The non-wandering set Ω(f) for a graph map f is investigated. It is showed that Ω(f) is contained in the closure of the set ER(f) of eventually recurrent points of f and ω-limit set ω(Ω(f)) of Ω(f) is containe...The non-wandering set Ω(f) for a graph map f is investigated. It is showed that Ω(f) is contained in the closure of the set ER(f) of eventually recurrent points of f and ω-limit set ω(Ω(f)) of Ω(f) is contained in the closure of the set R(f) of recurrent points of f.展开更多
The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the gr...The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001.The difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transformation is defined by means of combinatorial operations.They discuss its advantages over the graph homotopy transformation.As its applications,they investigate the mapping class group of a graph and the 1-order M P-homotopy group of a pointed simple graph.Moreover,they show that the 1-order M P-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.展开更多
Let G be a graph and f ： G → G be a continuous map. Denote by P（f）, R（f）, SA（f） and UF（f） the sets of periodic points, recurrent points, special α-limit points and unilateral γ-limit points of f, respectiv...Let G be a graph and f ： G → G be a continuous map. Denote by P（f）, R（f）, SA（f） and UF（f） the sets of periodic points, recurrent points, special α-limit points and unilateral γ-limit points of f, respectively. In this paper, we show that R（f） SA（f） = UP（f） ∪ P（f） R（f）.展开更多
Let G be a graph （i.e., a finite one-dimensional polyhedron） and f ： G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non-wandering point; every accumulatio...Let G be a graph （i.e., a finite one-dimensional polyhedron） and f ： G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non-wandering point; every accumulation point of the set of non-wandering points of f with infinite orbit is a two-order accumulation point of the set of recurrent points of f; the derived set of an ω-limit set of f is equal to the derived set of an the set of recurrent points of f; and the two-order derived set of non-wandering set of f is equal to the two-order derived set of the set of recurrent points of f.展开更多
Let G be a graph and f:G→G be continuous.Denote by R(f) andΩ(f) the set of recurrent points and the set of non-wandering points of f respectively.LetΩ_0(f) = G andΩ_n(f)=Ω(f|_(Ω_(n-1)(f))) for all n∈N.The minim...Let G be a graph and f:G→G be continuous.Denote by R(f) andΩ(f) the set of recurrent points and the set of non-wandering points of f respectively.LetΩ_0(f) = G andΩ_n(f)=Ω(f|_(Ω_(n-1)(f))) for all n∈N.The minimal m∈NU {∞} such thatΩ_m(f)=Ω_(m+1)(f) is called the depth of f.In this paper,we show thatΩ_2 (f)=(?) and the depth of f is at most 2.Furthermore,we obtain some properties of non-wandering points of f.展开更多
相位展开是磁共振成像技术应用中最关键的环节之一,可以为磁共振的某些重要临床应用提供精确的相位信息。然而,由于临床磁共振成像过程中,部分区域真实的相位存在急剧变化,同时伴有不同性态的噪声污染,导致相位展开时存在信息的高度不...相位展开是磁共振成像技术应用中最关键的环节之一,可以为磁共振的某些重要临床应用提供精确的相位信息。然而,由于临床磁共振成像过程中,部分区域真实的相位存在急剧变化,同时伴有不同性态的噪声污染,导致相位展开时存在信息的高度不一致性。为了有效地解决上述难题,基于马尔可夫-最大后验(Markov Random Field& Maximum A Posterioi,MRF-MAP)模型,首次将相位展开看作计算机视觉中的标记问题,并结合磁共振相位数据的特点,设计出相位图的模糊质量图,完成相位展开的能量函数构建。针对能量函数的优化求解,采用高效的图割算法进行。展开更多
A concept map is a diagram depicting relationships among concepts which is used as a knowledge representation tool in many knowledge domains. In this paper, we build on the modeling framework of Hui et al. (2008) in o...A concept map is a diagram depicting relationships among concepts which is used as a knowledge representation tool in many knowledge domains. In this paper, we build on the modeling framework of Hui et al. (2008) in order to develop a concept map suitable for testing the empirical evidence of theories. We identify a theory by a set of core tenets each asserting that one set of independent variables affects one dependent variable, moreover every variable can have several operational definitions. Data consist of a selected sample of scientific articles from the empirical literature on the theory under investigation. Our “tenet map” features a number of complexities more than the original version. First the links are two-layer: first-layer links connect variables which are related in the test of the theory at issue;second-layer links represent connections which are found statistically significant. Besides, either layer matrix of link-formation probabilities is block-symmetric. In addition to a form of censoring which resembles the Hui et al. pruning step, observed maps are subject to a further censoring related to second-layer links. Still, we perform a full Bayesian analysis instead of adopting the empirical Bayes approach. Lastly, we develop a three-stage model which accounts for dependence either of data or of parameters. The investigation of the empirical support and consensus degree of new economic theories of the firm motivated the proposed methodology. In this paper, the Transaction Cost Economics view is tested by a tenet map analysis. Both the two-stage and the multilevel models identify the same tenets as the most corroborated by empirical evidence though the latter provides a more comprehensive and complex insight of relationships between constructs.展开更多
In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph fo...In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph for the single-valued mapping whose conversion makes the results and proofs concise and straightforward, and then we propose an <em>SG</em>-contraction definition for set-valued mapping which is more general than some recent contraction’s definition. The results obtained in this paper extend and unify some recent results of other authors. Our method to discuss the N-order fixed point unifies <em>N</em>-order fixed point theory of set-valued and single-valued mappings.展开更多
基金The first author is supported by the Natural Science Foundation of the Committee of Education ofJiangsu Province ( 0 2 KJB1 1 0 0 0 8)
文摘The non-wandering set Ω(f) for a graph map f is investigated. It is showed that Ω(f) is contained in the closure of the set ER(f) of eventually recurrent points of f and ω-limit set ω(Ω(f)) of Ω(f) is contained in the closure of the set R(f) of recurrent points of f.
