• The Mathematical Education
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• v.49 no.2
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• pp.161-174
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• 2010

The purpose of the study is to analyze various types of errors appeared in true-false proof problems of matrix and to find out correction method. In order to achieve this purpose, error test was conducted to the subject of 87 second grade students who were chosen from D high schoool. It was shown from this test that the most frequent error type was caused by the lack of understanding about concepts and essential facts of matrix(35.3%), and then caused by the invalid logically reasoning (27.4%), and then caused by the misusing conditions(18.7%). Through three hours of correction lessons with 5 students, the following correction teaching method was proposed. First, it is stressed that the operation rules and properties satisfied in real number system can not be applied in matrix. Second, it is taught that the analytical proof method and the reductio ad absurdum method are useful in the proof problem of matrix. Third, it is explained that the counter example of E=$\begin{pmatrix}1\;0\\0\;1 \end{pmatrix}$, -E should be found in proof of the false statement. Fourth, it is taught that the determinant condition should be checked for the existence of the inverse matrix.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.195-204
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• 2016

We prove, in this note, that a Zabavsky ring R is an elementary divisor ring if and only if R is a $B{\acute{e}}zout$ ring. Many known results are thereby generalized to much wider class of rings, e.g. [4, Theorem 14], [7, Theorem 4], [9, Theorem 1.2.14], [11, Theorem 4] and [12, Theorem 7].

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.1-9
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• 2000

An algorithmic approach to degree elevation of B-spline curves is presented. The new algorithms are based on the blossoming process and its matrix representation. The elevation method is introduced that consists of the following steps: (a) decompose the B-spline curve into piecewise $B{\acute{e}}zier$ curves, (b) degree elevate each $B{\acute{e}}zier$ piece, and (c) compose the piecewise $B{\acute{e}}zier$ curves into B-spline curve.

• Elastomers and Composites
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• v.32 no.1
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• pp.29-36
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• 1997

The change of elastic modulus(E'), loss modulus(E"), and loss $tangent(tan{\delta})$ were investigated on condition of double strain amplitude (DSA) at temperature of $-40{\sim}80^{\circ}C$ for carbon black filled natural rubber. E', E", and $tan{\delta}$ were increased as it closed to the glass transition temperature due to decrease of rubber network flexibility and carbon black agglomerate interaction. In the micro strain range, energy loss showed maximum value because of the chain slippage in rubber matrix, but the regeneration of carbon black agglomerate and rubber matrix affected decrease of energy loss over the mid-range strain. As a results of regression analysis, $E'\;_{max}$ correlation with ${\Delta}E'$ $(E'\;_{0.4%DSA}-E'\;_{2.0%DSA})$ showed linear relationship.

• Korean Journal of Soil Science and Fertilizer
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• v.46 no.3
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• pp.163-172
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• 2013

The aquatic insect collected at six areas (each 2 for mountain area, plain field, and urban area) from 2009 to 2011 were classified to analyze the distribution and diversity of species. Frequency (number of aquatic insect: N), number of species (S), similarity index (C), richness index (R1, R2), variety index (V1, V2), evenness index (E1, E2, E3, E4, E5), and dominance index (D1) were investigated. Total N and S were 143 and 84, respectively. C matrix of 153 combinations was constructed with the average of 0.542. The average C of 3 years (0.659) was 9.9% P, more higher than the average C of 6 areas (0.560). The average values of the index of 18 plots were 2.28, 0.17, 1.24, 1.08, 0.07, 0.06, 0.01, 0.87, 0.31, 0.93 for R1, R2, V1, V2, E1, E2, E3, E4, E5, D1, respectively. The order in the coefficient of variation (CV) of the indicator for 18 plots was N (70.0%) > E3 (54.9%) > E1 (49.6%) > R2 (40.5%) > S (35.3%) > R1 (33.7%) > E2 (28.4%) > E5 (15.9%) > V1 (11.1%) > E4 (6.3%) > V2 (5.1%) > D1 (4.8%). The correlation matrix with 66 combinations between the indexes was constructed with statistical significance for 33 combinations. However, R1, V1, E2 and D1 were the proper indexes to represent species diversity of aquatic insect based on the correlation matrix and the theory of statistical independence. The richness index was highest in mountain, variety index in urban area, and evenness index in plain field. However, the dominance index was lowest in urban area.

