The Weyl algebra as a fixed ring

The magnetic-liquid double suspension bearing (MLDSB) is a new type of suspension bearing, with electromagnetic suspension as the main part and hydrostatic supports as the auxiliary part. It can greatly improve the bearing capacity and stiffness of rotor-bearing systems and is suitable for a medium speed, heavy load, and frequent starting occasions. Compared with the active electromagnetic bearing system, the traditional protective bearing device is replaced by the hydrostatic system in MLDSB, and the impact-rubbing phenomenon can be restrained and buffered. Thus, the probability and degree of friction and wear between the rotor and the magnetic pole are reduced drastically when the electromagnetic system fails. In order to explore the difference in the dynamic behavior law of the impact-rubbing phenomenon between the traditional protection device and hydrostatic system, the dynamic equations of the rotor impact-rubbing in three kinds of protection devices (fixed ring/deep groove ball bearing/hydrostatic system) under electromagnetic failure mode are established, and the axial trajectory and motion law of the rotor are numerically simulated. Finally, the dynamic behavior characteristics of the rotor are compared and analyzed. The results show that: Among the three kinds of protection devices (fixed ring/deep groove ball bearing/hydrostatic system), the hydrostatic system has the least influence on bouncing time, impact-rubbing force, and impact-rubbing degree, and the maximum impact-rubbing force of MLDSB is greatly reduced. Therefore, the protective bear is not required to be installed in the MLDSB. This study provides the basis for the theory of the “gap impact-rubbing” of MLDSB under electromagnetic failure, and helps to identify electromagnetic faults.

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Quantum relativistic Toda chain at root of unity: isospectrality, modifiedQ-operator, and functional Bethe ansatz

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171202105059 ◽

2002 ◽

Vol 31 (9) ◽

pp. 513-553 ◽

Cited By ~ 3

Author(s):

Stanislav Pakuliak ◽

Sergei Sergeev

Keyword(s):

Bethe Ansatz ◽

Weyl Algebra ◽

Separation Of Variables ◽

Toda Chain ◽

Special Choice ◽

Finite Dimensional Representation ◽

Classical Counterpart ◽

Discrete Integrable System ◽

Root Of Unity ◽

Finite Dimensional

We investigate anN-state spin model called quantum relativistic Toda chain and based on the unitary finite-dimensional representations of the Weyl algebra withqbeingNth primitive root of unity. Parameters of the finite-dimensional representation of the local Weyl algebra form the classical discrete integrable system. Nontrivial dynamics of the classical counterpart corresponds to isospectral transformations of the spin system. Similarity operators are constructed with the help of modified Baxter'sQ-operators. The classical counterpart of the modifiedQ-operator for the initial homogeneous spin chain is a Bäcklund transformation. This transformation creates an extra Hirota-type soliton in a parameterization of the chain structure. Special choice of values of solitonic amplitudes yields a degeneration of spin eigenstates, leading to the quantum separation of variables, or the functional Bethe ansatz. A projector to the separated eigenstates is constructed explicitly as a product of modifiedQ-operators.

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Path decompositions of digraphs and their applications to Weyl algebra

Advances in Applied Mathematics ◽

10.1016/j.aam.2015.03.005 ◽

2015 ◽

Vol 67 ◽

pp. 36-54 ◽

Cited By ~ 3

Author(s):

Askar Dzhumadil'daev ◽

Damir Yeliussizov

Keyword(s):

Weyl Algebra ◽

Path Decompositions

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Specht polynomials and modules over the Weyl algebra

Afrika Matematika ◽

10.1007/s13370-018-0642-9 ◽

2018 ◽

Vol 30 (1-2) ◽

pp. 279-290

Author(s):

Ibrahim Nonkané

Keyword(s):

Weyl Algebra

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The classical limit of a state on the Weyl algebra

Journal of Mathematical Physics ◽

10.1063/1.5013249 ◽

2018 ◽

Vol 59 (11) ◽

pp. 112102 ◽

Cited By ~ 3

Author(s):

Benjamin H. Feintzeig

Keyword(s):

Classical Limit ◽

Weyl Algebra

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The Group of Automorphisms of the Algebra of one-Sided Inverses of a Polynomial Algebra. II

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091514000303 ◽

2015 ◽

Vol 58 (3) ◽

pp. 543-580

Author(s):

V. V. Bavula

Keyword(s):

Weyl Algebra ◽

Differential Operators ◽

Polynomial Algebra ◽

Group Of Automorphisms ◽

Algebra Ii ◽

Noetherian Property

AbstractThe algebra of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting left (but not two-sided) inverses of the canonical generators of the algebra Pn. The algebra is isomorphic to the algebra of scalar integro-differential operators provided that char(K) = 0. Ignoring the non-Noetherian property, the algebra belongs to a family of algebras like the nth Weyl algebra An and the polynomial algebra P2n. Explicit generators are found for the group Gn of automorphisms of the algebra and for the group of units of (both groups are huge). An analogue of the Jacobian homomorphism AutK-alg (Pn) → K* is introduced for the group Gn (notice that the algebra is non-commutative and neither left nor right Noetherian). The polynomial Jacobian homomorphism is unique. Its analogue is also unique for n > 2 but for n = 1, 2 there are exactly two of them. The proof is based on the following theorem that is proved in the paper:

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