• 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.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.459-465
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• 2022

We exhibit various properties of the weighted Berezin operator T_α and its iteration T^k_α on L^p(𝜏), where α > -1 and 𝜏 is the invariant measure on the complex unit ball B_n. Iterations of T_α on L¹_R(𝜏) the space of radial integrable functions have performed important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. We show differences between the case of 1 < p < ∞ and p = 1, ∞ under the infinite iteration of T_α or the infinite summation of iterations, most of which are extensions or related assertions to the propositions of the previous results.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.811-825
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• 2022

Given a compact subset P ⊂ (ℝ⁺)^d and a compact set K in ℂ^d. We concern with the Bernstein-Markov properties of the triple (P, K, 𝜇) where 𝜇 is a finite positive Borel measure with compact support K. Our approach uses (global) P-extremal functions which is inspired by the classical case (when P = Σ the unit simplex) in [7].

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.433-448
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• 2022

The Cartan's second curvature tensor Pⁱ_jkh is a positively homogeneous of degree-1 in yⁱ, where yⁱ represent a directional coordinate for the line element in Finsler space. In this paper, we discuss the decomposition of Cartan's second curvature tensor Pⁱ_jkh in two spaces, a generalized 𝔅P-recurrent space and generalized 𝔅P-birecurrent space. We obtain different tensors which satisfy the recurrence and birecurrence property under the decomposition. Also, we prove the decomposition for different tensors are non-vanishing. As an illustration of the applicability of the obtained results, we finish this work with some illustrative examples.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.2
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• pp.59-70
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• 2024

In this paper we present the approximation method of the circular helix by G² cubic polynomial curves. The approximants are G¹ Hermite interpolation of the circular helix and their approximation order is four. We obtain numerical examples to illustrate the geometric continuity and the approximation order of the approximants. The method presented in this paper can be extended to approximating the elliptical helix. Using the property of affine transformation invariance we show that the approximant has G² continuity and the approximation order four. The numerical examples are also presented to illustrate our assertions.

• Progress in Superconductivity and Cryogenics
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• v.24 no.3
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• pp.30-34
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• 2022

Effects of electron beam (EB) irradiation on the mechanical strength of Cu (conducting sheath) and Nb (diffusion barrier) of Cu/Nb/MgB₂ superconducting was investigated. Wire- and tape-type Cu/Nb/MgB₂ samples were irradiated at E-beam energy of 2.5 MeV and 5 mA and a maximum E-beam dose was 5×10¹⁷ e/m². The hardness value of Cu and Nb region was measured by the Vickers micro-hardness method. In the case of the wire sample, the hardness of Cu and Nb increased proportionally as the dose was increased up to 5×10¹⁷ e/m², whereas in the case of the tape sample, the hardness increased up to a dose of 0.5×10¹⁷ e/m², and decreased slightly 5×10¹⁷ e/m². The hardness increase of Cu and Nb is believed to be due to the decrease of the deformability of Cu and Nb due to the defects formed inside the materials by E-beam irradiation.

• Journal of Practical Agriculture & Fisheries Research
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• v.19 no.1
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• pp.91-97
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• 2017

This study was carried out to establish a proper cultivation site and to diagnose the drought tolerance of Heracleum moellendorffii leaves by using pressure-volume curves. As a result of analysing data measured, the leaf of H. moellendorffii showed the osmotic pressure at full turgor (Ψ_o^sat) was -1.0MPa, and that at incipient plasmolysis (Ψ_o^tlp) -1.2MPa. Then, the value of maximum bulk modulus of elasticity Emax was 28MPa, showing the sightly strong drought tolerance of H. moellendorffii. Furthermore, the values of relative water contents RWC^tlp and RWC^* were above 88%, showing that the function of osmoregulation is somewhat better. Thus, responses to water relations such as Ψ_o^sat, Ψ_o^tlp, E_max, RWC^tlp and RWC^* of H. moellendorffii showed it's slightly high drought tolerance property.

