This paper presents a fault-detection method based on the phase space reconstruction and data mining approaches for the complex electronic system. The approach for the phase space reconstruction of chaotic time series...This paper presents a fault-detection method based on the phase space reconstruction and data mining approaches for the complex electronic system. The approach for the phase space reconstruction of chaotic time series is a combination algorithm of multiple autocorrelation and F-test, by which the quasi-optimal embedding dimension and time delay can be obtained. The data mining algorithm, which calculates the radius of gyration of unit-mass point around the centre of mass in the phase space, can distinguish the fault parameter from the chaotic time series output by the tested system. The experimental results depict that this fault detection method can correctly detect the fault phenomena of electronic system.展开更多
In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure i...In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure is assumed as an algebra instead of a topology.As to obtain the algebraic quotient operator,the granulation must be uniquely determined by a congruence relation,and all the congruence relations form a complete semi-order lattice,which is the theoretical basis of granularities ' completeness.When the given equivalence relation is not a congruence relation,it defines the concepts of upper quotient and lower quotient,and discusses some of their properties which demonstrate that falsity preserving principle and truth preserving principle are still valid.Finally,it presents the algorithms and example of upper quotient and lower quotient.The work extends the quotient space theory from structure,and provides theoretical basis for the combination of the quotient space theory and the algebra theory.展开更多
For a long time it was a common opinion that hyperbolic attractors are artificial mathematical constructions. However, in the recent papers there were proposed physically realizable systems that possess, in their phas...For a long time it was a common opinion that hyperbolic attractors are artificial mathematical constructions. However, in the recent papers there were proposed physically realizable systems that possess, in their phase space, the set with features that are very similar to hyperbolic type of attractors. As is known, invariant sets are called hyperbolic attractors of the dynamical system if they are closed, topologically transitive subsets, and every their trajectory possesses uniform hyperbolicity. Very familiar types of the hyperbolic attractors are Smale-Williams＇ solenoid and Plykin＇s attractor. Further, it is well known that chaotic systems are very sensitive to the external perturbations. This property is used for controlling nonlinear systems and chaos suppression. Thus, an important question arises： Is it possible to suppress chaos in systems with hyperbolic attractors because these attractors are structurally stable subsets？ In the present contribution we study the possibility of stabilization of chaotic oscillations in systems with the Smale-Williams hyperbolic attractors by means of the Pyragas method with a delay. It is shown that by means of external perturbation the dynamical system could be controllable： the hyperbolic attractor degenerates into a periodic one.展开更多
In this paper the linearly topological structure of Menger Probabilistic inner product space is discussed. In virtue of these, some more general convergence theorems, Pythagorean theorem, and the orthogonal projective...In this paper the linearly topological structure of Menger Probabilistic inner product space is discussed. In virtue of these, some more general convergence theorems, Pythagorean theorem, and the orthogonal projective theorem are established.展开更多
Infinitesimal prolongation theorem is extended from sequences to nets based on κ-saturated nonstandard model. As its an application, a main property about topology of uniform convergence is proved. The proof is much ...Infinitesimal prolongation theorem is extended from sequences to nets based on κ-saturated nonstandard model. As its an application, a main property about topology of uniform convergence is proved. The proof is much simpler than it was, meanwhile the nonstandard characteristics of convergence with respect to u.c. topology is given.展开更多
In this paper,we calculated the spatial local-averaged velocity strains along the streamwise direction at four spatial scales according to the concept of spatial local-averaged velocity structure function by using the...In this paper,we calculated the spatial local-averaged velocity strains along the streamwise direction at four spatial scales according to the concept of spatial local-averaged velocity structure function by using the three-dimensional three-component database of time series of velocity vector field in the turbulent boundary layer measured by tomographic time-resolved particle image velocimetry.An improved quadrant splitting method,based on the spatial local-averaged velocity strains together with a new conditional sampling phase average technique,was introduced as a criterion to detect the coherent structure topology.Furthermore,we used them to detect and extract the spatial topologies of fluctuating velocity and fluctuating vorticity whose center is a strong second-quadrant event(Q2) or a fourth-quadrant event(Q4).Results illustrate that a closer similarity of the multi-scale coherent structures is present in the wall-normal direction,compared to the one in the other two directions.The relationship among such topological coherent structures and Reynolds stress bursting events,as well as the fluctuating vorticity was discussed.When other burst events are surveyed(the first-quadrant event Q1 and the third-quadrant event Q3),a fascinating bursting period circularly occurs:Q4-S-Q2-Q3-Q2-Q1-Q4-S-Q2-Q3-Q2-Q1 in the center of such topological structures along the streamwise direction.In addition,the probability of the Q2 bursting event occurrence is slightly higher than that of the Q4 event occurrence.The spatial instable singularity that almost simultaneously appears together with typical Q2 or Q4 events has been observed,which is the main character of the mutual induction mechanism and vortex auto-generation mechanism explaining how the turbulence is produced and maintained.展开更多
