• Korean Journal of Materials Research
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• v.18 no.11
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• pp.577-582
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• 2008

Directional solidification experiments were carried out at $1-300\;{\mu}m/sec$ solidification rates in the single crystal superalloy, CMSX 10. The solid/liquid interface morphology changed from planar to dendritic, and the dendrite spacing became finer as the solidification rate increased. The pool size of the ${\gamma}/{\gamma}'$ eutectic, formed between dendrites, reduced as the solidification rate increased. The phase formation temperatures, such as the solidus, liquidus and eutectic, were estimated by differential scanning calorimetry (DSC) analysis. The morphology of the ${\gamma}/{\gamma}'$ phase, known to be eutectic, showed ${\gamma}'$ cells with a $\gamma$ intercellular network, and this ${\gamma}/{\gamma}'$ was composed of coarse and fine ${\gamma}/{\gamma}'$ regions. In this study, it is suggested that the ${\gamma}/{\gamma}'$ phase was a coupled peritectic.The solidification procedure of the ${\gamma}/{\gamma}'$ between dendrites is also discussed.

• Journal of the Korean Society for Heat Treatment
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• v.19 no.5
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• pp.249-256
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• 2006

Structural studies have been performed on precipitation hardening found in $L1_2$ ordered ${\gamma}^{\prime}-Ni_3(Al,Ti)$ alloys using transmission electron microscopy. A uniform solid solution of ${\gamma}^{\prime}-L1_2$ ordered phase supersaturated with Ni can be obtained by solution annealing in a suitable temperature range. The ${\gamma}^{\prime}$ phase hardens appreciably by the fine precipitation of disordered ${\gamma}$. The shape of ${\gamma}$ precipitates formed during aging is initially spherical or round-cubic and grow into platelets as aging proceeds. High resolution electron microscopy revealed that the ${\gamma}$ precipitates are perfectly coherent with the matrix ${\gamma}^{\prime}$ as long as the ${\gamma}$-precipitates are plates. The loss of coherency initiates by the introduction of dislocations at the ${\gamma}/{\gamma}^{\prime}$ interface followed by the step formation at the dislocations. The ${\gamma}$ precipitates become globular after the loss of coherency. The strength of ${\gamma}^{\prime}-Ni_3(Al,Ti)$ increases over the temperature range of experiment by the precipitation of fine ${\gamma}$ particles. The peak temperature where a maximum strength was obtained shifted to higher temperature.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.245-250
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• 2019

In this paper, the notion of ${\gamma}$-operation on a supratopological space is introduced. We found that the ${\gamma}$-operation induces a supratopology (topology) containing a given supratopology. We also introduce the notions of (${\gamma}$, S)-continuous function and almost ${\Gamma}$-supracompact defined by ${\gamma}$-operation on a supratopological space and investigate some properties for such notions.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.145-150
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• 2010

In this paper, we introduce the concepts of faintly ${\gamma}$-continuity and extremely ${\gamma}$-closed graph. And we study characterizations of such functions and relationships between faintly ${\gamma}$-continuity and extremely ${\gamma}$-closed graph.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.457-471
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• 2009

Let S = {a, b, c, ...} and ${\Gamma}$ = {${\alpha}$, ${\beta}$, ${\gamma}$, ...} be two nonempty sets. S is called a ${\Gamma}$-semigroup if $a{\alpha}b{\in}S$, for all ${\alpha}{\in}{\Gamma}$ and a, b ${\in}$ S and $(a{\alpha}b){\beta}c=a{\alpha}(b{\beta}c)$, for all a, b, c ${\in}$ S and for all ${\alpha}$, ${\beta}$ ${\in}$ ${\Gamma}$. An element $e{\in}S$ is said to be an ${\alpha}$-idempotent for some ${\alpha}{\in}{\Gamma}$ if $e{\alpha}e$ = e. A ${\Gamma}$-semigroup S is called an E-inversive ${\Gamma}$-semigroup if for each $a{\in}S$ there exist $x{\in}S$ and ${\alpha}{\in}{\Gamma}$ such that a${\alpha}$x is a ${\beta}$-idempotent for some ${\beta}{\in}{\Gamma}$. A ${\Gamma}$-semigroup is called a right E-${\Gamma}$-semigroup if for each ${\alpha}$-idempotent e and ${\beta}$-idempotent f, $e{\alpha}$ is a ${\beta}$-idempotent. In this paper we investigate different properties of E-inversive ${\Gamma}$-semigroup and right E-${\Gamma}$-semigroup.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1647-1659
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• 2008

