• Korean Journal of Optics and Photonics
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• v.35 no.3
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• pp.115-120
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• 2024

Magneto-optical (MO) materials have attracted much attention, since they can be utilized for various optical applications, such as magnetic field sensors, optical current sensors, optical isolators, and optical circulators. In this study, alumino-borosilicate (ABS) glasses with high concentrations of Dy³⁺ ions were fabricated by a conventional melt-quenching technique, and the dependence of their thermal, optical, and magneto-optical properties on Dy³⁺ ion concentration was investigated. The MO property of the glasses was investigated by measurement of Faraday rotation at 1550 nm. The Faraday rotation angle increased linearly with the increase of Dy³⁺ ion concentration in the glasses. A very high Verdet constant of -6.86 rad/(T·m) was obtained for glass with a Dy³⁺ ion concentration of 30 mol%. In addition, the ABS-Dy glasses showed good thermal stability of greater than 128 ℃ against crystallization, and high optical transmission of 70% in the visible to near-infrared windows of 480-720, 1390-1560, and 1800-2400 nm. Due to the high Verdet constant and good thermal stability, the ABS-Dy glasses in this study could be candidate optical materials for MO device applications at 1550 nm.

• Korean Journal of Mathematics
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• v.19 no.1
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• pp.61-64
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• 2011

Let $\mathcal{A}^*$ denotes the class of operators satisfying $|T^2|{\geq}|T^*|^2$. In this paper, we show if the restriction to a non-trivial invariant subspace $\mathcal{M}$ of an operator $T{\in}\mathcal{A}^*$ is normal, then $\mathcal{M}$ reduces T.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.1
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• pp.36-43
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• 2002

We analyze bulk service $M/G^{b}/1$ queues using the arrival time approach of Chae et al. (2001). As a result, the decomposition property of the M/G/1 queue with generalized vacations is extended to the $M/G^{b}/1$ queue in which the batch size is exactly a constant b. We also demonstrate that the arrival time approach is useful for relating the time-average queue length PGF to that of the departure time, both for the $M/G^{b}/1$queue in which the batch size is as big as possible but up to the maximum of constant b. The case that the batch size is a random variable is also briefly mentioned.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.387-400
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• 2014

We prove that the set of k-type nonwandering points of a Z2-action T can be decomposed into a disjoint union of closed and T-invariant sets $B_1,{\ldots},B_l$ such that $T|B_i$ is topologically k-type transitive for each $i=1,2,{\ldots},l$, if T is expansive and has the shadowing property.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.163-172
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• 2003

In this paper we study the property of harmonic vector fields. We call a vector fields ${\xi}$ harmonic if it is a harmonic map from the manifold into its tangent bundle with the Sasaki metric. We show that the characteristic polynomial of operator $A={\nabla}{\xi}\;in\;S^{2n+1}\;is\;(x^2+1)^n$.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.233-237
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• 2003

An asymptotic property of the ordinary least squares estimator of the disturbance variance is considered in the regression model with correlated errors. It is shown that the convergence in probability of S$^2$ is equivalent to the asymptotic unbiasedness. Beyond the assumption on the design matrix or the variance-covariance matrix of disturbances error, the result is quite general and simplify the earlier results.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.519-525
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• 2008

Let f be a diffeomorphisms of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper, we prove that if generically, f is tame diffeomorphims then the following conditions are equivalent: (i) f is ${\Omega}$-stable, (ii) f has the $C^1$-stable shadowing property (iii) f has the $C^1$-stable inverse shadowing property.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1355-1375
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• 2021

The n-dimensional generalized Hartogs triangles ℍⁿ_𝐩 with n ≥ 2 and 𝐩 := (p₁, …, p_n) ∈ (ℝ⁺)ⁿ are the domains defined by ℍⁿ_𝐩 := {z = (z₁, …, z_n) ∈ ℂⁿ : |z₁|^p₁ < ⋯ < |z_n|^p_n < 1}. In this paper, we study the L^p Sobolev mapping properties for the Bergman projections on the n-dimensional generalized Hartogs triangles ℍⁿ_𝐩, which can be viewed as a continuation of the work by S. Zhang in [25] and a higher-dimensional generalization of the work by L. D. Edholm and J. D. McNeal in [16].

• Korean Journal of Materials Research
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• v.31 no.7
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• pp.397-402
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• 2021

In this study, binderless-WC, WC-6 wt%Co, WC-6wt% 1 and 2.5 B₄C materials are fabricated by spark plasma sintering process (SPS process). Each fabricated WC material is almost completely dense, with a relative density up to 99.5 % after the simultaneous application of pressure of 60 MPa. The WC added Co and Co-B₄C materials resulted in crystalline growth. The WC with HCP crystal structure has respective interfacial energy (basal facet direction: 1.07 ~ 1.34 J·m^-2, prismatic direction: 1.43 ~ 3.02 J·m^-2) that depends on the grain growth direction. It is confirmed that the continuous grain growth, biased by the basal facet, which has relatively low energy, is promoted at the WC/Co interface. As abnormal grain growth takes place, the grain size increases more than twice from 0.37 to 0.8 um. It is found through analysis that the hardness property also greatly decreases from about 2661.4 to 1721.4 kg/mm², along with the grain growth.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.391-403
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• 2023

In this work, we establish common fixed point results by utilizing a variant of F-contraction in the framework of C^*-algebra valued metric spaces. We utilize E.A. and C.L.R. property possessed by the mappings to prove common fixed point results in the same metric settings. To validate the applicability of these common fixed point results, we provide illustrative examples too.