• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1555-1566
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• 2023

A Hilbert space operator A ∈ B(H) is a generalised n-projection, denoted A ∈ (G-n-P), if A^*n = A. (G-n-P)-operators A are normal operators with finitely countable spectra σ(A), subsets of the set $\{0\}\,{\cup}\,\{\sqrt[n+1]{1}\}.$ The Aluthge transform à of A ∈ B(H) may be (G - n - P) without A being (G - n - P). For doubly commuting operators A, B ∈ B(H) such that σ(AB) = σ(A)σ(B) and ${\parallel}A{\parallel}\,{\parallel}B{\parallel}\;{\leq}\;{\parallel}{\tilde{AB}}{\parallel},$ ${\tilde{AB}}\;{\in}\;(G\,-\,n\,-\,P)$ if and only if $A\;=\;{\parallel}{\tilde{A}}{\parallel}\,(A_{00}\,{\oplus}\,(A_0\,{\oplus}\,A_u))$ and $B\;=\;{\parallel}{\tilde{B}}{\parallel}\,(B_0\,{\oplus}\,B_u),$ where A₀₀ and B₀, and A₀ ⊕ A_u and B_u, doubly commute, A₀₀B₀ and A₀ are 2 nilpotent, A_u and B_u are unitaries, A^*n_u = A_u and B^*n_u = B_u. Furthermore, a necessary and sufficient condition for the operators αA, βB, αà and ${\beta}{\tilde{B}},\;{\alpha}\,=\,\frac{1}{{\parallel}{\tilde{A}}{\parallel}}$ and ${\beta}\,=\,\frac{1}{{\parallel}{\tilde{B}}{\parallel}},$ to be (G - n - P) is that A and B are spectrally normaloid at 0.

• Journal of Korea Society of Digital Industry and Information Management
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• v.7 no.4
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• pp.119-131
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• 2011

In this paper, we explore the application of 2-D dual-tree discrete wavelet transform (DDWT), which is a directional and redundant transform, for image coding. DDWT main property is a more computationally efficient approach to shift invariance. Also, the DDWT gives much better directional selectivity when filtering multidimensional signals. The dual-tree DWT of a signal is implemented using two critically-sampled DWTs in parallel on the same data. The transform is 2-times expansive because for an N-point signal it gives 2N DWT coefficients. If the filters are designed is a specific way, then the sub-band signals of the upper DWT can be interpreted as the real part of a complex wavelet transform, and sub-band signals of the lower DWT can be interpreted as the imaginary part. The quincunx lattice is a sampling method in image processing. It treats the different directions more homogeneously than the separable two dimensional schemes. Quincunx lattice yields a non separable 2D-wavelet transform, which is also symmetric in both horizontal and vertical direction. And non-separable wavelet transformation can generate sub-images of multiple degrees rotated versions. Therefore, non-separable image processing using DDWT services good performance.

• Earthquakes and Structures
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• v.16 no.2
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• pp.165-175
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• 2019

Incremental dynamic analysis (IDA), as an accurate method to evaluate the parameters of structural performance levels, requires many non-linear time history analyses, using a set of ground motion records which are scaled to different intensity levels. Therefore, this method is very computationally demanding. In this study, a new method is presented to estimate the summarized (16%, 50%, and 84% fractiles) IDA curves of a first-mode dominated structure using discrete wavelet transform and bees optimization algorithm. This method reduces the number of required ground motion records for the prediction of the summarized IDA curves. At first, a subset of first list ground motion records is decomposed by means of discrete wavelet transform which have a low dispersion estimating the summarized IDA curves of equivalent SDOF system of the main structure. Then, the bees algorithm optimizes a series of factors for each level of detail coefficients in discrete wavelet transform. The applied factors change the frequency content of original ground motion records which the generated ground motions records can be utilized to reliably estimate the summarized IDA curves of the main structure. At the end, to evaluate the efficiency of the proposed method, the seismic behavior of a typical 3-story special steel moment frame, subjected to a set of twenty ground motion records is compared with this method.

