• Honam Mathematical Journal
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• v.30 no.2
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• pp.343-358
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• 2008

The primitive orders in a quaternion algebra play a central role of the theory of Hecke operators. In this paper, we study theta series generated by Brandt matrices and its applications to almost Ramanujan graphs.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.3
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• pp.25-33
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• 2015

As a reversible Jacket is having the compatibility of two sided wearing, the matrix that both the inside and the outside are compatible is called Jacket matrix, and the matrix is having both inside and outside by the processes of element-wise inverse and block-wise inverse. This concept had been completed by one of the authors Moon Ho Lee in 1989, and finally that resultant matrix has been christened as Jacket matrix, in 2000. This is the most generalized extension of the well known Hadamard matrices, which includes both orthogonal and non-orthogonal matrices. This matrix addresses many problems in information and communication theories. we investigate the properties of the Jacket matrix, i.e. determinants, eigenvalues, and kronecker product. These computations are very useful for signal processing and orthogonal codes design. In our proposal, we provide some results to calculate these values by using a very simple mathematical model with less complexity.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.1
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• pp.717-724
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• 2016

This paper proposes a change detection method based on the covariance matrices of color and edge gradient in a color video. The YCbCr color format was used instead of RGB. The color covariance matrix was calculated from the CbCr-channels and the edge gradient covariance matrix was calculated from the Y-channels. The covariance matrices were effectively calculated at each pixel by calculating the sum, squared sum, and sum of two values' multiplication of a rectangle area using the integral images from a background image. The background image was updated by a running the average between the background image and a current frame. The change areas in a current frame image against the background were detected using the Mahalanobis distance, which is a measure of the statistical distance using covariance matrices. The experimental results of an expressway color video showed that the proposed approach can effectively detect change regions for color and edge gradients against the background.

• Steel and Composite Structures
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• v.51 no.5
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• pp.473-485
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• 2024

This paper proposes a composite form of fuzzy adaptive control plan based on a robust observer. The fuzzy 2D control gains are regulated by the parameters in the LMIs. Then, control and learning performance indices with weight matrices are constructed as the cost functions, which allows the regulation of the trade-off between the two performance by setting appropriate weight matrices. The design of 2D control gains is equivalent to the LMIs-constrained multi-objective optimization problem under dual performance indices. By using this proposed smart tracking design via fuzzy nonlinear criterion, the data link can be further extended. To evaluate the performance of the controller, the proposed controller was compared with other control technologies. This ensures the execution of the control program used to track position and trajectory in the presence of great model uncertainty and external disturbances. The performance of monitoring and control is verified by quantitative analysis. The goals of this paper are towards access to adequate, safe and affordable housing and basic services, promotion of inclusive and sustainable urbanization and participation, implementation of sustainable and disaster-resilient buildings, sustainable human settlement planning and manage. Therefore, the goal is believed to achieved in the near future by the ongoing development of AI and control theory.

• IEIE Transactions on Smart Processing and Computing
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• v.6 no.2
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• pp.117-123
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• 2017

N-continuous orthogonal frequency division multiplexing (OFDM) is a precoding method for sidelobe suppression of OFDM signals and seamlessly connects OFDM symbols up to the high-order derivative for sidelobe suppression, which is suitable for suppressing out-of-band radiation. However, it severely degrades the error rate as it increases the continuous derivative order. Two schemes for orthogonal precoding of N-continuous OFDM have been proposed to achieve an ideal error rate while maintaining sidelobe suppression performance; however, the large size of the precoder matrices in both schemes causes very high computational complexity for precoding and decoding. This paper proposes matrix decomposition of precoder matrices with a large size in the orthogonal precoding schemes in order to reduce computational complexity. Numerical experiments show that the proposed method can drastically reduce computational complexity without any performance degradation.

• Structural Engineering and Mechanics
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• v.36 no.1
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• pp.37-55
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• 2010

For large-scale structures, the calculation of the eigensolution and the eigensensitivity is usually very time-consuming. This paper develops the Kron's substructuring method to compute the first-order derivatives of the eigenvalues and eigenvectors with respect to the structural parameters. The global structure is divided into several substructures. The eigensensitivity of the substructures are calculated via the conventional manner, and then assembled into the eigensensitivity of the global structure by performing some constraints on the derivative matrices of the substructures. With the proposed substructuring method, the eigenvalue and eigenvector derivatives with respect to an elemental parameter are computed within the substructure solely which contains the element, while the derivative matrices of all other substructures with respect to the parameter are zero. Consequently this can reduce the computation cost significantly. The proposed substructuring method is applied to the GARTEUR AG-11 frame and a highway bridge, which is proved to be computationally efficient and accurate for calculation of the eigensensitivity. The influence of the master modes and the division formations are also discussed.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.5
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• pp.39-49
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• 2015

Some characters and construction theorems of Pseudo Jacket Matrix which is generalized from Jacket Matrix introduced by Jacket Matrices: Construction and Its Application for Fast Cooperative Wireless signal Processing[27] was announced. In this paper, we proposed some examples of Pseudo inverse Jacket matrix, such as $2{\times}4$, $3{\times}6$ non-square matrix for the MIMO channel. Furthermore we derived MIMO singular value decomposition (SVD) pseudo inverse channel and developed application to utilize SVD based on channel estimation of partitioned antenna arrays. This can be also used in MIMO channel and eigen value decomposition (EVD).

• The Journal of Engineering Research
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• v.3 no.1
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• pp.85-95
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• 1998

In this study, we consider a recursive procedure to obtain the stationary probability distribution for analyzing Coxian queueing networks with finite queues. This network deals with multiple class customers. Due to the state space representing multiple class customers, the sub-matrices corresponding to states can not be square matrices and can not be inverted. Therefore, we introduce more complex recursive method to avoid the singular problem. The open queueing network that we study consists of 3 parallel first-level sources linked to a single second level queue. We consider two types of schemes for entering a queue. The first scheme is assumed to be the first-blocked-first-enter (FBFE) and the second scheme is the higher-priority-first-enter (HPFE). Arrival and service times are assume to have a Coxian distribution with two phases. Comparison between the resulting using Gauss-Seidel method and recursive procedure will be shown.

• Korean Journal of Food Science and Technology
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• v.53 no.5
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• pp.527-534
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• 2021

The demand for sustainable extraction of bioactive compounds from food matrices has been increasing. Water extraction of anthocyanins in aronia was investigated using conventional and ultrasonic-assisted methods. The optimum extraction conditions for the conventional method included a sample-to-water ratio of 1:40 g/mL, extraction temperature 71℃, and extraction time of 39 min. The optimized conditions for ultrasonic-assisted extraction were a sample-to-water ratio of 1:40 g/mL, extraction temperature 80℃, extraction time of 20 min, and an amplitude of 87.2 ㎛. The anthocyanin contents of the two extracts were 155.32 and 158.02 mg/100 g fresh weight, respectively. The major anthocyanins were cyanidin 3-galactoside (65% of the total) and cyanidin 3-arabinoside (30% of the total). The contents of individual anthocyanins and phenolic acids were not significantly different between the two optimized extracts.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.345-353
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• 2023

Reduced solutions of size 2 and degree n of the Tarry-Escott problem over M₂(ℚ) are determined. As an application, the diophantine equation αAⁿ + βBⁿ = αCⁿ + βDⁿ, where α, β are rational numbers satisfying α + β ≠ 0 and n ∈ {1, 2}, is completely solved for A, B, C, D ∈ M₂(ℚ).