• East Asian mathematical journal
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• v.29 no.5
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• pp.467-479
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• 2013

We develop a Fourier-Feynman theory for Fourier-type functionals ${\Delta}^kF$ and $\widehat{{\Delta}^kF}$ on Wiener space. We show that Fourier-Feynman transform and convolution of Fourier-type functionals exist. We also show that the Fourier-Feynman transform of the convolution product of Fourier-type functionals is a product of Fourier-Feynman transforms of each functionals.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.231-246
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• 2008

In this paper, we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish several integration formulas for generalized analytic Feynman integrals generalized analytic Fourier-Feynman transforms and generalized integral transforms of functionals in the class of functionals ${\mathbb{E}}_0$. Finally, we use these integration formulas to obtain several generalized Feynman integrals involving the generalized analytic Fourier-Feynman transform and the generalized integral transform of functionals in ${\mathbb{E}}_0$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.8
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• pp.1715-1721
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• 1997

Wavelet transform is not applicable to arbitrarily-shaped region (or object) in images, due to the nature of its global decomposition. In this paper, the arbitrarily-shaped wavelet transform(ASWT) is proposed in order to solve this problem and its properties are investigated. Computation complexity of the ASWT is also examined and it is shown that the ASWT requires significantly fewer computations than conventional wavelet transform, since the ASWT processes only the object region in the original image. Experimental resutls show that any arbitrarily-shaped image segment can be decomposed using the ASWT and perfectly reconstructed using the inverse ASWT.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.4
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• pp.715-717
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• 2008

The connectivity weighted Hough transform is a useful method for detecting well-connected short lines without generating false lines yet requires extensive computation. This letter describes a method that reduces the computation of the connectivity weighted Hough transform by removing unnecessary weight calculations using the gradient angles of feature points. In simulations with synthetic images and experiments with liquid crystal display panel images, the proposed method showed significantly improved speed without compromising detectability.

• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.369-382
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• 2009

In this paper we establish various relationships among the generalized integral transform, the generalized convolution product and the first variation for functionals in a Banach algebra S($L_{a,b}^2$[0, T]) introduced by Chang and Skoug in [14]. We then derive an inverse integral transform and obtain several relationships involving inverse integral transforms.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05a
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• pp.282-287
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• 1996

We. develop in this study a wavelet transform method to apply to the flux reconstruction problem in reactor analysis. When we reconstruct pinwise heterogeneous flux by iterative methods, a difficulty arises due to the near singularity of the matrix as the mesh size becomes finer. Here we suggest a wavelet transform to tower the spectral radius of the near singular matrix and thus to converge by a standard iterative scheme. We find that the spectral radios becomes smatter than one after the wavelet transform is performed on sample problems.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.119-142
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• 2021

In this paper, we first introduce a new L_p analytic Fourier-Feynman transform with respect to subordinate Brownian motion (AFFTSB), which extends the Fourier-Feynman transform in the Wiener space. We next examine several relationships involving the L_p-AFFTSB, the convolution product, and the gradient operator for several types of functionals.

• Journal of the Semiconductor & Display Technology
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• v.19 no.4
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• pp.77-83
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• 2020

The Linear system analysis for physical system is very powerful tool for system diagnostic utilizing relationship between the input signal and output signal. This method utilized generally to investigate physical properties of system and the nondestructive test by ultrasonic signals. This method can be explained by linear system theory. In this paper the Continuous Wavelets Transform is utilized to search the relation between the linear system and continuous wavelets transform.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.521-536
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• 2023

This paper is a further development of the recent results by the author and coworker on the generalized sequential Fourier-Feynman transform for functionals in a Banach algebra Ŝ and some related functionals. We establish existence of the generalized first variation of these functionals. Also we investigate various relationships between the generalized sequential Fourier-Feynman transform, the generalized sequential convolution product and the generalized first variation of the functionals.

• The KIPS Transactions:PartD
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• v.13D no.4 s.107
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• pp.513-524
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• 2006

Normalization transform is very useful for finding the overall trend of the time-series data since it enables finding sequences with similar fluctuation patterns. The previous subsequence matching method with normalization transform, however, would incur index overhead both in storage space and in update maintenance since it should build multiple indexes for supporting arbitrary length of query sequences. To solve this problem, we propose a single index approach for the normalization transformed subsequence matching that supports arbitrary length of query sequences. For the single index approach, we first provide the notion of inclusion-normalization transform by generalizing the original definition of normalization transform. The inclusion-normalization transform normalizes a window by using the mean and the standard deviation of a subsequence that includes the window. Next, we formally prove correctness of the proposed method that uses the inclusion-normalization transform for the normalization transformed subsequence matching. We then propose subsequence matching and index building algorithms to implement the proposed method. Experimental results for real stock data show that our method improves performance by up to $2.5{\sim}2.8$ times over the previous method. Our approach has an additional advantage of being generalized to support many sorts of other transforms as well as normalization transform. Therefore, we believe our work will be widely used in many sorts of transform-based subsequence matching methods.