• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2007.11a
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• pp.448-449
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• 2007

The PMMA plates with periodic ~200 nm nanosized patterned array were fabricated through the nanoimprint technique with their proper Ni stamper. The computer coding was also made with the Mathematica language software via RCWA (Rigorous Continuous Wave Analysis) and it is confirmed that simulation results are in good agreement with the experimental ones.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.49-56
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• 2006

A convergence behavior is under investigation near a simple real zero for the k-fold pseudo-Olver's method defined by extending the classical Olver's method. The order of convergence is shown to be at least k+3. The asymptotic error constant is explicitly given in terms of k and the corresponding simple zero. Various numerical examples with a proposed zero-finding algorithm are successfully confirmed with the use of symbolic and computational ability of Mathematica.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.5.3-5
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• 2003

The boundary of a typical period-2 component in the degree-3 bifurcation set is formulated by a parametrization of its image which is the unit circle under the multiplier map, Some properties on the geometry of the boundary are investigated including the root point, the cusp, the component center and the length as well as the area bounded by the boundary curve. An algorithm drawing the boundary curve with Mathematica codes is proposed and its implementation exhibits a good agreement with the analysis presented here.

• Communications for Statistical Applications and Methods
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• v.18 no.3
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• pp.295-300
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• 2011

The Bayesian nonparametric estimation of two uniformly stochastically ordered distributions is studied. We propose a restricted Dirichlet Process. Among many types of restriction we consider only uniformly stochastic ordering in this paper since the computation of integrals is relatively easy. An explicit expression of the posterior distribution is given. When square loss function is used the posterior distribution can be obtained by easy integration using some computer program such as Mathematica.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.613-626
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• 2016

In this article, we study skew ruled surfaces by using the geodesic Frenet trihedron of its generator. We obtained some conditions on this surface to ensure that this ruled surface is flat, II-flat, minimal, II-minimal and Weingarten surface. Moreover, the parametric equations of asymptotic and geodesic lines on this ruled surface are determined and illustrated through example using the program of mathematica.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.87-94
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• 2002

Trot(1999) considered how to calculate the expected area of a random triangle in the unit square $[0,1]{\times}[0,1]$. He used the Mathematica software package for the computational part. In this article, we study various aspects of the probability distribution of a triangle randomly chosen inside the circle of radius r. A simulation activity that can be conducted in statistics and probability classrooms is also considered.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.201-209
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• 2008

In this paper we introduce two products of tempered distributions with positive support. These products are based in the Laguerre representation of distributions. We calculate some products as, $[{\delta}]x^{\lambda}_+={\delta}[x^{\lambda}_+]=0\;and\;[x^{\lambda}_+]x^{\mu}_+=x^{{\lambda}+{\mu}}_+$ for appropriate ${\lambda}$ and ${\mu}$.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.35-46
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• 2006

The concept of convolution is a fundamental mathematical concept in a wide variety of disciplines and applications including probability, image processing, physics, and many more. The visualization of convolution for the continuous case is generally predetermined. On the other hand, the convolution structure embedded in the discrete case is often subtle and its visualization is non- trivial. This paper purports to develop the CAS techniques in visualizing the logical structure in the concept of a discrete convolution.

• Journal of KSNVE
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• v.6 no.1
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• pp.45-56
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• 1996

Frequency equation for clamped-free circular cylindrical thin shell is derived by the application of Rayleigh-Ritz method using the Sanders shell equation. The cubic frequency equation is solved for each axial and circumferential mode number. Integration of the beam characteristic funcitions was performed via Mathematica which results in more accurate integration of the beam functions that affect the accuracy of the frequency. The natural frequencies from this calculation are compared with existing results. It shows that this calculation predicts natural frequencies closer to the test results than existing results.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.768-771
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• 2002

A method to derive the constitutive relations of a piezoelectric bender actuator is developed here. The constitutive relations are derived from the geometry, material properties of the actuator. The very complicated constitutive relations can be easily calculated by use of symbolic function in Mathematica. The developed program can calculate the constitutive relations for the unimorph bender made by attaching a short piezoelectric beam on a longer metal beam. The program can also calculate the constitutive relations of a piezoelectric bender with spring at its end.