• Journal of Astronomy and Space Sciences
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• 제37권2호
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• pp.131-142
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• 2020

As the laws of physics are expressed in a manner that makes their invariance under coordinate transformations manifest, they should be written in terms of tensors. Furthermore, tensors make manifest the characteristics and behaviors of electromagnetic fields through inhomogeneous, anisotropic, and compressible media. Electromagnetic fields are expressed completely in tensor form, F^αβ, which implies both electric field ${\overrightarrow{E}}$ and magnetic field ${\overrightarrow{B}}$ rather than separately in the vector fields. This study presents the Mathematica platform that generates and transforms a second-rank antisymmetric field-strength tensor F^αβ and whiskbroom pattern in Minkowski space. The platforms enhance the capabilities of students and researchers in tensor analysis and improves comprehension of the elegant features of complete structure in physics.

• Journal of Astronomy and Space Sciences
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• 제31권1호
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• pp.91-99
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• 2014

The atmospheric flow in the 3-Cell model of global atmosphere circulation is described by the Lagrange's equation of the non-inertial frame where pressure force, frictional force and fictitious force are mixed in complex form. The Coriolis force is an important factor which requires calculation of fictitious force effects on atmospheric flow viewed from the rotating Earth. We make new Mathematica platform to solve Lagrange's equation by numerical analysis in order to analyze dynamics of atmospheric general circulation in the non-inertial frame. It can simulate atmospheric circulation process anywhere on the earth. It is expected that this pedagogical platform can be utilized to help students studying the atmospheric flow understand the mechanisms of atmospheric global circulation.

• Journal of Astronomy and Space Sciences
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• 제32권2호
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• pp.151-159
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• 2015

The fundamental conception in physics of the propagation of the electromagnetic wave polarization in matter is newly understood as the cardinal keyword in free-space quantum communication technology and cosmology in astrophysics. Interactive visualization of the propagation mechanism of polarized electromagnetism in a medium with its helicity has accordingly received attention from scientists exploiting the protocol of quantum key distribution (QKD) to guarantee unconditional security in cryptography communication. We have provided a dynamic polarization platform for presenting the polarization modes of a transverse electromagnetic wave, converting the state of polarization through the arrangement of optical elements, using Jones vectors calculations in Methematica. The platform graphically simulates the mechanism of production and propagation of the polarized waves in a medium while satisfying Maxwell's equations.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권2호
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• pp.85-90
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• 2007

Arguably the most important internet technology of today is RIA (rich internet application), whose prime advantage is in improving the user experience on the web. However, the scope and variety of the RIA technology demand an eclectic guideline to build the mathematical services such as mathematical text, graphs, and animations. This paper sorts out and simplifies the complicated roadmap of the RIA technologies by presenting three design patterns for exposing the functionality of the CAS (computer algebra system) with the web browser as the user interface platform.

• 한국방사선학회논문지
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• 제13권7호
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• pp.901-907
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• 2019

이 연구의 목적은 기능성 질환의 감마나이프 시상하핵파괴술(또는 담창구파괴술, 시상파괴술)에서 렉셀 감마플랜의 표적 위치측정의 능력을 평가하는 것이다. 렉셀 감마플랜의 위치 설정의 정확성을 평가하기 위해 본원에서 뇌심부 자극술 수술을 받은 10명의 환자에 대해 렉셀 감마플랜(또는 렉셀 써지플랜)과 저자의 알고리즘에 의해 계산된 표적 좌표들의 차이 Δr가 평가 되었다. Δr는 0.0244663 mm에서 0.107961 mm까지 범위의 값을 가졌다. Δr의 평균은 0.054398 mm이었다. 또한 정위 공간과 뇌지도 공간 두 좌표계 사이의 위치 관계를 결정하기 위하여 좌표변환 행렬을 매스매티카(Mathematica)의 의사역행렬 또는 특이값 분해를 사용하여 계산하였다. 정교한 정위틀 장착에도 불구하고 요(yaw)는 -3.44739 도에서 1.82243 도, 피치(pitch)는 -4.57212 도에서 0.692063 도, 롤(roll)은 -6.38239 도에서 7.21426 도까지의 정렬 불량(misalignment)이 나타났다. 결론적으로, 사내 알고리즘을 사용하여 감마나이프 플랫폼에서 렉셀 감마플랜(또는 렉셀 써지플랜)의 위치 설정에 대한 정확도를 확인함으로써 뇌심부 자극술에 금기 사항이 있는 개인이나 노인과 같이 종래 수술에 고위험으로 간주되는 환자에 대한 난치성 운동이상 질환의 대체 치료법으로 안전과 효능을 가진 감마나이프 시상하핵파괴술(또는 담창구파괴술, 시상파괴술)이 추천된다. 향후 기능성 질환의 표적 위치측정을 위해 제안된 알고리즘은 여러 감마나이프 센터의 운동이상 질환 치료에 기여할 것이라 사료된다.