• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.07a
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• pp.791-794
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• 2001

We described a method resonant mode identification in dielectric-disc loaded cylindrical cavity resonators. The characteristic equation is solved by using the ContourPlot graph of Mathematica. Contour graph method uses graphical method. It is comparable with numerical method. The numerical method is very difficult a mode identification. The analysis based on the approximated electromagnetic representation. This kinds of studies only concentrated on the calculation of resonant frequencies, and a mode identification of resonant frequencies have not been covered. But, the contour graph method to analyze the characteristic equations is simple and all parts of resonant frequency graph can be easily drawn, it is possible to calculate precise resonant frequencies and to identify the mode of resonant frequencies.

• Electrical & Electronic Materials
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• v.9 no.5
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• pp.498-505
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• 1996

In the present work, we have developed the simulator to optimize the process conditions of the AR(antireflection) and HR(high-reflection) coatings for the high power laser diode. The simulator can run on the PC. After making the simple optical model, we establish the Maxwell equations for the model by the operator conversion. By using the Mathematica, we derive a matrix for the multilayer system by applying the equations to the model and optimize the AR and HR coating process conditions by obtaining the reflection rate from the matrix. We also prove the validity of the simulator by comparing the simulation with the characteristics of the laser diode which is AR and HR coated according to the optimized conditions.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.07a
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• pp.1069-1072
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• 2001

We described a method resonant mode identification in dielectric-rod loaded cylindrical cavity resonators. Resonant frequency of dielectric loaded cavity is calculated by analyzing the characteristic equation. The characteristic equation is solved by using the ContourPlot graph of Mathematica. As the result of comparing calculation value and experimental value of resonant frequencies, we know that the field representation of non-decaying mode is exact. The contour graph method is not a method using approximated representation of electromagnetic field variation at the outer area of dielectric in the resonators but a method using exact representation.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.133-139
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• 2006

By combining the classical Newton's method with the pseudo-secant method, pseudo-secant-Newton's method is constructed and its order and rate of convergence are investigated. Given a function $f:\mathbb{R}{\rightarrow}\mathbb{R}$ that has a simple real zero ${\alpha}$ and is sufficiently smooth in a small neighborhood of ${\alpha}$, the convergence behavior is analyzed near ${\alpha}$ for pseudo-secant-Newton's method. The order of convergence is shown to be cubic and the rate of convergence is proven to be $\(\frac{f^{{\prime}{\prime}}(\alpha)}{2f^{\prime}(\alpha)}\)^2$. Numerical experiments show the validity of the theory presented here and are confirmed via high-precision programming in Mathematica.

• Proceedings of the KSMRM Conference
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• 2001.11a
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• pp.146-146
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• 2001

목적： 해상도가 우수한 경직장 영상을 위한 소아용 two-turn 표면형 수신 코일, 안장 수신 코일을 제작하여 이를 이용하여 얻은 고양이의 경직장 영상을 비교한다. 대상 및 방법： 지금까지 소아의 경직장 영상은 주로 초음파를 이용하여 얻었으나 해상도가 떨어지며 아직까지 소아용 탐촉자는 개발되지 않았다. 소아의 항문직장 기형의 진단을 위해서는 해상도가 우수한 영상이 필요하고, 이를 위해 소아용 직장 RF 코일로 원주형 two-turn 표면형 코일, 안장 코일을 제작하였다. 크기는 직경 7mm, 길이 6cm와, 직경 10mm, 길이 l0cm 하였고, 코일의 구리선 바깥으로는 두께 1mm의 테프론 tube로 감쌌다. 균일한 시험 시료(phantom)로 마요네즈를 이용하여 T1 강조 영상(Spin echo TR/TE= 500/11 msec, FOV=12cm, 영상행렬 256$\times$256)을 얻어서 신호 강도의 profile을 얻는다. 이를 Mathematica를 이용하여 구한 RF 자기장 세기의 분포와 비교했다. 두 종류의 코일을 각각 사용하여 얻은 고양이 항문 괄약근 영상에서 외부 괄약근, 내부 괄약근 등을 구분, 비교하였다.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.9
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• pp.159-165
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• 2003

Most engineers interested in stress singularities have focused mainly on the research of power stress singularities for v-notched cracks in dissimilar materials. The logarithmic stress singularity was discussed a little in Bogy's paper. The power-logarithmic stress singularity was reported by Dempsey and Sinclair. It was indicated that the logarithmic singularity is only a special case of power-logarithmic stress singularities. Then, Dempsey reported specific cases which have power-logarithmic singularities even fur homogeneous boundary conditions. It was known that logarithmic stress singularities for v-notched cracks in dissimilar materials occurs when the surfaces of a v-notched crack have constant tractions. In this paper, using the complex potential method, the stresses and displacements having logarithmic stress singularities were obtained and the coefficients vectors were calculated by a numerical program code: Mathematica. It was shown that our analysis models don't have logarithmic stress singularities under the constant tractions, although the coefficient vectors are existing.

• Journal of Power System Engineering
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• v.15 no.6
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• pp.47-52
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• 2011

In this study, an accurate 2-noded hybrid-mixed element for continuous fiber-reinforced laminated beams is newly proposed. The present element including the effect of shear deformation is based on Hellinger-Reissner variational principle, and introduces additional consistent node less degrees for displacement field interpolation in order to enhance the numerical performance. The micromechanical and lamination theory are employed in the finite element description to consider the effects of the laminate stacking sequences, material orthotropy, and fiber volume fraction, etc. The element stiffness matrix can be explicitly derived through the stationary condition and static condensation using Mathematica program. Several numerical examples confirm the accuracy of the present hybrid-mixed element and also show in detail the effects of the continuous fiber volume fraction, stacking sequences and boundary condition on the bending behavior of laminated beams.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.217-227
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• 2009

Assuming that a given nonlinear function f : $\mathbf{R}{\rightarrow}\mathbf{R}$ has a zero $\alpha$with integer multiplicity $m{\geq}1$ and is sufficiently smooth in a small neighborhood of $\alpha$, we define extended leap-frogging Newton's method. We investigate the order of convergence and the asymptotic error constant of the proposed method as a function of multiplicity m. Numerical experiments for various test functions show a satisfactory agreement with the theory presented in this paper and are throughly verified via Mathematica programming with its high-precision computability.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.905-915
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• 2000

In this article we discuss some aspects of operational Tau Method on delay differential equations and then we apply this method on the differential delay equation defined by $\omega(u)\;=\frac{1}{u}\;for\;1\lequ\leq2$ and $(u\omega(u))'\;=\omega(u-1)\;foru\geq2$, which was introduced by Buchstab. As Khajah et al.[1] applied the Recursive Tau Method on this problem, they had to apply that Method under the Mathematica software to get reasonable accuracy. We present very good results obtained just by applying the Operational Tau Method using a Fortran code. The results show that we can obtain as much accuracy as is allowed by the Fortran compiler and the machine-limitations. The easy applications and reported results concerning the Operational Tau are again confirming the numerical capabilities of this Method to handle problems in different applications.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.165-180
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• 2017

In this study, Taylor matrix algorithm is designed for the approximate solution of linear and non-linear differential equation systems. The algorithm is essentially based on the expansion of the functions in differential equation systems to Taylor series and substituting the matrix forms of these expansions into the given equation systems. Using the Mathematica program, the matrix equations are solved and the unknown Taylor coefficients are found approximately. The presented numerical approach is discussed on samples from various linear and non-linear differential equation systems as well as stiff systems. The computational data are then compared with those of some earlier numerical or exact results. As a result, this comparison demonstrates that the proposed method is accurate and reliable.