• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.625-628
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• 2010

The purpose of this paper is to show that there exists a unit whose p-th root generates the first layer of anti-cyclotomic ${\mathbb{Z}}_p$-extension of certain imaginary quadratic number fields.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.475-486
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• 2001

In this paper we give a relationship among the Minkowski units, for all odd prime number including $\infty$, of 2-periodic knot is $S^3$, its factor knot, and the 2-component link consisting of the factor knot and the set of fixed points of the periodic action.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.1-4
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• 2009

In this paper we explicitly compute a Minkowski unit of a real abelian field and give a criterion when the first layer of anti-cyclotomic ${\mathbb{Z}}_3$-extension of an imaginary quadratic field is unramified everywhere.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1103-1107
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• 2018

Let M be a complete spacelike hypersurface in the (n + 1)-dimensional Minkowski space ${\mathbb{L}}^{n+1}$. Suppose that every unit speed curve X(s) on M satisfies ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}{\geq}-1/r^2$ and there exists a point $p{\in}M$ such that for every unit speed geodesic X(s) of M through the point p, ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}=-1/r^2$ holds. Then, we show that up to isometries of ${\mathbb{L}}^{n+1}$, M is the hyperbolic space $H^n(r)$.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1299-1320
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• 2023

In the present paper, firstly we obtain the general expression of the canal hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres, pseudo hyperbolic hyperspheres and null hyper-cones whose centers lie on a non-null curve with non-null Frenet vector fields in E⁴₁ and give their some geometric invariants such as unit normal vector fields, Gaussian curvatures, mean curvatures and principal curvatures. Also, we give some results about their flatness and minimality conditions and Weingarten canal hypersurfaces. Also, we obtain these characterizations for tubular hypersurfaces in E⁴₁ by taking constant radius function and finally, we construct some examples and visualize them with the aid of Mathematica.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.735-740
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• 2001

Let K be a convex body of constant relative breadth and let $K^*$ be its polar dual with respect to the Euclidean unit circle. In this paper we obtain the lower bound for the volume of the pedal body $PK^*P $K^{*}$ of K^*.$ Using this, we also obtain the lower bound for the volume product V$(PK^*)$V(PK) for planar bodies.s.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.1
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• pp.1-8
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• 2016

In this study, an WiFi fingerprinting method based on the k-nn algorithm was applied to improve the accuracy of location tracking of a moving train on a platform and evaluate the performance to minimize the estimation error of location tracking. The data related to the position of the moving train are monitored by the control center for trains and used widely for the safety and comfort of passengers. The train location tracking methods based on WiFi installed by telecom companies were evaluated. In this study, a simulator was developed to consider the environments of two cases; in already installed WiFi devices and new installed WiFi devices. The developed simulator can simulate the localized estimation of the position under a variety of conditions, such as the number of WiFi devices, the area of platform and entry velocity of train. To apply location tracking algorithms, a k-nn algorithm and fuzzy k-nn algorithm were applied selectively according to the underlying condition and also four distance measurement algorithms were applied to compare the error of location tracking. In conclusion, the best method to estimate train location tracking is a combination of the k-nn algorithm and Minkoski distance measurement at a 0.5m grid unit and 8 WiFi AP installed.