• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.335-340
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• 2019

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. Some variants of energy can also be found in the literature, in which the energy is defined for the Laplacian matrix, Distance matrix, Commonneighbourhood matrix or Seidel matrix. The Seidel matrix of the graph G is the square matrix in which $ij^{th}$ entry is -1 or 1, if the vertices $v_i$ and $v_j$ are adjacent or non-adjacent respectively, and is 0, if $v_i=v_j$. The Seidel energy of G is the sum of the absolute values of the eigenvalues of its Seidel matrix. We present here some families of pairs of graphs whose Seidel matrices have different eigenvalues, but who have the same Seidel energies.

• 상하수도학회지
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• 제20권1호
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• pp.35-43
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• 2006

Concerns related to protecting, identifying, and isolating of subsystems of a water distribution network have led to the realization of the increased importance of valves in the system. The most important purpose of valves in water distribution systems is to isolate a subsystem due to breakage, maintenance activities, or contamination. A subsystem called segment is isolated by the closure of adjacent valves. Minimizing the pipe failure impact, an efficient algorithm is required to identify adjacent valves quickly. In this paper, an algorithm to identify adjacent valves to be closed to isolate a subsystem from the remainder of a network when a pipe failure is presented. The algorithm is operated on a matrix called the valve location matrix containing the information of valve locations. An application to an existing water distribution system demonstrates the developed algorithm efficiently locates the adjacent valves for the isolation of a broken pipe.

• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2008년도 춘계 종합학술대회 논문집
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• pp.771-775
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• 2008

상수관망의 유지보수와 파괴부분의 수리를 위해서 상수관망의 일부분을 차폐할 경우가 자주 발생한다. 상수관망의 노후화로 인하여 이와 같은 부분차폐의 필요성은 증대되고 있다. 상수관망의 부분적인 차폐는 설치된 제수밸브를 닫아야 한다. 그러나 상수관망에 설치된 제수밸브의 위치와 갯수를 미리 파악하여 대처하는 것이 추가적인 피해를 방지하는데 필수적이다. 본 연구에서는 차폐하고자하는 상수관망의 위치에 따라서 필요한 제수밸브를 결정하기 위하여 세가지 matrix에 기반을 둔 알고리즘을 개발하였다. 세가지 matrix는 상수관망의 network topology를 반영하는 node-arc matrix, 제수밸브의 위치정보를 담고 있는 valve location matrix, 그리고 제수밸브가 설치되지 않은 위치정보를 담고 있는 valve deficiency matrix로 구성된다. 개발된 제수밸브 결정 알고리즘을 캐나다 오타와시의 상수관망에 적용하여 이의 적용성과 효율성을 검증하였다.

• 한국정보통신학회논문지
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• 제22권11호
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• pp.1538-1543
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• 2018

원 상에 n개의 점들의 쌍 (a,b)이 존재할 때, 두 점 a와 b를 연결하는 직선 선분을 코드라고 한다. 이러한 n개의 코드들은 새로운 그래프 G를 정의한다. 각 코드는 G의 한 정점을 정의하고 두 코드가 교차하는 경우에 대응되는 정점들 간에 간선을 연결한다. 이렇게 만들어진 그래프 G를 원 그래프라고 부른다. 본 논문에서는 원 그래프에서 연결 요소를 찾는 문제를 다룬다. 연결 요소란 그래프 G의 부분 그래프 H로서 H안의 임의의 두 정점 간에 경로가 존재한다는 조건을 만족하는 최대 부분 그래프이다. 그래프 G가 인접 행렬로 주어지는 경우, 연결 요소를 찾는 문제는 깊이 우선 탐색 또는 너비 우선 탐색을 통해서 해결할 수 있다. 하지만 원 그래프의 경우에 코드들을 정의하는 n개의 점들의 쌍 정보만 입력으로 주어질 때, 인접 행렬을 구하는데 ${\Omega}(n^2)$ 시간이 소요됨을 알 수 있다. 본 논문에서는 인접 행렬을 만들지 않고 원 그래프의 연결 요소를 $O(n{\log}^2n)$시간에 찾는 알고리즘을 고안한다.

• 한국컴퓨터정보학회논문지
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• 제24권4호
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• pp.169-176
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• 2019

