Additive Property of Drazin Invertibility of Elements

In this article, we investigate additive properties of the Drazin inverse of elements in rings and algebras over an arbitrary field. Under the weakly commutative condition of $ab = \lambda ba$, we show that $a-b$ is Drazin invertible if and only if $aa^{D}(a-b)bb^{D}$ is Drazin invertible. Next, we give explicit representations of $(a+b)^{D}$, as a function of $a, b, a^{D}$ and $b^{D}$, under the conditions $a^{3}b = ba$ and $b^{3}a = ab$.Comment: 17 page

Comparison of Halbach magnetized brushless machines based on discrete magnet segments or a single ring magnet

This paper compares the air-gap field distribution, cogging torque, back-electromotive-force waveform, and efficiency of brushless machines having a Halbach magnetization produced by either discrete magnet segments or a single ring magnet. Results deduced from finite-element analyses are compared with measurements, and the performance of Halbach magnetized machines is compared with that of machines equipped with radially magnetized magnets

Analytical magnetic field analysis of Halhach magnetized permanent-magnet machines

We develop analytical models for predicting the magnetic field distribution in Halbach magnetized machines. They are formulated in polar coordinates and account for the relative recoil permeability of the magnets. They are applicable to both internal and external rotor permanent-magnet machines with either an iron-cored or air-cored stator and/or rotor. We compare predicted results with those obtained by finite-element analyses and measurements. We show that the air-gap flux density varies significantly with the pole number and that an optimal combination of the magnet thickness and the pole number exists for maximum air-gap flux density, while the back iron can enhance the air-gap field and electromagnetic torque when the radial thickness of the magnet is small

R-mode instability in compact stars

R-mode oscillations have been identified as viable and promising targets for continuous gravitational wave searches, meanwhile, it would allow us to probe the interior of compact stars directly. As well as emitting gravitational wave, r-modes would strongly affect the thermal and spin evolution of compact stars. In this paper, we reviewed the theory behind the gravitational wave driven r-mode instability in a rapidly rotating compact star. In particular, we will focus on r-mode instability window, r-mode evolution and detectability of r-mode.Comment: contribution to the AIP Proceedings of the Xiamen-CUSTIPEN Workshop on the EOS of Dense Neutron-Rich Matter in the Era of Gravitational Wave Astronomy, Jan. 3-7, 2019, Xiamen, China. arXiv admin note: text overlap with arXiv:0806.1005, arXiv:1510.07051, arXiv:1209.5962 by other author