• 전자공학회논문지B
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• 제29B권3호
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• pp.16-24
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• 1992

In this paper, we solve the problem of designing a robust optimal controller which minimizes the H$\infty$-norm of the mixed sensitivity function matrix for linear multivariable systems. For a given minimized value, ${\gamma}$>o, an algorithm of finding all stabilizing controllers, such that the H$\infty$-norm of the mixed sensitivity function matrix is less than ${\gamma}$, is developed. The proposed algorithm, which is based on the model-matching and the interpolation theory, can be used for the H$\infty$-optimization problem.

• 대한수학회논문집
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• 제18권4호
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• pp.653-659
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• 2003

Let $1{\;}\leq{\;}p{\;}\infty{\;}and{\;}{\alpha}{\;}>{\;}-1$. If f is a holomorphic self-map of the open unit disc U of C with f(0) = 0, then the quantity $\int_U\;\{\frac{$\mid$f'(z)$\mid$}{1\;-\;$\mid$f(z)$\mid$^2}\}^p\;(1\;-\;$\mid$z$\mid$)^{\alpha+p}dxdy$ is equivalent to the operator norm of the composition operator $C_f{\;}:{\;}B{\;}\rightarrow{\;}A^{p,{\alpha}$ defined by $C_fh{\;}={\;}h{\;}\circ{\;}f{\;}-{\;}h(0)$, where B and $A^{p,{\alpha}$ are the Bloch space and the weighted Bergman space on U respectively.

• 한국방사성폐기물학회:학술대회논문집
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• 한국방사성폐기물학회 2018년도 추계학술논문요약집
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• pp.525-526
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• 2018

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.605-614
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• 2008

In this paper, we find the matrix representation of multi-degree reduction by $L_{\infty}$ of $B{\acute{e}}zier$ curves with constraints of endpoints continuity. Using the basis transformation between Chebyshev polynomials and Bernstein polynomials we can derive the matrix representation of multi-degree reduction of $B{\acute{e}}zier$ with respect to $L_{\infty}$ norm.

• Fisheries and Aquatic Sciences
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• 제19권4호
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• pp.21.1-21.11
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• 2016

Background: The evaluation of suitable reference genes as normalization controls is a prerequisite requirement for launching quantitative reverse transcription-PCR (RT-qPCR)-based expression study. In order to select the stable reference genes in abalone Haliotis discus hannai tissues (gill and hepatopancreas) under heavy metal exposure conditions (Cu, Zn, and Cd), 12 potential candidate housekeeping genes were subjected to expression stability based on the comprehensive ranking while integrating four different statistical algorithms (geNorm, NormFinder, BestKeeper, and ${\Delta}CT$ method). Results: Expression stability in the gill subset was determined as RPL7 > RPL8 > ACTB > RPL3 > PPIB > RPL7A > EF1A > RPL4 > GAPDH > RPL5 > UBE2 > B-TU. On the other hand, the ranking in the subset for hepatopancreas was RPL7 > RPL3 > RPL8 > ACTB > RPL4 > EF1A > RPL5 > RPL7A > B-TU > UBE2 > PPIB > GAPDH. The pairwise variation assessed by the geNorm program indicates that two reference genes could be sufficient for accurate normalization in both gill and hepatopancreas subsets. Overall, both gill and hepatopancreas subsets recommended ribosomal protein genes (particularly RPL7) as stable references, whereas traditional housekeepers such as ${\beta}-tubulin$ (B-TU) and glyceraldehyde-3-phosphate dehydrogenase (GAPDH) genes were ranked as unstable genes. The validation of reference gene selection was confirmed with the quantitative assay of MT transcripts. Conclusions: The present analysis showed the importance of validating reference genes with multiple algorithmic approaches to select genes that are truly stable. Our results indicate that expression stability of a given reference gene could not always have consensus across tissue types. The data from this study could be a good guide for the future design of RT-qPCR studies with respect to metal regulation/detoxification and other related physiologies in this abalone species.

