• Korean Journal of Mathematics
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• 제27권2호
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• pp.487-503
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• 2019

In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper.

• 대한수학회보
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• 제44권2호
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• pp.281-290
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• 2007

We deal with Bergman functions defined on the half-plane. We study integral operators, and some relationship between Berezin transforms and Toeplitz operators, and also show that some Berezin transforms are Mobius invariant.

• 대한수학회논문집
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• 제31권4호
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• pp.779-790
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• 2016

Using the extended generalized integral transform given by Luo et al. [6], we introduce some new generalized integral transforms to investigate such their (potentially) useful properties as inversion formulas and Parseval-Goldstein type relations. Classical integral transforms including (for example) Laplace, Stieltjes, and Widder-Potential transforms are seen to follow as special cases of the newly-introduced integral transforms.

• 충청수학회지
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• 제21권2호
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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 ${\mathbb{E}}_0$.

• 대한수학회논문집
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• 제31권4호
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• pp.791-809
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• 2016

By introducing two fractional convolutions, we obtain the convolution theorems for fractional Fourier cosine and sine transforms. Applying these convolutions, we construct two Boehmian spaces and then we extend the fractional Fourier cosine and sine transforms from these Boehmian spaces into another Boehmian space with desired properties.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2005년도 추계학술대회
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• pp.171-176
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• 2005

An infinite dam with compound Poisson inputs and a state-dependent release rate is considered. We build the Kolmogorov's backward differential equation and solve it to obtain the Laplace transforms of the first exit times for this dam.

• 충청수학회지
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• 제29권1호
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• pp.123-135
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• 2016

In this article, we introduce the transforms of Pythagorean and quadratic means of weighted shifts. We then explore how the transforms of weighted shifts behaves, in comparison with the Aluthge transform.

• 호남수학학술지
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• 제35권1호
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• pp.51-71
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• 2013

In the present paper, we evaluate the analytic conditional Fourier-Feynman transforms and convolution products of unbounded function which is the product of the cylinder function and the function in a Banach algebra which is defined on an analogue o Wiener space and useful in the Feynman integration theories and quantum mechanics. We then investigate the inverse transforms of the function with their relationships and finally prove that th analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the product of the conditional Fourier-Feynman transforms of each function.

• 대한수학회논문집
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• 제31권3호
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• pp.591-601
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• 2016

Integral transforms and fractional integral formulas involving well-known special functions are interesting in themselves and play important roles in their diverse applications. A large number of integral transforms and fractional integral formulas have been established by many authors. In this paper, we aim at establishing some (presumably) new integral transforms and fractional integral formulas for the generalized hypergeometric type function which has recently been introduced by Luo et al. [9]. Some interesting special cases of our main results are also considered.

• 한국정보통신학회논문지
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• 제16권6호
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• pp.1273-1278
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• 2012

본 논문에서는 무손실 영상 압축에서 쓰이는 변형된 정수 변환들을 설명하고 이를 2차원으로 확장한 것에 대한 성능 분석을 제시한다. 변형된 정수 변환들은 2차원으로 확장하는 방법에 따라서 그 성능 및 복잡도가 다른 면이 있다. 따라서 본 논문에서는 분리 가능한 형태로 확장한 변형 H.264 정수 변환 및 리프팅 구조를 이용한 가역 정수 변환과 분리 가능하지 않은 형태로 확장한 JPEG XR의 PCT변환에 대한 성능 및 복잡도를 비교 분석하여 제시하고, 이에 관련된 실험 결과를 제공한다. 실험 결과는 리프팅 구조를 이용하여 변형된 가역 정수 변환을 분리 가능한 형태로 확장하는 방법이 압축 효율면에서 가장 우수함을 보여준다.