The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what des...The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what described by the well-known technology "Li-Yorke chaos". The concept "sensitive dependency on initial conditions" has been generalized, and the chaotic phenomena has been discussed for transitive systems with the generalized sensitive dependency property.展开更多
For a prime p at least 5,let T=PSL(2,p).This paper gives a classification of the connected arc-transitive cubic Cayley graphs on T and a determination of the gener- ated pairs ((?),(?)) of T such that o((?))=2 and o((...For a prime p at least 5,let T=PSL(2,p).This paper gives a classification of the connected arc-transitive cubic Cayley graphs on T and a determination of the gener- ated pairs ((?),(?)) of T such that o((?))=2 and o((?))=3.展开更多
Load spectra research for bogie frame requires establishing the load?stress relationship on working condition, which has been omitted by the researchers. With the load?stress of the bogie frame of an intercity Electri...Load spectra research for bogie frame requires establishing the load?stress relationship on working condition, which has been omitted by the researchers. With the load?stress of the bogie frame of an intercity Electric Multiple Unit(Hereinafter referred to as EMU) as the research object, an optimization model of the load?stress transfer relationship is established. The load?stress coe cient for EMU bogie frame was calibrated in the laboratory bench and online test was arranged on Dazhou?Chengdu line. Comparison of nonlinear and linear neural networks proves that the linear transitive relation between the load and stress of the bogie frame in the operating process is highly suitable. An optimization model of the load?stress transfer coe cient is obtained. The data calculated with the modified coe cient are closer to the dynamic stress results in the actual operating process than the data calculated with the calibration coe cient. The coe cient of the modified transitive relation is una ected by operating area, empty load, heavy load, or other conditions in the operating process of the intercity EMU. The real loads in actual situations are obtained. The model of online load?stress relationship that is highly suitable for line stress calculation is finally established. The research is helpful for further damage calculation and inferring the time history signal of the load in load spectra research.展开更多
The possibility of developing a complete graph invariant computable in polynomial time remains an open question. Consequently, creating efficient algorithms to verify non-isomorphism, including heuristic approaches, i...The possibility of developing a complete graph invariant computable in polynomial time remains an open question. Consequently, creating efficient algorithms to verify non-isomorphism, including heuristic approaches, is essential. Effective implementation of these heuristics necessitates both the adaptation of existing graph invariants and the invention of novel ones, which continues to be a relevant challenge. Numerous current invariants are capable of distinguishing a significant number of graphs rapidly in real-time scenarios. In this study, we present an invariant tailored for tournaments, a specific class of directed graphs. Tournaments are particularly intriguing because the count of distinct tournaments for a given number of vertices aligns with that of undirected graphs of the same size. The introduced invariant evaluates all possible tournament subsets derived from the original digraph that share the identical arc set. For each subset tournament, standard rankings are computed and aggregated to produce the final vertex scores, which serve as the new invariant. Our analysis indicates that this newly proposed invariant diverges from the most straightforward tournament invariant, which typically assigns scores to each participant. Preliminary computational tests demonstrate that the minimal correlation between the sequences generated by these two invariants occurs at a vertex count of 15.展开更多
Let X be a finite simple undirected graph and G an automorphism group of X. If G is transitive on s-arcs but not on （s ＋ 1）-arcs then X is called （G, s）-transitive. Let X be a connected （G, s）-transitive graph ...Let X be a finite simple undirected graph and G an automorphism group of X. If G is transitive on s-arcs but not on （s ＋ 1）-arcs then X is called （G, s）-transitive. Let X be a connected （G, s）-transitive graph of a prime valency p, and Gv the vertex stabilizer of a vertex v E V（X） in G. For the case p = 3, the exact structure of Gv has been determined by Djokovid and Miller in [Regular groups of automorphisms of cubic graphs, J. Combin. Theory （Ser. B） 29 （1980） 195-230]. For the case p = 5, all the possibilities of Gv have been given by Guo and Feng in [A note on pentavalent s-transitive graphs, Discrete Math. 312 （2012） 2214-2216]. In this paper, we deal with the case p = 7 and determine the exact structure of the vertex stabilizer Gv.展开更多
In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a trip...In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang （J. Combin. Designs, 4 （1996）, 301-321）. As an application, we obtain an LRDTS（4·3^n） for any integer n ≥ 1, which provides an infinite family of even orders.展开更多
Water quality assessment of lakes is important to determine functional zones of water use.Considering the fuzziness during the partitioning process for lake water quality in an arid area,a multiplex model of fuzzy clu...Water quality assessment of lakes is important to determine functional zones of water use.Considering the fuzziness during the partitioning process for lake water quality in an arid area,a multiplex model of fuzzy clustering with pattern recognition was developed by integrating transitive closure method,ISODATA algorithm in fuzzy clustering and fuzzy pattern recognition.The model was applied to partition the Ulansuhai Lake,a typical shallow lake in arid climate zone in the west part of Inner Mongolia,China and grade the condition of water quality divisions.The results showed that the partition well matched the real conditions of the lake,and the method has been proved accurate in the application.展开更多
