• Journal of Power Electronics
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• 제9권1호
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• pp.61-67
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• 2009

In this paper, a simple technique is presented for robust stability testing of perturbed DC-DC converters having multi-linear uncertainty structure. This technique provides a necessary and sufficient condition for testing robust stability. It is based on the corollary of Routh criterion and gridding of parameters. The previous work based on parametric control theory using Kharitonov's theorem and Hermite Biehler theorem gives conservative results and only the sufficient condition of stability, whereas the proposed method provides the necessary and sufficient condition for testing robust stability and it is computationally efficient. The superiority of the method is compared with the Edge theorem.

• 한국통신학회논문지
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• 제11권6호
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• pp.388-395
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• 1986

Spectral domain에서 hybrid mode 분석과 Galerkin method를 사용하여 차폐된 단일, 결합 및 edge-offset 마이크로 스트립 구조의 분산특성을 고찰하였다. 진행방향의 스트립 전류에 대한 새로운 2개의 basis function이 제안되었으며 그들을 사용한 수치해의 수렵속도를 비교하였다. 결합 마이크로 스트립의 전류분포는 단일 마이크로 스트입의 전류분포로부터 Fourier변환의 shift theorem을 이용하여 얻었으며 off-centered 스트립의 분산에 대한 영향이 논의되었다. 수치 결과들은 여러가지 구조 parameter 들을 포함하여 다른 유용한 data 들과 비교한 결과 잘 일치함을 알 수 있었다.

• 한국통신학회논문지
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• 제13권1호
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• pp.63-73
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• 1988

본 논문에서는 확률적 방향성 그래프에서 시점(source node)과 종점(terminal node) 간의 통신할 수 있는 확률인 단점간 신뢰도를 계정하는 알고리즘을 제시하였다. Satyanarayana의 factoring $theorem^{(7)}$을 이용하여 확률적 방향성 그래프에서 시점에 연결되어 있는 에지(edge)를 개방(open)과 단락(short)상태로 감축하여 원래의 그래프를 2개의 감축된 그래프로 분리한 후, 본 논문이 제시한 에지제거법과 일반적인 직, 병렬 감축법을 분리된 그래프에 적용한다. 이 에지 감축(edge reduction)을 source node와 terminal node가 단일 에지로 연결될때까지 반복한다. 또한 복잡하고 규모가 큰 망에 대한 단점간 신뢰도를 계정하기 위해서 전산기 프로그램을 제시하였다.

• 호남수학학술지
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• 제36권4호
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• pp.787-794
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• 2014

We prove three convex hull theorems on triangles and circles. Given a triangle ${\triangle}$ and a point p, let ${\triangle}^{\prime}$ be the triangle each of whose vertices is the intersection of the orthogonal line from p to an extended edge of ${\triangle}$. Let ${\triangle}^{{\prime}{\prime}}$ be the triangle whose vertices are the centers of three circles, each passing through p and two other vertices of ${\triangle}$. The first theorem characterizes when $p{\in}{\triangle}$ via a distance duality. The triangle algorithm in [1] utilizes a general version of this theorem to solve the convex hull membership problem in any dimension. The second theorem proves $p{\in}{\triangle}$ if and only if $p{\in}{\triangle}^{\prime}$. These are used to prove the third: Suppose p be does not lie on any extended edge of ${\triangle}$. Then $p{\in}{\triangle}$ if and only if $p{\in}{\triangle}^{{\prime{\prime}}$.

• East Asian mathematical journal
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• 제31권4호
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• pp.459-481
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• 2015

In this study, we investigated whether the theorem is established even if we replace a 'square' element in the Euclidean proof of the Pythagorean theorem with different figures. At this time, we used different figures as equilateral, isosceles triangle, (mutant) a right triangle, a rectangle, a parallelogram, and any similar figures. Pythagorean theorem implies a relationship between the three sides of a right triangle. However, the procedure of Euclidean proof is discussed in relation between the areas of the square, which each edge is the length of each side of a right triangle. In this study, according to the attached figures, we found that the Pythagorean theorem appears in the following three cases, that is, the relationship between the sides, the relationship between the areas, and one case that do not appear in the previous two cases directly. In addition, we recognized the efficiency of Euclidean proof attached the square. This proving activity requires a mathematical process, and a generalization of this process is a good material that can experience the diversity and rigor at the same time.

• 대한수학회보
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• 제33권1호
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• pp.119-126
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• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.

• Journal of Information Processing Systems
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• 제19권4호
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• pp.450-464
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• 2023

To address the problems of large system overhead and low timeliness when dealing with task scheduling in mobile edge cloud computing, a task scheduling and resource management strategy for edge cloud computing based on an improved genetic algorithm was proposed. First, a user task scheduling system model based on edge cloud computing was constructed using the Shannon theorem, including calculation, communication, and network models. In addition, a multi-objective optimization model, including delay and energy consumption, was constructed to minimize the sum of two weights. Finally, the selection, crossover, and mutation operations of the genetic algorithm were improved using the best reservation selection algorithm and normal distribution crossover operator. Furthermore, an improved legacy algorithm was selected to deal with the multi-objective problem and acquire the optimal solution, that is, the best computing task scheduling scheme. The experimental analysis of the proposed strategy based on the MATLAB simulation platform shows that its energy loss does not exceed 50 J, and the time delay is 23.2 ms, which are better than those of other comparison strategies.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1998년도 춘계학술발표회논문집(2)
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• pp.160-165
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• 1998

Under the heavy irradiation, when the production and the recombination of interstitials and vacancies are included, the diffusion equations become nonlinear. An effort has been made to arrange an appropriated transformation of these nonlinear differential equations to soluble Poisson's equations, so that analytical solutions for simultaneously calculating the concentrations of interstitials and vacancies in the angular dependent Cottrell's potential of the edge dislocation have been derived from the well-known Green's theorem and perturbation theory.

• Nuclear Engineering and Technology
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• 제31권2호
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• pp.151-156
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• 1999

Under the heavy irradiation of crystalline materials when the production and the recombination of interstitials and vacancies are included, the diffusion equations become nonlinear. An effort has been made to arrange an appropriate transformation of these nonlinear differential equations to more solvable Poisson's equations, finally analytical solutions for simultaneously calculating the concentrations of interstitials and vacancies in the angular dependent Cottrell's potential of the edge dislocation have been derived from the well-known Green's theorem and perturbation theory.

• EDISON SW 활용 경진대회 논문집
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• 제6회(2017년)
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• pp.376-382
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• 2017

Graphene nanoribbons with zigzag-shaped edge (zGNRs) are predicted to be magnetic insulator at the ground state, attracting significant interest in view of spintronic applications [1]. On the other hand, although they are energetically and thermodynamically more favored than zGNRs [2], graphene nanoribbons with armchair-shaped edge (aGNRs) have been less spotlighted than zGNRs due to the absence of magnetism. Herein, based on the combined density functional theory (DFT) and matrix Green's function (MGF) approach, we consider aGNRs functionalized with various molecular groups, and show that the spin polarizations develop for some of the considered aGNR edge functionalization cases. The origin of the induced magnetism will be discussed within the Lieb's theorem [3]. This work will provide a novel guidance for the development of graphene-based spintronic devices.