• Journal of the Korean Professional Engineers Association
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• v.22 no.2
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• pp.19-25
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• 1989

Utilizing a cosine transform in image compression has several recognized performance benefits, resulting in the ability to attain large compression ratio with small quality loss. Also, various models incorporating Human Visual System (HVS) to Discrete Cosine Trans-form (DCT) scheme are considered. Using the exact frequency components of DCT basis function, the optimum modulation transfer function (MTF) is obtained analytically. The errors at a block boundary which is important factor in transform coder are criteria for error measurement. The HVS weight coding results in perceptually higher quality images compared with the unweighted scheme.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.471-480
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• 2005

This paper deals with some useful methods of solving the one-dimensional integral equation of Fredholm type. Application of the reduction techniques with a view to inverting a class of integral equation with Lauricella function in the kernel, Riemann-Liouville fractional integral operators as well as Weyl operators have been made to reduce to this class to generalized Stieltjes transform and inversion of which yields solution of the integral equation. Use of Mellin transform technique has also been made to solve the Fredholm integral equation pertaining to certain polynomials and H-functions.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1221-1235
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• 2023

In this paper, we use an infinite dimensional conditioning function to define a conditional Fourier-Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functions which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.

• The Pure and Applied Mathematics
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• v.30 no.2
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• pp.155-167
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• 2023

In this paper, we use a vector-valued conditioning function to define a conditional Fourier-Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functionals which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.151.1-151
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• 2001

This paper establishes some integral equalities formulated by zeros located in the convergence region of Laplace transformable function. Using the definition of Laplace transform, it is shown that time-domain integral equalities have to be satisfied by the function, and those can be applied to understanding of the fundamental limitations of the control system represented by the transfer function, which has been Laplace transform. In the unity-feedback control scheme, another integral equality is also derived on the output response of the system with open-loop poles and zeros located in the convergence region.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.505-519
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• 2018

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.597-605
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• 2020

In this article, we discuss the global uniqueness problem for the Radon transform. It is not sufficient for the global uniqueness for the Radon transform to assume that the Radon transform Rf for a function f absolutely converges on any hyperplane. It is also known that it is sufficient to assume that f ∈ L¹ for the global uniqueness to hold. There exists a big gap between the above two conditions, to fill which is our purpose in this paper. We shall give a better sufficient condition for the global uniqueness of the Radon transform.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.273-289
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• 2011

In this paper we dene the concept of a conditional generalized Fourier-Feynman transform on very general function space $C_{a,b}$[0, T]. We then establish the existence of the conditional generalized Fourier-Feynman transform for functionals in a Fresnel type class. We also obtain several results involving the conditional transform. Finally we present functionals to apply our results. The functionals arise naturally in Feynman integration theories and quantum mechanics.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.425-435
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• 2023

The classical Hardy Theorem on R states that a function f and its Fourier transform cannot be simultaneously very small; this fact was generalized by Miyachi in terms of L¹ + L^∞ and log⁺-functions. In this paper, we consider the k-Hankel transform, which is a deformation of the Hankel transform by a parameter k > 0 arising from Dunkl's theory. We study Miyachi's theorem for the k-Hankel transform on ℝ^d.

• Proceedings of the KSRS Conference
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• 2008.10a
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• pp.169-172
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• 2008

Land-use or land-cover classification of satellite images is one of the important tasks in remote sensing application and many researchers have been tried to enhance classification accuracy. Previous studies show that the classification technique based on wavelet transform is more effective than that of traditional techniques based on original pixel values, especially in complicated imagery. Various wavelets can be used in wavelet transform. Wavelets are used as basis functions in representing other functions, like sinusoidal function in Fourier analysis. In these days, some basis functions such as Haar, Daubechies, Coiflets and Symlets are mainly used in 2D image processing. Selecting adequate wavelet is very important because different results could be obtained according to the type of basis function in classification. However, it is not easy to choose the basis function which is effective to improve classification accuracy. In this study, we computed the wavelet coefficients of satellite image using 10 different basis functions, and then classified test image. After evaluating classification results, we tried to ascertain which basis function is the most effective for image classification. We also tried to see if the optimum basis function is decided by energy parameter before classifying the image using all basis function. The energy parameter of signal is the sum of the squares of wavelet coefficients. The energy parameter is calculated by sub-bands after the wavelet decomposition and the energy parameter of each sub-band can be a favorable feature of texture. The decision of optimum basis function using energy parameter in the wavelet based image classification is expected to be helpful for saving time and improving classification accuracy effectively.