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.239-251
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• 2007

We show how the minimization can be used to solve the quadratic matrix equation and then compare two different types of conjugate gradient method which are Polak and Ribi$\acute{e}$re version and Fletcher and Reeves version. Finally, some results of the global and local convergence are shown.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.487-498
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• 2007

In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.

• Journal of Life Science
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• v.33 no.11
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• pp.851-858
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• 2023

Unique cartilage matrix-associated protein (UCMA) is an extrahepatic vitamin K-dependent protein rich in γ-carboxylated (Gla) residues. UCMA has been recognized for its ability to promote osteoblast differentiation and enhance bone formation; however, its impact on osteoblasts under hyperglycemic stress remains unknown. In this paper, we investigated the effect of UCMA on MC3T3-E1 osteoblastic cells under hyperglycemic conditions. After exposure to high glucose, the MC3T3-E1 cells were treated with recombinant UCMA proteins. CellROX and MitoSOX staining showed that the production of reactive oxygen species (ROS), which initially increased under high-glucose conditions in MC3T3-E1 cells, decreased after UCMA treatment. Additionally, quantitative polymerase chain reaction revealed increased expression of antioxidant genes, nuclear factor erythroid 2-related factor 2 and superoxide dismutase 1, in the MC3T3-E1 cells exposed to both high glucose and UCMA. UCMA treatment downregulated the expression of heme oxygenase-1, which reduced its translocation from the cytosol to the nucleus. Moreover, the expression of dynamin-related protein 1, a mitochondrial fission marker, was upregulated, and AKT signaling was inhibited after UCMA treatment. Overall, UCMA appears to mitigate ROS production, increase antioxidant gene expression, impact mitochondrial dynamics, and modulate AKT signaling in osteoblasts exposed to high-glucose conditions. This study advances our understanding of the cellular mechanism of UCMA and suggests its potential use as a novel therapeutic agent for bone complications related to metabolic disorders.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.365-380
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• 2012

Non-negative matrix factorization (NMF) is a very efficient method to explain the relationship between functions for finding basis information of multivariate nonnegative data. The multiplicative update (MU) algorithm is a popular approach to solve the NMF problem, but it fails to approach a stationary point and has inner iteration and zero divisor. So the elementwisely alternating projected gradient (eAPG) algorithm was proposed to overcome the defects. In this paper, we use the fact that the equilibrium point is stable to prove the convergence of the eAPG algorithm. By using a classic model, the equilibrium point is obtained and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the eAPG algorithm are obtained, which can accelerate the convergence. In addition, the conditions, which satisfy that the non-zero equilibrium point exists and is stable, can cause that the algorithm converges to different values. Both of them are confirmed in the experiments. And we give the mathematical proof that the eAPG algorithm can reach the appointed precision at the least iterations compared to the MU algorithm. Thus, we theoretically illustrate the advantages of the eAPG algorithm.

• Environmental Engineering Research
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• v.14 no.1
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• pp.63-67
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• 2009

Escherichia coli K-12 (E. coli K-12) is a representative indicator globally used for distinguishing and monitoring dynamic fates of pathogenic microorganisms in the environment. This study investigated how to most critically quantify lacZ ($\beta$-galactosidase) gene in E. coli K-12 by two different real-time polymerase chain reaction (real-time PCR) in association with three different DNA extraction practices. Three DNA extractions, i.e., sodium dodecyl sulfate (SDS)/proteinase K, magnetic beads and guanidium thiocyanate (GTC)/silica matrix were each compared for extracting total genomic DNA from E. coli K-12. Among them, GTC/silica matrix and magnetic beads beating similarly worked out to have the highest (22-23 ng/${\mu}L$) concentration of DNA extracted, but employing SDS/proteinase K had the lowest (10 ng/${\mu}L$) concentration of DNA retrieved. There were no significant differences in the quantification of the copy numbers of lacZ gene between SYBR Green I qPCR and QProbe-qPCR. However, SYBR Green I qPCR obtained somewhat higher copy number as $1{\times}10^8$ copies. It was decided that GTC/silica matrix extraction or magnetic beads beating in combination with SYBR Green I qPCR can be preferably applied for more effectively quantifying specific gene from a pure culture of microorganism.