• 대한수학회보
• /
• 제56권3호
• /
• pp.681-689
• /
• 2019

The $M{\ddot{o}}bius$ homogeneous submanifold in ${\mathbb{S}}^{n+1}$ is an orbit of a subgroup of the $M{\ddot{o}}bius$ transformation group of ${\mathbb{S}}^{n+1}$. In this note, We prove that a compact $M{\ddot{o}}bius$ homogeneous submanifold in ${\mathbb{S}}^{n+1}$ is the image of a $M{\ddot{o}}bius$ transformation of the isometric homogeneous submanifold in ${\mathbb{S}}^{n+1}$.

• 한국통신학회논문지
• /
• 제38B권9호
• /
• pp.715-721
• /
• 2013

RF소자의 소형화 기법으로는 헤리컬 구조를 적용하는 방법, Meta Material을 사용하는 방법 및 적층구조를 적용하는 방법 등 여러 방법들이 적용되고 있다. 그러나 헤리컬 구조는 한 번의 원주의 회전이 있을 때 마다 공진주파수가 생김에 따라 단일 공진주파수 특성을 가지는 RF회로의 소형화 기법에는 맞지 않으며, Meta Material과 적층구조를 적용하는 방법들은 구조가 복잡하며 비용이 많이 드는 단점이 있다. 또한, 3차원 구조의 기본적인 뫼비우스 스트립을 활용한 논문과 뫼비우스 스트립의 특성을 활용한 평판형 구조의 논문이 제안되었으나 완전한 평판형구조가 아니고, 선로결합효과(coupling effect) 현상의 문제점이 있었다. 따라서 본 논문은 기존 M$\ddot{o}$bius Strip과 위상동형인 Quasi M$\ddot{o}$bius Strip과 via hole구조를 응용함으로써, RF회로의 소형화와 선로결합효과를 완화한 안테나를 제시하였다. 본 논문의 시뮬레이션 결과에 의하면, 2.4GHz의 공진주파수 일 때, 기존의 링 안테나와 대비하여 물리적 원주의 길이는 1/3배로 소형화 되었다. 그리고 기존의 헤리컬 안테나의 다중공진특성이 아니라 단일 주파수에서의 공진특성을 보인다. 또한, 2.4GHz의 공진주파수 근처에서 선로결합 효과 현상이 거의 발생하지 않았다.

• 대한수학회보
• /
• 제49권4호
• /
• pp.685-692
• /
• 2012

Consider a hypersurface $M^n$ in $\mathbb{R}^{n+1}$ with $n$ distinct principal curvatures, parametrized by lines of curvature with vanishing Laplace invariants. (1) If the lines of curvature are planar, then there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations Dupin hypersurfaces with constant M$\ddot{o}$bius curvature. (2) If the principal curvatures are given by a sum of functions of separated variables, there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations, Dupin hypersurfaces with constant M$\ddot{o}$bius curvature.

• Investigative Magnetic Resonance Imaging
• /
• 제23권2호
• /
• pp.167-171
• /
• 2019

$M\ddot{o}bius$ syndrome is a rare congenital condition, characterized by abducens and facial nerve palsy, resulting in limitation of lateral gaze movement and facial diplegia. However, to our knowledge, there have been few studies on evaluation of cranial nerves, on MR imaging in $M\ddot{o}bius$ syndrome. Herein, we describe a rare case of $M\ddot{o}bius$ syndrome representing limitation of lateral gaze, and weakness of facial expression, since the neonatal period. In this case, high-resolution MR imaging played a key role in diagnosing $M\ddot{o}bius$ syndrome, by direct visualization of corresponding cranial nerves abnormalities.

• 대한수학회보
• /
• 제54권4호
• /
• pp.1159-1171
• /
• 2017

The purpose of this paper is twofold. The first is to show that two meromorphic functions f and g must be linked by a quasi-$M{\ddot{o}}bius$ transformation if they share a pair of small functions regardless of multiplicity and share other three pairs of small functions with multiplicities truncated to level 4. We also show a quasi-$M{\ddot{o}}bius$ transformation between two meromorphic functions if they share four pairs of small functions with multiplicities truncated by 4, where all zeros with multiplicities at least k > 865 are omitted. Moreover the explicit $M{\ddot{o}}bius$-transformation between such f and g is given. Our results are improvement of some recent results.

• 충청수학회지
• /
• 제30권1호
• /
• pp.15-19
• /
• 2017

We introduce the $M{\ddot{o}}bius$ functions ${\mu}k$ of order k and give the asymptotic formula for the summatory function associated to theses functions in function field case.

• 대한수학회논문집
• /
• 제35권3호
• /
• pp.927-933
• /
• 2020

We characterize Möbius functions mapping the unit disc of the complex plane contractively into itself. We then give a procedure to produce Möbius iterated function systems on the unit disc.

• 대한수학회보
• /
• 제51권4호
• /
• pp.1187-1193
• /
• 2014

We will characterize the boundedness and compactness of weighted composition operators on the minimal M$\ddot{o}$bius invariant space.

• Kyungpook Mathematical Journal
• /
• 제47권2호
• /
• pp.165-714
• /
• 2007

The basis number of a graph G is the least positive integer $k$ such that G has a $k$-fold basis. In this paper, we prove that the basis number of the cartesian product of a path with a circular ladder, a M$\ddot{o}$bius ladder and path with a net is exactly 3. This improves the upper bound of the basis number of these graphs for a general theorem on the cartesian product of graphs obtained by Ali and Marougi, see [2]. Also, by this general result, the cartesian product of a theta graph with a M$\ddot{o}$bius ladder is at most 5. But in section 3 we prove that it is at most 4.

• International Journal of CAD/CAM
• /
• 제2권1호
• /
• pp.45-54
• /
• 2002

Given a set of three generator circles in a plane, we want to find a circumcircle of these generators. This problem is a part of well-known Apollonius' $10^{th}$ Problem and is frequently encountered in various geometric computations such as the Voronoi diagram for circles. It turns out that this seemingly trivial problem is not at all easy to solve in a general setting. In addition, there can be several degenerate configurations of the generators. For example, there may not exist any circumcircle, or there could be one or two circumcircle(s) depending on the generator configuration. Sometimes, a circumcircle itself may degenerate to a line. We show that the problem can be reduced to a point location problem among the regions bounded by two lines and two transformed circles via $M{\ddot{o}}bius$ transformations in a complex space. The presented algorithm is simple and the required computation is negligible. In addition, several degenerate cases are all incorporated into a unified framework.