• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.573-582
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• 1995

J.Milnor[Mi2] has introduced the notion of directional entropy in his study of Cellular Automata. Cellular Automaton map can be considered as a continuous map from a space $K^Z^n$ to itself which commute with the translation of the lattice $Z^n$. Since the space $K^Z^n$ is compact, map S is uniformly continuous. Hence S is a block map(a finite code)[He]. (S is said to have a finite memory.) In the case of n = 1, we have a shift map, T on $K^Z$, and a block map S and they together generate a $Z^2$ action.

• Journal of Magnetics
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• v.1 no.1
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• pp.1-3
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• 1996

The $YBa_2Cu_3O_{7-x}$ structure has been fluorinated by a gas phase exchange technique. The ${^19}F$NMR (nuclear magnetic resonance) spin-lattice relaxation rate (1/T1) measurements on a fluorinated sample gave superconducting energy gap of $2\Delta=4.6kT_c$.

• Journal of Magnetics
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• v.2 no.2
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• pp.35-37
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• 1997

A sample of YBa2Cu3O7-x fluorinated by a high temperature (400$^{\circ}C$) gas exchange technique has been investigated by means of 19F NMR (nuclear magneti resonance) measurements in both superconducting and normal state. As a result, behaviors characteristic of the superconductor, including a peculiarity in the spin-lattice relaxation rate (1/T1) around 250 K, were observed.

• Proceedings of the Korean Magnestics Society Conference
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• 2002.12a
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• pp.190-191
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• 2002

Granular feromagnets는 non-magnetic maxtrix 안에 nanometer-sized의 ferromagnetic grain들 구성된다. Co-Cu,Co-Ag, Fe-Ag, NiFe-Ag $^1$을 포함하는 이미 알려진 다른 Granular 금속 합금들의 giant magnetoresistance 에 관계하여 Granular feromagnets 에 대해 조사하였다. Bulk상태의 NiFe와 Mn 혼화되기 쉽다.$^2$ 그리고 Mn은 열처리된 다층박막의 NiFe의 lattice에 쉽게 수용되어진다.$^3$ 이번 실험에서는 metastable한 fcc solid solution NiFe-Mn 박막이 열처리 하에서 NiFe과 Mn으로 분리되었다. (중략)

• Nuclear Engineering and Technology
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• v.52 no.10
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• pp.2285-2289
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• 2020

Protactinium contamination is a mayor issue in the thorium fuel cycle. We investigate, in this work, the consequences of Pa incorporation in vacancy defects and interstitials in Th, ThC and ThN. We calculate charge transfers and lattice distortions due to these incorporations as well as migration paths and energies involved in the diffusion of Pa.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.173-184
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• 2022

We investigated the invariant subspaces of the fractional integral operator in the Sobolev space W^k_p[0, 1] and prove unicellularity of the operator J^α by using the Duhamel product.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.35-51
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• 2022

We give secure parameter suggestions to use sparse secret vectors in LWE based encryption schemes. This should replace existing security parameters, because homomorphic encryption (HE) schemes use quite different variables from the existing parameters. In particular, HE schemes using sparse secrets should be supported by experimental analysis, here we summarize existing attacks to be considered and security levels for each attacks. Based on the analysis and experiments, we compute optimal scaling factors for CKKS.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1121-1148
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• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

• Nuclear Engineering and Technology
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• v.49 no.1
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• pp.1-5
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• 2017

The heavy water zero power reactor (HWZPR), which is a critical assembly with a maximum power of 100 W, can be used in different lattice pitches. The last change of core configuration was from a lattice pitch of 18-20 cm. Based on regulations, prior to the first operation of the reactor, a new core was simulated with MCNP (Monte Carlo N-Particle)-4C and WIMS (Winfrith Improved Multigroup Scheme)-CITATON codes. To investigate the criticality of this core, the effective multiplication factor ($K_{eff}$) versus heavy water level, and the critical water level were calculated. Then, for safety considerations, the reactivity worth of $D_2O$, the reactivity worth of safety and control rods, and temperature reactivity coefficients for the fuel and the moderator, were calculated. The results show that the relevant criteria in the safety analysis report were satisfied in the new core. Therefore, with the permission of the reactor safety committee, the first criticality operation was conducted, and important physical parameters were measured experimentally. The results were compared with the corresponding values in the original core.

• Nuclear Engineering and Technology
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• v.55 no.9
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• pp.3450-3463
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• 2023

In the two-step analysis of Pebble-Bed type High-Temperature Gas-Cooled Reactor (PB-HTGR), the lattice physics calculation for the generation of homogenized cross-sections is based on the fuel pebble. However, the randomly-dispersed fuel particles in the fuel pebble introduce double heterogeneity and randomness. Compared to the deterministic method, the Monte Carlo method which is flexible in geometry modeling provides a high-fidelity treatment. Therefore, the Monte Carlo code NECP-MCX is extended in this study to perform the lattice physics calculation of the PB-HTGR. Firstly, the capability for the simulation of randomly-dispersed media, using the explicit modeling approach, is developed in NECP-MCX. Secondly, the capability for the generation of the homogenized cross-section is also developed in NECP-MCX. Finally, simplified PB-HTGR problems are calculated by a two-step neutronics analysis tool based on Monte Carlo homogenization. For the pebble beds mixed by fuel pebble and graphite pebble, the bias is less than 100 pcm when compared to the high-fidelity model, and the bias is increased to 269 pcm for pebble bed mixed by depleted fuel pebble. Numerical results show that the Monte Carlo lattice physics calculation for the two-step analysis of PB-HTGR is feasible.