• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.173-176
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• 1987

This paper presents a simple factorization of the Hadamard matrix which is used to develop a fast algorithm for the Hadamard transform. This matrix decomposition is of the kronecker products of identity matrices and successively lower order Hadamard matrices. This following shows how the Kronecker product can be mathematically defined and efficiently implemented using a factorization matrix methods.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.917-925
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• 2020

It has been shown that the geometric mean A#B of positive definite Hermitian matrices A and B is the maximal element X of Hermitian matrices such that $$\(\array{A&X\\X&B}\)$$ is positive semi-definite. As an extension of this result for the 2 × 2 block matrix, we consider in this article the block matrix [[A#w_ijB]] whose (i, j) block is given by the Riemannian geodesics of positive definite Hermitian matrices A and B, where w_ij ∈ ℝ for all 1 ≤ i, j ≤ m. Under certain assumption of the Loewner order for A and B, we establish the equivalent condition for the parameter matrix ω = [w_ij] such that the block matrix [[A#w_ijB]] is positive semi-definite.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1667-1682
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• 2017

In this paper, the Hermitian positive definite solutions of the matrix equation $X^s+A^*X-^tA=Q$, where Q is an $n{\times}n$ Hermitian positive definite matrix, A is an $n{\times}n$ nonsingular complex matrix and $s,t{\in}[1,{\infty})$ are discussed. We find a matrix interval which contains all the Hermitian positive definite solutions of this equation. Also, a necessary and sufficient condition for the existence of these solutions is presented. Iterative methods for obtaining the maximal and minimal Hermitian positive definite solutions are proposed. The theoretical results are illustrated by numerical examples.

• Journal of Life Science
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• v.6 no.4
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• pp.286-292
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• 1996

Angiogenesis is a fundamental process by which new blood vessels are formed. It is essential in embryo development, and wound healing. Furthermore, malignant tumor growth and metastasis are also angiogenesis-dependent. In the catilage tissue, normal angiogenesis process is suppressed. In fact, it was reported that angiogenesis-inhibitory substances were isolated from the extracts of cow and shark catilage tissue. In order to isolate genes involved in the regulation of angiogenesis from a catilage fish, we constructed a shark cDNA library from Scylliohinus torazame. We then screened the library using hyman tissue inhibitor of matrix metalloproteinase-1 (TIMP-1) gene as a probe. Among the 4 X 10$^{4}$ plaques screened, we isolated 2 positive clones (T-1, T-2). Restriction enzyme analysis revealed that the T-1 clone contains 0.8 kb cDNA insert, and the T-2 clone contains 1.2 kb and 2.2 kb inserts, respectively. Further DNA sequence analysis shows that the DNA sequence of the T-1 clone is 53% homologous to that of the human TIMP-1 gene.

• Korean Management Science Review
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• v.24 no.2
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• pp.177-196
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• 2007

For better predictions and classifications in customer recommendation, this study proposes an integrative model that efficiently combines the currently-in-use statistical and artificial intelligence models. In particular, by integrating the models such as Association Rule, Frequency Matrix, and Rule Induction, this study suggests an integrative prediction model. Integrated models consist of four models: ASFM model which combines Association Rule(A) and Frequency Matrix(B), ASRI model which combines Association Rule(A) and Rule Induction(C), FMRI model which combines Frequency Matrix(B) and Rule Induction(C), and ASFMRI model which combines Association Rule(A), Frequency Matrix(B), and Rule Induction(C). The data set for the tests is collected from a convenience store G, which is the number one in its brand in S. Korea. This data set contains sales information on customer transactions from September 1, 2005 to December 7, 2005. About 1,000 transactions are selected for a specific item. Using this data set. it suggests an integrated model predicting whether a customer buys or not buys a specific product for target marketing strategy. The performance of integrated model is compared with that of other models. The results from the experiments show that the performance of integrated model is superior to that of all other models such as Association Rule, Frequency Matrix, and Rule Induction.

• Journal of Pharmaceutical Investigation
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• v.29 no.1
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• pp.7-12
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• 1999

The captopril matrix tablets composed of polyethylene oxide(PEO) was prepared and administered to beagle dogs. Captopril matrix tablets were prepared using direct compressed method and wet granulation compressed method with various ratios of drug to PEO. The diffusion rate of captopril matrix tablets followed on the Higuchi's diffusion model. With increasing hardness of captopril matrix tablets, release rate was decreased. Each formulation was evaluated by the area under the curve (AUC) and time course of plasma captopril concentration after oral administration to beagle dogs. The $AUC_{0-12}$ were $9.126\;{\mu}g\;h/ml$ and $6.417\;{\mu}g\;h/ml$ for the matrix tablets and conventional tablets, respectively. Therefore, the bioavailability of captopril matrix tablets was greater than that of commercial product. It is suggested that captopril matrix tablets using PEO is a useful sustained release formulation.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.5
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• pp.1-11
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• 1994

In computer graphics since objects atre constructed by lines and curves, the high-speed curve generator is indispensible for computer aided design and simulatation. Since the functions of graphic generation can be represented as a series of matrix operations, in this paper, two kind of the high-speed Bezier curve generator that uses matrix equation and a recursive relation for Bezier polynomials are designed. And B-spline curve generator is designed using interdependence of B-spline blending functions. As the result of the comparison of designed curve generator and reference [5], [6] in the operation time and number of operators, the curve generator with 1-dimensional systolic array processor for matrix vector operation that uses matrix equation for Bezier curve is more effective.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.969-990
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• 2011

Assume that X, partitioned into $2{\times}2$ block form, is a solution of the system of quaternion matrix equations $A_1XB_1$ = $C_1,A_2XB_2=C_2$. We in this paper give the maximal and minimal ranks of the submatrices in X, and establish necessary and sufficient conditions for the submatrices to be zero, unique as well as independent. As applications, we consider the common inner inverse G, partitioned into $2{\times}2$ block form, of two quaternion matrices M and N. We present the formulas of the maximal and minimal ranks of the submatrices of G, and describe the properties of the submatrices of G as well. The findings of this paper generalize some known results in the literature.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.97-109
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• 2001

This article is devoted to “forgotten” and rarely used technique of matrix analysis, introduced in 60-70th and enhanced by authors. We will study the matrix trace operator and it’s differentiability. This idea generalizes the notion of scalar derivative for matrix computations. The list of the most common derivatives is given at the end of the article. Additionally we point out a close connection of this technique with a least square problem in it’s classical and generalized case.