• 대한수학회보
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• 제47권6호
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• pp.1275-1283
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• 2010

If the Wiener-Hopf $C^*$-algebra W(G,M) for a discrete group G with a semigroup M has the uniqueness property, then the structure of it is to some extent independent of the choice of isometries on a Hilbert space. In this paper we show that if the Wiener-Hopf $C^*$-algebra W(G,M) of a partially ordered group G with the positive cone M has the uniqueness property, then (G,M) is weakly unperforated. We also prove that the Wiener-Hopf $C^*$-algebra W($\mathbb{Z}$, M) of subsemigroup generating the integer group $\mathbb{Z}$ is isomorphic to the Toeplitz algebra, but W($\mathbb{Z}$, M) does not have the uniqueness property except the case M = $\mathbb{N}$.

• 대한수학회지
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• 제49권2호
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• pp.405-417
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• 2012

We find the Hilbert function and the minimal free resolution of a star-configuration in $\mathbb{P}^n$. The conditions are provided under which the Hilbert function of a star-configuration in $\mathbb{P}^2$ is generic or non-generic We also prove that if $\mathbb{X}$ and $\mathbb{Y}$ are linear star-configurations in $\mathbb{P}^2$ of types t and s, respectively, with $s{\geq}t{\geq}3$, then the Artinian k-algebra $R/(I_{\mathbb{X}}+I_{\mathbb{Y})$ has the weak Lefschetz property.

• 충청수학회지
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• 제30권4호
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• pp.435-443
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• 2017

We find a graded minimal free resolution of the union of two star configurations ${\mathbb{X}}$ and ${\mathbb{Y}}$ (not necessarily linear star configurations) in ${\mathbb{P}}^n$ of type s and t for s, $t{\geq}2$, and $n{\geq}3$. As an application, we prove that an Artinian ring $R/(I_{\mathbb{X}}+I_{\mathbb{Y}})$ of two linear star configurations ${\mathbb{X}}$ and ${\mathbb{Y}}$ in ${\mathbb{P}}^3$ of type s and t has the weak Lefschetz property for $s{\geq}{\lfloor}\frac{1}{2}(^t_2){\rfloor}$ and $t{\geq}2$.

• 대한수학회지
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• 제60권3호
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• pp.565-586
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• 2023

We study the Dirichlet problem for the degenerate nonlocal parabolic equation u_t - a(||∇u||²_L²(Ω))∆u = C_b ||u||^β_L²(Ω) |u|^q(x,t)-2 u log |u| + f in Q_T, where Q_T := Ω × (0, T), T > 0, Ω ⊂ ℝ^N, N ≥ 2, is a bounded domain with a sufficiently smooth boundary, q(x, t) is a measurable function in Q_T with values in an interval [q^-, q⁺] ⊂ (1, ∞) and the diffusion coefficient a(·) is a continuous function defined on ℝ₊. It is assumed that a(s) → 0 or a(s) → ∞ as s → 0⁺, therefore the equation degenerates or becomes singular as ||∇u(t)||2 → 0. For both cases, we show that under appropriate conditions on a, β, q, f the problem has a global in time strong solution which possesses the following global regularity property: ∆u ∈ L²(Q_T) and a(||∇u||²_L²(Ω))∆u ∈ L²(Q_T ).

• Korean Journal of Radiology
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• 제24권6호
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• pp.564-573
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• 2023

Objective: To investigate the feasibility of assessing the viscoelastic properties of the brain using magnetic resonance elastography (MRE) and a novel MRE transducer to determine the relationship between the viscoelastic properties and glymphatic function in neurologically normal individuals. Materials and Methods: This prospective study included 47 neurologically normal individuals aged 23-74 years (male-to-female ratio, 21:26). The MRE was acquired using a gravitational transducer based on a rotational eccentric mass as the driving system. The magnitude of the complex shear modulus |G^*| and the phase angle 𝛗 were measured in the centrum semiovale area. To evaluate glymphatic function, the Diffusion Tensor Image Analysis Along the Perivascular Space (DTI-ALPS) method was utilized and the ALPS index was calculated. Univariable and multivariable (variables with P < 0.2 from the univariable analysis) linear regression analyses were performed for |G^*| and 𝛗 and included sex, age, normalized white matter hyperintensity (WMH) volume, brain parenchymal volume, and ALPS index as covariates. Results: In the univariable analysis for |G^*|, age (P = 0.005), brain parenchymal volume (P = 0.152), normalized WMH volume (P = 0.011), and ALPS index (P = 0.005) were identified as candidates with P < 0.2. In the multivariable analysis, only the ALPS index was independently associated with |G^*|, showing a positive relationship (β = 0.300, P = 0.029). For 𝛗, normalized WMH volume (P = 0.128) and ALPS index (P = 0.015) were identified as candidates for multivariable analysis, and only the ALPS index was independently associated with 𝛗 (β = 0.057, P = 0.039). Conclusion: Brain MRE using a gravitational transducer is feasible in neurologically normal individuals over a wide age range. The significant correlation between the viscoelastic properties of the brain and glymphatic function suggests that a more organized or preserved microenvironment of the brain parenchyma is associated with a more unimpeded glymphatic fluid flow.

• Journal of the Korean Data and Information Science Society
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• 제13권2호
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• pp.209-216
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• 2002

In this paper, we introduce a concept of (H)-property which generalize that of increasing(decreasing) property of binary operation. We also treat some works related to operations on fuzzy numbers and generalize earlier results of Kawaguchi and Da-te(1994).

• Journal of the Korean Wood Science and Technology
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• 제32권3호
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• pp.59-65
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• 2004

This paper reports the mechanical properties of bending, compression and hardness of woodceramics manufactured at different carbonizing temperatures (600℃, 800℃, 1000℃, 1200℃ and 1500℃) in a vacuum sintering furnace using sawdust boards of Pinus densiflora, Pinus koraiensis and Larix kaemferi. The highest values of bending MOR (MOR_b) were 104 kgf/cm² (1200℃), 91 kgf/cm² (1500℃) and 86 kgf/cm² (1500℃), the highest values of compression strength were 152 kgf/cm²(1200℃)), 160 kgf/cm²(1000℃) and 189 kgf/cm²(1000℃), the highest values of hardness were 2.00 kgf/mm²(800℃), 2.01 kgf/mm² (1200℃) and 2.28 kgf/mm² (1000℃) in P. densifora, L. kaemferi and P. koraiensis, respectively. The carbonizing temperature of 600℃ was not proper to the mechanical properties for three kinds of sawdust boards and the highest values of mechanical properties were different from the kinds of mechanical properties and species of sawdust boards. Therefore, it is necessary to manufacture woodceramics at a proper temperature for particular species of sawdust boards to obtain good mechanical properties.

• Korean Journal of Mathematics
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• 제28권3호
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• pp.449-457
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• 2020

We focus on the interations of the weighted Berezin transform T_α on L^p(τ), where 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 played important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. Here, we introduce more properties on iterations of T_α on L¹_R(τ) and observe differences between the iterations of T_α on L1(τ) and L^p(τ) for 1 < p < ∞.

• 대한수학회보
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• 제57권4호
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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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• 제30권3호
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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.