络中应用.通过对网络拓扑结构的分析,本文提出一种基于节点交互度(interacting degree of nodes,IDN)的社会网络链路预测方法.该方法首先根据网络中节点间的路径特征,引入了节点效率的概念,从而提高对于没有公共邻居节点之间链路预测的准确性;为了进一步挖掘节点间共同邻居的相关属性,借助分析节点间共同邻居的拓扑结构,该方法还创新性地整合了路径特征和局部信息,提出了社会网络节点交互度的定义,准确刻画出节点间的相似度,从而增强网络链路的预测能力;最后,本文借助6个真实网络数据集对IDN方法进行验证,实验结果表明,相比于目前的主流算法,本文提出的方法在AUC和Precision两个评价指标上均表现出更优的预测性能,预测结果平均分别提升22%和54%.因此节点交互度的提出在链路预测方面具有很高的可行性和有效性.

THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN

In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.

基于文本挖掘的WUI火灾致灾因子网络构建及特征分析

为预防和减少WUI火灾的发生,挖掘WUI火灾关键致灾因子,厘清致灾因子间的作用机制.本文首先基于本文挖掘技术从WUI火灾事故案例中得到致灾因子,使用Apriori算法得到致灾因子之间的关联规则.然后使用复杂网络理论构建WUI火灾致灾因子网络,计算网络拓扑特征参数,探析WUI火灾致灾因子网络特征.最后引入WUI火灾致因链风险度指标,挖掘出高风险连边,并提出断链措施.结果表明:WUI火灾致灾因子网络具有小世界特性,高温、强风、干旱等对其他致灾因子影响较大.燃烧废弃物、植物起火、应急响应速度、人为纵火、强风在不同致灾因子转换中具有重要作用,应加强管控.网络中风险度最高的边是燃烧废弃物→植物起火,通过颁布禁止擅自燃烧废弃物等规定,即可切断该风险链,实现对WUI火灾的预防和主动控制.

Robust measurement of orbital angular momentum of a partially coherent vortex beam under amplitude and phase perturbations

The ability to overcome the negative effects,induced by obstacles and turbulent atmosphere,is a core challenge of long-distance information transmission,and it is of great significance in free-space optical communication.The spatial-coherence structure,that characterizes partially coherent fields,provides a new degree of freedom for carrying information.However,due to the influence of the complex transmission environment,the spatial-coherence structure is severely damaged during the propagation path,which undoubtedly limits its ability to transmit information.Here,we realize the robust far-field orbital angular momentum(OAM)transmission and detection by modulating the spatial-coherence structure of a partially coherent vortex beam with the help of the cross-phase.The cross-phase enables the OAM information,quantified by the topological charge,hidden in the spatial-coherence structure can be stably transmitted to the far field and can resist the influence of obstructions and turbulence within the communication link.This is due to the self-reconstruction property of the spatial-coherence structure embedded with the cross-phase.We demonstrate experimentally that the topological charge information can be recognized well by measuring the spatial-coherence structure in the far field,exhibiting a set of distinct and separated dark rings even under amplitude and phase perturbations.Our findings open a door for robust optical signal transmission through the complex environment and may find application in optical communication through a turbulent atmosphere.

一类p-Laplacian问题正径向解的存在性与多解性

研究了p-Laplacian问题{-div(|∇u|^(p-2)∇u)=q(|x|)f(u),|x|>1,x∈R^(N),u(x)=b,|x|=1,u(x)→a,|x|→+∞,其中,1<p<N,a,b为正参数,q∈L^(1)_(loc)((1,+∞),[0,+∞)),f∈C([0,+∞),[0,+∞))。运用锥上的不动点定理、上下解方法和拓扑度理论,获得了p-Laplacian问题正解的存在性和多解性结果。