• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.105-122
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• 2023

We present explicit formulas for the spectra of higher spin operators on the subbundle of the bundle of spinor-valued trace free symmetric tensors that are annihilated by Clifford multiplication over the standard sphere in odd dimension. In the even dimensional case, we give the spectra of the square of such operators. The Dirac and Rarita-Schwinger operators are zero-form and one-form cases, respectively. We also give eigenvalue formulas for the conformally invariant differential operators of all odd orders on the subbundle of the bundle of spinor-valued forms that are annihilated by Clifford multiplication in both even and odd dimensions on the sphere.

• Journal of Magnetics
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• v.17 no.1
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• pp.13-18
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• 2012

Starting with Kubo's formula and using the projection operator technique introduced by Kawabata, EPR lineprofile function for a $Mn^{2+}$-doped wurtzite structure GaN semiconductor was derived as a function of temperature at a frequency of 9.49 GHz (X-band) in the presence of external electromagnetic field. The line-width is barely affected in the low-temperature region because there is no correlation between the resonance fields and the distribution function. At higher temperature the line-width increases with increasing temperature due to the interaction of electrons with acoustic phonons. Thus, the present technique is considered to be more convenient to explain the resonant system as in the case of other optical transition systems.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.999-1021
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• 2023

Using the results in the paper [12], we give an estimate for the first positive and negative Dirac eigenvalue on a 7-dimensional Sasakian spin manifold. The limiting case of this estimate can be attained if the manifold under consideration admits a Sasakian Killing spinor. By imposing the eta-Einstein condition on Sasakian manifolds of higher dimensions 2m + 1 ≥ 9, we derive some new Dirac eigenvalue inequalities that improve the recent results in [12, 13].