• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.200-202
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• 2010

In this paper, we introduce the concept of fuzzy ${\gamma}$-quasi open sets which are generalizations of fuzzy ${\gamma}$-open sets, and obtain some basic properties of such fuzzy sets. Also we introduce and study the concepts of fuzzy ${\gamma}$-quasi continuous mapping and fuzzy ${\gamma}$-quasi open(closed) mapping.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.211-222
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• 2001

In this paper, we prove the existence and uniqueness of a $\delta(\Gamma)$-conformal density on the limit set of $\Gamma$ acting on visibility manifold H for a Fuchsian group $\Gamma$.

• The Korean Journal of Nuclear Medicine Technology
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• v.19 no.2
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• pp.108-111
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• 2015

Purpose Lately, in accordance with the increasing interest about Healthcare accreditation program and International laboratory accreditation scheme, requirements about the instrument quality management are gradually taking shape. In nuclear medicine In vitro laboratory, the most typical instruments are multi detector gamma counter and automatic dispensing system. Each laboratory continue with the quality control adequate for circumstances. The purpose of this study is to application and establish the new Calibrator[I-125]Set which is efficient at standardization of equipment quality management. Materials and Methods Deviation between detectors were measured with 12 solid samples of the Calibrator[I-125]Set. their activities differ from each other by less than 1%. Multi detector gamma counters are GAMMA-10;Shinjin medics. Inc, Goyansi, Korea(Gamma counter A), SR300;Stratec biomedical systems AG, Gewerbestr, Germany(Gamma counter B) and COBRA II; Packard Instrument Co. Inc, Meriden, USA(Gamma counter C). Evaluation of two automatic dispensing system used A, B liquid tracer of the Calibrator[I-125]Set. After dispensing and counting, calculated using the ratio of the measured value and proposed value. We used solution A for 20, 25ul and solution B for 50, 100ul. Method of data analysis and reference range was provided by kit documentation. Furthermore, we could calculate our counter efficiency indirectly. Results The CV(%) of measured values by Gamma counter A, B, C are 0.34, 0.70, 1.30. Calculated value are 1.05314, 2.10419, 4.08485. Provided reference range is less than 3. A dispensing system's calculated values are 0.986, 0.989, 1.023, 1.017 and B are 0.874, 0.725, 1.021, 0.904. Provided reference range is from 0.95 to 1.05. Also, counter's efficiency are 74.18, 72.79, 74.32% at counter A, B, C and efficiency of the one detector counter is 79.26%. Conclusion If using this Calibrator[I-125]Set after verifying whether quality assurance, is applicable to equipment quality management on behalf of the role of gold standard.

• East Asian mathematical journal
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• v.22 no.2
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• pp.131-149
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• 2006

In this paper we introduce the concept of $\gamma$-preopen sets in a topological space together with its corresponding $\gamma$-preclosure and $\gamma$-preinterior operators and a new class of topology $\tau_{{\gamma}p}$ which is generated by the class of $\gamma$-preopen sets. Also we introduce $\gamma$-pre $T_i$ spaces(i=0, $\frac{1}{2}$, 1, 2) and study some of its properties and we proved that if $\gamma$ is a regular operation, then$(X,\;{\tau}_{{\gamma}p})$ is a $\gamma$-pre $T\frac{1}{2}$ space. Finally we introduce $(\gamma,\;\beta)$-precontinuous mappings and study some of its properties.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.1013-1018
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• 2009

Let * be an e.a.b. star operation on an integrally closed domain D, and let $K\gamma$(D, *) be the Kronecker function ring of D. We show that if D is a P*MD, then the mapping $D_{\alpha}{\mapsto}K{\gamma}(D_{\alpha},\;{\upsilon})$ is a bijection from the set {$D_{\alpha}$} of *-linked overrings of D into the set of overrings of $K{\gamma}(D,\;{\upsilon})$. This is a generalization of [5, Proposition 32.19] that if D is a Pr$\ddot{u}$fer domain, then the mapping $D_{\alpha}{\mapsto}K_{\gamma}(D_{\alpha},\;b)$ is a one-to-one mapping from the set {$D_{\alpha}$} of overrings of D onto the set of overrings of $K_{\gamma}$(D, b).

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.1031-1051
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• 2012

In this paper, we will investigate the concept of the torsion-graph of an R-module M, in which the set $T(M)^*$ makes up the vertices of the corresponding torsion graph, ${\Gamma}(M)$, with any two distinct vertices forming an edge if $[x:M][y:M]M=0$. We prove that, if ${\Gamma}(M)$ contains a cycle, then $gr({\Gamma}(M)){\leq}4$ and ${\Gamma}(M)$ has a connected induced subgraph ${\overline{\Gamma}}(M)$ with vertex set $\{m{\in}T(M)^*{\mid}Ann(m)M{\neq}0\}$ and diam$({\overline{\Gamma}}(M)){\leq}3$. Moreover, if M is a multiplication R-module, then ${\overline{\Gamma}}(M)$ is a maximal connected subgraph of ${\Gamma}(M)$. Also ${\overline{\Gamma}}(M)$ and ${\overline{\Gamma}}(S^{-1}M)$ are isomorphic graphs, where $S=R{\backslash}Z(M)$. Furthermore, we show that, if ${\overline{\Gamma}}(M)$ is uniquely complemented, then $S^{-1}M$ is a von Neumann regular module or ${\overline{\Gamma}}(M)$ is a star graph.

• 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.4 no.2
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• pp.131-135
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• 1997

We give the relation between the semilattice congruence N and the set of prime ideals of the ordered $\Gamma$-semigroup M.