• 호남수학학술지
• /
• 제23권1호
• /
• pp.113-132
• /
• 2001

We prove an equality that holds on G-invariant minimal hypersurfaces with constant scalar curvatures in $S^5$.

• 대한수학회지
• /
• 제28권1호
• /
• pp.79-86
• /
• 1991

• 대한수학회논문집
• /
• 제37권4호
• /
• pp.1131-1146
• /
• 2022

In this paper we present another characterization of the norming set of T ∈ 𝓛(²𝒍²_∞) in terms of Norm(T) ∩ Ω whose proofs are more systematic than those of Kim [6], where Ω = {((1, 1), (1, 1)), ((1, 1), (1, -1)), ((1, -1), (1, 1)), ((1, -1), (1, -1))}.

• 방사선산업학회지
• /
• 제17권2호
• /
• pp.161-172
• /
• 2023

Coal-fired power plants handle large quantities of coal, one of the most prominent NORM, and the coal ash produced after the coal is burned can be tens of times more radioactive than the coal. Workers in these industries may be exposed to internal exposure by inhalation of particles while handling NORM. This study evaluated the size, concentration, particle shape and density, and radioactivity concentrations of airborne suspended particles in the main processes of a coal-fired power plant. Finally, the internal radiation dose to workers from particle inhalation was evaluated. For this purpose, airborne particles were collected by size using a multi-stage particle collector to determine the size, shape, and concentration of particles. Samples of coal and coal ash were collected to measure the density and radioactivity of particles. The dose conversion factor and annual radionuclide inhalation amount were derived based on the characteristics of the particles. Finally, the internal radiation dose due to particle inhalation was evaluated. Overall, the internal radiation dose to workers in the main processes of coalfired power plants A and B ranged from 1.47×10^-5~1.12×10^-3 mSv y^-1. Due to the effect of dust generated during loading operations, the internal radiation dose of fly ash loading processes in both coal-fired power plants A and B was higher than that of other processes. In the case of workers in the coal storage yard at power plants A and B, the characteristic values such as particle size, airborne concentration, and working time were the same, but due to the difference in radioactivity concentration and density depending on the origin of the coal, the internal radiation dose by origin was different, and the highest was found when inhaling coal imported from Australia among the five origins. In addition, the main nuclide contributing the most to the internal radiation dose from the main processes in the coal-fired power plants was thorium due to differences in dose conversion factors. However, considering the external radiation dose of workers in coal-fired power plants presented in overseas research cases, the annual effective dose of workers in the main processes of power plants A and B does not exceed 1mSv y^-1, which is the dose limit for the general public notified by the Nuclear Safety Act. The results of this study can be utilized to identify the internal exposure levels of workers in domestic coal-fired power plants and will contribute to the establishment of a data base for a differential safety management system for NORM-handling industries in the future.

• 충청수학회지
• /
• 제34권4호
• /
• pp.369-378
• /
• 2021

In this paper, we give an upper bound for the fundamental tone of stable constant mean curvature hypersurfaces in hyperbolic space. Let M be an n-dimensional complete non-compact constant mean curvature hypersurface with finite L²-norm of the traceless second fundamental form. If M is weakly stable, then λ₁(M) is bounded above by n² + O(n^2+s) for arbitrary s > 0.

• 충청수학회지
• /
• 제4권1호
• /
• pp.61-69
• /
• 1991

By $C^{(1)}$[0, 1] we denote the Banach algebra of complex valued continuously differentiable functions on [0, 1] with norm given by $${\parallel}f{\parallel}=\sup_{x{\in}[0,1]}({\mid}f(x){\mid}+{\mid}f^{\prime}(x){\mid})\text{ for }f{\in}C^{(1)}$$. By A we denote the sub algebra of $C^{(1)}$ defined by $$A=\{f{\in}C^{(1)}:f(0)=f(1)\text{ and }f^{\prime}(0)=f^{\prime}(1)\}$$. By an isometry of A we mean a norm-preserving linear map of A onto itself. The purpose of this article is to describe the isometries of A. More precisely, we show tht any isometry of A is induced by a point map of the interval [0, 1] onto itself.

