Isotropic polynomial invariants of Hall tensor

doi:10.1007/s10483-018-2398-9

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (12): 1845-1856.doi: https://doi.org/10.1007/s10483-018-2398-9

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Isotropic polynomial invariants of Hall tensor

Jinjie LIU¹, Weiyang DING², Liqun QI¹, Wennan ZOU³

1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China;
2. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China;
3. Institute for Advanced Study, Nanchang University, Nanchang 330031, China

Received:2018-06-22 Revised:2018-08-03 Online:2018-12-01 Published:2018-12-01
Contact: Liqun QI E-mail:maqilq@polyu.edu.hk
Supported by:
Project supported by Hong Kong Baptist University RC's Start-up Grant for New Academics, the Hong Kong Research Grant Council (Nos. PolyU 15302114, 15300715, 15301716, and 15300717), and the National Natural Science Foundation of China (No. 11372124)

Abstract

Abstract: The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.

Key words: vibration nonlinear differential, periodic solution Schauder’sprinciple, characteristic equation results by computer, isotropic polynomial invariant, irreducibility, function basis, integrity basis, Hall tensor

2010 MSC Number:

15A69
15A72

Jinjie LIU, Weiyang DING, Liqun QI, Wennan ZOU. Isotropic polynomial invariants of Hall tensor. Applied Mathematics and Mechanics (English Edition), 2018, 39(12): 1845-1856.

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References

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