• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1303-1314
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• 2013

An injective coloring of a graph G is an assignment of colors to the vertices of G so that any two vertices with a common neighbor receive distinct colors. A graph G is said to be injectively $k$-choosable if any list $L(v)$ of size at least $k$ for every vertex $v$ allows an injective coloring ${\phi}(v)$ such that ${\phi}(v){\in}L(v)$ for every $v{\in}V(G)$. The least $k$ for which G is injectively $k$-choosable is the injective choosability number of G, denoted by ${\chi}^l_i(G)$. In this paper, we obtain new sufficient conditions to be ${\chi}^l_i(G)={\Delta}(G)$. Maximum average degree, mad(G), is defined by mad(G) = max{2e(H)/n(H) : H is a subgraph of G}. We prove that if mad(G) < $\frac{8k-3}{3k}$, then ${\chi}^l_i(G)={\Delta}(G)$ where $k={\Delta}(G)$ and ${\Delta}(G){\geq}6$. In addition, when ${\Delta}(G)=5$ we prove that ${\chi}^l_i(G)={\Delta}(G)$ if mad(G) < $\frac{17}{7}$, and when ${\Delta}(G)=4$ we prove that ${\chi}^l_i(G)={\Delta}(G)$ if mad(G) < $\frac{7}{3}$. These results generalize some of previous results in [1, 4].

• Journal of Astronomy and Space Sciences
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• v.40 no.4
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• pp.259-266
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• 2023

The Standard Model (SM) does not provide an information for 26% of dark matter of the universe. In the dark sector, dark matter is supposed to be linked with the hypothetical particles called dark photons that have similar role to photons in electromagnetic interaction in the SM. Besides astronomical observation, there are studies to find dark matter candidates using accelerators. In this paper, we searched for dark photons using future electron-positron colliders, including Circular Electron Positron Collider (CEPC)/CEPC, Future Circular Collider (FCC-ee)/Innovative Detector for Electron-positron Accelerator (IDEA), and International Linear Collider (ILC)/International Large Detector (ILD). Using the parameterized response of the detector simulation of Delphes, we studied the sensitivity of a double dark photon mode at each accelerator/detector. The signal mode is double dark photon decay channel, e⁺e^- → A'A', where A' (dark photon with spin 1) decaying into a muon pair. We used MadGraph5 to generate Monte Carlo (MC) events by means of a Simplified Model. We found the dark photon mass at which the cross-sections were the highest for each accelerator to obtain the maximum number of events. In this paper we show the expected number of dark photon signal events and the detector efficiency of each accelerator. The results of this study can facilitate in the dark photon search by future electron-positron accelerators.

• International Journal of Contents
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• v.17 no.3
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• pp.67-73
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• 2021

Dark matter is barely known because it cannot be explained using the Standard Model. In addition, dark matter has not been detected yet. It is currently being explored through various ways. In this paper, we studied dark matter in an electron-positron collider using MadGraph5. The signal channel is e⁺e^- → 𝜇⁺𝜇^-A' where A' decays to dimuon. We studied the cross-section by increasing the center-of-mass energy. Central processing unit (CPU) time of simulation was compared with that using a local Linux machine and a KISTI-5 supercomputer (Knight Landing and Skylake). Furthermore, one or more cores were used for comparing CPU time among machines. Results of this study will enable the exploration of dark matter in electron-positron experiments. This study also serves as a reference for optimizing high-energy physics simulation toolkits.

• Journal of Astronomy and Space Sciences
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• v.39 no.1
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• pp.1-10
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• 2022

The universe is thought to be filled with not only Standard Model (SM) matters but also dark matters. Dark matter is thought to play a major role in its construction. However, the identity of dark matter is as yet unknown, with various search methods from astrophysical observartion to particle collider experiments. Because of the cross-section that is a thousand times smaller than SM particles, dark matter research requires a large amount of data processing. Therefore, optimization and parallelization in High Performance Computing is required. Dark matter in hypothetical hidden sector is though to be connected to dark photons which carries forces similar to photons in electromagnetism. In the recent analysis, it was studied using the decays of a dark photon at collider experiments. Based on this, we studies double dark photon decays at lepton colliders. The signal channels are e⁺e^- → A'A' and e⁺e^- → A'A'γ where dark photon A' decays dimuon. These signal channels are based on the theory that dark photons only decay into heavily charged leptons, which can explain the muon magnetic momentum anomaly. We scanned the cross-section according to the dark photon mass in experiments. MadGraph5 was used to generate events based on a simplified model. Additionally, to get the maximum expected number of events for the double dark photon channel, the detector efficiency for several center of mass (CM) energy were studied using Delphes and MadAnalysis5 for performance comparison. The results of this study will contribute to the search for double dark photon channels at lepton colliders.

• Journal of Astronomy and Space Sciences
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• v.38 no.1
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• pp.55-63
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• 2021

The universe is well known to be consists of dark energy, dark matter and the standard model (SM) particles. The dark matter dominates the density of matter in the universe. The dark matter is thought to be linked with dark photon which are hypothetical hidden sector particles similar to photons in electromagnetism but potentially proposed as force carriers. Due to the extremely small cross-section of dark matter, a large amount of data is needed to be processed. Therefore, we need to optimize the central processing unit (CPU) time. In this work, using MadGraph5 as a simulation tool kit, we examined the CPU time, and cross-section of dark matter at the electron-positron collider considering three parameters including the center of mass energy, dark photon mass, and coupling constant. The signal process pertained to a dark photon, which couples only to heavy leptons. We only dealt with the case of dark photon decaying into two muons. We used the simplified model which covers dark matter particles and dark photon particles as well as the SM particles. To compare the CPU time of simulation, one or more cores of the KISTI-5 supercomputer of Nurion Knights Landing and Skylake and a local Linux machine were used. Our results can help optimize high-energy physics software through high-performance computing and enable the users to incorporate parallel processing.

• The Journal of the Korea Contents Association
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• v.8 no.12
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• pp.176-189
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• 2008

The purpose of this study was to analyze self-regulation about changing heart rate and perceived arousal variation when actors start their performance. Object of this study were 5 actors who belong to the theater selected using the purposive sampling method. This study used a measuring instrument of heart rate to measure arousal status, used behavior observation paper to observe and record self-regulation behavior and executed personal consultation after ending performance. There was graph mad by variation transition which calculated average and standard deviation about variation of heart rate each time of performance. The results of this study were as follows. First, there were high variation of awake level that actor's heart rates were rising before starting performance and the most high level of arousal was from 20minutes to 5minutes before starting performance. Second, there were self-regulation behaviors appeared such as deep breathing, breath controling, self talking, talking with other actors, concentrating an script, going to toilet, smoking, checking closes before starting performance. Third, when performance start, actors used psychological self-regulational method such as relaxation, self concentration, confidence reinforcement, coping with state or accommodation for controling raised arousal status.