Let M be a closed smooth manifold M, and let f ： M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set A of f. We show that if f has the C^1-stably average shadowing property on A, then A...Let M be a closed smooth manifold M, and let f ： M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set A of f. We show that if f has the C^1-stably average shadowing property on A, then A admits a dominated splitting.展开更多
In the present paper, we define sensitive pairs via Furstenberg families and discuss the relation of three definitions： sensitivity, F -sensitivity and F -sensitive pairs, see Theorem 1. For transitive systems, we gi...In the present paper, we define sensitive pairs via Furstenberg families and discuss the relation of three definitions： sensitivity, F -sensitivity and F -sensitive pairs, see Theorem 1. For transitive systems, we give some sufficient conditions to ensure the existence of F -sensitive pairs. In particular, each non-minimal E system （M system, P system） has positive lower density （ Fs , Fr resp.）-sensitive pairs almost everywhere. Moreover, each non-minimal M system is Fts -sensitive. Finally, by some examples we show that： （1） F -sensitivity can not imply the existence of F -sensitive pairs. That means there exists an F -sensitive system, which has no F -sensitive pairs. （2） There is no immediate relation between the existence of sensitive pairs and Li-Yorke chaos, i.e., there exists a system （X, f ） without Li-Yorke scrambled pairs, which has κ B -sensitive pairs almost everywhere. （3） If the system （G, f ） is sensitive, where G is a finite graph, then it has κ B -sensitive pairs almost everywhere.展开更多
In this paper, we classify the m-ovoids of finite classical polar spaces that admit a transitive automorphism group acting irreducibly on the ambient vector space. In particular, we obtain several new infinite familie...In this paper, we classify the m-ovoids of finite classical polar spaces that admit a transitive automorphism group acting irreducibly on the ambient vector space. In particular, we obtain several new infinite families of transitive m-ovoids.展开更多
Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectr...Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectrum of T and T={λ∈C:|λ|=1},and that there is a non-hypercyclic,sensitive system(X,T) which is not syndetically sensitive.We also show that there is a transitively sensitive system(X,T) which is mean sensitive but not multi-transitively sensitive.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.10171034).
文摘The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what described by the well-known technology "Li-Yorke chaos". The concept "sensitive dependency on initial conditions" has been generalized, and the chaotic phenomena has been discussed for transitive systems with the generalized sensitive dependency property.
基金supported by the National natural Science Foundation of China(Grant No.10371003)Beijing Natural Science Foundation(Grant no.1052005)BMCE(Grant No.KM 2004 10028001).
文摘For a prime p at least 5,let T=PSL(2,p).This paper gives a classification of the connected arc-transitive cubic Cayley graphs on T and a determination of the gener- ated pairs ((?),(?)) of T such that o((?))=2 and o((?))=3.
基金Supported by National Natural Science Foundation of China(Grant No.U1134201)National Key Research and Development Program of China(Grant No.2016YFB1200404-08)National Key Research and Development Program of China(Grant No.2016YFB1200505-11)
文摘Load spectra research for bogie frame requires establishing the load?stress relationship on working condition, which has been omitted by the researchers. With the load?stress of the bogie frame of an intercity Electric Multiple Unit(Hereinafter referred to as EMU) as the research object, an optimization model of the load?stress transfer relationship is established. The load?stress coe cient for EMU bogie frame was calibrated in the laboratory bench and online test was arranged on Dazhou?Chengdu line. Comparison of nonlinear and linear neural networks proves that the linear transitive relation between the load and stress of the bogie frame in the operating process is highly suitable. An optimization model of the load?stress transfer coe cient is obtained. The data calculated with the modified coe cient are closer to the dynamic stress results in the actual operating process than the data calculated with the calibration coe cient. The coe cient of the modified transitive relation is una ected by operating area, empty load, heavy load, or other conditions in the operating process of the intercity EMU. The real loads in actual situations are obtained. The model of online load?stress relationship that is highly suitable for line stress calculation is finally established. The research is helpful for further damage calculation and inferring the time history signal of the load in load spectra research.
文摘The possibility of developing a complete graph invariant computable in polynomial time remains an open question. Consequently, creating efficient algorithms to verify non-isomorphism, including heuristic approaches, is essential. Effective implementation of these heuristics necessitates both the adaptation of existing graph invariants and the invention of novel ones, which continues to be a relevant challenge. Numerous current invariants are capable of distinguishing a significant number of graphs rapidly in real-time scenarios. In this study, we present an invariant tailored for tournaments, a specific class of directed graphs. Tournaments are particularly intriguing because the count of distinct tournaments for a given number of vertices aligns with that of undirected graphs of the same size. The introduced invariant evaluates all possible tournament subsets derived from the original digraph that share the identical arc set. For each subset tournament, standard rankings are computed and aggregated to produce the final vertex scores, which serve as the new invariant. Our analysis indicates that this newly proposed invariant diverges from the most straightforward tournament invariant, which typically assigns scores to each participant. Preliminary computational tests demonstrate that the minimal correlation between the sequences generated by these two invariants occurs at a vertex count of 15.
