• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.741-752
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• 2015

We introduce the warping crossing polynomial of an oriented knot diagram by using the warping degrees of crossing points of the diagram. Given a closed transversely intersected plane curve, we consider oriented knot diagrams obtained from the plane curve as states to take the sum of the warping crossing polynomials for all the states for the plane curve. As an application, we show that every closed transversely intersected plane curve with even crossing points has two independent canonical orientations and every based closed transversely intersected plane curve with odd crossing points has two independent canonical orientations.

• 제어로봇시스템학회논문지
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• 제17권3호
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• pp.236-240
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• 2011

The terminal sliding mode control schemes have been studied a lot since they can guarantee that the state error gets to zero in a finite time. However, the conventional terminal sliding surfaces have been designed using power function whose exponent is a rational number between 0 and 1, and whose numerator and denominator should be odd integers. It is clearly restrictive. Thus, in this paper, we propose a novel terminal sliding surface using power function whose exponent can be a real number between 0 and 1.

• 한국CDE학회논문집
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• 제7권2호
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• pp.75-80
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• 2002

This paper details a robust and efficient algorithm for point classification with respect to a polygon in 2D real number domain. The concept of tolerance makes this algorithm robust and consistent. It enables to define‘on-boundary’ , which can be interpreted as either‘in-’or‘out-’side region, and to manage rounding errors in floating point computation. Also the tolerance is used as a measure of reliability of point classifications. The proposed algorithm is based on a ray-intersection technique known as the most efficient, in which intersections between a ray originating from a given test point and the boundary of a region are counted. An odd number of intersections indicates that the point is inside region. For practical examples the algorithm is most efficient because most edges of the polygon region are processed by simple bit operations.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.321-330
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• 2023

Let G = (V, E) be a graph. Consider the group S₃. Let g : V (G) → S₃ be a function. For each edge xy assign the label 1 if ${\lceil}{\frac{o(g(x))+o(g(y))}{2}}{\rceil}$ is odd or 0 otherwise. g is a group S₃ mean cordial labeling if |v_g(i) - v_g(j)| ≤ 1 and |e_g(0) - e_g(1)| ≤ 1, where vg(i) and e_g(y)denote the number of vertices labeled with an element i and number of edges labeled with y (y = 0, 1). The graph G with group S₃ mean cordial labeling is called group S₃ mean cordial graph. In this paper, we discuss group S3 mean cordial labeling for star related graphs.

• Journal of Power Electronics
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• 제14권4호
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• pp.671-677
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• 2014

In this paper, a new basic unit is proposed. Then, a cascaded multilevel inverter basded on the series connection of n number of these new basic units is proposed. In order to generate all of the voltage levels (even and odd) at the output, three different algorithms to determine the magnitude of the dc voltage source are proposed. Reductions in the number of power switches, driver circuits and dc voltage sources in addition to increases in the numbr of output voltage levels are some of the advantages of the proposed cascaded multilevel inverter. These results are obtained through a comparison of the proposed inverter and its algorithms with an H-bridge cascaded multilevel inverter from the point of view of the number of power electronic devices. Finally, the capability of the proposed topology with its proposed algorithms in generating all of the voltage levels is verified through experimental results on a laboratorary prototype of a 49-level inverter.

• Korean Journal of Mathematics
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• 제7권2호
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• pp.227-233
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• 1999

Let $k$ be a real abelian field and $k_{\infty}={\bigcup}_{n{\geq}0}k_n$ be its $\mathbb{Z}_p$-extension for an odd prime $p$. For each $n{\geq}0$, we denote the class number of $k_n$ by $h_n$. The following is a well known theorem: Theorem. Suppose $p$ remains inert in $k$ and the prime ideal of $k$ above $p$ totally ramifies in $k_{\infty}$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$ for all $n{\geq}0$. The aim of this paper is to generalize above theorem: Theorem 1. Suppose $H^1(G_n,E_n){\simeq}(\mathbb{Z}/p^n\mathbb{Z})^l$, where $l$ is the number of prime ideals of $k$ above $p$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$. Theorem 2. Let $k$ be a real quadratic field. Suppose that $H^1(G_1,E_1){\simeq}(\mathbb{Z}/p\mathbb{Z})^l$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$ for all $n{\geq}0$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권7호
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• pp.2610-2630
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• 2021

The aim of this paper is to propose the alternative algorithm to finish the process in public key cryptography. In general, the proposed method can be selected to finish both of modular exponentiation and point multiplication. Although this method is not the best method in all cases, it may be the most efficient method when the condition responds well to this approach. Assuming that the binary system of the exponent or the multiplier is considered and it is divided into groups, the binary system is in excellent condition when the number of groups is small. Each group is generated from a number of 0 that is adjacent to each other. The main idea behind the proposed method is to convert the exponent or the multiplier as the subtraction between two integers. For these integers, it is impossible that the bit which is equal to 1 will be assigned in the same position. The experiment is split into two sections. The first section is an experiment to examine the modular exponentiation. The results demonstrate that the cost of completing the modular multiplication is decreased if the number of groups is very small. In tables 7 - 9, four modular multiplications are required when there is one group, although number of bits which are equal to 0 in each table is different. The second component is the experiment to examine the point multiplication process in Elliptic Curves Cryptography. The findings demonstrate that if the number of groups is small, the costs to compute point additions are low. In tables 10 - 12, assigning one group is appeared, number of point addition is one when the multiplier of a point is an even number. However, three-point additions are required when the multiplier is an odd number. As a result, the proposed method is an alternative way that should be used when the number of groups is minimal in order to save the costs.

