• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.291-296
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• 2011

Cs$\'{a}$sz$\'{a}$r [3] introduced the notions of ${\gamma}$-compact and ${\gamma}$-operation on a topological space. In this paper, we introduce the notions of almost ${\Gamma}$-compact, (${\gamma},{\tau}$)-continuous function and (${\gamma},{\tau}$)-open function defined by ${\gamma}$-operation on a topological space and investigate some properties for such notions.

• Nuclear Engineering and Technology
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• v.55 no.8
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• pp.2873-2878
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• 2023

The purpose of this study is to perform radiation monitoring by acquiring gamma images and real-time optical images for ^99mTc vial source using charge couple device (CCD) cameras equipped with the proposed compact gamma camera. The compact gamma camera measures 86×65×78.5 mm³ and weighs 934 g. It is equipped with a metal 3D printed diverging collimator manufactured in a 45 field of view (FOV) to detect the location of the source. The circuit's system uses system-on-chip (SoC) and field-programmable-gate-array (FPGA) to establish a good connection between hardware and software. In detection modules, the photodetector (multi-pixel photon counters) is tiled at 8×8 to expand the activation area and improve sensitivity. The gadolinium aluminium gallium garnet (GAGG) measuring 0.5×0.5×3.5 mm³ was arranged in 38×38 arrays. Intrinsic and extrinsic performance tests such as energy spectrum, uniformity, and system sensitivity for other radioisotopes, and sensitivity evaluation at edges within FOV were conducted. The compact gamma camera can be mounted on unmanned equipment such as drones and robots that require miniaturization and light weight, so a wide range of applications in various fields are possible.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.435-442
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• 2008

We introduce the concepts of weakly ${\gamma}$-continuity, strongly ${\gamma}$-closed graph and ${\gamma}-T_2$ spaces. And we study some characterizations and properties or such concepts.

• Journal of Radiation Protection and Research
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• v.42 no.2
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• pp.91-97
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• 2017

Background: A gamma energy identifying algorithm using spectral decomposition combined with smoothing method was suggested to confirm the existence of the artificial radio isotopes. The algorithm is composed by original pattern recognition method and smoothing method to enhance the performance to identify gamma energy of radiation sensors that have low energy resolution. Materials and Methods: The gamma energy identifying algorithm for the compact radiation sensor is a three-step of refinement process. Firstly, the magnitude set is calculated by the original spectral decomposition. Secondly, the magnitude of modeling error in the magnitude set is reduced by the smoothing method. Thirdly, the expected gamma energy is finally decided based on the enhanced magnitude set as a result of the spectral decomposition with the smoothing method. The algorithm was optimized for the designed radiation sensor composed of a CsI (Tl) scintillator and a silicon pin diode. Results and Discussion: The two performance parameters used to estimate the algorithm are the accuracy of expected gamma energy and the number of repeated calculations. The original gamma energy was accurately identified with the single energy of gamma radiation by adapting this modeling error reduction method. Also the average error decreased by half with the multi energies of gamma radiation in comparison to the original spectral decomposition. In addition, the number of repeated calculations also decreased by half even in low fluence conditions under $10^4$ ($/0.09cm^2$ of the scintillator surface). Conclusion: Through the development of this algorithm, we have confirmed the possibility of developing a product that can identify artificial radionuclides nearby using inexpensive radiation sensors that are easy to use by the public. Therefore, it can contribute to reduce the anxiety of the public exposure by determining the presence of artificial radionuclides in the vicinity.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.269-273
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• 2010

We introduce the concepts of strongly $s{\gamma}$-closed graph, $s{\gamma}$-compactness and $s{\gamma}-T_2$ space and study the relationships between such concepts and weakly $s{\gamma}$-continuous functions.

• Journal of Korean Neurosurgical Society
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• v.67 no.4
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• pp.431-441
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• 2024

Objective : Gamma Knife radiosurgery (GKRS) is an effective and noninvasive treatment for high-risk arteriovenous malformations (AVMs). Since differences in GKRS outcomes by nidus type are unknown, this study evaluated GKRS feasibility and safety in patients with brain AVMs. Methods : This single-center retrospective study included patients with AVM who underwent GKRS between 2008 and 2021. Patients were divided into compact- and diffuse-type groups according to nidus characteristics. We excluded patients who performed GKRS and did not follow-up evaluation with magnetic resonance imaging or digital subtraction angiography within 36 months from the study. We used univariate and multivariate analyses to characterize associations of nidus type with obliteration rate and GKRS-related complications. Results : We enrolled 154 patients (mean age, 32.14±17.17 years; mean post-GKRS follow-up, 52.10±33.67 months) of whom 131 (85.1%) had compact- and 23 (14.9%) diffuse-type nidus AVMs. Of all AVMs, 89 (57.8%) were unruptured, and 65 (42.2%) had ruptured. The mean Spetzler-Martin AVM grades were 2.03±0.95 and 3.39±1.23 for the compact- and diffuse-type groups, respectively (p<0.001). During the follow-up period, AVM-related hemorrhages occurred in four individuals (2.6%), three of whom had compact nidi. Substantial radiation-induced changes and cyst formation were observed in 21 (13.6%) and one patient (0.6%), respectively. The AVM complete obliteration rate was 46.1% across both groups. Post-GKRS complication and complete obliteration rates were not significantly different between nidus types. For diffuse-type nidus AVMs, larger AVM size and volume (p<0.001), lower radiation dose (p<0.001), eloquent area location (p=0.015), and higher Spetzler-Martin grade (p<0.001) were observed. Conclusion : GKRS is a safe and feasible treatment for brain AVMs characterized by both diffuse- and compact-type nidi.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1051-1060
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• 2009

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.775-784
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• 2024

Let (X, m, 𝓗) be a hereditary m-space and γ : m → P(X) be an operation on m. A subset A of X is said to be γ𝓗-compact relative to X [3] if for every cover {U_𝛼 : 𝛼 ∈ 2206;} of A by m-open sets of X, there exists a finite subset ∆₀ of ∆ such that A ⧵ ∪{γ(U_𝛼) : 𝛼 ∈ ∆₀} ∈ 𝓗. In this paper, we define and investigate two kinds of strong forms of γ𝓗-compact relative to X.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.481-485
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• 2009

Gabai's sutured manifold theory has produced many remarkable results in knot theory. Let M be the compact oriented 3-manifold and (M, ${\gamma}$) be sutured manifold. The aim of this note is to show that there exist a sutured manifold decomposition and a surface of M which defines a sutured manifold decomposition.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.671-686
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• 1994

다양체 M은 매끈하고(smooth) 콤팩트(compact) n 차원 리만다양체이고, 실가함수 f는 M상에서 미분가능 함수임을 가정한다. Morse 함수는 임계점(critical point)들이 모두 비퇴화(non-degenerate)인 실가함수이다. 만약 함수 f가 Morse 함수이고, 임의의 점 $x \in M$에서 $\gamma_x$는 x를 통과하는 흐름(flow)이면 $$ (*) \frac{d\gamma_x(t)}{dt} + \bigtriangledown_{\gamma x(t)}(f) = 0 $$ 이다. 여기서 $\bigtriangledown(f)$는 함수 f에 의해서 정의되는 기울기 벡터장이고 초기조건 $\gamma_x(0) = x$ 이다.