Wireless sensor networks are used to monitor and control areas in a variety of military and civilian areas such as battlefield surveillance, intrusion detection, disaster recovery, biological detection, and environmental monitoring. Since the sensor nodes are randomly placed in the area of interest, separation of the sensor network area may occur due to environmental obstacles or a sensor may not exist in some areas. Also, in the situation where the sensor node is placed in a non-relocatable place, some node may exhaust energy or physical hole of the sensor node may cause coverage hole. Coverage holes can affect the performance of the entire sensor network, such as reducing data reliability, changing network topologies, disconnecting data links, and degrading transmission load. It is possible to solve the problem that occurs in the coverage hole by finding a coverage hole in the sensor network and further arranging a new sensor node in the detected coverage hole. The existing coverage hole detection technique is based on the location of the sensor node, but it is inefficient to mount the GPS on the sensor node having limited resources, and performing other location information processing causes a lot of message transmission overhead. In this paper, we propose an Adjacent Matrix-based Hole Coverage Discovery(AMHCD) scheme based on connectivity of neighboring nodes. The method searches for whether the connectivity of the neighboring nodes constitutes a closed shape based on the adjacent matrix, and determines whether the node is an internal node or a boundary node. Therefore, the message overhead for the location information strokes does not occur and can be applied irrespective of the position information error.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2005년도 춘계학술대회 논문집
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• pp.435-440
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• 2005

This study describes a new method of constructing Reconfigurable machine tools configurations from a set of modules or components. This proposed method defines combinability vector for each module and mutual combinability coefficient matrix for adjacent two modules. All of machine configurations possible to be generated from any two adjacent modules can be determined by quadratic form of two associated combinability vectors. Furthermore, all of possible RMT configurations generating from a series of multiple modules also can be obtained by multiplying quadratic form of two adjacent conbinability vectors recursively. Our proposed RMT configuration generating method can be successfully applied to determining all of possible machine configurations from several modules or components at conceptual- or preliminary- design stage.

• 대한약학회:학술대회논문집
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• 대한약학회 2003년도 Proceedings of the Convention of the Pharmaceutical Society of Korea Vol.2-1
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• pp.100-101
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• 2003

Cell-cell and cell-matrix interaction is clearly required for metazoans not only to hold their cells together but also to conduct more sophisticated biological processes. Each cell has adhesion molecules on its cell membrane to link extracellular matrix and adjacent cells to the intracellular cytoskeleton, and also to transduce signals. In complex metazoans, information is transmitted from one cell to another by mechanisms such as direct intercellular communication, soluble signal molecules among distant cells, and local cellular environments formed by highly specialized extracellular matrix. (omitted)

• 조명전기설비학회논문지
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• 제28권1호
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• pp.69-78
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• 2014

In this paper, characteristics of wireless power transfer (WPT) systems using magnetically coupled resonance scheme with relay coils are investigated and modeled. Especially, asymmetric frequency splitting characteristics in over-coupled region of WPT with relays are measured and accurately modeled. Transmitter, receiver, and relay coils are modeled with R, L, C equivalent circuits. Using these circuit models and mutual inductances between coils, a WPT system is described with a linear matrix equation. For under-coupled region, a matrix is simplified considering only mutual inductances between adjacent coils. An analytical transfer characteristic of WPT system vs. distance is extracted using an inverse matrix that is acquired by Gauss elimination method for the simplified matrix. For over-coupled region, a matrix considering mutual inductances between non-adjacent coils is used to predict a frequency splitting characteristics accurately. A 6.3MHz WPT system with relay coils is implemented and measured. An accuracy of the model is investigated by comparing the output of the model with the measured results.

• 대한수학회보
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• 제53권4호
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• pp.1017-1031
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• 2016

Let R be a commutative ring with the non-zero identity and n be a natural number. ${\Gamma}^n_R$ is a simple graph with $R^n{\setminus}\{0\}$ as the vertex set and two distinct vertices X and Y in $R^n$ are adjacent if and only if there exists an $n{\times}n$ lower triangular matrix A over R whose entries on the main diagonal are non-zero such that $AX^t=Y^t$ or $AY^t=X^t$, where, for a matrix B, $B^t$ is the matrix transpose of B. ${\Gamma}^n_R$ is a generalization of Cayley graph. Let $T_n(R)$ denote the $n{\times}n$ upper triangular matrix ring over R. In this paper, for an arbitrary ring R, we investigate the properties of the graph ${\Gamma}^n_{T_n(R)}$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권11호
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• pp.5616-5630
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• 2019

Fully homomorphic encryption allows a third-party to perform arbitrary computation over encrypted data and is especially suitable for secure outsourced computation. This paper investigates secure outsourced computation of multiple matrix multiplication based on fully homomorphic encryption. Our work significantly improves the latest Mishra et al.'s work. We improve Mishra et al.'s matrix encoding method by introducing a column-order matrix encoding method which requires smaller parameter. This enables us to develop a binary multiplication method for multiple matrix multiplication, which multiplies pairwise two adjacent matrices in the tree structure instead of Mishra et al.'s sequential matrix multiplication from left to right. The binary multiplication method results in a logarithmic-depth circuit, thus is much more efficient than the sequential matrix multiplication method with linear-depth circuit. Experimental results show that for the product of ten 32×32 (64×64) square matrices our method takes only several thousand seconds while Mishra et al.'s method will take about tens of thousands of years which is astonishingly impractical. In addition, we further generalize our result from square matrix to non-square matrix. Experimental results show that the binary multiplication method and the classical dynamic programming method have a similar performance for ten non-square matrices multiplication.