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A GENERAL VERSION OF KALTON'S CLOSED GRAPH THEOREM 被引量:2
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作者 丘京辉 《Acta Mathematica Scientia》 SCIE CSCD 1995年第2期161-170,共10页
By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which a... By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which are convenient for application. Particularly we improve some results of Kalton. 展开更多
关键词 Locally convex spaces Mackey spaces closed graph theorems.
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AN IMPROVED NONLINEAR CLOSED GRAPH THEOREM
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作者 Lei Qiang Li Ronglu 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第2期226-228,共3页
In this paper, a new nonlinear closed graph theorem is established, whose result improves substantially a recent-known important conclusion.
关键词 closed graph Fréchet space CONTINUITY
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A NEW CLASS OF LOCALLY CONVEX SPACES AND THE GENERALIZATION OF KALTON'S CLOSED GRAPH THEOREM
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作者 丘京辉 《Acta Mathematica Scientia》 SCIE 1985年第4期389-397,共9页
By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the clo... By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given. 展开更多
关键词 A NEW CLASS OF LOCALLY CONVEX SPACES AND THE GENERALIZATION OF KALTON’S closed graph THEOREM
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Theorems of Helly's Type for Partially-closed Half-spaces
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作者 Liu Jian-Guo Guo Qi 《Communications in Mathematical Research》 CSCD 2018年第2期117-124,共8页
In this article, under quite weaker conditions, theorems of Helly’s type for(not necessarily finite) family of partially closed half-spaces are presented in both analytic and geometric forms. Examples are also provid... In this article, under quite weaker conditions, theorems of Helly’s type for(not necessarily finite) family of partially closed half-spaces are presented in both analytic and geometric forms. Examples are also provided to show that these conditions cannot be omitted in general. 展开更多
关键词 Helly's theorem partially-closed half-space affine function convex set
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关于The Closed Graph定理的一点注记
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作者 姚喜妍 《郧阳师范高等专科学校学报》 2001年第3期5-6,共2页
The Closed Graph定理是泛函分析中的基本定理,在数学领域内用途比较广泛.文章研究了定理的条件中被忽视的问题并给出了相应的反例.
关键词 闭图象 闭算子 连续算子
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边加权有限图的Weil-Riemann-Roch定理
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作者 曹廷彬 刘洁 《南昌大学学报(理科版)》 CAS 2024年第2期103-107,共5页
Riemann-Roch定理是数学中的一个重要结论,并有了广泛的应用。在有限图和边加权有限图等图中也有对应的Riemann-Roch定理以及应用,但所有这些工作都有一个共同点,那就是它们都聚焦于在除子或和除子线性等价的线丛的情况下,也就是秩为1... Riemann-Roch定理是数学中的一个重要结论,并有了广泛的应用。在有限图和边加权有限图等图中也有对应的Riemann-Roch定理以及应用,但所有这些工作都有一个共同点,那就是它们都聚焦于在除子或和除子线性等价的线丛的情况下,也就是秩为1的情况。为了得到高维秩的情形,可以借助多重除子的术语来描述。本文利用还原群GLn的root datum的概念给出了边加权有限图上主GLn-丛——向量丛的定义,并用多重除子的术语来描述向量丛,进而给出了边加权有限图的Weil-Riemann-Roch定理以及证明,推广了GROSS A.ULIRSCH M.和ZAKHAROV D的结果。 展开更多
关键词 边加权有限图 Riemann-Roch定理 向量丛 多重除子
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一类特殊复积分的探讨
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作者 马建清 《高等数学研究》 2024年第3期11-12,共2页
本文从教学中两个具体的例子出发,总结出一类积分值为零的复积分的特点,并给出理论证明.