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introductio...The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.展开更多
Magnetic topological quantum materials(TQMs) provide a fertile ground for the emergence of fascinating topological magneto-electric effects. Recently, the discovery of intrinsic antiferromagnetic(AFM) topological insu...Magnetic topological quantum materials(TQMs) provide a fertile ground for the emergence of fascinating topological magneto-electric effects. Recently, the discovery of intrinsic antiferromagnetic(AFM) topological insulator MnBi_(2)Te_(4) that could realize quantized anomalous Hall effect and axion insulator phase ignited intensive study on this family of TQM compounds. Here, we investigated the AFM compound Mn Bi4 Te7 where Bi_(2)Te_(3) and MnBi_(2)Te_(4) layers alternate to form a superlattice. Using spatial-and angleresolved photoemission spectroscopy, we identified ubiquitous(albeit termination dependent) topological electronic structures from both Bi_(2)Te_(3) and MnBi_(2)Te_(4) terminations. Unexpectedly, while the bulk bands show strong temperature dependence correlated with the AFM transition, the topological surface states with a diminishing gap show negligible temperature dependence across the AFM transition.Together with the results of its sister compound MnBi_(2)Te_(4), we illustrate important aspects of electronic structures and the effect of magnetic ordering in this family of magnetic TQMs.展开更多
文摘This paper presents a fault-detection method based on the phase space reconstruction and data mining approaches for the complex electronic system. The approach for the phase space reconstruction of chaotic time series is a combination algorithm of multiple autocorrelation and F-test, by which the quasi-optimal embedding dimension and time delay can be obtained. The data mining algorithm, which calculates the radius of gyration of unit-mass point around the centre of mass in the phase space, can distinguish the fault parameter from the chaotic time series output by the tested system. The experimental results depict that this fault detection method can correctly detect the fault phenomena of electronic system.
基金Supported by the National Natural Science Foundation of China(No.61173052)the Natural Science Foundation of Hunan Province(No.14JJ4007)
文摘In the quotient space theory of granular computing,the universe structure is assumed to be a topology,therefore,its application is still limited.In this study,based on the quotient space model,the universe structure is assumed as an algebra instead of a topology.As to obtain the algebraic quotient operator,the granulation must be uniquely determined by a congruence relation,and all the congruence relations form a complete semi-order lattice,which is the theoretical basis of granularities ' completeness.When the given equivalence relation is not a congruence relation,it defines the concepts of upper quotient and lower quotient,and discusses some of their properties which demonstrate that falsity preserving principle and truth preserving principle are still valid.Finally,it presents the algorithms and example of upper quotient and lower quotient.The work extends the quotient space theory from structure,and provides theoretical basis for the combination of the quotient space theory and the algebra theory.
文摘For a long time it was a common opinion that hyperbolic attractors are artificial mathematical constructions. However, in the recent papers there were proposed physically realizable systems that possess, in their phase space, the set with features that are very similar to hyperbolic type of attractors. As is known, invariant sets are called hyperbolic attractors of the dynamical system if they are closed, topologically transitive subsets, and every their trajectory possesses uniform hyperbolicity. Very familiar types of the hyperbolic attractors are Smale-Williams＇ solenoid and Plykin＇s attractor. Further, it is well known that chaotic systems are very sensitive to the external perturbations. This property is used for controlling nonlinear systems and chaos suppression. Thus, an important question arises： Is it possible to suppress chaos in systems with hyperbolic attractors because these attractors are structurally stable subsets？ In the present contribution we study the possibility of stabilization of chaotic oscillations in systems with the Smale-Williams hyperbolic attractors by means of the Pyragas method with a delay. It is shown that by means of external perturbation the dynamical system could be controllable： the hyperbolic attractor degenerates into a periodic one.
基金Supported by the Natural Science Foundation of the Education Committee ofJiangsu Province
文摘In this paper the linearly topological structure of Menger Probabilistic inner product space is discussed. In virtue of these, some more general convergence theorems, Pythagorean theorem, and the orthogonal projective theorem are established.
基金Supported by the Speaial Science Foundation of the Edneational Committee of Shaanxi Province(oojk207).
