• Korean Journal of Mathematics
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• 제22권1호
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• pp.123-131
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• 2014

The purpose of this paper is to study the perturbation analysis of the matrix equation $X=I-A^*X^{-1}A+B^*X^{-1}B$. Based on the matrix differentiation, we give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the shrpness of the perturbation bound.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.197-204
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• 2005

For two distinct rank-1 matrices A and B, a rank-1 matrix C is called a separating matrix of A and B if the rank of A + C is 2 but the rank of B + C is 1 or vice versa. In this case, rank-1 matrices A and B are said to be separable. We show that every pair of distinct Boolean rank-l matrices are separable.

• 융복합기술연구소 논문집
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• 제9권1호
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• pp.1-6
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• 2019

Matrix multiplication is a fundamental mathematical operation that has numerous applications across most scientific fields. In this paper, we presents a parallel GPU computation algorithm for dense matrix-matrix multiplication using OpenGL compute shader, which can play a very important role as a fundamental building block for many high-performance computing applications. Experimental results on NVIDIA Quad 4000 show that the proposed algorithm runs about 208 times faster than previous CPU algorithm and achieves performance of 75 GFLOPS in single precision for dense matrices with matrix size 4,096. Such performance proves that our algorithm is practical for real applications.

• 대한수학회보
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• 제41권1호
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• pp.125-135
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• 2004

One of the intriguing and fundamental algorithmic graph problems is the computation of the strongly connected components of a directed graph G. In this paper we first introduce a simple procedure for determining the location of the nonzero elements occurring in $B^{-1}$ without fully inverting B, where EB\;{\equiv}\;(b_{ij)\;and\;B^T$ are diagonally dominant matrices with $b_{ii}\;>\;0$ for all i and $b_{ij}\;{\leq}\;0$, for $i\;{\neq}\;j$, and then, as an application, show that all of the strongly connected components of a directed graph G can be recognized by the location of the nonzero elements occurring in the matrix $C(G)\;=\;(D\;-\;A(G))^{-1}$. Here A(G) is an adjacency matrix of G and D is an arbitrary scalar matrix such that (D - A(G)) becomes a diagonally dominant matrix.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1493-1499
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• 2009

Let $A_1$ and $A_2$ be nonzero complex idempotent and tripotent matrix, respectively. Denote a linear combination of the two matrices by A = $c_1A_1$ + $c_2A_2$, where $c_1,\;c_2$ are nonzero complex scalars. In this paper, under an assumption of $A_1A_2$ = $A_2A_1$, we characterize all situations in which the linear combination is tripotent. A statistical interpretation of this tripotent problem is also pointed out. Moreover, In [2], Baksalary characterized all situations in which the above linear combination is idem-potent by using the property of decomposition of a tripotent matrix, i.e. if $A_2$ is tripotent, then $A_2$ = $B_1-B_2$, where $B^2_i=B_i$, i = 1, 2 and $B_1B_2=B_2B_1=0$. While in this paper, by utilizing a method different from the one used by Baksalary in [2], we prove the theorem 1 in [2] again.

• 시스템엔지니어링학술지
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• 제12권1호
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• pp.1-5
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• 2016

Most of systems engineers make a traceability matrix and attach it to their technical documents as a result of systems engineering activities. I have been working in the field of systems engineering for many years and have been watching traceability matrices created by systems engineers or developers from various companies. I have been thinking that some of them are not suitable in terms of purposes of traceability matrix. In this paper, I would like to suggest a right template for the traceability matrix in conformance to traceability purposes. The key is that traceability matrix should be created from higher level of requirements to current level of requirements.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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• pp.73-88
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• 2004

A punctured torus $\Sigma(1,1)$ is a building block of oriented surfaces. The goal of this paper is to formulate the matrix presentations of elements of the Teichmuller space of a punctured torus. Let $\cal{C}$ be a matrix presentation of the boundary component of $\Sigma(1,1)$.In the level of the matrix group $\mathbb{SL}$($\mathbb2,R$) we shall show that the trace of $\cal{C}$ is always negative.