关键词 复积分 复合闭路定理 留数定理
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一种鲁棒闭环的增量式Graph SLAM算法 被引量:4
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作者 张国良 姚二亮 +1 位作者 岳亚南 孙一杰 《电光与控制》 北大核心 2015年第7期28-33,共6页
针对常规增量式Graph SLAM算法的后端优化无法高效排除错误闭环影响的问题,基于i SAM算法和SC算法,提出一种鲁棒闭环的增量式Graph SLAM算法R-i SAM。R-i SAM在增量式过程中对当前时刻引入的闭环约束的转换变量进行初步近似计算,得到合... 针对常规增量式Graph SLAM算法的后端优化无法高效排除错误闭环影响的问题,基于i SAM算法和SC算法,提出一种鲁棒闭环的增量式Graph SLAM算法R-i SAM。R-i SAM在增量式过程中对当前时刻引入的闭环约束的转换变量进行初步近似计算,得到合理的机器人节点位姿。在离线式过程中对当前时期的所有闭环约束转换变量进行精确计算,判断当前时期闭环的正确性,并作为以后优化节点的基础。对公开的数据集进行的算法实验表明,在添加不同类型、不同数量的错误闭环条件下,所提算法对不同数据集具有良好适应性,且收敛速度满足增量式SLAM实时性要求,证明了算法的有效性。 展开更多
关键词 同步定位与地图构建 图优化 鲁棒闭环 增量式
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从一道普特南竞赛题看高等代数课程中的图论方法
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作者 刘乐乐 汪毅 《黄山学院学报》 2024年第5期102-106,共5页
以一道普特南数学竞赛试题作为切入点,探讨图论思想如何融入高等代数课程中,展示图论课程与高等代数课程之间的联系。进一步分析图论在解决高等代数问题中的多元应用,如矩阵横贯、逆序数、矩阵幂计算及向量组线性相关性等。通过图论视角... 以一道普特南数学竞赛试题作为切入点,探讨图论思想如何融入高等代数课程中,展示图论课程与高等代数课程之间的联系。进一步分析图论在解决高等代数问题中的多元应用,如矩阵横贯、逆序数、矩阵幂计算及向量组线性相关性等。通过图论视角,深化对高等代数知识的理解与运用。 展开更多
关键词 图论 高等代数 横贯 Hall定理
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Dynamics of Advantageous Mutant Spread in Spatial Death-Birth and Birth-Death Moran Models
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作者 Jasmine Foo Einar Bjarki Gunnarsson +1 位作者 Kevin Leder David Sivakoff 《Communications on Applied Mathematics and Computation》 EI 2024年第1期576-604,共29页
The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized tha... The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world applications, the population usually has an explicit spatial structure which can significantly influence the dynamics. In the context of cancer initiation in epithelial tissue, several recent works have analyzed the dynamics of advantageous mutant spread on integer lattices, using the biased voter model from particle systems theory. In this spatial version of the Moran model, individuals first reproduce according to their fitness and then replace a neighboring individual. From a biological standpoint, the opposite dynamics, where individuals first die and are then replaced by a neighboring individual according to its fitness, are equally relevant. Here, we investigate this death-birth analogue of the biased voter model. We construct the process mathematically, derive the associated dual process, establish bounds on the survival probability of a single mutant, and prove that the process has an asymptotic shape. We also briefly discuss alternative birth-death and death-birth dynamics, depending on how the mutant fitness advantage affects the dynamics. We show that birth-death and death-birth formulations of the biased voter model are equivalent when fitness affects the former event of each update of the model, whereas the birth-death model is fundamentally different from the death-birth model when fitness affects the latter event. 展开更多
关键词 Spatial death-birth models Spatial birth-death models Spatial evolutionary models Spatial cancer models Evolutionary graph theory Stochastic processes Biased voter model Dual process Fixation probability Shape theorem
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复变函数与积分变换的渐进式教学研究——以含奇点复积分解法为例
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作者 池建成 《科技风》 2024年第5期97-99,共3页
文章主要通过复合闭路定理、柯西积分公式、留数定理三种方法去处理几类积分路径内含有奇点的积分问题,并对它们的适用条件进行了比较.在教学中,有助于对这三个知识点的引入与讲解.
