• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.655-663
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• 2012

Based on the elegant properties of the spectral norm and Thompson metric, we firstly give two perturbation estimates for the positive definite solution of the nonlinear matrix equation $$X-\sum^m_{i=1}A^{\ast}_iX^{\delta_i}A_i=Q(0<|{\delta}_i|<1)$$ which arises in an optimal interpolation problem.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.593-605
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• 2015

In this study, we define r-circulant, circulant, Hankel and Toeplitz matrices involving the integer sequence with recurrence relation U_n = pU_n-1 + U_n-2, with U₀ = a, U₁ = b. Moreover, we obtain special norms of above mentioned matrices. The results presented in this paper are generalizations of some of the results of [1, 10, 11].

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.2343-2346
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• 2003

The spatial resolution of multispectral images can be improved by merging them with higher resolution image data. A fundamental problem frequently occurred in existing fusion processes, is the distortion of spectral information. This paper presents a spatially adaptive image fusion algorithm which produces visually natural images and retains the quality of local spectral information as well. High frequency information of the high resolution image to be inserted to the resampled multispectral images is controlled by adaptive gains to incorporate the difference of local spectral characteristics between the high and the low resolution images into the fusion. Each gain is estimated to minimize the l$_2$-norm of the error between the original and the estimated pixel values defined in a spatially adaptive window of which the weight are proportional to the spectral correlation measurements of the corresponding regions. This method is applied to a set of co-registered Landsat7 ETM＋ panchromatic and multispectral image data.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.583-590
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• 2021

In this work we give new upper and lower bounds for the numerical radius of a complex square matrix A using the entries and the trace of A.

• Journal of the Optical Society of Korea
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• v.20 no.6
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• pp.752-761
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• 2016

Hyperspectral images are often contaminated with stripe noise, which severely degrades the imaging quality and the precision of the subsequent processing. In this paper, a variational model is proposed by employing spectral-spatial adaptive unidirectional variation and a sparse representation. Unlike traditional methods, we exploit the spectral correction and remove stripes in different bands and different regions adaptively, instead of selecting parameters band by band. The regularization strength adapts to the spectrally varying stripe intensities and the spatially varying texture information. Spectral correlation is exploited via dictionary learning in the sparse representation framework to prevent spectral distortion. Moreover, the minimization problem, which contains two unsmooth and inseparable $l_1$-norm terms, is optimized by the split Bregman approach. Experimental results, on datasets from several imaging systems, demonstrate that the proposed method can remove stripe noise effectively and adaptively, as well as preserve original detail information.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.3
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• pp.813-829
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• 2022

In multi-view subspace clustering, how to integrate the complementary information between perspectives to construct a unified representation is a critical problem. In the existing works, the unified representation is usually constructed in the original data space. However, when the data representation in each view is very diverse, the unified representation derived directly in the original data domain may lead to a huge information loss. To address this issue, different to the existing works, inspired by the latest revelation that the data across all perspectives have a very similar or close spectral block structure, we try to construct the unified representation in the spectral embedding domain. In this way, the complementary information across all perspectives can be fused into a unified representation with little information loss, since the spectral block structure from all views shares high consistency. In addition, to capture the global structure of data on each view with high accuracy and robustness both, we propose a novel low-rank approximation via the tight lower bound on the rank function. Finally, experimental results prove that, the proposed method has the effectiveness and robustness at the same time, compared with the state-of-art approaches.

• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1503-1511
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• 2013

This paper deals with the analysis of leakage current characteristics of silicone rubber insulator in order to develop a new condition monitoring tool to identify the flashover of outdoor insulators. In this work, laboratory based pollution performance tests are carried out on silicone rubber insulator under ac voltage at different pollution levels and relative humidity conditions with sodium chloride (NaCl) as a contaminant. Min-Norm spectral analysis is adopted to calculate the higher order harmonics and Signal Noise Ratio (SNR). Choi-Williams Distribution (CWD) function is employed to understand the time frequency characteristics of the leakage current signal. Reported results on silicone rubber insulators show that the flashover development process of outdoor polymer insulators could be identified from the higher order harmonics and signal noise ratio values of leakage current signals.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1273-1283
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• 2019

In matrix analysis, the Wielandt-Mirsky conjecture states that $$dist({\sigma}(A),{\sigma}(B)){\leq}{\parallel}A-B{\parallel}$$ for any normal matrices $A,B{\in}{\mathbb{C}}^{n{\times}n}$ and any operator norm ${\parallel}{\cdot}{\parallel}$ on $C^{n{\times}n}$. Here dist(${\sigma}(A),{\sigma}(B)$) denotes the optimal matching distance between the spectra of the matrices A and B. It was proved by A. J. Holbrook (1992) that this conjecture is false in general. However it is true for the Frobenius distance and the Frobenius norm (the Hoffman-Wielandt inequality). The main aim of this paper is to study the Hoffman-Wielandt inequality and some weaker versions of the Wielandt-Mirsky conjecture for matrix polynomials.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.481-487
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• 1998

Let (equation omitted) denote the closure of the set (equation omitted) of dominant operators in the norm topology. We show that the Weyl spectrum of an operator T $\in$ (equation omitted) satisfies the spectral mapping theorem for analytic functions, which is an extension of [5, Theorem 1]. Also we show that an operator approximately equivalent to an operator of class (equation omitted) is of class (equation omitted).

• Honam Mathematical Journal
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• v.38 no.4
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• pp.725-738
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• 2016

In this paper, the explicit determinants of the circulant and negacyclic matrix involving Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$ are expressed by using only Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$. Also euclidean norms and spectral norms of circulant and negacyclic matrices have been obtained.