• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.719-722
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• 2022

In this paper, we present some estimates for the norm of a multilinear form T ∈ 𝓛(^m𝑙ⁿ_p) for 1 ≤ p ≤ ∞ and n, m ≥ 2.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.569-576
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• 2020

An element x ∈ E is called a norming point of P ∈ P(ⁿE) if ║x║ = 1 and |P(x)| = ║P║. For P ∈ P(ⁿE), we define Norm(P) = {x ∈ E : x is a norming point of P}. Norm(P) is called the norming set of P. We classify Norm(P) for P ∈ 𝒫(²𝑙²_∞).

• Journal of Radiation Industry
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• v.18 no.3
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• pp.183-193
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• 2024

As part of the social response to the radon bed incident in 2018, the Nuclear Safety and Security Commission took measures to collect and dispose of all radon beds. The Waste Management Act provides landfill disposal as one of the disposal methods for natural radioactive product waste, which is one of the NORM wastes. When NORM wastes are landfilled, workers and the public at the landfill site are exposed to radiation through various pathways, such as leaching of radionuclides through soil and groundwater, and multiple exposure factors are involved simultaneously. In order to improve the reliability of radiological impact assessment, the values of main exposure factors should be selected more accurately. Therefore, before developing the main exposure factors for site characteristics, it is necessary to prioritize main exposure factors reflecting domestic characteristics of NORM waste landfills. Therefore, in this study, the main exposure factors for NORM waste landfill were derived using NDD analysis. To derive the main exposure factors, the analysis tool was first selected as RESRAD-ONSITE computer code, and the exposure scenarios were mainly selected as a resident farmer and suburban resident scenario, recreation scenario, and industrial worker scenario. Then, the priority 1 and 2 factors were selected for sensitivity analysis, and a Korean standard model was established to reflect Korean characteristics. Finally, the sensitivity analysis was conducted through NDD, and the main exposure factors were derived based on this. In the resident farmer scenario, the contaminated zone distribution coefficients of ²²⁶Ra, ²¹⁰Pb, ²³²Th, ²²⁸Ra, ²³⁴U, and ²³⁸U, as well as precipitation and evapotranspiration factors, were derived as the main exposure factors. In the suburban resident scenario, the contaminated zone distribution coefficients of ²²⁶Ra, ²¹⁰Pb, ²³²Th, ²²⁸Ra, ²³⁴U, and ²³⁸U, as well as precipitation and evapotranspiration coefficients, were derived as the main exposure factors. In the recreation scenario, the contaminated zone distribution coefficient of ²³²Th was derived as the main exposure factor. For the industrial worker scenario, the erosion rate was derived as the main exposure factor. The main exposure factors for each scenario were analyzed to be different depending on the scenario characteristics. The results of this study can be utilized as a basis for radiological environmental impact assessment of NORM waste landfill in Korea.

• Journal of Radiation Industry
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• v.18 no.3
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• pp.195-207
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• 2024

International organizations such as IAEA and EC recommend graded approach by identifying NORM industries requiring radiation protection. In Korea, single regulation rather than graded regulation for NORM industry is applied. Therefore, it consumes more manpower and costs than necessary for both regulators and workers, and is not optimized. The purpose of this study is to analyze domestic and foreign NORM industry regulatory standards and radiological characteristics for graded approach of NORM industry in Korea. Safety reports and publications such as SRS 49 and ICRP 142 published by international organizations were investigated, and domestic and foreign NORM regulatory guidelines and legislation such as Health Canada and the Act on Protective Action Guidelines Against Radiation in the Natural Environment were investigated to indicate NORM industries and regulatory standards. The radioactivity concentration of raw materials or by-products, radiation dose by industrial process of the NORM industry identified in IAEA and Korea were investigated. Nine NORM industries in Korea were identified based on the NORM industry from IAEA and KINS survey report. Foreign countries such as Canada, UK and Denmark were executing graded approach such as classification of dose level or licensing, registration, notification based on safety assessment. Radioactivity concentration of domestic and foreign NORM industries were widespread up to 200 Bq g^-1 or higher based on industrial process and work type, and numerous NORM industries that exceeded radiation dose of 1 mSv y^-1 were indicated. Therefore, it is necessary to consider handling materials and work types of identified NORM industry when establishing graded approach for NORM industry in Korea considering domestic situation. The results of this study are expected to be used as basic data for developing methodology of graded approach for NORM industry in Korea.

