• Nuclear Engineering and Technology
• /
• v.56 no.10
• /
• pp.4384-4389
• /
• 2024

NORM is used as a raw material in various industries worldwide. According to the IAEA, radiological effects may occur in the environment due to raw materials and by-products generated from NORM industries. The objective of this study was to assess radiological environmental impact of the phosphate processing industry to identify the radiological effects on the general public. The resident farmer scenario was chosen as the exposure scenario due to the living characteristics of the public around the facility and the conservatism of the assessment. The RESRAD-OFFSITE code was used to evaluate the radiation dose to the public. The maximum radiation dose to the public was 6.13 × 10^-3 mSv/y. Main exposure pathways were aquatic food ingestion, radon inhalation, and meat ingestion. The uranium series accounted for about 99 % of the total radiation dose, while the thorium series and K-40 nuclides accounted for less than 1 %. These study results can be used for management of radiological impact to the public around domestic NORM industries.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.443-447
• /
• 2020

For n ≥ 2, we characterize the smooth points of the unit ball of 𝓛_s(ⁿ𝑙²_∞).

• Journal of Radiation Protection and Research
• /
• v.47 no.1
• /
• pp.16-21
• /
• 2022

Background: Epidemiological observations such as mental retardation, physical deformities, etc., in children besides different types of cancer in the adult population of the Malwa region have been reported. The present study is designed to get insight into the role of naturally occurring radioactive material (NORM) in causing detrimental health effects observed in the general population of this region. Materials and Methods: Deep soil samples were collected from different locations in the Malwa region. Their activity concentrations were determined using low-level background gammaray spectrometry. High efficiency and high purity germanium detector capped in a lead-shielded chamber having a resolution of 1.8 keV at 1,173 keV and 2.0 keV at the 1,332 keV line of ⁶⁰Co was used in the present work. Data were evaluated with Genie-2000 software. Results and Discussion: Mean activity concentrations of ²³⁸U, ²³²Th, and ⁴⁰K in deep soil were found to be 101.3 Bq/kg, 65.8 Bq/kg, and 688.6 Bq/kg, respectively. The mean activity concentration of ²³⁸U was found to be three and half times higher than the global average prescribed by the United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR). It was further observed that the activity concentration of ²³²Th and ⁴⁰K has a magnitude that is nearly one and half times higher than the global average prescribed by UNSCEAR. In addition, the radioisotope ¹³⁷Cs which is likely to have its origin in radiation fallout was also observed. It is postulated that the NORM present in high quantity in deep soil somehow get mobilized into the water aquifers used by the general population and thereby causing harmful health problems. Conclusion: It can be stated that the present work has been able to demonstrate the use of low background gamma-ray spectrometry to understand the role of NORM in causing health-related effects in a general population of the Malwa region of Punjab, India.

• Communications of the Korean Mathematical Society
• /
• v.22 no.1
• /
• pp.111-119
• /
• 2007

We consider the growth norm of a measurable function f defined by defined by $${\parallel}f{\parallel}-\sigma=ess\;sup\{\delta_D(z)^\sigma{\mid}f(z)\mid:z{\in}D\}$$, where $\delta_D(z)$ denote the distance from z to ${\partial}D$. We prove some kind of optimal growth norm estimates for a on convex domains.

• Journal of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.553-569
• /
• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• Honam Mathematical Journal
• /
• v.31 no.3
• /
• pp.381-398
• /
• 2009

Let $G\;=\;O(k){\times}O(k){\times}O(q)$ and let $M^n$ be a closed G-invariant minimal hypersurface with constant scalar curvature in $S^{n+1}$. Then we obtain a theorem: If $M^n$ has 2 distinct principal curvatures at some point p, then the square norm of the second fundamental form of $M^n$, S = n.

• Communications of the Korean Mathematical Society
• /
• v.9 no.2
• /
• pp.303-315
• /
• 1994

Let X be a real Banach space with norm ∥ㆍ∥. Let T > 0, r ≥a be fixed constants. We denote by L/sup p/ the usual L/sup p/( -r, 0; X) with norm ∥ㆍ∥/sub p/ for 1 ≤p < ∞. Our object is to study the existence of solutions of nonlinear functional evolution equations of the type (FDE) x'(t) ＋ A(t)x(t) = G(t, x/sub t/), 0 ≤t ≤T, x/sub 0/ = ø.(omitted)

• Kyungpook Mathematical Journal
• /
• v.53 no.4
• /
• pp.515-540
• /
• 2013

Let $G=O(2){\times}O(2){\times}O(2)$. Then a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$ is a product of spheres, i.e., the square norm of its second fundamental form, S = 4.

• Journal of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.69-90
• /
• 2021

In this paper, we prove weighted norm inequalities for rough singular integrals along surfaces with radial kernels h and sphere kernels Ω by assuming h ∈ △γ(ℝ+) and Ω ∈ ����β(Sn-1) for some γ > 1 and β > 1. Here Ω ∈ ����β(Sn-1) denotes the variant of Grafakos-Stefanov type size conditions on the unit sphere. Our results essentially improve and extend the previous weighted results for the rough singular integrals and the corresponding maximal truncated operators.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.877-884
• /
• 2021

We prove that if a compact convex hypersurface of ℝⁿ⁺¹ has almost maximal extinction time when it is evolved by the mean curvature flow, then it must be nearly round in the C⁰-norm.