• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.575-582
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• 2015

The Newton-Raphson method is used to compute the q-th roots of a p-adic number for a prime number q. The sufficient conditions for the convergence of this method are obtained. The speed of its convergence and the number of iterations to obtain a number of corrected digits in the approximation are calculated.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.769-772
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• 2022

Given a prime number p and a natural number m not divisible by p, we propose the problem of finding the smallest number r₀ such that for r ≥ r₀, every group G of order p^rm has a non-trivial normal p-subgroup. We prove that we can explicitly calculate the number r₀ in the case where every group of order p^rm is solvable for all r, and we obtain the value of r₀ for a case where m is a product of two primes.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.5
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• pp.263-269
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• 2014

In this paper, I disprove Hadwiger conjecture of the vertex coloring problem, which asserts that "All $K_k$-minor free graphs can be colored with k-1 number of colors, i.e., ${\chi}(G)=k$ given $K_k$-minor." Pursuant to Hadwiger conjecture, one shall obtain an NP-complete k-minor to determine ${\chi}(G)=k$, and solve another NP-complete vertex coloring problem as a means to color vertices. In order to disprove Hadwiger conjecture in this paper, I propose an algorithm of linear time complexity O(V) that yields the exact solution to the vertex coloring problem. The proposed algorithm assigns vertex with the minimum degree to the Maximum Independent Set (MIS) and repeats this process on a simplified graph derived by deleting adjacent edges to the MIS vertex so as to finally obtain an MIS with a single color. Next, it repeats the process on a simplified graph derived by deleting edges of the MIS vertex to obtain an MIS whose number of vertex color corresponds to ${\chi}(G)=k$. Also presented in this paper using the proposed algorithm is an additional algorithm that searches solution of ${\chi}^{{\prime}{\prime}}(G)$, the total chromatic number, which also remains NP-complete. When applied to a $K_4$-minor graph, the proposed algorithm has obtained ${\chi}(G)=3$ instead of ${\chi}(G)=4$, proving that the Hadwiger conjecture is not universally applicable to all the graphs. The proposed algorithm, however, is a simple algorithm that directly obtains an independent set minor of ${\chi}(G)=k$ to assign an equal color to the vertices of each independent set without having to determine minors in the first place.

• Journal of the Korean Society for Heat Treatment
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• v.13 no.2
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• pp.85-90
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• 2000

The influence of transformation cycles (${\alpha}^{\prime}{\leftrightarrow}{\gamma}^{\prime}$) on the microstructure and mechanical properties of lath and lenticular martensites has been studied in Fe-Ni alloys. The width of lath in Fe-15%Ni alloy decreased with increasing the number of transformation cycles, while no appreciable change in dislocation density inside the lath was observed. In case of Fe-31%Ni alloy, a number of dislocations were additionally introduced into the martensite plate after the transformation cycling. Tensile strength and Vickers hardness of lath martensite decreased with the increase in number of transformation cycles, whereas those of lenticular martensite increased up to 1 cycle and then remained constant. Elongation of two alloys was deteriorated after 1 transformation cycling, corresponding to the tensile strength. But the decrement of elongation in Fe-31%Ni alloy was smaller than that in Fe-15%Ni alloy.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1463-1481
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• 2021

Divisibility properties of harmonic numbers by a prime number p have been a recurrent topic. However, finding the exact p-adic orders of them is not easy. Using class numbers of number fields and Bernoulli numbers, we compute the exact p-adic orders of harmonic type sums. Moreover, we obtain an asymptotic formula for generalized harmonic numbers whose p-adic orders are exactly one.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.937-941
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• 2023

For each positive integer n, a square congruence graph S(n) is the graph with vertex set H = {1, 2, 3,...., n} and two vertices a, b are adjacent if they are distinct and a² ≡ b² (mod n). In this paper we investigate some structural properties of square congruence graph and we obtain the relationship between clique number, chromatic number and maximum degree of square congruence graph. Also we study square congruence graph with p vertices or 2p vertices for any prime number p.

