• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.595-608
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• 2013

Let G = (V, E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V (G) and E = E(G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The distance between the vertices $u$ and $v$ in V (G) of graph G is the number of edges in a shortest path connecting them, we denote by $d(u,v)$. In graph theory, we have many invariant polynomials for a graph G. In this paper, we focus on the Schultz polynomial, Modified Schultz polynomial, Hosoya polynomial and their topological indices of a molecular graph circumcoronene series of benzenoid $H_k$ and specially third member from this family. $H_3$ is a basic member from the circumcoronene series of benzenoid and its conclusions are base calculations for the Schultz polynomial and Hosoya polynomial of the circumcoronene series of benzenoid $H_k$ ($k{\geq}3$).

• 대한수학회지
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• 제52권2호
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• pp.389-402
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• 2015

A symmetric union is a diagram of a knot, obtained from diagrams of a knot in the 3-space and its mirror image, which are symmetric with respect to an axis in the 2-plane, by connecting them with 2-tangles with twists along the axis and 2-tangles with no twists. This paper presents an invariant of knots with symmetric union presentations, which is called the minimal twisting number, and the minimal twisting number of $10_{42}$ is shown to be two. This paper also presents a sufficient condition for non-amphicheirality of a knot with a certain symmetric union presentation.

• 한국군사과학기술학회지
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• 제4권2호
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• pp.105-111
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• 2001

The shrinking generator is simple and stateable, and known that has good security properties. The bits of one output( $R_1$) are used to determine whether the corresponding bits of the second output will be used as part of the overall keystream. Two LFSRs consisting the generator generate pseudorandom sequences satisfying Golomb's postulates. We used this property to analyze the stream of LFSR $R_1$ of the generator.

• 자동차안전학회지
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• 제11권3호
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• pp.30-36
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• 2019

This paper suggests a car-following algorithm for urban environment, with multiple target candidates. Until now, advanced driver assistant systems (ADASs) and self-driving technologies have been researched to cope with diverse possible scenarios. Among them, car-following driving has been formed the groundwork of autonomous vehicle for its integrity and flexibility to other modes such as smart cruise system (SCC) and platooning. Although the field has a rich history, most researches has been focused on the shape of target trajectory, such as the order of interpolated polynomial, in simple single-lane situation. However, to introduce the car-following mode in urban environment, realistic situation should be reflected: multi-lane road, target's unstable driving tendency, obstacles. Therefore, the suggested car-following system includes both in-lane preceding vehicle and other factors such as side-lane targets. The algorithm is comprised of three parts: path candidate generation and optimal trajectory selection. In the first part, initial guesses of desired paths are calculated as polynomial function connecting host vehicle's state and vicinal vehicle's predicted future states. In the second part, final target trajectory is selected using quadratic cost function reflecting safeness, control input efficiency, and initial objective such as velocity. Finally, adjusted path and control input are calculated using model predictive control (MPC). The suggested algorithm's performance is verified using off-line simulation using Matlab; the results shows reasonable car-following motion planning.

• 한국컴퓨터정보학회논문지
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• 제18권11호
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• pp.159-165
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• 2013

본 논문은 NP-완전 문제인 간선 색칠과 그래프 부류 결정 문제를 동시에 해결하는 O(E)의 다항시간 알고리즘을 제안하였다. 제안된 알고리즘은 최대차수-최소차수 정점 쌍 간선을 단순히 선택하는 방법으로 간선 채색수 ${\chi}^{\prime}(G)$를 결정하였다. 결정된 ${\chi}^{\prime}(G)$는 ${\Delta}(G)$ 또는 ${\Delta}(G)+1$을 얻는다. 결국, 알고리즘 수행 결과 얻은 ${\chi}^{\prime}(G)$로부터 ${\chi}^{\prime}(G)={\Delta}(G)$이면 부류 1, ${\chi}^{\prime}(G)={\Delta}(G)+1$이면 부류 2로 분류할 수 있다. 또한, 미해결 문제로 알려진 "최대차수가 6인 단순, 평면 그래프는 부류 1이다."라는 Vizing의 평면 그래프 추정도 증명하였다.

• 제어로봇시스템학회논문지
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• 제20권2호
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• pp.223-231
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• 2014

Humanoid robot is the most suitable robot platform for effective human interaction and various intelligent services. The present work addresses development of real time wireless control application of humanoid robot's forward and backward walks, and turning in walking. For convenience of human users, the application is developed on Android OS (Operating System) working on his or her smartphone. To this end, theoretic background on various-directional biped walking is proposed based on joint trajectories for forward walking, which have been shaped with a global optimization method. In this paper, backward walking is scheduled by interchange of angles and angular velocities and additional change of signs in angular velocities at all the via-points connecting cubic polynomial trajectories. Turning direction in walking is also implemented by activating the transversal hip joint initially located in the support leg in two stages. After validation of the proposed walking schemes with Matlab simulator, a smartphone application for the omnidirectional walking has been developed to control a humanoid robot platform named DARwIn-OP interconnected via Wi-Fi. Experiment result of the present wireless control of a humanoid robot with smartphone is successful, and the application will be released in application market near future.

• 전자공학회논문지
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• 제51권2호
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• pp.173-181
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• 2014

본 논문은 흉부 CT에서 폐, 기관지 및 폐혈관을 자동으로 분할 할 수 있는 알고리즘을 제안 하였다. 제안된 방법은 3단계로 진행된다. 첫째는 최적 임계값과 3차원 레이블링을 통한 영역성장법으로 폐 및 기관지를 분할한다. 둘째는 기관지의 형태학적 정보를 활용하여 기관지의 첫 번째 분기점(용골)까지는 차감연산으로, 이후부터는 가변적 임계값 기법을 적용하여 기관지를 분할한다. 셋째는 폐에 대한 복원 과정으로 좌/우측 폐를 분리하고, 개선된 롤링 볼 알고리즘을 적용하여 폐 외곽의 이상 유무를 확인하며, 이상이 발견되면 그 부분을 제거하고, 2차 다항식 형태로 폐 외곽을 연결시킴으로서 정상적인 폐로 복원한다. 마지막으로 폐혈관은 임계 값 기법의 3 차원 레이블링과 3 차원 영역성장법을 적용하여 분할하였다. 시뮬레이션 결과 폐 주변조직의 손실 없이 정확하게 분할됨을 확인 할 수 있었다.

• 한국인터넷방송통신학회논문지
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• 제24권3호
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• pp.95-101
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• 2024

주어진 숫자 쌍 간에 빈 셀을 경유하는 선을 연결함에 있어 다른 숫자의 연결선과 교차가 발생하지 않도록 하는 숫자 연결 퍼즐은 다항시간으로 퍼즐을 풀 수 있는 방법이 알려져 있지 않은 NP-완전 문제이다. 지금까지는 임의의 숫자를 선정하여 시행착오 법으로 퍼즐을 풀고 있다. 본 논문은 주어진 문제에 대해 빈 셀을 정점으로, 인접 셀들 간에 간선으로 연결한 격자 그래프로 변환하였다. 다음으로 숫자 쌍 들 간에 직선을 긋고, 교차가 발생한 숫자 그룹으로 분할하였다. 교차 숫자 그룹에서 교차를 회피하는 우회 경로를 설정하였다. 제안된 알고리즘을 18개의 벤치마킹 데이터들에 적용한 결과 모든 데이터에 대해 퍼즐을 O(n)의 선형시간 복잡도로 풀 수 있음을 보였다.