Let R be a ring with identity, X the set of all nonzero, nonunits of R and G the group of all units of R. First, we investigate some connected conditions of the zero-divisor graph $\Gamma(R)$ of a noncommutative ring R as follows: (1) if $\Gamma(R)$ has no sources and no sinks, then $\Gamma(R)$ is connected and diameter of $\Gamma(R)$, denoted by diam($\Gamma(R)$) (resp. girth of $\Gamma(R)$, denoted by g($\Gamma(R)$)) is equal to or less than 3; (2) if X is a union of finite number of orbits under the left (resp. right) regular action on X by G, then $\Gamma(R)$ is connected and diam($\Gamma(R)$) (resp. g($\Gamma(R)$)) is equal to or less than 3, in addition, if R is local, then there is a vertex of $\Gamma(R)$ which is adjacent to every other vertices in $\Gamma(R)$; (3) if R is unit-regular, then $\Gamma(R)$ is connected and diam($\Gamma(R)$) (resp. g($\Gamma(R)$)) is equal to or less than 3. Next, we investigate the graph automorphisms group of $\Gamma(Mat_2(\mathbb{Z}_p))$ where $Mat_2(\mathbb{Z}_p)$ is the ring of 2 by 2 matrices over the galois field $\mathbb{Z}_p$ (p is any prime).

• Journal of Radiation Protection and Research
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• v.26 no.3
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• pp.287-290
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• 2001

The 9.17MeV gamma-rays from the $^{13}C(p,\;{\gamma})^{14}N,\;^{14}N({\gamma},\;{\gamma})^{14}N$ reactions were measured. The incident 9.17MeV gamma-ray was produced from the $^{13}C(p,\;{\gamma})^{14}N$ reaction at Ep=1.75MeV resonance. The 1.75MeV proton beam was accelerated using the 3MV SNU-AMS Tandetron and 1.7MV KIGAM Tandem accelerators. The enriched 13C target was $121{\mu}g/cm^2$ self-supporting foil, and we used liquid nitrogen as a resonant absorption target. We used a HP-Ge detector with 30% efficiency and less 2keV energy resolution. We developed new method to detect the scattered 9.17MeV gamma-ray from the nitrogen target by using the energy difference between the Doppler shifted gamma-ray from the $^{13}C(p,\;{\gamma})^{14}N$ reaction and the resonant absorbed and rescattered gamma-ray from the $^{14}N({\gamma},\;{\gamma})^{14}N$ reaction.

• Water for future
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• v.13 no.4
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• pp.41-50
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• 1980

The prupose of this study are the theoretical examination of Gamma distribution function and its application to hydraulic engineering, that is studying the simulation of monthly streamflow by the Gamma distribtution function model(Gamma Model) based on Monte Carlo technique. In the analysis, monthly streamflow data in the Nak Dong River, the Han River, and the Keum River were used and the data were changed to modular coefficient in order to make the analysis convenient. At first, the fitness of monthly streamflow to 2-Parameter Gamma distribution was tested by Chi-square and Kolmogrov-Smironov test, by which it was found the monthly streamflow were fit well to this Gamma distribution function. Then, the Gamma Model based on the Gamma distribution and Monte Carlo Method was used in the simulation of monthly streamflow, and simulateddata showed that all their stastical characteristics were preserved well in the simulation. Consequently, it can be concluded that the Gamma Model is suitable for the simulation of monthly streamflow series directly by using the Mote Carlo technique.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.93-108
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• 2018

In this paper, we introduce the notion of ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals of ${\Gamma}$-semihypergroups by a new approach called soft intersection (briefly, S. I.). It is proved that in regular ${\Gamma}$-semihypergroups the ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and the ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals coincide. Further, we introduce the concept of ($\xi$, ${\zeta}$)-soft simple ${\Gamma}$-semihypergroup and characterize the simple ${\Gamma}$-semihypergroups in terms of ($\xi$, ${\zeta}$)-soft ${\Gamma}$-hyperideals and ($\xi$, ${\zeta}$)-soft interior ${\Gamma}$-hyperideals.

• Journal of Radiation Protection and Research
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• v.43 no.4
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• pp.137-142
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• 2018

Background: Gamma-ray detectors having a thin window of a material with low atomic number can increase the true coincidence summing effects for radionuclides emitting X-rays or gamma-rays. This effect can make efficiency calibration or spectrum analysis more complicated. In this study, a Cu shield was tested as an X-ray filter to neglect the true coincidence summing effect by X-rays and gamma-rays in gamma-ray spectrometry, in order to simplify gamma-ray energy spectrum analysis. Materials and Methods: A Cu shield was designed and applied to an n-type high-purity germanium detector having an $X-{\gamma}$ summing effect during efficiency calibration. This was tested using a commercial, certified mixed gamma-ray source. The feasibility of a Cu shield was evaluated by comparing efficiency calibration results with and without the shield. Results and Discussion: In this study, the thickness of a Cu shield needed to avoid true coincidence summing effects due to $X-{\gamma}$ was tested and determined to be 1 mm, considering the detection efficiency desired for higher energy. As a result, the accuracy of the detection efficiency calibration was improved by more than 13% by reducing $X-{\gamma}$ summing. Conclusion: The $X-{\gamma}$ summing effect should be considered, along with ${\gamma}-{\gamma}$ summing, when a detection efficiency calibration is implemented and appropriate shielding material can be useful for simplifying analysis of the gamma-ray energy spectra.