• Journal of the Korean School Mathematics Society
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• v.7 no.2
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• pp.81-97
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• 2004

This paper is a study on the understanding process of「Matrix and Graph」on discrete mathematics using TI-92 calculator. For this purpose, we investigated the understanding process of two middle school students learning the concepts of matrix and graph using TI-92 calculator. In this process, we collected qualitative data using recorder and video camera. Then we categorized these data as follows: students' attitude related to using technology, understanding process of meaning, expression and operation of matrix and graph, mathematical communication, etc. From this, we have the following conclusions: First, students inquired out the meaning and role of matrix by themselves using calculator. We could see that calculator can do the role of good learning partner to them. Second, students realized their own mistakes when they used calculator on the process of learning matrix. So we found that calculator could form the self-leading learning circumstance on learning matrix. Third, calculators reinforce the mathematical communication in learning matrix and graph. That is, calculator could be a good mediator to reinforce mathematical communication between teacher and students, among students on learning matrix and graph.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.75-86
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• 1996

Let G be a finite simple connected graph with vertex set V(G) and edge set E(G). Let A(G) be the adjacency matrix of G. The characteristic polynomial of G is the characteristic polynomial $\Phi(G;\lambda) = det(\lambda I - A(G))$ of A(G). A zero of $\Phi(G;\lambda)$ is called an eigenvalue of G.

• The Journal of the Acoustical Society of Korea
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• v.30 no.2
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• pp.80-85
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• 2011

Speaker change detection involves the identification of time indices of an audio stream, where the identity of the speaker changes. In this paper, we propose novel measures for the speaker change detection based on a graph-partitioning criterion over the pairwise distance matrix of feature-vector stream. Experiments on both synthetic and real-world data were performed and showed that the proposed approach yield promising results compared with the conventional statistical measures.

• Journal of the Korean Data and Information Science Society
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• v.25 no.5
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• pp.1107-1116
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• 2014

In this paper, we review recent developments in network analysis using the graph theory, and introduce ongoing research area with relevant theoretical results. In specific, we introduce basic notations in graph, and conditional and marginal approach in constructing the adjacency matrix. Also, we introduce the Marcenko-Pastur law, the Tracy-Widom law, the white Wishart distribution, and the spiked distribution. Finally, we mention the relationship between degrees and eigenvalues for the detection of hubs in a network.

• 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.

• ETRI Journal
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• v.29 no.3
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• pp.381-389
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• 2007

In this paper we propose a graph-theoretic method based on linear congruence for constructing low-density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ${\rho}$)-regular quasi-cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit-error-rate performance with iterative decoding in additive white Gaussian noise channels.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1137-1145
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• 1996

A Steinhaus graph is a labelled graph whose adjacency matrix $A = (a_{i,j})$ has the Steinhaus property : $a_{i,j} + a{i,j+1} \equiv a_{i+1,j+1} (mod 2)$. We consider random Steinhaus graphs with n labelled vertices in which edges are chosen independently and with probability $\frac{1}{2}$. We prove that almost all Steinhaus graphs are Hamiltonian like as in random graph theory.

• International conference on construction engineering and project management
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• 2005.10a
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• pp.383-388
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• 2005

In the construction industry, complex works are carried out with significant resources under non-linear circumstances where clear concepts of project management could be of benefit to all parties and personnel involved. In this paper, we define the optimum project management configuration for construction management by using DSM (Design Structure Matrix). Furthermore DSM can be visualized as a network model, and then Graph Theory provides us the numerical results.

• The Transactions of the Korea Information Processing Society
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• v.5 no.8
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• pp.2061-2074
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• 1998

In pattern recognition and image analysis upplications, a graph is a useful tool for complex obect representation and recognition. However it takes much time to pair proper nodes between the prototype graph and an input data graph. Futhermore it is difficult to decide whether the two graphs in a class are the same hecause real images are degradd in general by noise and other distortions. In this paper we propose a matching algorithm using a matrix. The matrix is suiable for simple and easily understood representation and enables the ordering and matching process to be convenient due to its predefined matrix manipulation. The nodes which constitute a gaph are ordered in the matrix by their geometrical positions and this makes it possible to save much comparison time for finding proper node pairs. for the classification, we defined a distance measure thatreflects the symbo's structural aspect that is the sum of the mode distance and the relation distance; the fornet is from the parameters describing the node shapes, the latter from the relations with othes node in the matrix. We also introduced a subdivision operation to compensate node merging which is mainly due t the prepreocessing error. The proposed method is applied to the recognition of musteal symbols and the result is given. The result shows that almost all, except heavily degraded symbols are recognized, and the recognition rate is approximately 95 percent.

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.255-263
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• 2023

In general, the rigidity problem of braced rectangular frameworks is determined by the connectivity of the bipartite graph induced by given rectangular framework. In this paper, we study how to solve the rigidity problem of the braced rectangular framework using the Laplacian matrix of the matrix induced by a braced rectangular framework.