• Journal of Korea Society of Digital Industry and Information Management
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• v.10 no.3
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• pp.237-247
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• 2014

This paper describes a 2D discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the image signal to which it is applied. The tunable Q-factor wavelet transform (TQWT) is a fully-discrete wavelet transform for which the Q-factor, Q, of the underlying wavelet and the asymptotic redundancy (over-sampling rate), r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can be real-valued. Therefore, by tuning Q, the oscillatory behavior of the wavelet can be chosen to match the oscillatory behavior of the signal of interest, so as to enhance the sparsity of a sparse signal representation. The TQWT is well suited to fast algorithms for sparsity-based inverse problems because it is a Parseval frame, easily invertible, and can be efficiently implemented. The TQWT can also be used as an easily-invertible discrete approximation of the continuous wavelet transform. The transform is based on a real valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e. g. 3-4 times overcomplete) being sufficient for the analysis/synthesis functions to be well localized. Therefore, This method services good performance in image processing fields.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.12
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• pp.1236-1248
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• 1991

A new fast algorithm for computing the discrete cosine transform(DCT) Is developed decomposing N-point DCT into an N /2-point DCT and two N /4 point transforms(transpose of an N /4-point DCT. TN/t'and)It has an important characteristic that in this method, the roundoff noise power for a fixed point arithmetic can be reduced significantly with respect to the wellknown fast algorithms of Lee and Chen. since most coefficients for multiplication are distributed at the nodes close to the output and far from the input in the signal flow graph In addition, it also shows three other versions of factorization of DCT matrix with the same number of operations but with the different distributions of multiplication coefficients.

• Kyungpook Mathematical Journal
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• v.17 no.2
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• pp.211-214
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• 1977

• The KIPS Transactions:PartB
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• v.12B no.7 s.103
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• pp.729-736
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• 2005

In this paper. the proposed method for the digital watermarking is based on the multiresolution wavelet transform. The 1-level Discrete Wavelet Transform(DWT) coefficients of a $2N_{wx}{\times}2N_{wy}$ binary logo image used as a watermarks. The LL band and middle frequency band of the host image that the 3-level DWT has been performed are divided into $N_{wx}{\times}N_{wy}$ size and we use large coefficients at the divided blocks to make threshold. we set the thresholds that completely insert the watermark in each frequency of the host image. The thresholds in each frequency of the host image differ each other. The watermarks where is the same positions are added to the larger coefficients than threshold in the blocks at LL band and middle frequency band in order to prevent the quality deterioration of the host image. The watermarks are inserted in LL band and middle frequency band of the host image. In order to be invisibility of the watermark, the Human Visual System(HVS) is applied to the watermark. We prove the proper embedding method by experiment. We rapidly detect the watermark using this watermarking method. And because the small size watermarks are inserted by HVS, the results confirm the superiority of the proposed method on invisibility and robustness.

• The Journal of the Acoustical Society of Korea
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• v.15 no.4E
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• pp.53-57
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• 1996

An extension of the well-known Fourier transform is developed in this paper. It is denoted as the generalized Fourier transform(GFT), since it encompasses the Fourier transform as its special case. The first idea of this extension can be found on [1]. In the definition of the N-point discrete GFT, it first construct a passband in time which functions as a window in the time domain. An appropriate interpretation of each variables are introduced during the definition of the GFT, followed by the formal derivation of the inverse GFT. This transform pair is similar to the windowing in the frequency domain such as the subband coding technique (or filter bank approach) and could be extended to the wavelet transform.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.593-601
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• 2022

Let C(Q) denote Yeh-Wiener space, the space of all real-valued continuous functions x(s, t) on Q ≡ [0, S] × [0, T] with x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. For each partition τ = τ_m,n = {(s_i, t_j)|i = 1, . . . , m, j = 1, . . . , n} of Q with 0 = s₀ < s₁ < . . . < s_m = S and 0 = t₀ < t₁ < . . . < t_n = T, define a random vector X_τ : C(Q) → ℝ^mn by X_τ (x) = (x(s₁, t₁), . . . , x(s_m, t_n)). In this paper we study the conditional integral transform and the conditional convolution product for a class of cylinder type functionals defined on K(Q) with a given conditioning function X_τ above, where K(Q)is the space of all complex valued continuous functions of two variables on Q which satify x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. In particular we derive a useful equation which allows to calculate the conditional integral transform of the conditional convolution product without ever actually calculating convolution product or conditional convolution product.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.10a
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• pp.363-368
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• 1993

Hilbert Transform has been used for detection of nonlinearity in modal analysis. HTD(Hilbert Transform Describers) are used to quantify and identify nonlinearity. Mottershead and Stanway method for identification of N-th power velocity nonlinear damping are extended to P-th power displacement stiffness, N-th power velocity damping and dry friction. Time domain and frequency domain data are used and HTD and Mottershead methods are combined for identification of nonlinear parameters in this paper. Computer simulations and experimental results are shown to verify nonlinear structure identification methods.