• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.681-698
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• 2016

In this paper, we investigate relative essential spectra of $2{\times}2$ block operator matrix using the Fredholm perturbation theory. Furthermore, an example for two-group transport equations is presented to illustrate the validity of the main results.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1139-1150
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• 2009

We obtain necessary and sufficient conditions for $2{\tims}2$ block operator valued matrices to be Moore-Penrose (MP) invertible and give new representations of such MP inverses in terms of the individual blocks.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1351-1370
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• 2018

In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order ${\alpha}$ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.

• Transactions on Control, Automation and Systems Engineering
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• v.3 no.4
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• pp.242-249
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• 2001

In this paper, the open-loop state response of the two-time-scale systems by unified approach using the $\delta$-operator is presented with an example of the aircraft longitudinal dynamics. First, the $\delta$-operator system unifies both the continuous system and the discrete system simultaneously, and the $\delta$-operator approach improves the finite word-length characteristics. This saves more computing time than that of the discrete system. Second, the singular perturbation method by block diagonalization reduces the sizes and orders of the systems. This also reduces the floating-point operations (flops). The advantage of those two approaches is shown by comparing our results with the earlier ones in the illustrative example of the longitudinal motion of F-8 aircraft.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.237-252
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• 2014

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space $L^2_a(\mathbb{D},\mathbb{C}^n)$. We also show some necessary conditions for the hyponormality of $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.427-430
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• 1989

For on-line ARMA spectral estimation, the fast transversal filter algorithm of extended least squares method(ETS FTF) is presented. The projection operator, a key tool for geometric approach, is used in the derivation of the algorithm. ELS FTF is a fast time update recursion which is based on the fact that the correlation matrix of ARMA model satisfies the shift invariance property in each block, and thus it takes 10N+31 MADPR.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.831-843
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• 2010

Let $\cal{H}$ and $\cal{K}$ be Hilbert spaces and let T, $\tilde{T}$ = T + ${\delta}T$ be bounded operators from $\cal{H}$ into $\cal{K}$. In this article, two facts related to the perturbation bounds are studied. The first one is to find the upper bound of $\parallel\tilde{T}^+\;-\;T^+\parallel$ which extends the results obtained by the second author and enriches the perturbation theory for the Moore-Penrose inverse. The other one is to develop explicit representations of projectors $\parallel\tilde{T}\tilde{T}^+\;-\;TT^+\parallel$ and $\parallel\tilde{T}^+\tilde{T}\;-\;T^+T\parallel$. In addition, some spectral cases related to these results are analyzed.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.2
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• pp.329-334
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• 2014

This paper proposes the hardware architecture of high performance multi-mode 2D forward transform for HEVC which has same number of cycles for processing any type of four TUs and yield high throughput. In order to make the original image which has high pixel and high resolution into highly compressed image effectively, the transform technique of HEVC supports 4 kinds of pixel units, TUs and it finds the optimal mode after performs each transform computation. As the proposed transform engine uses the common computation operator which is produced by analyzing the relationship among transform matrix coefficients, it can process every 4 kinds of TU mode matrix operation with 35cycles equally. The proposed transform block was designed by Verilog HDL and synthesized by using TSMC 0.18um CMOS processing technology. From the results of logic synthesis, the maximum operating frequency was 400MHz and total gate count was 214k gates which has the throughput of 10-Gpels/cycle with the $4k(3840{\times}2160)@30fps$ image.

• The Transactions of the Korea Information Processing Society
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• v.2 no.6
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• pp.937-946
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• 1995

We proposed and efficient block segmentation and classification method for the document analysis using SGLDM(spatial gray level dependence matrix) and BP (back Propagation) neural network. Seven texture features are extracted directly from the SGLDM of each gray-level block image, and by using the nonlinear classifier of neural network BP, we can classify document blocks into 9 categories. The proposed method classifies the equation block, the table block and the flow chart block, which are mostly composed of the characters, out of the blocks that are conventionally classified as non-character blocks. By applying Sobel operator on the gray-level document image beforebinarization, we can reduce the effect of the background noises, and by using the additional horizontal-vertical smoothing as well as the vertical-horizontal smoothing of images, we can obtain an effective block segmentation that does not lead to the segmentation into small pieces. The result of experiment shows that a document can be segmented and classified into the character blocks of large fonts, small fonts, the character recognigible candidates of tables, flow charts, equations, and the non-character blocks of photos, figures, and graphs.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.3
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• pp.39-49
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• 2003

The delta operator approach and the singular perturbation technique are introduced. The former reduces the round-off error in the numerical computation. The latter reduces computing time by decoupling the original system into the fast and slow sub-systems. The aircraft dynamics consists of the Phugoid and short-period motions whether its model is longitudinal or lateral. In this paper, an approximated solutions of lateral dynamic model of Beaver obtained by using those two methods in compared with the exact solution. For open-loop system and closed-loop system, and approximated solution gets identical to the exact solution with only one iteration and without iteration, respectively. Therefore, it is shown that implementing those approaches is very effective in the flight dynamic and control.