关键词 奇点 复合闭路定理 柯西积分公式 留数定理
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ON RANGE DECOMPOSITION THEOREMS
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作者 吴利生 《苏州大学学报(自然科学版)》 CAS 1990年第2期119-123,共5页
We prove the following theorems.Theorem 1.Suppose f:X→Y is a closed map.X is a ωγ and β space,then Y=Y0∪(∪n=1^∞Yn),where f^-1(y) is countably compact for each y ∈Y0 and Yn is closed discrete in Y for each n≥1... We prove the following theorems.Theorem 1.Suppose f:X→Y is a closed map.X is a ωγ and β space,then Y=Y0∪(∪n=1^∞Yn),where f^-1(y) is countably compact for each y ∈Y0 and Yn is closed discrete in Y for each n≥1,Theorem 2-3:Suppose f:X→Y is a closed map,X is stratifable space,then Y=Y0 ∪(∪n=1^∞Yn),where f^-1(y) is compact for each y∈Y0 and Yn is closed discrete in Y for each n≥1. 展开更多
关键词 闭映射 分解定理 半可层化 拟完全原象
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A Computational Synthesis Approach of Mechanical Conceptual Design Based on Graph Theory and Polynomial Operation 被引量:1
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作者 Lin Han Geng Liu +1 位作者 Xiaohui Yang Bing Han 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2020年第1期60-74,共15页
The design synthesis is the key issue in the mechanical conceptual design to generate the design candidates that meet the design requirements.This paper devotes to propose a novel and computable synthesis approach of ... The design synthesis is the key issue in the mechanical conceptual design to generate the design candidates that meet the design requirements.This paper devotes to propose a novel and computable synthesis approach of mechanisms based on graph theory and polynomial operation.The graph framework of the synthesis approach is built firstly,and it involves:(1)the kinematic function units extracted from mechanisms;(2)the kinematic link graph that transforms the synthesis problem from mechanical domain into graph domain;(3)two graph representations,i.e.,walk representation and path representation,of design candidates;(4)a weighted matrix theorem that transforms the synthesis process into polynomial operation.Then,the formulas and algorithm to the polynomial operation are presented.Based on them,the computational flowchart to the synthesis approach is summarized.A design example is used to validate and illustrate the synthesis approach in detail.The proposed synthesis approach is not only supportive to enumerate the design candidates to the conceptual design of a mechanical system exhaustively and automatically,but also helpful to make that enumeration process computable. 展开更多
关键词 DESIGN SYNTHESIS CONCEPTUAL DESIGN graph theory POLYNOMIAL operation KINEMATIC link graph Weighted matrix theorem
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TRANSFER OPEN OR CLOSED SETVALUED MAPPING AND GENERALIZ-ATION OF H-KKM THEOREM WITH APPLICATIONS
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作者 李秉友 苏家宝 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第10期981-987,共7页
In this paper ,we introduce a class of generalized mapping called transfer open orclosed valued mapping to generalize the KKM theorem on H-space.Then asapplications,using our H-KKM theorem,we prove some coincidence th... In this paper ,we introduce a class of generalized mapping called transfer open orclosed valued mapping to generalize the KKM theorem on H-space.Then asapplications,using our H-KKM theorem,we prove some coincidence theorems.matching theorems and vector valued minimax inequalities which generalize slightly thecorresponding results in[1,2,4,5,6,7]. 展开更多
关键词 transfer closed or open setvalued mapping coincidence theorem.H-KKM mapping matching theorem
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Bernstein type theorem of minimal Lagrangian graphs in quaternion Euclidean space H^n
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作者 HAN Ying-bo 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2009年第1期114-118,共5页
In this paper, a Bernstein type theorem for minimal Lagrangian submanifolds in quaternion Euclidean space H^n is studied.