• Journal of the Korea Society of Computer and Information
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• v.20 no.4
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• pp.95-102
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• 2015

This paper proposes a simple algorithm for circuit minimization. There are currently two effective heuristics for circuit minimization, namely manual Karnaugh maps and computable Quine-McCluskey algorithm. The latter, however, has a major defect: the runtime and memory required grow $3^n/n$ times for every increase in the number of variables n. The proposed algorithm, however, extracts the prime implicants (PI) that cover minterms of a given Boolean function by deriving an implicants table based on frequency. From a set of the extracted prime implicants, the algorithm then eliminates redundant PIs again based on frequency. The proposed algorithm is therefore capable of minimizing circuits polynomial time when faced with an increase in n. When applied to various 3-variable and 4-variable cases, it has proved to swiftly and accurately obtain the optimal solutions.

• Korean Journal of Plant Taxonomy
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• v.35 no.4
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• pp.337-364
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• 2005

The vascular flora of Mt. Deokhang (a.s.l. 1072.5m, $37^{\circ}17^{\prime}{\sim}37^{\circ}20^{\prime}N$, $128^{\circ}09^{\prime}{\sim}129^{\circ}03^{\prime}E$), one of the limestone areas in Korea and is located between Samcheok-si and Taebaek-si, Gangwon-do, is surveyed from 10 Oct. 2003 to 4 Oct. 2005. The characteristics of the flora from the phytogeographical point of view is also discussed. The number of the vascular plant taxa identified in this study is 590 in total which belongs to 90 families, 337 genera, 537 species, 4 subspecies, 46 varieties and 3 forms. Of them, 30 taxa are endemic to Korea, 4 taxa are legally protected ones, and 17 taxa are generally regarded as rare and endangered species in Korea. Naturalized plants are 19 taxa. The phytogeographical importance and the conservation strategy of the flora of Mt. Deokhang focusing on either rare, endemic or phytogeographically important species are discussed.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.33.3-34
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• 2016

We explored the GALEX UV properties of optical red sequence galaxies in 4 rich Abell clusters at z ~ 0.1. In particular, we tried to find a hint of merger-induced recent star formation (RSF) in red sequence galaxies. Based on the NUV - r' colors of the galaxies, about 36% of the post-merger galaxies were classified as RSF galaxies with a conservative criterion (NUV - $r^{\prime}{\leq}5$), and that number was doubled (~ 72%) when using a generous criterion (NUV - $r^{\prime}{\leq}5.4$). Post-merger galaxies with strong UV emission showed more violent, asymmetric features on the deep optical images. Also it turned out that all massive RSF galaxies (Mr' < -22 and NUV - $r^{\prime}{\leq}5$) exhibited post-merger signatures. Our results suggested that only 30% of RSF red sequence galaxies show morphological hints of recent galaxy mergers. This implies that internal processes (e.g., stellar mass-loss or hot gas cooling) for the supply of cold gas to early-type galaxies may play a significant role in the residual star formation of early-type galaxies at a recent epoch.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.63.2-63.2
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• 2019

Eight hundred thousand asteroids in the solar system have been identified so far under extensive sky surveys. Kilometer to sub-km sized asteroids, however, are still waiting for discovery, and their size and orbital distribution will provide a better understanding of the collisional and dynamical evolution of the solar system. In order to study the number of asteroids which is detectable with 1.6 m telescope and their orbital distribution, we conducted a small observation campaign as a part of Deep Ecliptic Patrol of the Southern Sky (DEEP-South) project, which is an asteroid survey in the southern hemisphere with Korea Microlensing Telescope Network (KMTNet). We observed the ecliptic plane near opposition ($2^{\circ}{\times}2^{\circ}$ field of view centering on ${\alpha}=22h40m31s$, ${\delta}=-08^{\circ}22^{\prime}58^{{\prime}{\prime}}$) in August 2018, and identified 464 moving objects by visual inspection. As a result, 266 of 464 moving objects turn out to be previously unknown asteroids, and their signal to noise ratio is below two on numerous occasions. Most of the newly detected objects are main belt asteroids (MBAs), while three Hildas, one Jupiter trojan, and two Hungarias are also identified. In this meeting, we report the differences in the orbital distributions between the previously known asteroids and newly discovered ones using statistical methods. We also talk about the observational bias of this survey and suggest future works.