• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.45-57
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• 2005

An efficient algorithm for finding the inverse and the group inverse of the FLS $\gamma-circulant$ matrix is presented by Euclidean algorithm. Extension is made to compute the inverse of the FLS $\gamma-retrocirculant$ matrix by using the relationship between an FLS $\gamma-circulant$ matrix and an FLS $\gamma-retrocirculant$ matrix. Finally, some examples are given.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.197-205
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• 2018

In this note we give a relationship between the degree and coprime-ness of matrix-valued rational functions.

• Animal Bioscience
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• v.34 no.4
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• pp.516-524
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• 2021

Objective: The genetic evaluation of Santa Inês sheep was performed for resistance to gastrointestinal nematode infection (RGNI) and body size using different relationship matrices to assess the efficiency of including genomic information in the analyses. Methods: There were 1,637 animals in the pedigree and 500, 980, and 980 records of RGNI, thoracic depth (TD), and rump height (RH), respectively. The genomic data consisted of 42,748 SNPs and 388 samples genotyped with the OvineSNP50 BeadChip. The (co)variance components were estimated in single- and multi-trait analyses using the numerator relationship matrix (A) and the hybrid matrix H, which blends A with the genomic relationship matrix (G). The BLUP and single-step genomic BLUP methods were used. The accuracies of estimated breeding values and Spearman rank correlation were also used to assess the feasibility of incorporating genomic information in the analyses. Results: The heritability estimates ranged from 0.11±0.07, for TD (in single-trait analysis using the A matrix), to 0.38±0.08, for RH (using the H matrix in multi-trait analysis). The estimates of genetic correlation ranged from -0.65±0.31 to 0.59±0.19, using A, and from -0.42±0.30 to 0.57±0.16 using H. The gains in accuracy of estimated breeding values ranged from 2.22% to 75.00% with the inclusion of genomic information in the analyses. Conclusion: The inclusion of genomic information will benefit the direct selection for the traits in this study, especially RGNI and TD. More information is necessary to improve the understanding on the genetic relationship between resistance to nematode infection and body size in Santa Inês sheep. The genetic evaluation for the evaluated traits was more efficient when genomic information was included in the analyses.

• Journal of Chest Surgery
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• v.44 no.6
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• pp.387-391
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• 2011

Background: The relationship between the degree of expression of matrix metalloproteinases or tissue inhibitor of metalloproteinases and venous reflux remains to be investigated. Materials and Methods: Primary varicose vein tissues were obtained from 23 patients, 18 females and 5 males, aged from 19 to 73. Cephalic or basilic veins were obtained for the control group from 10 patients who underwent vascular access for maintenance hemodialysis. Two operative techniques (high ligation with stripping or endovenous laser coagulation) were used. The expression of matrix metalloproteinase-2 and 13 and tissue inhibitor of metalloproteinase-4 in the varicose vein group and control group was assessed semi-quantitatively by immunohistochemical slides stained with primary antibodies. Results: Twenty (87%) of the varicose vein group patients had greater or lesser saphenous vein diseases with reflux. The focal weak (+) stain for matrix metalloproteinases-2, and 13, and tissue inhibitor of matrix metalloproteinase-4 was dominant in the varicose vein group; the focal or diffuse strong stain (++ or +++) was prevalent in the control group. The differences were statistically significant (p<0.01). The degree of reflux and the duration of symptoms were not significantly related to the expression of MMP-13 (p=0.317 and p=0.654, respectively). Conclusion: Further study should be performed to investigate the relationship between the clinical characteristics related to venous hypertension or reflux and expression of MMPs and TIMP in varicose veins.

• Honam Mathematical Journal
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• v.7 no.1
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• pp.129-133
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• 1985

The object of this note is to discuss the relationship between some matrix transformations that naturally occur involving prime numbers in the theory of Summability.

• Journal of Korean Institute of Industrial Engineers
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• v.34 no.1
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• pp.42-48
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• 2008

The house of quality (HOQ) involves subjective and ambiguous information typically through a likert scale, It isimportant to validate consistency of such input in the HOQ before rating the fmal importance of technicalrequirements, Previously, a methodology was developed to test the consistency of relationship strengths in theHOQ between roof matrix and relationship matrix. We described disadvantages of the previous method andpropose a new approach based on the permutation test. Advantages of the proposed method are illustrated withan example.

• Journal of Korean Institute of Industrial Engineers
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• v.12 no.2
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• pp.45-55
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• 1986

A method for forming production cells in cellular manufacturing systems is presented. The basic approach is based on part-machine group formation by using relationship matrix calculated from the original part-machine matrix. The cases of exceptional elements and bottleneck machines are discussed. The proposed method can work with any starting form of part-machine matrix and provides the same solution regardless of the changes of starting form of part-machine matrix for any given problem.

