• Steel and Composite Structures
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• 제23권6호
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• pp.683-690
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• 2017

In the stability and sensitivity design and diagnosis approaches, there are various methodologies available. Bond graph modeling by lumping technique is one of the universal methodologies in methodical analysis used by many researchers in all over the world. The accuracy of the method is validated in different arenas. Bond graphs are a concise, pictorial representation of the energy storage, dissipation and exchange mechanisms of interacting dynamic systems, subsystems and components. This paper proposes a bond graph modeling for distributed parameter systems using lumping techniques. Therefore, a steel frame structure was modeled to analyze employing bond graph modeling of distributed system using lumping technique. In the analytical part, the effectiveness of bond graphs to model this system is demonstrated. The dynamic responses of the system were computed and compared with those computed from the finite element analysis. The calculated maximum deflection time histories were found to be comparable. The sensitivity and the stability of the steel frame structure was also studied in different aspects. Thus, the proposed methodology, with its simplicity, can be used for stability and sensitivity analyses as alternative to finite element method for steel structures. The major value brought in the practical design is the simplicity of the proposed method for steel structures.

• 로봇학회논문지
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• 제12권3호
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• pp.339-349
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• 2017

In this paper, we present a finite-time sliding mode control (FSMC) with an integral finite-time sliding surface for applying the concept of graph theory to a distributed wheeled mobile robot (WMR) system. The kinematic and dynamic property of the WMR system are considered simultaneously to design a finite-time sliding mode controller. Next, consensus and formation control laws for distributed WMR systems are derived by using the graph theory. The kinematic and dynamic controllers are applied simultaneously to compensate the dynamic effect of the WMR system. Compared to the conventional sliding mode control (SMC), fast convergence is assured and the finite-time performance index is derived using extended Lyapunov function with adaptive law to describe the uncertainty. Numerical simulation results of formation control for WMR systems shows the efficacy of the proposed controller.

• 한국정보통신학회논문지
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• 제10권12호
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• pp.2187-2192
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• 2006

본 논문에서는 De Bruijn그래프에 기초한 다중처리기 구성 방법에 대해 논의하였다. 유한체 상의 수학적 성질과 그래프의 성질을 사용하여 변환연산자에 대해 논의하였으며, 이들 변환연산자를 이용하여 De Buijn그래프의 변환표를 도출하였다. 그리고, 이 변환표로부터 유한체 상의 De Bruijn 그래프를 도출하였다. 제안한 다중처리기는 유한체 상에서의 임의 소수와 양의 정수에 대해 구성할 수 있으며 고장허용컴퓨팅 시스템, 파이프라인 시스템, 병렬처리 네트워크, 스위칭 함수와 이의 회로, 차세대 디지털논리 시스템 및 컴퓨터 구조 등에 적 용할 수 있다.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 1993년도 추계학술대회발표논문집; 서강대학교, 서울; 25 Sep. 1993
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• pp.118-118
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• 1993

We consider a discrete event dynamic system called periodic job shop, where an identical mixture of items called minimal part set(MPS) is repetitively produced in the same processing order and the primary performance measure is the cycle time. The precedence relationships among events(starts of operations) are represented by a directed graph with rocurront otructure. When each operation starts as soon as all its preceding operations complete(called earliest starting), the occurrences of events are modeled in a linear system using a special algebra called minimax algebra. By investigating the eigenvalues and the eigenvectors, we develop conditions on the directed graph for which a stable steady state or a finite eigenvector exists. We demonstrate that each finite eigenvector, characterized as a finite linear combination of a class of eigenvalue, is the minimum among all the feasible schedules and an identical schedule pattern repeats every MPS. We develop an efficient algorithm to find a schedule among such schedules that minimizes a secondary performance measure related to work-in-process inventory. As a by-product of the linear system approach, we also propose a way of characterizing stable steady states of a class of discrete event dynamic systems.

• 대한수학회논문집
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• 제22권2호
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• pp.277-287
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• 2007

We prove that if a graph G of bounded degree has finitely many p-hyperbolic ends($1) in which every bounded energy finite p-harmonic function is asymptotically constant for almost every path, then the set $\mathcal{HBD}_p(G)$ of all bounded energy finite p-harmonic functions on G is in one to one corresponding to $\mathbf{R}^l$, where $l$ is the number of p-hyperbolic ends of G. Furthermore, we prove that if a graph G' is roughly isometric to G, then $\mathcal{HBD}_p(G')$ is also in an one to one correspondence with $\mathbf{R}^l$.

• 대한수학회지
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• 제48권2호
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• pp.301-309
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• 2011

Let R = $Mat_2(F)$ be the ring of all 2 by 2 matrices over a finite field F, X the set of all nonzero, nonunits of R and G the group of all units of R. After investigating some properties of orbits under the left (and right) regular action on X by G, we show that the graph automorphisms group of $\Gamma(R)$ (the zero-divisor graph of R) is isomorphic to the symmetric group $S_{|F|+1}$ of degree |F|+1.

• 대한수학회논문집
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• 제35권4호
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• pp.1045-1056
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• 2020

Let R be a commutative ring with unity. The extension of annihilating-ideal graph of R, $^{\bar{\mathbb{AG}}}$(R), is the graph whose vertices are nonzero annihilating ideals of R and two distinct vertices I and J are adjacent if and only if there exist n, m ∈ ℕ such that IⁿJ^m = (0) with Iⁿ, J^m ≠ (0). First, we differentiate when 𝔸𝔾(R) and $^{\bar{\mathbb{AG}}}$(R) coincide. Then, we have characterized the diameter and the girth of $^{\bar{\mathbb{AG}}}$(R) when R is a finite direct products of rings. Moreover, we show that $^{\bar{\mathbb{AG}}}$(R) contains a cycle, if $^{\bar{\mathbb{AG}}}$(R) ≠ 𝔸𝔾(R).

• Korean Journal of Mathematics
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• 제28권1호
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• pp.123-136
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• 2020

In this paper, we give an explicit formula as a rational function for the Ihara zeta function of every finite connected graph without degree one vertices whose circuit rank is two.

• 한국정보통신학회논문지
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• 제12권12호
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• pp.2201-2206
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• 2008

본 논문에서는 유한체의 수학적 성질과 그래프이론을 바탕으로 GF(P)상의 선형디지털스위칭함수구성을 효과적으로 구성하는 한가지 방법을 제안하였다. 제안한 방법은 주어진 임의의 디지털스위칭함수의 입출력 사이의 연관관계특성으로 부터 DCG를 도출한 후에 노드의 개수를 인수분해한다. 이때 행렬방정식을 해당 차수보다 낮은 기약다항식으로 인수분해하여 그 결과를 부분회로실현한 다음 선형결합함으로써 최종 선형디지털스위칭함수를 구성하였다. 그 결과 기존의 방법에 비해 선형디지털스위칭함수구성을 상당히 간단화 할 수 있었으며 회로구성은 유한체 GF(P)내에서 정의된 가산기와 계수곱셈기를 사용하여 용이하게 실현 할 수 있다.

• 대한수학회지
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• 제53권3호
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• pp.519-532
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• 2016

The zero-divisor graph of a noncommutative ring R, denoted by ${\Gamma}(R)$, is a graph whose vertices are nonzero zero-divisors of R, and there is a directed edge from a vertex x to a distinct vertex y if and only if xy = 0. Let $R=M_2(F_q)$ be the $2{\times}2$ matrix ring over a finite field $F_q$. In this article, we investigate the automorphism group of ${\Gamma}(R)$.