• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.197-204
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• 2022

In this article, we define a modified Koszul complex, which we call a quantized Koszul complex, on a quantum space ring, and we also prove that it is an acyclic complex.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.461-464
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• 1998

We generalize the Artin-Rees Theorem about the AR-property and study linking diagram in the set of prime ideals of the coordinate ring of quantum affine space.

• Journal of the Korea Convergence Society
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• v.8 no.5
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• pp.161-167
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• 2017

We have fabricated and characterized $32{\times}32$ photonic quantum ring (PQR) laser arrays uniformly operable with $0.98{\mu}A$ per ring at room temperature. The typical threshold current, threshold current density, and threshold voltage are 20 mA, $0.068A/cm^2$, and 1.38 V. The top surface emitting PQR array contains GaAs multiquantum well active regions and exhibits uniform characteristics for a chip of $1.65{\times}1.65mm^2$. The peak power wavelength is $858.8{\pm}0.35nm$, the relative intensity is $0.3{\pm}0.2$, and the linewidth is $0.2{\pm}0.07nm$. We also report the wavelength division multiplexing system experiment using angle-dependent blue shift characteristics of this laser array. This photonic quantum ring laser has angle-dependent multiple-wavelength radial emission characteristics over about 10 nm tuning range generated from array devices. The array exhibits a free space detection as far as 6 m with a function of the distance.

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.322-325
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• 1999

We report fiber guiding experiments on the Photonic Quantum Ring(PQR) laser diode. In the 1km transmission measurements, we find that the PQR performs much better than the VCSEL. This suggests that the PQR laser is very promising candidate for LAN-range optical data communications. On the other hand, we have also fabricated 8$\times$8 PQR laser arrays and measured spatial decays for free space properties without using any guiding optics, which showed about 1m distance of spectral angle sensing.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.933-943
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• 2020

Let M be a Fano manifold, and H^🟉(M; ℂ) be the quantum cohomology ring of M with the quantum product 🟉. For 𝜎 ∈ H^🟉(M; ℂ), denote by [𝜎] the quantum multiplication operator 𝜎🟉 on H^🟉(M; ℂ). It was conjectured several years ago [7,8] and has been proved for many Fano manifolds [1,2,10,14], including our cases, that the operator [c₁(M)] has a real valued eigenvalue 𝛿₀ which is maximal among eigenvalues of [c₁(M)]. Galkin's lower bound conjecture [6] states that for a Fano manifold M, 𝛿₀ ≥ dim M + 1, and the equality holds if and only if M is the projective space ℙⁿ. In this note, we show that Galkin's lower bound conjecture holds for Lagrangian and orthogonal Grassmannians, modulo some exceptions for the equality.