文摘Infinitesimal prolongation theorem is extended from sequences to nets based on κ-saturated nonstandard model. As its an application, a main property about topology of uniform convergence is proved. The proof is much simpler than it was, meanwhile the nonstandard characteristics of convergence with respect to u.c. topology is given.
基金supported by the National Basic Research Program of China(Grant No.2012CB720101)the National Natural Science Foundation of China(Grant No.10832001)the Opening Subject of State Key Laboratory of Nonlinear Mechanics,Institute of Mechanics,Chinese Academy of Sciences
文摘In this paper,we calculated the spatial local-averaged velocity strains along the streamwise direction at four spatial scales according to the concept of spatial local-averaged velocity structure function by using the three-dimensional three-component database of time series of velocity vector field in the turbulent boundary layer measured by tomographic time-resolved particle image velocimetry.An improved quadrant splitting method,based on the spatial local-averaged velocity strains together with a new conditional sampling phase average technique,was introduced as a criterion to detect the coherent structure topology.Furthermore,we used them to detect and extract the spatial topologies of fluctuating velocity and fluctuating vorticity whose center is a strong second-quadrant event(Q2) or a fourth-quadrant event(Q4).Results illustrate that a closer similarity of the multi-scale coherent structures is present in the wall-normal direction,compared to the one in the other two directions.The relationship among such topological coherent structures and Reynolds stress bursting events,as well as the fluctuating vorticity was discussed.When other burst events are surveyed(the first-quadrant event Q1 and the third-quadrant event Q3),a fascinating bursting period circularly occurs:Q4-S-Q2-Q3-Q2-Q1-Q4-S-Q2-Q3-Q2-Q1 in the center of such topological structures along the streamwise direction.In addition,the probability of the Q2 bursting event occurrence is slightly higher than that of the Q4 event occurrence.The spatial instable singularity that almost simultaneously appears together with typical Q2 or Q4 events has been observed,which is the main character of the mutual induction mechanism and vortex auto-generation mechanism explaining how the turbulence is produced and maintained.
基金supported by National Natural Science Foundation of China (Grant No.10871016)
文摘The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures.This paper includes eight sections.Section 1 is a longer introduction,which gives a brief introduction to random metric theory,risk measures and conditional risk measures.Section 2 gives the central framework in random metric theory,topological structures,important examples,the notions of a random conjugate space and the Hahn-Banach theorems for random linear functionals.Section 3 gives several important representation theorems for random conjugate spaces.Section 4 gives characterizations for a complete random normed module to be random reflexive.Section 5 gives hyperplane separation theorems currently available in random locally convex modules.Section 6 gives the theory of random duality with respect to the locally L0-convex topology and in particular a characterization for a locally L0-convex module to be L0-pre-barreled.Section 7 gives some basic results on L0-convex analysis together with some applications to conditional risk measures.Finally,Section 8 is devoted to extensions of conditional convex risk measures,which shows that every representable L∞-type of conditional convex risk measure and every continuous Lp-type of convex conditional risk measure(1 ≤ p < +∞) can be extended to an L∞F(E)-type of σ,λ(L∞F(E),L1F(E))-lower semicontinuous conditional convex risk measure and an LpF(E)-type of T,λ-continuous conditional convex risk measure(1 ≤ p < +∞),respectively.
基金supported by the National Key Research and Development Program of China (2017YFA0305400, 2017YFA0304600, 2018YFA0307100, and 2018YFA0305603)the National Natural Science Foundation of China (11774190, 11674229, 11634009, 11774427, 51788104, and 11874035)+1 种基金EPSRC Platform Grant (EP/M020517/1)the support from the Shanghai Pujiang Program (17PJ1406200)。
文摘Magnetic topological quantum materials(TQMs) provide a fertile ground for the emergence of fascinating topological magneto-electric effects. Recently, the discovery of intrinsic antiferromagnetic(AFM) topological insulator MnBi_(2)Te_(4) that could realize quantized anomalous Hall effect and axion insulator phase ignited intensive study on this family of TQM compounds. Here, we investigated the AFM compound Mn Bi4 Te7 where Bi_(2)Te_(3) and MnBi_(2)Te_(4) layers alternate to form a superlattice. Using spatial-and angleresolved photoemission spectroscopy, we identified ubiquitous(albeit termination dependent) topological electronic structures from both Bi_(2)Te_(3) and MnBi_(2)Te_(4) terminations. Unexpectedly, while the bulk bands show strong temperature dependence correlated with the AFM transition, the topological surface states with a diminishing gap show negligible temperature dependence across the AFM transition.Together with the results of its sister compound MnBi_(2)Te_(4), we illustrate important aspects of electronic structures and the effect of magnetic ordering in this family of magnetic TQMs.