关键词 Bernstein type theorem minimal Lagrangian graph
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面向数字孪生流域的知识平台构建关键技术 被引量:18
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作者 冯钧 朱跃龙 +1 位作者 王云峰 周思源 《人民长江》 北大核心 2023年第3期229-235,共7页
数字孪生流域中的知识平台需要支撑物理流域全映射与孪生流域可互动等应用要求。针对知识平台中的水利知识图谱、历史场景模式、业务规则、专家经验等建设内容,提出了一种基于知识图谱的数字孪生流域知识体系架构。在该架构中,利用图模... 数字孪生流域中的知识平台需要支撑物理流域全映射与孪生流域可互动等应用要求。针对知识平台中的水利知识图谱、历史场景模式、业务规则、专家经验等建设内容,提出了一种基于知识图谱的数字孪生流域知识体系架构。在该架构中,利用图模型描述业务场景中实体概念间的关联关系,以事件为视角描述事件演化背后的机理与模式,以业务为导向形成业务-事件-要素间的关联网络,最终构建形成全景式耦合网络。基于全景式耦合网络,进一步建立了物理空间与数字空间、业务层与支撑层互动关联的闭环式应用架构。将此架构应用至数字孪生流域平台中,以事件为驱动,通过数据反馈形成决策闭环,从而达到支撑水利业务智能管理与决策的目的。 展开更多
关键词 数字孪生 知识图谱 计算机仿真 智能模型 闭环系统
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Note on Faudree-Schelp Theorem in Path Connected Graphs and Ore Theorem in Hamilton Connected Graphs
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作者 ZHAOKe-wen ZENGKe-yang 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第2期175-177,共3页
In this note more short proofs are given for Faudree-Schelp theorem and Ore theorem.
关键词 Faudree-Schelp theorem Ore theorem Hamilton connected graphs
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Biggs Theorem for Directed Cycles and Topological Invariants of Digraphs
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作者 Michael Hecht Ivo F. Sbalzarini 《Advances in Pure Mathematics》 2021年第6期573-594,共22页
We generalize Biggs Theorem to the case of directed cycles of multi-digraphs allowing to compute the dimension of the directed cycle space independently of the graph representation with linear runtime complexity. By c... We generalize Biggs Theorem to the case of directed cycles of multi-digraphs allowing to compute the dimension of the directed cycle space independently of the graph representation with linear runtime complexity. By considering two-dimensional CW complex of elementary cycles and deriving formulas for the Betti numbers of the associated cellular homology groups, we extend the list of representation independent topological inavariants measuring the graph structure. We prove the computation of the 2nd Betti number to be sharp #<em>P</em> hard in general and present specific representation invariant sub-fillings yielding efficiently computable homology groups. Finally, we suggest how to use the provided structural measures to shed new light on graph theoretical problems as <em>graph embeddings</em>, <em>discrete Morse theory </em>and<em> graph clustering</em>. 展开更多
关键词 Biggs Theorem Elementary and Simple Cycles CW Complexes of graphs Cellular and Singular Homology Betti Numbers
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基于图论法和贝叶斯理论的供水管网漏损定位方法 被引量:4
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作者 王彤 康炳卿 +5 位作者 李钟毓 朱多林 王晴怡 赵红斌 许德伦 洪磊 《水电能源科学》 北大核心 2023年第8期135-138,125,共5页
目前大多数漏损定位方法都依赖于管网水力模型,但当水力模型精度无法达到要求或由于基础资料缺失无法建立模型时,基于模型的方法就会失效。为此,以压力监测数据为基础进行供水管网漏损定位研究,即基于图论法建模理论得出插值估计管网节... 目前大多数漏损定位方法都依赖于管网水力模型,但当水力模型精度无法达到要求或由于基础资料缺失无法建立模型时,基于模型的方法就会失效。为此,以压力监测数据为基础进行供水管网漏损定位研究,即基于图论法建模理论得出插值估计管网节点压力,通过分析各节点压力监测值和漏损发生后实测值的残差估计漏损位置,并借助贝叶斯理论对定位结果进行时序推理,将一定时段内概率最大的节点视为发生漏损的位置。借助L镇案例对管网发生单点漏损时的状态进行模拟,验证了漏损定位方法的可行性和定位性能。 展开更多
关键词 供水管网 漏损定位 图论法 贝叶斯理论 压力监测数据
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Generalized S-KKM Theorems and Minimax Inequalities in FC-Spaces
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作者 张红玲 范翠丽 《Journal of Southwest Jiaotong University(English Edition)》 2008年第3期303-307,共5页
The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is t... The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value. 展开更多
关键词 Generalized S-KKM type theorem Finitely continuous topological space FC-closed value Minimax inequalities
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