基金supported by the National Natural Science Foundation of China(No.11771116)。
文摘The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001.The difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transformation is defined by means of combinatorial operations.They discuss its advantages over the graph homotopy transformation.As its applications,they investigate the mapping class group of a graph and the 1-order M P-homotopy group of a pointed simple graph.Moreover,they show that the 1-order M P-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.
基金supported by National Natural Science Foundation of China (Grant No.10861002)Natural Science Foundation of Guangxi Province (Grnat Nos. 2010GXNSFA013106,2011GXNSFA018135)SF of Education Department of Guangxi Province (Grant No. 200911MS212)
文摘Let G be a graph and f ： G → G be a continuous map. Denote by P（f）, R（f）, SA（f） and UF（f） the sets of periodic points, recurrent points, special α-limit points and unilateral γ-limit points of f, respectively. In this paper, we show that R（f） SA（f） = UP（f） ∪ P（f） R（f）.
基金NSF of the Committee of Education of Jiangshu Province of China (02KJB110008)supported by NNSF of China(19961001)the Support Program for 100 Young and Middle-aged Disciplinary Leaders in Guangxi Higher Education Institutions
文摘Let G be a graph （i.e., a finite one-dimensional polyhedron） and f ： G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non-wandering point; every accumulation point of the set of non-wandering points of f with infinite orbit is a two-order accumulation point of the set of recurrent points of f; the derived set of an ω-limit set of f is equal to the derived set of an the set of recurrent points of f; and the two-order derived set of non-wandering set of f is equal to the two-order derived set of the set of recurrent points of f.
基金This work was supported by the Special Foundation of National Prior Basis Researches of China (Grant No.G1999075108)the National Natural Science Foundation of China (Grant No.10461001)the Natural Science Foundation of Guangxi (Grant Nos.0728002,0640205)
文摘Let G be a graph and f:G→G be continuous.Denote by R(f) andΩ(f) the set of recurrent points and the set of non-wandering points of f respectively.LetΩ_0(f) = G andΩ_n(f)=Ω(f|_(Ω_(n-1)(f))) for all n∈N.The minimal m∈NU {∞} such thatΩ_m(f)=Ω_(m+1)(f) is called the depth of f.In this paper,we show thatΩ_2 (f)=(?) and the depth of f is at most 2.Furthermore,we obtain some properties of non-wandering points of f.
文摘相位展开是磁共振成像技术应用中最关键的环节之一,可以为磁共振的某些重要临床应用提供精确的相位信息。然而,由于临床磁共振成像过程中,部分区域真实的相位存在急剧变化,同时伴有不同性态的噪声污染,导致相位展开时存在信息的高度不一致性。为了有效地解决上述难题,基于马尔可夫-最大后验(Markov Random Field& Maximum A Posterioi,MRF-MAP)模型,首次将相位展开看作计算机视觉中的标记问题,并结合磁共振相位数据的特点,设计出相位图的模糊质量图,完成相位展开的能量函数构建。针对能量函数的优化求解,采用高效的图割算法进行。
文摘A concept map is a diagram depicting relationships among concepts which is used as a knowledge representation tool in many knowledge domains. In this paper, we build on the modeling framework of Hui et al. (2008) in order to develop a concept map suitable for testing the empirical evidence of theories. We identify a theory by a set of core tenets each asserting that one set of independent variables affects one dependent variable, moreover every variable can have several operational definitions. Data consist of a selected sample of scientific articles from the empirical literature on the theory under investigation. Our “tenet map” features a number of complexities more than the original version. First the links are two-layer: first-layer links connect variables which are related in the test of the theory at issue;second-layer links represent connections which are found statistically significant. Besides, either layer matrix of link-formation probabilities is block-symmetric. In addition to a form of censoring which resembles the Hui et al. pruning step, observed maps are subject to a further censoring related to second-layer links. Still, we perform a full Bayesian analysis instead of adopting the empirical Bayes approach. Lastly, we develop a three-stage model which accounts for dependence either of data or of parameters. The investigation of the empirical support and consensus degree of new economic theories of the firm motivated the proposed methodology. In this paper, the Transaction Cost Economics view is tested by a tenet map analysis. Both the two-stage and the multilevel models identify the same tenets as the most corroborated by empirical evidence though the latter provides a more comprehensive and complex insight of relationships between constructs.
文摘In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph for the single-valued mapping whose conversion makes the results and proofs concise and straightforward, and then we propose an <em>SG</em>-contraction definition for set-valued mapping which is more general than some recent contraction’s definition. The results obtained in this paper extend and unify some recent results of other authors. Our method to discuss the N-order fixed point unifies <em>N</em>-order fixed point theory of set-valued and single-valued mappings.
