• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.925-942
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• 2016

We study the structure of rings whose principal right ideals contain a sort of two-sided ideals, introducing right ${\pi}$-duo as a generalization of (weakly) right duo rings. Abelian ${\pi}$-regular rings are ${\pi}$-duo, which is compared with the fact that Abelian regular rings are duo. For a right ${\pi}$-duo ring R, it is shown that every prime ideal of R is maximal if and only if R is a (strongly) ${\pi}$-regular ring with $J(R)=N_*(R)$. This result may be helpful to develop several well-known results related to pm rings (i.e., rings whose prime ideals are maximal). We also extend the right ${\pi}$-duo property to several kinds of ring which have roles in ring theory.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.10C
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• pp.1363-1369
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• 2004

LDPC(Low Density Parity Check) codes are described by bipartite graphs with bit nodes and parity-check nodes. Tanner derived minimum distance bounds of the regular LDPC code in terms of the eigenvalues of the associated adjacency matrix. In this paper we generalize the Tanner's results. We derive minimum distance bounds applicable to both regular and blockwise-irregular LDPC codes. The first bound considers the relation between bit nodes in a minimum-weight codeword, and the second one considers the connectivity between parity nodes adjacent to a minimum-weight codeword. The derived bounds make it possible to describe the distance property of the code in terms of the eigenvalues of the associated matrix.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.569-575
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• 2015

In this paper, we research some properties of quaternionic regular functions in Clifford analysis. We investigate the corresponding Cauchy-Riemann system and find regularities of some hypercomplex valued functions.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.33-48
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• 2011

The notion of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,s)}$ of type s, whose nonzero elements are generalized Fibonacci numbers, is introduced in the paper [23]. Regular case s = 0 is investigated in [23]. In the present article we consider singular case s = -1. Pseudoinverse of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,-1)}$ is derived. Correlations between the matrix $\mathcal{F}_n^{(a,b,-1)}$ and the Pascal matrices are considered. Some combinatorial identities involving generalized Fibonacci numbers are derived. A class of test matrices for computing the Moore-Penrose inverse is presented in the last section.

• East Asian mathematical journal
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• v.36 no.3
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• pp.417-424
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• 2020

Huang et al. proved that the n by n upper triangular matrix ring over a domain is weakly reversible-over-center by using the property of regular matrices. In this article we provide a concrete proof which is able to be available in the related study of centers. Next we extend an example of weakly reversible-over-center, which was argued by Huang et al., to the general case.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.495-509
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• 2002

We propose variants of the modified incomplete Cho1esky factorization preconditioner for a symmetric positive definite (SPD) matrix. Spectral properties of these preconditioners are discussed, and then numerical results of the preconditioned CG (PCG) method using these preconditioners are provided to see the effectiveness of the preconditioners.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.161-176
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• 2012

The authors [6] introduced the concept of a complete matrix of grade $g$ > 3 to describe a structure theorem for complete intersections of grade $g$ > 3. We show that a complete matrix can be used to construct the Eagon-Northcott complex [7]. Moreover, we prove that it is the minimal free resolution $\mathbb{F}$ of a class of determinantal ideals of $n{\times}(n+2)$ matrices $X=(x_{ij})$ such that entries of each row of $X=(x_{ij})$ form a regular sequence and the second differential map of $\mathbb{F}$ is a matrix $f$ defined by the complete matrices of grade $n+2$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.813-822
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• 2014

A ring R is called quasipolar if for every a 2 R there exists $p^2=p{\in}R$ such that $p{\in}comm^2{_R}(a)$, $ a+p{\in}U(R)$ and $ap{\in}R^{qnil}$. The class of quasipolar rings lies properly between the class of strongly ${\pi}$-regular rings and the class of strongly clean rings. In this paper, we determine when a $2{\times}2$ matrix over a local ring is quasipolar. Necessary and sufficient conditions for a $2{\times}2$ matrix ring to be quasipolar are obtained.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.1
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• pp.16-22
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• 2001

In this study for reduction degree of freedom of dynamic model, a mixed method to combined finite element method and transfer matrix method is presented. This offers the advantages of an automatic reduction in the size of the eigenvalues problem and of a straightforward means of dynamic substructuring. The analytical procedure in this method for dynamic analysis of 3-dimensional cantilevered box beam are described. the result of numerical example is shown to demonstate the efficiency and accuracy of this method. The result form this example agree well those obtained by ANSYS, By using this technique, the number of nodes required in the regular finite element method is reduced and therefore a smaller com-puter can be used.

• Structural Engineering and Mechanics
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• v.3 no.3
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• pp.245-253
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• 1995

A combination of Riccati transfer matrix method and finite element method is proposed for obtaining vibration frequencies of structures. This method reduces the propagation of round-off errors produced in the standard transfer matrix method and finds out the values of the frequency by Newton-Raphson method. By this technique, the number of nodes required in the regular finite element method is reduced and therefore a microcomputer may be used. Besides, no plotting of the value of the determinant versus assumed frequency is necessary. As the application of this method, some numerical examples are presented to demonstrate the accuracy as well as the capability of the proposed method for the vibration of structures.