• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.651-658
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• 2001

The projection matrix plays an important role in the linear model theory. In this paper we derive an algebraic relationship between the projection matrices of submatrices of the design matrix. Using this relationship we can easily obtain the projection matrices of any submatrices of the design matrix. Also we show that every projection matrix can be obtained as a linear combination of Kronecker products of identity matrices and matrices with all elements equal to 1.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.609-615
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• 2012

In the current paper, we establish the relationship between the powers of an invertible matrix and the powers of its inverse. More precisely, we prove that if A is an invertible matrix and, if $A^n\;=\;(A_{i,j}(n))$ for all positive integer n, then $A^{-n}\;=\;(A_{i,j}{(-n))$.

• Genomics & Informatics
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• v.12 no.4
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• pp.254-260
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• 2014

Best linear unbiased prediction (BLUP) has been used to estimate the fixed effects and random effects of complex traits. Traditionally, genomic relationship matrix-based (GRM) and random marker-based BLUP analyses are prevalent to estimate the genetic values of complex traits. We used three methods: GRM-based prediction (G-BLUP), random marker-based prediction using an identity matrix (so-called single-nucleotide polymorphism [SNP]-BLUP), and SNP-SNP variance-covariance matrix (so-called SNP-GBLUP). We used 35,675 SNPs and R package "rrBLUP" for the BLUP analysis. The SNP-SNP relationship matrix was calculated using the GRM and Sherman-Morrison-Woodbury lemma. The SNP-GBLUP result was very similar to G-BLUP in the prediction of genetic values. However, there were many discrepancies between SNP-BLUP and the other two BLUPs. SNP-GBLUP has the merit to be able to predict genetic values through SNP effects.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.2
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• pp.103-109
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• 2021

About the orthogonal Hadamard matrix announced by Hadamard in France in 1893, Professor Moon Ho Lee newly defined it as Center Weight Hadamard in 1989 and announced it, and discovered the Jacket matrix in 1998. The Jacket matrix is a generalization of the Hadamard matrix. In this paper, we propose a method of obtaining the Symmetric Jacket matrix, analyzing important properties and patterns, and obtaining the Jacket matrix's determinant and Eigenvalue, and proved it using Eigen decomposition. These calculations are useful for signal processing and orthogonal code design. To analyze the matrix system, compare it with DFT, DCT, Hadamard, and Jacket matrix. In the symmetric matrix of Galois Field, the element-wise inverse relationship of the Jacket matrix was mathematically proved and the orthogonal property AB=I relationship was derived.

• Journal of the Korea Society for Simulation
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• v.10 no.1
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• pp.13-24
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• 2001

We propose a divide-conquer method of Petri nets under the condition of one-boundedness for all the Petri nets. We introduce the P-invariant transitive matrix of Petri nets and relationship between them. The feature of the P-invariant transitive matrix is that each element stands for the transitive relationship between input place and output place through the firing of the enable transition.

• The Journal of the Acoustical Society of Korea
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• v.28 no.3E
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• pp.118-135
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• 2009

The level set based approach is one of active methods for contour extraction in image segmentation. Since Osher and Sethian introduced the level set framework in 1988, the method has made the great impact on image segmentation. However, there are some problems to be solved; such as multi-objects segmentation, noise filtering and much calculation amount. In this paper we address the drawbacks of the previous level set methods and propose an extension of the traditional fast level set to cope with the limitations. We introduce a relationship matrix, a new split-and-merge criterion, a modified Chan-Vese criterion and a novel filtering criterion into the traditional fast level set approach. With the segmentation experiments we evaluate the proposed method and show the promising results of the proposed method.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.239-246
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• 2021

In this article, a study of generalized Bateman's matrix polynomials is presented. We obtained partial differential equations by using differential operators in the generalized Bateman's matrix polynomials for two variables. Then we introduced some different recurrence relationships of the generalized Bateman's matrix polynomials. Finally present the relationship between the generalized Bateman's matrix polynomials of one and two variables.

• Earthquakes and Structures
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• v.22 no.4
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• pp.387-399
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• 2022

To study the seismic damage of masonry structures and understand the characteristics of the multi-intensity region, according to the Dujiang weir urbanization of China Wenchuan earthquake, the deterioration of 3991 masonry structures was summarized and statistically analysed. First, the seismic damage of multistory masonry structures in this area was investigated. The primary seismic damage of components was as follows: Damage of walls, openings, joints of longitudinal and transverse walls, windows (lower) walls, and tie columns. Many masonry structures with seismic designs were basically intact. Second, according to the main factors of construction, seismic intensity code levels survey, and influence on the seismic capacity, a vulnerability matrix calculation model was proposed to establish a vulnerability prediction matrix, and a comparative analysis was made based on the empirical seismic damage investigation matrix. The vulnerability prediction matrix was established using the proposed vulnerability matrix calculation model. The fitting relationship between the vulnerability prediction matrix and the actual seismic damage investigation matrix was compared and analysed. The relationship curves of the mean damage index for macrointensity and ground motion parameters were drawn through calculation and analysis, respectively. The numerical analysis was performed based on actual ground motion observation records, and fitting models of PGA, PGV, and MSDI were proposed.

• Korean Journal of Materials Research
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• v.18 no.7
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• pp.362-366
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• 2008

The precipitation behavior in Mg-6 wt%Zn-1 wt%Y alloy annealed at different temperatures of $200^{\circ}C$ and $400^{\circ}C$ has been characterized by high resolution transmission electron microscope. When the alloy is annealed at $200^{\circ}C$ for 6 hr, the plate- and the rod-shaped ${\beta}_2'$ phases are precipitated in the matrix. The orientation relationship of plate-shaped precipitates with the matrix exhibits a [$11{\bar{2}}0]{\beta}_2$ || [$10{\bar{1}}0$]Mg, $(0001){\beta}_2'$ || (0001)Mg. While the rod-shaped precipitates have two kinds of the orientation relationships with the matrix, i.e. $[11{\bar{2}}0]{\beta}_2'$||[0001] Mg, $(0001){\beta}_2'||(11{\bar{2}}0)$ Mg and $[11{\bar{2}}0]{\beta}_2'$||[0001] Mg, $({\bar{1}}106){\beta}_2'||(10{\bar{1}}0)$ Mg. With increasing annealing time at $200^{\circ}C$ the ${\beta}_1'$ phases are also precipitated in the matrix and the orientation relationship exhibits a $[010]{\beta}_1'$ || [0001]Mg, $(603){\beta}_1'$ || ($01{\bar{1}}0$)Mg between the ${\beta}_1'$ precipitate and the matrix. The icosahedral phases are precipitated in the alloy annealed at $400^{\circ}C$ and exhibit a $[I2]_I$ || [0001]Mg relationship with the matrix.

• Journal of Digital Convergence
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• v.10 no.5
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• pp.267-273
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• 2012

The semantic relationship structures hierarchically the huge amount of document objects which is usually not formatted. However, it is very difficult to structure relevant data from various distributed application domains. This paper proposed a new object management method to service the distributed domain objects by using semantic reference relationship. The proposed mechanism utilized the profile structure in order to extract the semantic similarity from application domain objects and utilized the joint matrix to decide the semantic relationship of the extracted objects. This paper performed the simulation to show the performance of the proposed method, and simulation results show that the proposed method has better retrieval performance than the existing text mining method and information extraction method.