Toda谱V(1)的自映射群

本文给出了由Ｔｏｄａ 谱Ｖ（１）的同伦群πＶ（１）确定出它的自映射群［ΣＶ（１），Ｖ（１）］的一般方法，并且由πＶ（１）的已知结果确定了［ΣＶ（１），Ｖ（１）］在次数＜ ２（ｐ２ ＋ ２ｐ）（ｐ－ １）－ ５ 时的全部Ｚｐ 基元，其中ｐ≥５

Turnout fault diagnosis based on DBSCAN/PSO-SOM

In order to diagnose the common faults of railway switch control circuit,a fault diagnosis method based on density-based spatial clustering of applications with noise(DBSCAN)and self-organizing feature map(SOM)is proposed.Firstly,the three-phase current curve of the switch machine recorded by the micro-computer monitoring system is dealt with segmentally and then the feature parameters of the three-phase current are calculated according to the action principle of the switch machine.Due to the high dimension of initial features,the DBSCAN algorithm is used to separate the sensitive features of fault diagnosis and construct the diagnostic sensitive feature set.Then,the particle swarm optimization(PSO)algorithm is used to adjust the weight of SOM network to modify the rules to avoid“dead neurons”.Finally,the PSO-SOM network fault classifier is designed to complete the classification and diagnosis of the samples to be tested.The experimental results show that this method can judge the fault mode of switch control circuit with less training samples,and the accuracy of fault diagnosis is higher than that of traditional SOM network.

When a smooth self-map of a semi-simple Lie group can realize the least number of periodic points

There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = min{#Fix（gn）;g - f; g smooth}. In general, NJDn（f） may be much greater than NFn（f）. We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NFn（f） = NJDn（f） holds for all n →← all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.

THE TRACE SPACE INVARIANT AND UNITARY GROUP OF C-ALGEBRA

Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometric if n = ∞) under certain condition of A.