• 대한수학회지
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• 제56권6호
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• pp.1515-1528
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• 2019

We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A{\subseteq}F^d_q$ and edges assigned the algebraic distance between pairs of vertices. We prove nontrivial results on locating specified subgraphs of maximum vertex degree at most t in dimensions $d{\geq}2t$.

• 대한수학회지
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• 제46권3호
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• pp.551-560
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• 2009

A theorem of Robert Blumenthal is used here in order to obtain a sufficient condition for a function between two Finsler manifolds to be a fibre bundle map. Our study is connected with two possible constructions: 1) a Finslerian generalization of usually Kaluza-Klein theories which use Riemannian metrics, the well-known particular case of Finsler metrics, 2) a Finslerian version of reduction process from geometric mechanics. Due to a condition in the Blumenthal's result the completeness of Euler-Lagrange vector fields of Finslerian type is discussed in detail and two situations yielding completeness are given: one concerning the energy and a second related to Finslerian fundamental function. The connection of our last framework, namely a regular Lagrangian having the energy as a proper (in topological sense) function, with the celebrated $Poincar{\acute{e}}$ Recurrence Theorem is pointed out.

• 충청수학회지
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• 제23권2호
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• pp.185-195
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• 2010

In the unified field theory(UFT), in order to find a solution of the Einstein's equation it is necessary and sufficient to study the torsion tensor. The main goal in the present paper is to obtain, using a given torsion tensor (3.1), the complete representation of a particular solution of the Einstein's equation in terms of the basic tensor $g_{{\lambda}{\nu}}$ in even-dimensional UFT $X_n$.

• 한국통신학회논문지
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• 제27권3A호
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• pp.240-248
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• 2002

본 논문에서는 연속영상에서 움직이는 객체의 motion에 기반하여 영상을 분할하는 새로운 알고리즘을 제안하였다. 전체적인 분할 과정은 2단계로 구성되어진다. 첫 단계는 '픽셀 레이블링' 단계이며, 두 번째 단계는 'motion 분할' 단계이다. '픽셀 레이블링' 단계에서는 optical flow에 의해 발생하는 속도 벡터들의 크기에 따라 영상의 각 픽셀에 레이블을 부여한다. 'Motion 분할' 단계에서는 첫 단계에서 생겨난 불필요한 잡음을 제거하기 위해 motion 필드를 마코프 랜덤 필드로 모델링하여 에너지 최소화를 통해 motion을 분할한다. 실험결과, 제안된 알고리즘이 연속영상에서 움직이는 객체의 motion을 효율적으로 분할함을 확인할 수 있었다.

• 대한수학회논문집
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• 제34권4호
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• pp.1279-1287
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• 2019

The main purpose of the paper is to prove that if a compact Riemannian manifold admits a gradient ${\rho}$-Einstein soliton such that the gradient Einstein potential is a non-trivial conformal vector field, then the manifold is isometric to the Euclidean sphere. We have showed that a Riemannian manifold satisfying gradient ${\rho}$-Einstein soliton with convex Einstein potential possesses non-negative scalar curvature. We have also deduced a sufficient condition for a Riemannian manifold to be compact which satisfies almost ${\eta}$-Ricci soliton.

• Journal of Astronomy and Space Sciences
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• 제37권2호
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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.

• 한국통신학회논문지
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• 제27권3A호
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• pp.221-230
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• 2002

본 논문에서는 마코프 랜덤 필드를 이용해 움직이는 객체를 분할하는 새로운 방법을 제안하였다. 제안된 방법은 신호 탐지 이론에 기반을 두고 있다. 즉, 영상에서의 모션의 존재 유무는 binary decision rule에 의해 결정되고 잘못된 결정은 마코프 랜덤 필드 모델에 의해 수정된다. 전체적인 분할 과정은 2단계로 나뉘어진다. 첫 단계는 '모션탐지' 단계이며, 두번째 단계는 '객체분할' 단계이다. '모션탐지' 단계에서는 optical flow에 의해 발생하는 속도 벡터들에 대하여 binary decision rule을 적용하여 모tus의 존재 유무를 결정하는 과정이다. '객체분할' 단계에서는 첫 단계에서 원치 않게 발생하는 잡음을 제거한다. 이때 마코프 랜덤 필드로 가정하고 베이스 규칙에 의해 잡음을 제거한다. 실험결과, 연속영상에서 움직이는 객체의 영역을 효율적으로 분할함을 확인할 수 있었다.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.547-554
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• 2021

The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.169-179
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• 2021

In this paper, we extend the definition of p-harmonic maps between two Riemannian manifolds. We prove a Liouville type theorem for generalized p-harmonic maps. We present some new properties for the generalized stress p-energy tensor. We also prove that every generalized p-harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a homothetic vector field satisfying some condition is constant.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2013년도 제44회 동계 정기학술대회 초록집
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• pp.153-153
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• 2013

Turbomolecular pump (TMP) is widely used to obtain and maintain high vacuum by spinning turbine rotors to migrate gas molecules to the exhaust of the pump. However, performance of the TMP has not been well observed when it is influenced by strong magnetic field. Such study may give useful information about magnetic field tolerance of TMP, development of magnetic shielding technique for key components of TMP, etc. For this purpose, magnetic field induced by a circular current source was firstly designed and investigated. Using spherical coordinates and vector potential, magnetic field throughout the space including axis of rotation was calculated. Due to the rotational symmetry of the circular current source, induced magnetic field is azimuthally symmetric and, thus, is analyzed by radial and polar components of the magnetic fields. In order to enhance the numerical accuracy for the calculation, magnetic field was expressed by complete elliptic integrals of first and second kinds. According to the calculation, when 1 A of DC-current passes through a 1 turned circular wire with 50 cm of diameter, overall magnitude of the inducedmagnetic field was about 0.02 Gauss, which was used to the determination of the current and the number of turns of wires to fabricate the coil for the study on the magnetic field tolerance of TMP.