• International journal of advanced smart convergence
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• v.9 no.4
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• pp.42-51
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• 2020

In this paper, the authors propose the pseudo complex correlation coefficient (PCCC) of the two complex random variables (RV), because the four real correlation coefficients (RCC) of the corresponding four real RVs cannot be obtained only from the complex correlation coefficient (CCC) of given two complex RV. Such observation is motivated by the general statement; "The complex jointly-Gaussian random M-vector cannot be completely described by the complex covariance matrix, even though the real Gaussian random 2M-vector can be completely descried by the real covariance matrix. Therefore, in order to describe completely the complex jointly-Gaussian random M-vector, we need an additional matrix, namely the complex pseudo-covariance matrix, along with the complex covariance matrix." Then, we apply PCCC to correlated information sources (CIS) for non-orthogonal multiple access (NOMA) in 5G system, and investigate impact of the proposed PCCC on the achievable data rate of the stronger channel user in the conventional successive interference cancellation (SIC) NOMA with CIS. It is shown that for the given same CCC, the achievable data rates with the different PCCC are different, because the corresponding RCC are different. We also show that as the absolute value of the same CCC increases, the impact of the different PCCC becomes more significant.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.487-497
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• 2020

In this paper, we establish a complex matrix representation of the Clifford algebra Cℓ_p,q. The size of our representation is significantly smaller than the size of the elements in L_p,q(ℝ). Additionally, we give detailed information about the spectrum of the constructed matrix representation.

• Food Science of Animal Resources
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• v.37 no.1
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• pp.147-152
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• 2017

A bioluminescent Lactobacillus plantarum (pLuc2) strain was constructed. The luminescent signal started to increase during the early exponential phase and reached its maximum in the mid-exponential phase in a batch culture of the strain. The signal detection sensitivity of the strain was the highest in PBS (phosphate buffered saline), followed by milk and MRS broth, indicating that the sensitivity was influenced by the matrix effect. The strain was used in millet seed fermentation which has a complex matrix and native lactic acid bacteria (LAB). The luminescent signal was gradually increased until 9 h during fermentation and abolished at 24 h, indicating that the strain could be specifically tracked in the complex matrix and microflora. Therefore, the bioluminescent labeling system can be used for monitoring LAB in food and dairy sciences and industries.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.49-53
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• 2011

In this paper, we adopt a numerical method to establish the smallest set to contain all Ger$\v{s}$gorin discs of a given complex matrix and its some similar matrices. With the smallest set, a new estimation for all eigenvalues of the matrix is obtained.

• KSBB Journal
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• v.10 no.2
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• pp.166-169
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• 1995

Spores of Trichoderma harzianum TCC 52445 for control of Rhlzocronia stem canker on potato were immobilized in various natural matrix, and germination rate and some rheological properties of the spore-matrix complex were Investigated. Germination rate of gelatin gel-spore complex and potato starch gel-spore complex were 2.8% and 2.9%, respectively, but hardness and cohesiveness of the gelstin gel-spoke complex were better than those of potato starch-spore complex. The hardness and cohesiveness were increased when the spores were immobilized in hybrid gelatin gel made by mixing several different types of natural matrix, but decreased their germination rate. Addition of corn steep liquor (1%) as spore nutrient in gelatin gel-spore complex was helpful for increasing the germination rate.

• East Asian mathematical journal
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• v.29 no.3
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• pp.327-335
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• 2013

In this paper we consider the quadratic matrix equation which can be defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown complex matrix, and A, B and C are $n{\times}n$ given matrices with complex elements. We first introduce a couple of condition numbers of the equation Q(X) and present normwise condition numbers. Finally, we compare the results and some numerical experiments are given.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.125-131
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• 2021

In the paper, we investigate the representation of the numerical range W(An) for the 2 × 2 complex matrix A, in terms of the numerical range W(A) of the matrix A, and the elements of A or the eigenvalue of A.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.8
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• pp.1586-1591
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• 2011

This paper considers synchronization problem of a complex dynamical network. For the problem, the virtual target node is chosen as one of nodes in the complex network and only one connection is needed between an isolate target node and virtual target node not any more connections. Moreover, our synchronization scheme does not need additional conditions and information of coupling matrix comparing with existing works. Based on Lyapunov stability theory, a design criterion for a novel adaptive feedback controller for the synchronization between the isolate target node and another nodes of the complex network is proposed. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our results.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.485-495
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• 2011

Let $A_1$ and $A_2$ be $n{\times}n$ nonzero complex matrices, denote a linear combination of the two matrices by $A=c_1A_1+c_2A_2$, where $c_1$, $c_2$ are nonzero complex numbers. In this paper, we research the problem of the linear combinations in the general case. We give a sufficient and necessary condition for A is an involutive matrix and s+1-potent matrix, respectively, where $A_1$ is a tripotent matrix, with $A_1A_2=A_2A_1$. Then, using the results, we also give the sufficient and necessary conditions for the involutory of the linear combination A, where $A_1$ is a tripotent matrix, anti-idempotent matrix, and involutive matrix, respectively, and $A_2$ is a tripotent matrix, idempotent matrix, and involutive matrix, respectively, with $A_1A_2=A_2A_1$.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.29A no.11
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• pp.14-18
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• 1992

A gradient matrix method in conjunction with the transmission-reflection method to determine the complex permittivity and permeability of a microwave material is presented. This method does not incur the phase ambiguity due to an improper sample length, and is applicable to the measurement of low-loss materials of a half wavelength. A gradient matrix for a coaxial cable sample is derived, and the results are illustrated.