• East Asian mathematical journal
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• v.10 no.2
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• pp.255-260
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• 1994

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.15-23
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• 1999

We obtain an efficient upper bound of the area of convex curves of constant relative breadth in the Minkowski plane. The estimation is given in terms of the Minkowski are length of pedal curve of original curve.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.521-529
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• 2003

In this paper, we get the measure of strips and lines in the Minkowski plane $M^2$ that meet a fixed compact convex body in $M^2$. From this we also investigate the probability that strips and lines meet a fixed compact convex body in $M^2$.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.375-385
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• 2020

Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.

• Korean Journal of Computational Design and Engineering
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• v.8 no.4
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• pp.243-253
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• 2003

This paper presents a new geometric morphing algorithm for polygons based on a simple geometric structure called direction map, which is mainly composed of a circular list of direction vectors defined by two neighboring vertices of a polygon. To generate a sequence of intermediate morphing shapes, first we merge direction maps of given control shapes based on a certain ordering rule of direction vectors, and scale the length of each direction vectors using Bezier or blossom controls. We show that the proposed algorithm is an improvement of the previous methods based on Minkowski sum (or convolution) in th aspects of computational efficiency and geometric properties.

• Journal of the Korean Institute of Telematics and Electronics
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• v.7 no.3
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• pp.12-18
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• 1970

In this paper, the radiation characteristics of a Circular Loop Antenna is studied in a moving homogeneous, isotropic and linear media with a constant velocity much less than the speed of light. In Stuffing the radiation characteristics, Srst vector potential on the loop antenna is derived in the moving media by appling Maxwell-Minkowaski's theory. Next, using the derived relations, the electric and magnetic Seld is calculated for the spec-i Sed wave length ana velocity of the media. The Seld patterns in the moving media are compared with those of stationary media. We find that the intensity of the field is reduced in the direction of the media velocity and increased in the opposite direction only for the component parallel with the plane of the antenna. The deviation from the stationary media is proportional to the velocity of the media and the frequency of source current.