• Kyungpook Mathematical Journal
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• v.59 no.2
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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.

• Journal of Korean Society of Water and Wastewater
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• v.20 no.1
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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.

• Proceedings of the Korea Contents Association Conference
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• 2008.05a
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• pp.771-775
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• 2008

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 subsystems due to breakage, maintenance activities, or contamination. A subsystem called segment is isolated by the closure of adjacent valves and an efficient algorithm should identify the adjacent valves to minimize the pipe failure impact. In this paper, an algorithm to identify adjacent valves to be closed to isolate a subsystem from the remainder of a network in case of a pipe failure is presented. An application to the water distribution system in Ottawa, Canada demonstrates the developed algorithm efficiently locates the adjacent valves for the isolation of a broken pipe.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.22 no.11
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• pp.1538-1543
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• 2018

For n pairs of points (a,b) on a circle, the line segment to connect two points is called a chord. These chords define a new graph G. Each chord corresponds to a vertex of G, and if two chords intersect, the two vertices corresponding to them are connected by an edge. This makes a graph, called by a circle graph. In this paper, we deal with the problem to find the connected components of a circle graph. The connected component of a graph G is a maximal subgraph H such that any two vertices in H can be connected by a path. When the adjacent matrix of G is given, the problem to find them can be solved by either the depth-first search or the breadth-first search. But when only the information for the chords is given as an input, it takes ${\Omega}(n^2)$ time to obtain the adjacent matrix. In this paper, we do not make the adjacent matrix and develop an $O(n{\log}^2n)$ algorithm for the problem.

• Journal of the Korea Society of Computer and Information
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• v.24 no.4
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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.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2005.05a
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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.

• Proceedings of the PSK Conference
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• 2003.10a
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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)

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.28 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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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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• v.13 no.11
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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.