• Korean Journal of Materials Research
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• v.27 no.10
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• pp.534-543
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• 2017

$Gd_2O_3:Eu^{3+}$ red phosphors were prepared by template method from crystalline cellulose impregnated by metal salt. The crystallite size and photoluminescence(PL) property of $Gd_2O_3:Eu^{3+}$ red phosphors were controlled by varying the calcination temperature and $Eu^{3+}$ mol ratio. The nano dispersion of $Gd_2O_3:Eu^{3+}$ was also conducted with a bead mill wet process. Dependent on the time of bead milling, $Gd_2O_3:Eu^{3+}$ nanosol of around 100 nm (median particle size : $D_{50}$) was produced. As the bead milling process proceeded, the luminescent efficiency decreased due to the low crystallinity of the $Gd_2O_3:Eu^{3+}$ nanoparticles. In spite of the low PL property of $Gd_2O_3:Eu^{3+}$ nanosol, it was observed that the photoluminescent property was recovered after re-calcination. In addition, in the dispersed nanosol treated at $85^{\circ}C$, a self assembly phenomenon between particles appeared, and the particles changed from spherical to rod-shaped. These results indicate that particle growth occurs due to mutual assembly of $Gd(OH)_3$ particles, which is the hydration of $Gd_2O_3$ particles, in aqueous solvent at $85^{\circ}C$.

• Journal of Powder Materials
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• v.24 no.6
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• pp.457-463
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• 2017

Nanosized $Gd_2O_3:Eu^{3+}$ red phosphor is prepared using a template method from metal salt impregnated into a crystalline cellulose and is dispersed using a bead mill wet process. The driving force of the surface coating between $Gd_2O_3:Eu^{3+}$ and mica is induced by the Coulomb force. The red phosphor nanosol is effectively coated on mica flakes by the electrostatic interaction between positively charged $Gd_2O_3:Eu^{3+}$ and negatively charged mica above pH 6. To prepare $Gd_2O_3:Eu^{3+}$-coated mica ($Gd_2O_3:Eu/mica$), the coating conditions are optimized, including the stirring temperature, pH, calcination temperature, and coating amount (wt%) of $Gd_2O_3:Eu^{3+}$. In spite of the low luminescence of the $Gd_2O_3:Eu/mica$, the luminescent property is recovered after calcination above $600^{\circ}C$ and is enhanced by increasing the $Gd_2O_3:Eu^{3+}$ coating amount. The $Gd_2O_3:Eu/mica$ is characterized using X-ray diffraction, field emission scanning electron microscopy, zeta potential measurements, and fluorescence spectrometer analysis.

• Nuclear Engineering and Technology
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• v.56 no.5
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• pp.1854-1862
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• 2024

This study aims to investigate the strain-dependent-deformation property of Gyeongju bentonite buffer material. A series of unconfined compressive tests were performed with cylindrical specimens prepared at varying dry densities (𝜌_d = 1.58 g/cm³ to 1.74 g/cm³) using cold isostatic pressing technique. It is found that as 𝜌_d increase, the unconfined compressive strength (q_u), failure strain, and elastic modulus (E) of Gyeongju compacted bentonite (GCB) increases. Normalized elastic modulus (E_sec/E_max) degradation curves of GCB specimens are fitted using Ramberg-Osgood model and the elastic threshold strain (𝜀_e,th) is determined through the fitted curves. The strain-dependency of E and Poisson's ratio (v) of GCB were observed. E and v were measured constant below 𝜀_e,th of 0.14 %. Then, E decreases while v increases after exceeding the strain threshold. The E_sec/E_max degradation curves of GCB in this study suggests wider linear range and higher linearity than those of sedimentary clay in previous study. On top of that, the influence of 𝜌_d is observed on E_sec/E_max degradation curves of GCB, showing a slight increase in 𝜀_e,th with increase in 𝜌_d. Furthermore, an empirical model of q_u with 𝜌_d and a correlation model between q_u and E are proposed for Gyeongju bentonite buffer materials.