基金This work was supported by the National Natural Science Foundation of China （11301154, 11271012, 11301159, 11101035, 11326056）, the Key Project of Education Department of Henan Province Scientific and Technological Research （13A110249） and the Scientific Re- search Foundation for Doctoral Scholars of HAUST （09001707）.
文摘Let X be a finite simple undirected graph and G an automorphism group of X. If G is transitive on s-arcs but not on （s ＋ 1）-arcs then X is called （G, s）-transitive. Let X be a connected （G, s）-transitive graph of a prime valency p, and Gv the vertex stabilizer of a vertex v E V（X） in G. For the case p = 3, the exact structure of Gv has been determined by Djokovid and Miller in [Regular groups of automorphisms of cubic graphs, J. Combin. Theory （Ser. B） 29 （1980） 195-230]. For the case p = 5, all the possibilities of Gv have been given by Guo and Feng in [A note on pentavalent s-transitive graphs, Discrete Math. 312 （2012） 2214-2216]. In this paper, we deal with the case p = 7 and determine the exact structure of the vertex stabilizer Gv.
文摘In this paper, we first define a doubly transitive resolvable idempotent quasigroup （DTRIQ）, and show that aDTRIQ of order v exists if and only ifv ≡0（mod3） and v ≠ 2（mod4）. Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang （J. Combin. Designs, 4 （1996）, 301-321）. As an application, we obtain an LRDTS（4·3^n） for any integer n ≥ 1, which provides an infinite family of even orders.
基金Supported by the National Natural Science Foundation of China (No.50269001, 50569002, 50669004)Natural Science Foundation of Inner Mongolia (No.200208020512, 200711020604)The Key Scientific and Technologic Project of the 10th Five-Year Plan of Inner Mongolia (No.20010103)
文摘Water quality assessment of lakes is important to determine functional zones of water use.Considering the fuzziness during the partitioning process for lake water quality in an arid area,a multiplex model of fuzzy clustering with pattern recognition was developed by integrating transitive closure method,ISODATA algorithm in fuzzy clustering and fuzzy pattern recognition.The model was applied to partition the Ulansuhai Lake,a typical shallow lake in arid climate zone in the west part of Inner Mongolia,China and grade the condition of water quality divisions.The results showed that the partition well matched the real conditions of the lake,and the method has been proved accurate in the application.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(Grant No.2011-0007649)supported by National Natural Science Foundation of China(Grant No.11026041)
文摘Let M be a closed smooth manifold M, and let f ： M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set A of f. We show that if f has the C^1-stably average shadowing property on A, then A admits a dominated splitting.
基金supported by NSFC (10771079 10871186+5 种基金 11071084 11026095)NSF of Guangdong Province (10451063101006332)supported by NSFC (11001071)Hefei University of Technology (GDBJ2008-024 2010HGXJ0200)
文摘In the present paper, we define sensitive pairs via Furstenberg families and discuss the relation of three definitions： sensitivity, F -sensitivity and F -sensitive pairs, see Theorem 1. For transitive systems, we give some sufficient conditions to ensure the existence of F -sensitive pairs. In particular, each non-minimal E system （M system, P system） has positive lower density （ Fs , Fr resp.）-sensitive pairs almost everywhere. Moreover, each non-minimal M system is Fts -sensitive. Finally, by some examples we show that： （1） F -sensitivity can not imply the existence of F -sensitive pairs. That means there exists an F -sensitive system, which has no F -sensitive pairs. （2） There is no immediate relation between the existence of sensitive pairs and Li-Yorke chaos, i.e., there exists a system （X, f ） without Li-Yorke scrambled pairs, which has κ B -sensitive pairs almost everywhere. （3） If the system （G, f ） is sensitive, where G is a finite graph, then it has κ B -sensitive pairs almost everywhere.
基金supported by National Natural Science Foundation of China (Grant No. 12171428)the Sino-German Mobility Programme M-0157Shandong Provincial Natural Science Foundation (Grant No. ZR2022QA069)。
文摘In this paper, we classify the m-ovoids of finite classical polar spaces that admit a transitive automorphism group acting irreducibly on the ambient vector space. In particular, we obtain several new infinite families of transitive m-ovoids.
文摘Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectrum of T and T={λ∈C:|λ|=1},and that there is a non-hypercyclic,sensitive system(X,T) which is not syndetically sensitive.We also show that there is a transitively sensitive system(X,T) which is mean sensitive but not multi-transitively sensitive.