• BMB Reports
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• 제55권12호
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• pp.627-632
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• 2022

Dickkopf-1 (DKK1) is a secreted protein that acts as an antagonist of the canonical WNT/β-catenin pathway, which regulates osteoblast differentiation. However, the role of DKK1 on osteoblast differentiation has not yet been fully clarified. Here, we investigate the functional role of DKK1 on osteoblast differentiation. Primary osteoprogenitor cells were isolated from human spinal bone tissues. To examine the role of DKK1 in osteoblast differentiation, we manipulated the expression of DKK1, and the cells were differentiated into mature osteoblasts. DKK1 overexpression in osteoprogenitor cells promoted matrix mineralization of osteoblast differentiation but did not promote matrix maturation. DKK1 increased Ca⁺ influx and activation of the Ca⁺/calmodulin-dependent protein kinase II Alpha (CAMK2A)-cAMP response element-binding protein 1 (CREB1) and increased translocation of p-CREB1 into the nucleus. In contrast, stable DKK1 knockdown in human osteosarcoma cell line SaOS2 exhibited reduced nuclear translocation of p-CREB1 and matrix mineralization. Overall, we suggest that manipulating DKK1 regulates the matrix mineralization of osteoblasts by Ca⁺-CAMK2A-CREB1, and DKK1 is a crucial gene for bone mineralization of osteoblasts.

• BMB Reports
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• 제55권4호
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• pp.192-197
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• 2022

Cell signals for growth factors depend on the mechanical properties of the extracellular matrix (ECM) surrounding the cells. Microtubule acetylation is involved in the transforming growth factor (TGF)-β-induced myofibroblast differentiation in the soft ECM. However, the mechanism of activation of α-tubulin acetyltransferase 1 (α-TAT1), a major α-tubulin acetyltransferase, in the soft ECM is not well defined. Here, we found that casein kinase 2 (CK2) is required for the TGF-β-induced activation of α-TAT1 that promotes microtubule acetylation in the soft matrix. Genetic mutation and pharmacological inhibition of CK2 catalytic activity specifically reduced microtubule acetylation in the cells cultured on a soft matrix rather than those cultured on a stiff matrix. Immunoprecipitation analysis showed that CK2α, a catalytic subunit of CK2, directly bound to the C-terminal domain of α-TAT1, and this interaction was more prominent in the cells cultured on the soft matrix. Moreover, the substitution of alanine with serine, the 236th amino acid located at the C-terminus, which contains the CK2-binding site of α-TAT1, significantly abrogated the TGF-β-induced microtubule acetylation in the soft matrix, indicating that the successful binding of CK2 and the C-terminus of α-TAT1 led to the phosphorylation of serine at the 236th position of amino acids in α-TAT1 and regulation of its catalytic activity. Taken together, our findings provide novel insights into the molecular mechanisms underlying the TGF-β-induced activation of α-TAT1 in a soft matrix.

• 한국세라믹학회지
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• 제29권8호
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• pp.587-592
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• 1992

Sheets of SiC-SiC whisker maxed matrix were prepared from the mixed slurry of SiC whisker and SiC matrix by the rolling method. With the increase of SiC whisker, the pore size, the porosity and the phosphoric acid absorbency of the matrix were increased, while the bubble pressure was decreased. The activation energy for the transfer of H+ ion was decreased with the increase of mixing ratio of SiC whisker to the SiC matrix from the measurement of hydrogen ion conductivity. The activation energy was evaluated as 0.25 eV when the mixing ratio of SiC whisker to the SiC matrix was 1 : 2 and the activation energy was 0.16 eV for the 2 : 1 matrix. It means that SiC whisker matrix contributes to attain a better microstructure for the diffusion of hydrogen ion. From the measurement of single cell performance of matrix with various mixing ratio, it is concluded that if SiC-SiC whisker maxed matrix has a sufficient bubble pressure to prevent the crossover of H2 gas, the current density of a fuel cell is increased with the increase of acid absorbency of the matrix. Current density was improved from 140 mA/$\textrm{cm}^2$ for 0.25 mm thickness of matrix to 170 mA/$\textrm{cm}^2$ for the 0.20 mm one at 700 mV.