• Journal of the Korea Institute of Information Security & Cryptology
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• v.17 no.3
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• pp.3-15
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• 2007

In this paper, we propose a simple scheme which produces a new S-box from a given S-box. We use well-known conversion technique between the polynomial functions over a finite field $F_{2^n}$ and the boolean functions from $F_2^n$ to $F_2$. We have applied this scheme to Rijndael S-box and obtained 29 new S-boxes, whose linear complexities are improved. We investigate their cryptographic properties via transform domain analysis.

• 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.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.693-722
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• 2016

In this paper, we characterize the support for the Dunkl transform on the generalized Lebesgue spaces via the Dunkl resolvent function. The behavior of the sequence of $L^p_k$-norms of iterated Dunkl potentials is studied depending on the support of their Dunkl transform. We systematically develop real Paley-Wiener theory for the Dunkl transform on ${\mathbb{R}}^d$ for distributions, in an elementary treatment based on the inversion theorem. Next, we improve the Roe's theorem associated to the Dunkl operators.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.129-151
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• 2015

In this paper, we prove an $L^p$ version of Donoho-Stark's uncertainty principle for the inverse of the hypergeometric Fourier transform on $\mathbb{R}^d$. Next, using the ultracontractive properties of the semigroups generated by the Heckman-Opdam Laplacian operator, we obtain an $L^p$ Heisenberg-Pauli-Weyl uncertainty principle for the inverse of the hypergeometric Fourier transform on $\mathbb{R}^d$.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.39-57
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• 2003

Some inequalities for the Hilbert transform of the product of two functions are given.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.555-560
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• 2012

In this paper, differential transform method (DTM) is considered to obtain solution to the generalized Fisher's equation. This method is easy to apply and because of high level of accuracy can be used to solve other linear and nonlinear problems. Furthermore, is capable of reducing the size of computational work. In the present work, the generalization of the two-dimensional transform method that is based on generalized Taylor's formula is applied to solve the generalized Fisher equation and numerical example demonstrates the accuracy of the present method.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1607-1619
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• 2015

We investigate some generalization of a class of Hankel-Clifford transformations having Fox H-function as part of its kernel on a class of Boehmians. The generalized transform is a one-to-one and onto mapping compatible with the classical transform. The inverse Hankel-Clifford transforms are also considered in the sense of Boehmians.

• Proceedings of the IEEK Conference
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• 2000.06c
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• pp.23-26
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• 2000

In this paper, to perform iris recognition, the iris is changed to 1-D iris signature and methods of efficient iris pattern transformation are discussed. To represent iris signature's frequency characteristics, Fourier transform, Gabor filtering, and wavelet transform are proposed. The consistency between same person's iris and the discrimination between different person's iris are defined by using correlation. Based on these, three transform methods are compared and analyzed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.1
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• pp.31-40
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• 2004

In this paper we point out an approximation for the Fourier transform for functions of bounded variation and study the approximation error of certain associated quadrature rules.

• International Journal of Reliability and Applications
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• v.3 no.4
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• pp.199-202
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• 2002

In this paper, we obtain an explicit formula of the Laplace transform of the forward recurrence time at finite time t > 0 in an alternating renewal process, by adopting a Markovian approach. As a consequence, we obtain the first two moments of the forward recurrence time.