• The Mathematical Education
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• v.25 no.1
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• pp.33-37
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• 1986

• The Mathematical Education
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• v.15 no.1
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• pp.22-26
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• 1976

• East Asian mathematical journal
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• v.7 no.2
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• pp.171-178
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• 1992

• Kyungpook Mathematical Journal
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• v.32 no.3_spc
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• pp.553-559
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• 1992

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.459-466
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• 2009

In this paper, a numerical scheme is introduced to solve the Cauchy problem for one-dimensional hyperbolic equations. The mesh points of the proposed scheme are distributed along characteristics so that the solution on the stencil can be easily and accurately computed. This is very important in reducing errors of the scheme because many numerical errors are generated when the solution is estimated over grid points. In addition, when characteristics intersect, the proposed scheme combines corresponding grid points into one and assigns new characteristic to the point in order to improve computational efficiency. Numerical experiments on the inviscid Burgers' equation have been presented.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.345-358
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• 2020

In this paper, we study the concepts of Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence, Wijsman lacunary ${\mathcal{I}}_2$-invariant convergence (${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$), Wijsman lacunary ${\mathcal{I}}^*_2$-invariant convergence (${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$), Wijsman p-strongly lacunary invariant convergence ([W₂N_σθ]_p) of double sequence of sets and investigate the relationships among Wijsman lacunary invariant convergence, [W₂N_σθ]_p, ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$ and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$. Also, we introduce the concepts of ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence of sets.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1996.06a
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• pp.9-15
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• 1996

In this paper, we propose a new detector based on the median-shift sign. We call it the median-shift sign (MSS) detector, which is an extension of the classical sign detector. We first analyze the problem of detecting a dc signal in noise of known probability density function (pdf). The MSS detector with the optimum median-shift value, the optimum MSS detector, performs better than the sign detector in Gaussian noise: it has the best performance among the detectors compared in Laplacian and Cauchy noise. It is shown that the MSS detectors with constant median-shift values are nearly equal to the optimum MSS detector. We also analyze the problem of detecting a dc signal when only partial information is available on the noise. The MSS detectors with constant median-shift values are almost equal to the sign detector in Gaussian noise: they perform better than the sign and Wilcoxon detectors for most signal ranges in Laplacian and Cauchy noise.

• Communications for Statistical Applications and Methods
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• v.21 no.5
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• pp.461-469
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• 2014

Characteristic functions play an important role in probability and statistics; however, a rigorous derivation of these functions requires contour integration, which is unfamiliar to most statistics students. Without resorting to contour integration, Datta and Ghosh (2007) derived the characteristic functions of normal, Cauchy, and double exponential distributions. Here, we derive the characteristic functions of t, truncated normal, skew-normal, and skew-t distributions. The characteristic functions of normal, cauchy distributions are obtained as a byproduct. The derivations are straightforward and can be presented in statistics masters theory classes.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.135-141
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• 2004

We studied the relation between the tangential Cauchy-Riemann operator ${\={\partial}}_b$ CR-manifolds and the derivation $d^{{\pi}^{0,\;1}}$ associated to the natural projection map ${\pi}^{0.1}\;:\;TM\;{\bigotimes}\;{\mathbb{C}}\;=\;T^{1,0}\;{\bigoplus}\;T^{0,\;1}\;{\rightarrow}\;T^{0,\;1}$. We found that these two differential operators agree only on the space of functions ${\Omega}^0(M),\;unless\;T^{1,\;0}$ is involutive as well. We showed that the difference is a derivation, which vanishes on ${\Omega}^0(M)$, and it is induced by the Nijenhuis tensor associated to ${\pi}^{0.1}$.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.111-118
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• 2008

Using the Hyers-Ulam-Rassias stability method, we investigate isomorphisms in quasi-Banach algebras and derivations on quasi-Banach algebras associated with the Cauchy-Jensen functional equation $$2f(\frac{x+y}{2}+z)$$=f(x)+f(y)+2f(z), which was introduced and investigated in [2, 17]. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias' stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Furthermore, isometries and isometric isomorphisms in quasi-Banach algebras are studied.