• Journal of the Korean Society for Heat Treatment
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• v.19 no.1
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• pp.10-19
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• 2006

Microstructure and morphology of precipitates in $Ni_3Al$- and TiAl-based intermetallics containing carbon have been investigated in terms of transmission electron microscopy(TEM). In an $L1_2$-ordered $Ni_3Al$ alloy with 4 mol.% of chromium and 0.2~3.0 mol.% of carbon, fine octahedral precipitates of $M_{23}C_6$ type carbide were formed in the matrix by aging at temperatures around 973 K after solution annealing at 1423 K. TEM examination revealed that the $M_{23}C_6$ phase and the matrix lattices have a cube-cube orientation relationship and keep partial atomic matching at the {111} interface. After prolonged aging or by aging at higher temperatures, the $M_{23}C_6$ precipitates then adopt a rod-like morphology elongated parallel to the <100> directions. In the $L1_0$-ordered TiAl containing 0.1~2.0 mol.% carbon, TEM observations revealed that needle-like precipitates, which lie only in one direction parallel to the [001] axis of the $L1_0$ matrix, appear in the matrix and preferentially at dislocations. Selected area electron diffraction(SAED) patterns analyses have shown that the needle-shaped precipitate is $Ti_3AlC$ of perovskite type. The orientation relationship between the $Ti_3AlC$ and the $L1_0$ matrix is found to be $(001)_{Ti3AlC}//(001)_{L10\;matrix}$ and $[010]_{Ti3AlC}//[010]_{L10\;matrix}$. By aging at higher temperatures or for longer period at 1073 K, plate-like precipitates of $Ti_2AlC$ with a hexagonal structure are formed on the {111} planes of the $L1_0$ matrix. The orientation relationship between the $Ti_2AlC$ and the $L1_0$ matrix is $(0001)_{Ti2AlC}//(111)_{L10\;matrix}$ and $_{Ti2AlC}//_{L10\;matrix}$.

• Korean Journal of Materials Research
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• v.18 no.1
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• pp.51-56
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• 2008

The crystal structures and morphologies of precipitates in $L1_0$-ordered TiAl intermetallics containing nitrogen were investigated by transmission electron microscopy (TEM). Under aging at an approximate temperature of 1073 K after quenching from 1423 K, TiAl hardens appreciably due to the nitride precipitation. TEM observations revealed that needle-like precipitates, which lie only in one direction parallel to the [001] axis of the $L1_0$-TiAl matrix, appear in the matrix preferentially at the dislocations. Selected area electron diffraction (SAED) pattern analyses showed that the needle-shaped precipitate is perovskite-type $Ti_3AlN$ (P-phase). The orientation relationship between the P-phase and the $L1_0$-TiAl matrix was found to be $(001)_P//(001)_{TiAl}\;and\;[010]_P//[010]_{TiAl}$. By aging at higher temperatures or for longer periods at 1073 K, plate-like precipitates of $Ti_2AlN$ (H-phase) with a hexagonal structure formed on the {111} planes of the $L1_0$-TiAl matrix. The orientation relationship between the $Ti_2AlN$ and the $L1_0$-TiAl matrix is $(0001)_H//(111)_{TiAl}\;and\;_H//_{TiAl}$.

• Asian-Australasian Journal of Animal Sciences
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• v.30 no.7
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• pp.907-911
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• 2017

Objective: Intramuscular fat is one of the meat quality traits that is considered in the selection strategies for Hanwoo (Korean cattle). Different methods are used to estimate the breeding value of selection candidates. In the present work we focused on accuracy of different genotype relationship matrices as described by forni and pedigree based relationship matrix. Methods: The data set included a total of 778 animals that were genotyped for BovineSNP50 BeadChip. Among these 778 animals, 72 animals were sires for 706 reference animals and were used as a validation dataset. Single trait animal model (best linear unbiased prediction and genomic best linear unbiased prediction) was used to estimate the breeding values from genomic and pedigree information. Results: The diagonal elements for the pedigree based coefficients were slightly higher for the genomic relationship matrices (GRM) based coefficients while off diagonal elements were considerably low for GRM based coefficients. The accuracy of breeding value for the pedigree based relationship matrix (A) was 13% while for GRM (GOF, G05, and Yang) it was 0.37, 0.45, and 0.38, respectively. Conclusion: Accuracy of GRM was 1.5 times higher than A in this study. Therefore, genomic information will be more beneficial than pedigree information in the Hanwoo breeding program.