• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.2351-2354
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• 2003

A new transform coder for arbitrarily shaped image segments is proposed. In the encoder, a block-based DCT is applied to the resulting image block after shifting pixels within the image segment to block border and padding the mean value of the pixels to empty region. For reducing the transmission bit rate, the transform coefficients located in padded region are truncated and only the remaining transform coefficients are transmitted to the decoder. In the decoder, the transform coefficients truncated in the encoder are recovered using received transform coefficients and a block-based inverse DCT is performed.

• 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.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.545-563
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• 2000

An integral transform with the Bessel function Jv(z) in the kernel is considered. The transform is relatd to a singular Sturm-Liouville problem on a half line. This relation yields a Plancherel's theorem for the transform. A Paley-Wiener-type theorem for the transform is also derived.

• 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.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.827-832
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• 2013

In this paper we apply the Catalan transform to the ${\kappa}$-Fibonacci sequence finding different integer sequences, some of which are indexed in OEIS and others not. After we apply the Hankel transform to the Catalan transform of the ${\kappa}$-Fibonacci sequence and obtain an unusual property.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.521-535
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• 2022

In this paper, we introduce the k-Hankel-Wigner transform on R in some problems of time-frequency analysis. As a first point, we present some harmonic analysis results such as Plancherel's, Parseval's and an inversion formulas for this transform. Next, we prove a Heisenberg's uncertainty principle and a Calderón's reproducing formula for this transform. We conclude this paper by studying an extremal function for this transform.

• 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.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.65-76
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• 2024

In this paper, the I-transform of the Mellin convolution type is presented. Based on the Mellin transform theory, a general integral transform of the Mellin convolution type is introduced. The generating operators for I-transform together with the corresponding operational relations are also presented.

• JSTS:Journal of Semiconductor Technology and Science
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• v.12 no.2
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• pp.175-185
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• 2012

Predictive watershed transform is a popular object segmentation algorithm which achieves a speed-up by identifying image regions that are different from the previous frame and performing object segmentation only for those regions. However, incorrect segmentation is often generated by the predictive watershed transform which uses only local information in merge-split decision on boundary regions. This paper improves the predictive watershed transform to increase the accuracy of segmentation results by using the additional information about the root of boundary regions. Furthermore, the proposed algorithm is processed in a block-based manner such that an image frame is decomposed into blocks and each block is processed independently of the other blocks. The block-based approach makes it easy to implement the algorithm in hardware and also permits an extension for parallel execution. Experimental results show that the proposed watershed transform produces more accurate segmentation results than the predictive watershed transform.