• Journal of Astronomy and Space Sciences
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• v.37 no.2
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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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• v.31 no.1
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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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• v.32 no.2
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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.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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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.

• Journal of the Korean Society of Radiology
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• v.13 no.7
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• pp.901-907
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• 2019

The aim of this study is to evaluate the ability of target localizations of Leksell GammaPlan(LGP) in Gamma Knife Subthalamotomy(or Pallidotomy, Thalamotomy) of functional diseases. To evaluate the accuracy of LGP's location settings, the difference Δr of the target coordinates calculated by LGP (or LSP) and author's algorithm was reviewed for 10 patients who underwent Deep Brain Stimulation(DBS) surgery. Δr ranged from 0.0244663 mm to 0.107961 mm. The average of Δr was 0.054398 mm. Transformation matrix between stereotactic space and brain atlas space was calculated using PseudoInverse or Singular Value Decomposition of Mathematica to determine the positional relationship between two coordinate systems. Despite the precise frame positioning, the misalignment of yaw from -3.44739 degree to 1.82243 degree, pitch from -4.57212 degree to 0.692063 degree, and rolls from -6.38239 degree to 7.21426 degree appeared. In conclusion, a simple in-house algorithm was used to test the accuracy for location settings of LGP(or LSP) in Gamma Knife platform and the possibility for Gamma Knife Subthalamotomy. The functional diseases can be treated with Gamma Knife Radiosurgery with safety and efficacy. In the future, the proposed algorithm for target localizations' QA will be a great contributor to movement disorders' treatment of several Gamma Knife Centers.