• Journal of applied mathematics & informatics
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• 제8권2호
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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.

• 충청수학회지
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• 제25권4호
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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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• 제12권4호
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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.

• 한국인터넷방송통신학회논문지
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• 제21권2호
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• pp.103-109
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• 2021

1893년 불란서 Hadamard가 발표한 직교 Hadamard 행렬에 대해 이문호교수는 1989년에 Center Weight Hadamard로 새롭게 정의하여 발표했고 1998년에는 Jacket 행렬을 발견했다. Jacket 행렬은 Hadamard 행렬을 일반화한 것이다. 본 논문에서는 Symmetric Jacket 행렬을 구해 중요한 속성과 패턴을 분석하고 Jacket 행렬의 행렬식과 Eigenvalue을 얻는 방법을 제시하며 Eigen decomposition를 사용하여 이를 증명했다. 이러한 계산은 신호 처리 및 직교 코드 설계에 유용하다. 행렬의 체계를 분석하기 위해 DFT, DCT, Hadamard, Jacket 행렬로 비교해 본다. Galois Field의 대칭 행렬에서 Jacket 행렬의 element-wise inverse 관계를 수학적으로 증명하고 직교 성질 AB=I 관계를 유도했다.

• 한국시뮬레이션학회논문지
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• 제10권1호
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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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• 제28권3E호
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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.

• 대한수학회논문집
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• 제36권2호
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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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• 제22권4호
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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.

• 한국재료학회지
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• 제18권7호
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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.

• 디지털융복합연구
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• 제10권5호
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• pp.267-273
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• 2012

시맨틱 관계성은 포맷되지 않은 많은 문서 객체들을 계층적으로 구조화한다. 그러나 분산 응용도메인에서 관련 데이터를 추출하여 구조화하기란 쉽지 않는 일이다. 이러한 문제를 해결하기 위하여 본 논문에서는 분산된 응용 도메인 객체들을 서비스할 수 있도록 시멘틱 참조 관련성을 이용한 새로운 객체 관리 기법을 제안하였다. 제안된 기법은 응용 도메인 객체들로부터 시멘틱 유사성을 추출하기 위하여 프로파일 구조를 이용하였으며, 추출된 객체들의 시멘틱 관계성을 결정하기 위하여 joint matrix를 이용하였다. 제안된 기법의 성능을 알아보기 위하여 시뮬레이션을 수행하였으며, 시뮬레이션 결과 제안된 기법이 기존의 텍스트 마이닝 기법과 정보추출기법에 비해서 검색 성능이 우수함을 알게 되었다.