• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.311-322
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• 2007

This paper deals with space Beltrami system with three characteristic matrices in even dimensions, which can be regarded as a generalization of space Beltrami system with one and two characteristic matrices. It is transformed into a nonhomogeneous $p$-harmonic equation $d^*A(x,df^I)=d^*B(x,Df)$ by using the technique of out differential forms and exterior algebra of matrices. In the process, we only use the uniformly elliptic condition with respect to the characteristic matrices. The Lipschitz type condition, the monotonicity condition and the homogeneous condition of the operator A and the controlled growth condition of the operator B are derived.

• 한국전자통신학회논문지
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• 제6권2호
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• pp.193-198
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• 2011

행렬들 중 그것의 성분으로 부호인 + 와 0 만을 갖는 행렬을 우리는 비음인 부호화 행렬이라 한다. 또한 비음인 부호화 행렬 A가 그것과 같은 부호를 갖는 실수 정규행렬 B가 존재하면 정규성을 허용한다고 한다. 본 논문은 참고문헌[1] 에서 밝힌 형태와 다른 특별한 형태를 조사했고, 실수 행렬 중 비음인 정규행렬을 구성하는 흥미로운 방법을 제공했다.

• Communications for Statistical Applications and Methods
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• 제13권1호
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• pp.113-123
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• 2006

Normal mixture model(NMM) frequently used to cluster genes on microarray gene expression data. In this paper some of component means of NMM are modelled by a linear regression model so that its design matrix presents the pattern between sample classes in microarray matrix. This modelling for the component means by given design matrices certainly has an advantage that we can lead the clusters that are previously designed. However, it suffers from 'overfitting' problem because in practice genes often are highly dimensional. This problem also arises when the NMM restricted by the linear model for component-means is fitted. To cope with this problem, in this paper, the use of the factor analyzer NMM restricted by linear model is proposed to cluster genes. Also several design matrices which are useful for clustering genes are provided.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권3호
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• pp.305-320
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• 2020

This study aims to generalize MINRES-N2 method [1]. It means that we tend to obtain an algorithm to transfer each normal matrix - that its eigenvalues belong to an algebraic curve of low degree k- to its condensed form through using a unitary similarity transformation. Then, we aim to obtain a method to solve a system of linear equations that its coefficient matrix is equal to such a matrix by utilizing it. Finally this method is compared to the well-known GMRES method through using numerical examples. The results obtained through examples show that the given method is more efficient than GMRES.

• 대한기계학회논문집A
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• 제24권2호
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• pp.472-480
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• 2000

A macroscopic yield criterion for porous solids with pressure-sensitive matrices modeled by Coulomb's yield criterion was obtained by generalizing Gurson's yield criterion with consideration of the hydrostatic yield stresses for a spherical thick-walled shell and by fitting the finite element results of a voided cube. The macroscopic yield criterion is valid for negative mean normal stresses as well as for positive mean normal stresses. From the yield criterion, a plastic potential function for the porous solids was derived either for plastic normality flow or for plastic non-normality flow of pressure- sensitive matrices. In addition, the elastic relation, an evolution equation of the plastic flow stress of the matrices and an evolution equation of the void volume fraction were presented to complete a set of constitutive relations. The set of constitutive relations was implemented into a finite element code ABAQUS to analyze the material behavior of rubber-toughened epoxies. The cavitation and the deformation behavior were analyzed around a crack tip under three-point bending and around notch tips under four-point bending. In the numerical analyses, the cavitation of rubber particles was considered via a stress-controlled nucleation model. The numerical results indicate that a reasonable cavitation zone can be obtained with void nucleation controlled by the macroscopic mean normal stress, and a plastic zone is smaller around a notch tip under compression than under tension. These numerical results agree well with corresponding experimental results on the cavitation and plastic zones.

• 충청수학회지
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• 제16권1호
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• pp.25-36
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• 2003

We study the question of whether a partial (0, 1)-normal matrix has a non-symmetric normal completion. Matrix sandwich problems are an important and special case of matrix completion problems. In this paper, we give some properties for the (0, 1)-normal matrices and some large classes that satisfies the normal sandwich completion.

• 음성과학
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• 제10권4호
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• pp.189-200
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• 2003

The objective of this study was to examine two new parameters by which we could screen people with malignant vocal folds. The new parameters were the difference sums and Pearson correlation coefficients between adjacent pairs of intensity level matrices of narrow-band spectra. Audio files from the Korean Disordered Speech Database were analyzed by Praat, a speech analysis software, to obtain matrices of 400 intensity levels at 16 time points of each sustained vowel spectra. We limited our study to 12 normal subjects and 20 patients with malignant vocal folds who recorded at least three Korean vowels at a sound-proofed booth in Busan National University Hospital. Results indicated that the average coefficients of the abnormal subjects were much lower than those of the normal subjects while the average difference sums of the patients were much higher than those of the normal ones. Also, we found that the degree of the malignancy of the vocal folds was related to the coefficients and sums. However, some subjects at the initial stages of cancerous vocal folds yielded almost comparable coefficients and difference sums to those of the normal speakers. Further studies on larger databases will be desirable to set certain criteria or threshold levels for screening people with vocal fold diseases.

• 충청수학회지
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• 제15권2호
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• pp.97-107
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• 2003

An efficient algorithm for the multiplication in a binary finite filed using a normal basis representation of $F_{2^m}$ is discussed and proposed for software implementation of elliptic curve cryptography. The algorithm is developed by using the storage scheme of sparse matrices.

• 대한수학회보
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• 제48권4호
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• pp.759-767
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• 2011

An element of a ring is called strongly nil clean provided that it can be written as the sum of an idempotent and a nilpotent element that commute. A ring is strongly nil clean in case each of its elements is strongly nil clean. We investigate, in this article, the strongly nil cleanness of 2${\times}$2 matrices over local rings. For commutative local rings, we characterize strongly nil cleanness in terms of solvability of quadratic equations. The strongly nil cleanness of a single triangular matrix is studied as well.

• 대한수학회보
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• 제49권3호
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• pp.589-599
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• 2012

An element of a ring is called strongly nil clean provided that it can be written as the sum of an idempotent and a nilpotent element that commute. We characterize, in this article, the strongly nil cleanness of $2{\times}2$ and $3{\times}3$ matrices over $R[x]/(x^2-1)$ where $R$ is a commutative local ring with characteristic 2. Matrix decompositions over fields are derived as special cases.