• 방사선산업학회지
• /
• 제17권2호
• /
• pp.151-160
• /
• 2023

The International Atomic Energy Agency (IAEA) proposes 11 industries that handle Naturally Occurring Radioactive Material (NORM) that are considered to need management. A water treatment facility is one of the above industries that takes in groundwater and produces drinking water through a water treatment process. Groundwater can accumulate natural radionuclides such as uranium and thorium in raw water by contacting rocks or soil containing natural radionuclides. Therefore, there is a possibility that workers in water treatment facilities will be exposed due to the accumulation of natural radionuclides in the water treatment process. The goal of this study is to evaluate the external radiation dose according to the working type of workers in water treatment facilities. In order to achieve the above goal, the study was conducted by dividing it into 1) analysis of the exposure environment, 2) measurement of the external radiation dose rate 3) evaluation of the external radiation dose. In the stage of analyzing the exposure environment, major processes that are expected to occur significantly were derived. In the measurement stage of the external radiation dose rate, a map of the external radiation dose rate was prepared by measuring the spatial radiation dose rate in major processes. Through this, detailed measurement points were selected considering the movement of workers. In the external radiation dose evaluation stage, the external radiation dose was evaluated based on the previously derived external radiation dose rate and working time. As a result of measuring the external radiation dose rate at the detailed points of water treatment facilities A to C, it was 1.90×10^-1 to 3.75×10⁰ μSv h^-1, and the external radiation dose was analyzed as 3.27×10^-3 to 9.85×10^-2 mSv y^-1. The maximum external radiation dose appeared during the disinfection and cleaning of activated carbon at facility B, and it is judged that natural radionuclides were concentrated in activated carbon. It was found that the external radiation dose of workers in the water treatment facility was less than 1mSv y^-1, which is about 10% of the dose limit for the public. As a result of this study, it was found that the radiological effect of external radiation dose of domestic water treatment facility workers was insignificant. The results are expected to contribute as background data to present optimized safety management measures for domestic NORM industries in the future.

• Nuclear Engineering and Technology
• /
• 제54권6호
• /
• pp.2230-2243
• /
• 2022

The tin tailing processing industry in Malaysia has operated with minimal regard and awareness for material management and working environment safety, impacting the environment and workers in aspects of radiation and heavy metal exposure. RIA was conducted where environmental samples were analyzed, revealing concentrations of ²²⁶Ra, ²³²Th and ⁴⁰K between the range of 0.1-10.0, 0.0-25.7, and 0.1-5.8 Bq/g respectively, resulting in the AED exceeding UNCEAR recommended value and regulation limit enforced by AELB (1 mSv/y). Ra_eq calculated indicates that samples collected pose a significant threat to human health from gamma-ray exposure. Assessment of heavy metal content via pollution indices of soil and sediment showed significant contamination and enrichment from processing activities conducted. As and Fe were two of the highest metals exposed both via soil ingestion with an average of 4.6 × 10^-3 mg/kg-day and 1.4 × 10^-4 mg/kg-day, and dermal contact with an average of 5.6 × 10^-4 mg/kg-day and 6.0 × 10^-4. mg/kg-day respectively. Exposure via accidental ingestion of soil and sediment could potentially cause adverse non-carcinogenic and carcinogenic health effect towards workers in the industry. Correlation analysis indicates the presence of a relationship between the concentration of NORM and trace elements.

• Nonlinear Functional Analysis and Applications
• /
• 제26권2호
• /
• pp.331-345
• /
• 2021

Let p(z)be a polynomial of degree n. Then Bernstein's inequality [12,18] is $${\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;n\;{\max_{{\mid}z{\mid}=1}{\mid}(z){\mid}}$$. For q > 0, we denote $${\parallel}p{\parallel}_q=\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}$$, and a well-known fact from analysis [17] gives $${{\lim_{q{\rightarrow}{{\infty}}}}\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}={\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p(z){\mid}$$. Above Bernstein's inequality was extended by Zygmund [19] into L^q norm by proving ║p'║_q ≤ n║p║_q, q ≥ 1. Let p(z) = a₀ + ∑ⁿ_𝜈=𝜇 a_𝜈z^𝜈, 1 ≤ 𝜇 ≤ n, be a polynomial of degree n having no zero in |z| < k, k ≥ 1. Then for 0 < r ≤ R ≤ k, Aziz and Zargar [4] proved $${\max\limits_{{\mid}z{\mid}=R}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;{\frac{nR^{{\mu}-1}(R^{\mu}+k^{\mu})^{{\frac{n}{\mu}}-1}}{(r^{\mu}+k^{\mu})^{\frac{n}{\mu}}}\;{\max\limits_{{\mid}z{\mid}=r}}\;{\mid}p(z){\mid}}$$. In this paper, we obtain the L^q version of the above inequality for q > 0. Further, we extend a result of Aziz and Shah [3] into L^q analogue for q > 0. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.

• Kyungpook Mathematical Journal
• /
• 제60권3호
• /
• pp.485-505
• /
• 2020

We present a complete description of all the extreme points of the unit ball of 𝓛_s(²𝑙³_∞) which leads to a complete formula for ║f║ for every f ∈ 𝓛_s(²𝑙³_∞)^∗. We also show that $extB_{{\mathcal{L}}_s(^2l^3_{\infty})}{\subset}extB_{{\mathcal{L}}_s(^2l^n_{\infty})}$ for every n ≥ 4. Using the formula for ║f║ for every f ∈ 𝓛_s(²𝑙³_∞)^∗, we show that every extreme point of the unit ball of 𝓛_s(²𝑙³_∞) is exposed. We also characterize all the smooth points of the unit ball of 𝓛_s(²𝑙³_∞).