• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1185-1189
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• 2008

In this paper we show that the polynomial of degree 9 called generalized algebraicity is a polynomial identity for $3{\times}3$ matrices. ([5])

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.751-755
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• 2008

Formanek([2]) proved that $M_n(K)$, the matrix algebra has a nontrivial central polynomial when char K = 0. Also Razmyslov([3]) showed the same result using the essential weak identity. In this article we explicitly compute Formanek's central polynomial for $M_2(\mathbb{C})$ and $M_3(\mathbb{C})$ and classify the coefficients of the central polynomial.

• Journal of the Korean Home Economics Association
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• v.48 no.9
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• pp.1-11
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• 2010

The purpose of this study was to investigate the effects of family-of-origin differentiation, ego identity, and attitudes toward children on marital intimacy among married men and women. The participants of this study were 261 married men and 274 married women whose marital period were less than 14 years, and whose first child was less than 12 years old and who were living in Chungbuk Province. Data were analyzed by frequency, percentages, ttest, F-test with Tukey test for post-hoc test, Cronbach ${\alpha}$ for reliability analysis, factor analysis, and Pearson's correlation using the SPSS program(12.0 version). The model test was done with analysis of correlational matrix by the AMOS 5.0 package using a maximum likelihood estimation. Family of origin differentiation, ego identity, and attitude toward children had different effects on marital intimacy according to gender. Also, ego identity was the strongest predictor of men's marital intimacy whereas attitude was the strongest for women's marital intimacy.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2468-2483
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• 2017

The construction of completely random sensing matrices of Compressive Sensing requires a large number of random numbers while that of deterministic sensing operators often needs complex mathematical operations. Thus both of them have difficulty in acquiring large signals efficiently. This paper focuses on the enhancement of the practicability of the structurally random matrices and proposes a semi-deterministic sensing matrix called Partial Kronecker product of Identity and Hadamard (PKIH) matrix. The proposed matrix can be viewed as a sub matrix of a well-structured, sparse, and orthogonal matrix. Only the row index is selected at random and the positions of the entries of each row are determined by a deterministic sequence. Therefore, the PKIH significantly decreases the requirement of random numbers, which has a complex generating algorithm, in matrix construction and further reduces the complexity of sampling. Besides, in order to process large signals, the corresponding fast sampling algorithm is developed, which can be easily parallelized and realized in hardware. Simulation results illustrate that the proposed sensing matrix maintains almost the same performance but with at least 50% less random numbers comparing with the popular sampling matrices. Meanwhile, it saved roughly 15%-35% processing time in comparison to that of the SRM matrices.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1603-1608
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• 2011

Let R be a ring with identity. If a, b, $c{\in}R$ such that a+b+c = 1, then the distributive laws from addition over multiplication hold in R, that is a+(bc) = (a+b)(a+c) when ab = ba, and (ab)+c = (a+c)(b+c) when ac = ca. An application to obtains, if A,B are idempotent matrices and AB = BA = 0 then there exists an idempotent matrix C such that A + BC = (A + B)(A + C), and also A + BC = (I - C)(I - B). Some other cases and applications are also presented.

• The Journal of the Acoustical Society of Korea
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• v.30 no.2
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• pp.80-85
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• 2011

Speaker change detection involves the identification of time indices of an audio stream, where the identity of the speaker changes. In this paper, we propose novel measures for the speaker change detection based on a graph-partitioning criterion over the pairwise distance matrix of feature-vector stream. Experiments on both synthetic and real-world data were performed and showed that the proposed approach yield promising results compared with the conventional statistical measures.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1251-1256
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• 2011

Consider a p-variate ($p{\geq}4$) normal distribution with mean ${\theta}$ and identity covariance matrix. Using a simple property of noncentral chi square distribution, the generalized Bayes estimators dominating the Lindley estimator under quadratic loss are given based on the methods of Brown, Brewster and Zidek for estimating a normal variance. This result can be extended the cases where covariance matrix is completely unknown or ${\Sigma}={\sigma}^2I$ for an unknown scalar ${\sigma}^2$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.71-78
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• 2009

An element of a ring R with identity is called strongly clean if it is the sum of an idempotent and a unit that commute, and R is called strongly clean if every element of R is strongly clean. Let R be a noncommutative local ring, a criterion in terms of solvability of a simple quadratic equation in R is obtained for $M_2$(R) to be strongly clean.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.423-432
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• 1998

Let p, q be integers such that 2 $\leq$ p, q $\leq$ n, and let $D_{p, q}$ denote the matrix obtained from $I_{n}$, the identity matrix of order n, by replacing each of the first p columns by an all 1's vector and by replacing each of the first two rows and each of the last q-2 rows by an all 1's vector. In this paper the permanent minimization problem over the face, determined by the matrix $D_{p, q}$, of the polytope of all n $\times$ n doubly stochastic matrices is treated.d.

• East Asian mathematical journal
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• v.14 no.2
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• pp.259-268
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• 1998

In this paper, for a commutative ring R with an identity, considering the endomorphism ring $End_R$(M) of left R-module $_RM$ which is (quasi-)injective or (quasi-)projective, some discriminations of prime endomorphism were found as follows: each epimorphism with the irreducible(or simple) kernel on a (quasi-)injective module and each monomorphism with maximal image on a (quasi-)projective module are prime. It was shown that for a field F, any given square matrix in $Mat_{n{\times}n}$(F) with maximal image and irreducible kernel is a prime matrix, furthermore, any given matrix in $Mat_{n{\times}n}$(F) for any field F can be factored into a product of prime matrices.