• Journal of the Korean Data and Information Science Society
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• v.22 no.5
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• pp.961-966
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• 2011

Circular variables are those that have a period in its range. Their examples include direction of animal migration, and time of drug administration, just to mention a few. Statistical analysis of circular variables is quite different from that of linear variable due to its periodic nature. In this paper, the author proposes new circular regression models using geodesic lines on the surface of the sample space of the response and the predictor variables.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.29 no.4
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• pp.329-341
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• 2011

The object of this paper is to compare the accuracy and the characteristic of various methods of solving the geodetic inverse problem for the geodesic lines which be in the standard case and special cases(antipodal, near antipodal, equatorial, and near equatorial situation) on the WGS84 reference ellipsoid. For this, the various algorithms (classical and recent solutions) to deal with the geodetic inverse problem are examined, and are programmed in order to evaluate the calculation ability of each method for the precise geodesic determination. The main factors of geodetic inverse problem, the distance and the forward azimuths between two points on the sphere(or ellipsoid) are determined by the 18 kinds of methods for the geodetic inverse solutions. After then, the results from the 17 kinds of methods in the both standard and special cases are compared with those from the Karney method as a reference. When judging these comparison, in case of the standard geodesics whose length do not exceed 100km, all of the methods show the almost same ability to Karney method. Whereas to the geodesics is longer than 4,000km, only two methods (Vincenty and Pittman) show the similar ability to the Karney method. In the cases of special geodesics, all methods except the Modified Vincenty method was not proper to solve the geodetic inverse problem through the comparison with Karney method. Therefore, it is needed to modify and compensate the algorithm of each methods by examining the various behaviors of geodesics on the special regions.

• Journal of The Korean Astronomical Society
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• v.46 no.3
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• pp.97-102
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• 2013

In the present work, we prove the validity of two theorems on null-paths in a version of absolute parallelismgeometry. A version of these theorems has been originally established and proved by Kermak, McCrea and Whittaker (KMW) in the context of Riemannian geometry. The importance of such theorems lies in their applications to derive a general formula for the redshift of spectral lines coming from distant objects. The formula derived in the present work can be applied to both cosmological and astrophysical redshifts. It takes into account the shifts resulting from gravitation, different motions of the source of photons, spin of the moving particle (photons) and the direction of the line of sight. It is shown that this formula cannot be derived in the context of Riemannian geometry, but it can be reduced to a formula given by KMW under certain conditions.