26 research outputs found
Geometric Schur Duality of Classical Type, II
We establish algebraically and geometrically a duality between the
Iwahori-Hecke algebra of type D and two new quantum algebras arising from the
geometry of N-step isotropic flag varieties of type D. This duality is a type D
counterpart of the Schur-Jimbo duality of type A and the Schur-like duality of
type B/C discovered by Bao-Wang. The new algebras play a role in the type D
duality similar to the modified quantum gl(N) in type A, and the modified
coideal subalgebras of quantum gl(N) in type B/C. We construct canonical bases
for these two algebras.Comment: 40 page
Differential operator realization of braid group action on quantum groups
We construct a unique braid group action on modified -Weyl algebra
. Under this action, we give a realization of the braid group
action on quasi-split quantum groups of type
. Furthermore, we directly construct a unique braid group action
on polynomial ring which is compatible with the braid group action
on and
Approach to health monitoring and assessment of rolling bearing
A bearing is the most common and vital element in the majority of rotating machinery. Condition monitoring and performance assessment of rolling bearing have recently attracted significant attention. This paper proposes a set of methodologies to realize the efficient health monitoring and assessment of rolling bearing. Considering the difficulties and disadvantages in detecting the fault signal of rolling bearing with background noise, this paper presents a method based on the Duffing oscillator and Hu’s moment invariant for health monitoring. The proposed method mainly combines the chaotic oscillator and moment invariant, fully utilizing the sensitivity of the former to detect the fault signal and taking the latter as a quantitative index for fault identification without the need for a qualitative artificial judgment on the Duffing oscillator phase trajectory map. To provide the optimal performance of Hu’s moment invariant in automatic recognition for the phase trajectory map, the influencing principle of different oscillator parameters was analyzed. Therefore, the health state of rolling bearing can be automatically monitored by quantitatively identifying the transition state of the phase trajectory map. A health assessment model was established to evaluate the health state of bearings. Wavelet packet transform was used to extract the features (approximate entropy) of bearing vibration signal, which were input into the self-organizing map (SOM) network. The health state of rolling bearings was then assessed using the SOM network and confidence values. A case study on health monitoring and assessment for rolling bearing was conducted to demonstrate the effectiveness and accuracy of the proposed methods