• Asian-Australasian Journal of Animal Sciences
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• 제27권4호
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• pp.471-478
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• 2014

Investigating gene expression of immune cells of whole blood or peripheral blood mononuclear cells (PBMC) under polyinosinic:polycytidylic acid (poly I:C) stimulation is valuable for understanding the immune response of organism to RNA viruses. Quantitative real-time PCR (qRT-PCR) is a standard method for quantification of gene expression studies. However, the reliability of qRT-PCR data critically depends on proper selection of reference genes. In the study, using two different analysis programs, geNorm and NormFinder, we systematically evaluated the gene expression stability of six candidate reference genes (GAPDH, ACTB, B2M, RPL4, TBP, and PPIA) in samples of whole blood and PBMC with or without poly I:C stimulation. Generally, the six candidate genes performed a similar trend of expression stability in the samples of whole blood and PBMC, but more stably expressed in whole blood than in PBMC. geNorm ranked B2M and PPIA as the best combination for gene expression normalization, while according to NormFinder, TBP was ranked as the most stable reference gene, followed by B2M and PPIA. Comprehensively considering the results from the two programs, we recommended using the geometric mean of the three genes, TBP, PPIA and B2M, to normalize the gene expression of whole blood and PBMC with poly I:C stimulation. Our study is the first detailed survey of the gene expression stability in whole blood and PBMC with or without poly I:C stimulation and should be helpful for investigating the molecular mechanism involved in porcine whole blood and PBMC in response to poly I:C stimulation.

• 지구물리와물리탐사
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• 제9권1호
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• pp.44-49
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• 2006

이 연구에서는 $CO_2$ 주입 모니터링에서의 전기비저항 토모그래피(ERT)의 분해능에 대해 조사한다. $CO_2$ 주입체 양쪽의 케이싱 없는 시추공에서 단극자 및 양극자 전극 배열이 사용된다. 주입 전 및 주입에 따른 3단계 모델에 대한 반응이 계산되고, 잡음이 더해진 후의 이론 값들이 L1 과 L2 norm을 사용해 역산된다. 역산결과는 어느 정도 수준이상의 $CO_2$ 부피가 확실히 감지됨을 보여준다. 대부분의 경우에 L1 norm의 경우가 L2에 비해 우월함이 판명되었다. 역산 결과를 주입 전 모델의 역산결과로 정규화하면 전기비저항이 변화하는 부분의 훌륭한 영상을 보여주며, 비저항의 전체적인 변화를 통합해서 판단하면 전체 주입된 부피에 대한 타당한 측정이 이루어짐이 입증된다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권2호
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• pp.107-121
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• 2016

We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and $Lov{\acute{a}}sz$ as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of $O(N^4{\log}B)$ multiplications (or, $O(N^5({\log}B)^2)$ bit operations) for a lattice basis matrix $H({\in}{\mathbb{R}}^{M{\times}N})$ where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm's complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.

• Kyungpook Mathematical Journal
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• 제54권2호
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• pp.189-195
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• 2014

Let X be a compact metric space, B be a unital commutative Banach algebra and ${\alpha}{\in}(0,1]$. In this paper, we first define the vector-valued (B-valued) ${\alpha}$-Lipschitz operator algebra $Lip_{\alpha}$ (X, B) and then study its structure and characterize of its maximal ideal space.

• ETRI Journal
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• 제36권1호
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• pp.42-50
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• 2014

Orthogonal frequency division multiplexing (OFDM) is a modulation technique that allows the transmission of high data rates over wideband radio channels subject to frequency selective fading by dividing the data into several narrowband and flat fading channels. OFDM has high spectral efficiency and channel robustness. However, a major drawback of OFDM is that the peak-to-average power ratio (PAPR) of the transmitted signals is high, which causes nonlinear distortion in the received data and reduces the efficiency of the high power amplifier in the transmitter. The most straightforward method to solve this problem is to use a nonlinear mapping algorithm to transform the signal into a new signal that has a smaller PAPR. One of the latest nonlinear methods proposed to reduce the PAPR is the $L_2$-by-3 algorithm, which is based on the discrete sliding norm transform. In this paper, a new algorithm based on the $L_2$-by-3 method is proposed. The proposed method is very simple and has a low complexity analysis. Simulation results show that the proposed method performs better, has better power spectral density, and is less sensitive to the modulation type and number of subcarriers than $L_2$-by-3.