• 한국측량학회지
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• 제31권2호
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• pp.151-157
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• 2013

1997년부터 도로명을 기준으로 주소를 나타내는 법적 근거가 마련되었다. 지번 방식의 주소에서 도로의 왼쪽에 위치한 건물에 홀수번호를 오른쪽에 위치한 건물에는 짝수번호를 부여하는 도로명 기준의 주소로 변화하는 것이다. 사람들이 거주하는 지역에 대해서는 도로명주소에 의한 위치표시는 가능하나, 전 답 산악 지역에 대한 위치표시체계는 미흡하여 범죄와 응급 구조에 신속히 대처할 수 없다. 이러한 비거주지역에서의 위치찾기 어려움의 도로명주소 약점을 보완하기 위해 국가지점번호가 도입되었다. 연구의 목적은 국가지점번호 도입을 돕기 위함이다. 본 연구에서는 국가지점번호를 위한 영토 중심의 기준점과 격자 범위, 그리고 부여체계로 두 글자의 한글과 x, y 좌표체계를 제안하였다. 또한, 지점번호 고시대상지역, 지점번호판 설치위치와 민간 및 공공분야 활용방안을 제시하였다.

• 공업화학
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• 제21권2호
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• pp.230-237
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• 2010

선상의 액정 다이머 동족체들인 ${\alpha},{\omega}$-비스(4-니트로아조벤젠-4'-카보닐옥시)알칸들(NATWESn, n = 2~8, 10, 유연격자 중의 메틸렌 단위들의 수)을 합성함과 동시에 이들의 열적 거동을 검토하였다. 모든 다이머들은 쌍방성 네마틱 상들을 형성하였다. 다이머들의 네마틱 상에서 액체 상으로의 전이온도들, 그리고 상 전이시의 엔트로피 변화는 n의 함수로서 커다란 홀수-짝수 효과를 나타냈다. 이러한 거동은 유연격자의 홀수-짝수의 변화에 의한 유연격자의 평균적인 형태변화의 견지에서 합리적으로 설명된다. NATWESn이 나타내는 네마틱 상의 열적 안정성과 질서도, 그리고 홀수-짝수의 크기는 니트로아조벤젠 그룹을 폴리메틸렌 유연격자를 통하여 에테르 결합으로 도입시켜 얻은 대칭 다이머들의 결과들과 거의 유사한 반면 모노메소겐 화합물들인 4-{4'-(니트로페닐아조펜옥시}알카노일 클로라이드들, 그리고 곁사슬형 액정 고분자인 폴리[1-{4-(4'-니트로페닐아조)펜옥시카보닐알카노일옥시}에틸렌]들의 결과들에 비해 판이하였다. 이들의 결과를 Imrie에 의한 'irtual trimer model'의 견지에서 검토하였다.

• 공업화학
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• 제22권4호
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• pp.358-366
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• 2011

선상의 액정 dimer 동족체인 ${\alpha},{\omega}$-(4-사이아노아조벤젠-4'-옥시)알케인(CATWETn, n = 2~10, 유연격자 중의 메틸렌 단위들의 수)을 합성함과 동시에 이들의 열방성 액정 거동을 검토하였다. n이 3, 6인 dimer들은 단방성 네마틱 상을 형성하는 반면 다른 유도체들은 양방성 네마틱 상을 형성하였다. Dimer들의 네마틱액체 전이온도와 상 전이시의 엔트로피 변화는 n의 함수로서 커다란 홀수-짝수 효과를 나타냈다. 이러한 상 전이 거동은 유연격자의 홀수-짝수의 변화에 의한 유연격자의 평균적인 형태변화의 견지에서 합리적으로 설명된다. CATWETn이 나타내는 네마틱 상의 열적 안정성과 질서도 그리고 홀수-짝수 효과는 메톡시, 니트로 그리고 펜틸기로 치환된 dimer에 대해 보고된 결과와 유사한 경향을 나타내는 반면 monomesogenic 화합물인 1-{4-(4'-사이아노페닐아조)펜옥시}알킬브롬 그리고 곁사슬형 액정 고분자인 폴리[1-{4-(4'-사이아노페닐아조)펜옥시알킬옥시}에틸렌]에 대해 보고된 결과와 현저히 달랐다. 이들의 결과를 Imirie에 의한 'virtural trimer model'의 견지에서 검토하였다.