• East Asian mathematical journal
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• v.24 no.3
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• pp.275-287
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• 2008

In this paper, using large deviation results for Gaussian processes, we establish some functional limit theorems for increments of a fractional Brownian motion in the usual sup-norm via estimating large deviation probabilities for increments of a fractional Brownian motion.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.71-96
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• 2024

In this paper we present many interesting results such as completeness and composition theorems in the 𝛼 norm. Moreover, under some conditions, we establish the existence and uniqueness of Cⁿ-(𝜇, 𝜈) pseudo-almost automorphic solutions of class r in the 𝛼-norm for some partial functional differential equations in Banach space when the delay is distributed. An example is given to illustrate our results.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.171-184
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• 2023

In this paper, we show that a complete translating soliton Σ^m in ℝⁿ for the mean curvature flow is stable with respect to weighted volume functional if Σ satisfies that the L^m norm of the second fundamental form is smaller than an explicit constant that depends only on the dimension of Σ and the Sobolev constant provided in Michael and Simon [12]. Under the same assumption, we also prove that under this upper bound, there is no non-trivial f-harmonic 1-form of L²_f on Σ. With the additional assumption that Σ is contained in an upper half-space with respect to the translating direction then it has only one end.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.693-715
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• 2024

Let n ∈ ℕ, n ≥ 2. An element (x₁, . . . , x_n) ∈ Eⁿ is called a norming point of T ∈ 𝓛(ⁿE) if ||x₁|| = ··· = ||x_n|| = 1 and |T(x₁, . . . , x_n)| = ||T||, where 𝓛(ⁿE) denotes the space of all continuous n-linear forms on E. For T ∈ 𝓛(ⁿE), we define Norm(T) = {(x₁, . . . , x_n) ∈ Eⁿ : (x₁, . . . , x_n) is a norming point of T}. Norm(T) is called the norming set of T. Let $0{\leq}{\theta}{\leq}{\frac{{\pi}}{4}}$ and ${\ell}^2_{{\infty},{\theta}}={\mathbb{R}}^2$ with the rotated supremum norm $${\parallel}(x,y){\parallel}_{({\infty},{\theta})}={\max}\{{\mid}x\;cos\;{\theta}+y\;sin\;{\theta}{\mid},\;{\mid}x\;sin\;{\theta}-y\;cos\;{\theta}|\}$$. In this paper, we characterize the norming set of T ∈ 𝓛(ⁿℓ²_(∞,θ)). Using this result, we completely describe the norming set of T ∈ 𝓛_s(ⁿℓ²_(∞,θ)) for n = 3, 4, 5, where 𝓛_s(ⁿℓ²_(∞,θ)) denotes the space of all continuous symmetric n-linear forms on ℓ²_(∞,θ). We generalizes the results from [9] for n = 3 and ${\theta}={\frac{{\pi}}{4}}$.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1769-1784
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• 2008

The group Hameo (M, $\omega$) of Hamiltonian homeomorphisms of a connected symplectic manifold (M, $\omega$) was defined and studied in [7] and further in [6]. In these papers, the authors consistently used the $L^{(1,{\infty})}$-Hofer norm (and not the $L^{\infty}$-Hofer norm) on the space of Hamiltonian paths (see below for the definitions). A justification for this choice was given in [7]. In this article we study the $L^{\infty}$-case. In view of the fact that the Hofer norm on the group Ham (M, $\omega$) of Hamiltonian diffeomorphisms does not depend on the choice of the $L^{(1,{\infty})}$-norm vs. the $L^{\infty}$-norm [9], Y.-G. Oh and D. McDuff (private communications) asked whether the two notions of Hamiltonian homeomorphisms arising from the different norms coincide. We will give an affirmative answer to this question in this paper.

• Nuclear Engineering and Technology
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• v.55 no.5
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• pp.1757-1762
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• 2023

Radiological hazards from external exposure of naturally occurring radioactive materials (NORM) scales residues, generated during the extraction process of oil and gas production in southern Algeria, are evaluated. The activity concentrations of ²²⁶Ra, ²³²Th, and ⁴⁰K were measured using high-purity gamma-ray spectrometry (GeHP). Mean activity concentration of ²²⁶Ra, ²³²Th and ⁴⁰K, found in scale samples are 4082 ± 41, 1060 ± 38 and 568 ± 36 Bq kg^-1, respectively. Radiological hazard parameters, such as radium equivalent (Ra_eq), external and internal hazard indices (H_ex, H_in), and gamma index (I_γ) are also evaluated. All hazard parameter values were greater than the permissible and recommended limits and the average annual effective dose value exceeded the dose constraint (0.3 mSv y^-1). However, for occasionally exposed workers, the dose rate of 0.65 ± 0.02 mSv y^-1 is lower than recommended limit of 1 mSv y^-1 for public.