• 호남수학학술지
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• 제23권1호
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• pp.71-90
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• 2001

In this paper, we introduce the MarKov chain and hyperplane arrangement. we prove some properties determined by a hyperplane arrangement and give an example as an application of them.

• 대한수학회지
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• 제37권3호
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• pp.455-461
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• 2000

The quantum hyperplane section theorem is explained for nonnegative decomposable concavex bundle spaces over generalized flag manifolds.

• 대한수학회보
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• 제54권2호
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• pp.375-382
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• 2017

We exhibit a one-to-one correspondence between 3-colored graphs and subarrangements of certain hyperplane arrangements denoted ${\mathcal{J}}_n$, $n{\in}{\mathbb{N}}$. We define the notion of centrality of 3-colored graphs, which corresponds to the centrality of hyperplane arrangements. Via the correspondence, the characteristic polynomial ${\chi}{\mathcal{J}}_n$ of ${\mathcal{J}}_n$ can be expressed in terms of the number of central 3-colored graphs, and we compute ${\chi}{\mathcal{J}}_n$ for n = 2, 3.

• 대한수학회지
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• 제54권5호
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• pp.1595-1604
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• 2017

We give a complete formula for the characteristic polynomial of hyperplane arrangements ${\mathcal{J}}_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $1{\leq}i$, j, k, $l{\leq}n$. The formula is obtained by associating hyperplane arrangements with graphs, and then enumerating central graphs via generating functions for the number of bipartite graphs of given order, size and number of connected components.

• Journal of Advanced Marine Engineering and Technology
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• 제14권3호
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• pp.42-51
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• 1990

A construction method of a switching hyperplane for the Variable Structure Systems, which have robustness for parameter variations and noises in sliding mode is presented. The problem of composing a switching hyperplane is considered as a special case of the pole assignment for a closed-loop system. It is shown that the condition for constructing arbitrarily a switching hyperplane matrix C is equivalent to the controllability of the pair matrix(A, B) for the system, and then an algorithm of obtaining the switching hyperplane is proposed. It is also proved that zeros of the system are invariable in the sliding mode, and the stability for the system dynamic is equivalent to the stability of PA $\textit{ker}$ C. The applicability of the method proposed in the paper is shown by the simulation results for an example system.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.1623-1628
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• 2004

In the 3-dimensional cyclic Lotka-Volterra equations, we show the solution on the invariant hyperplane. In addition, we show the existence of the invariant hyperplane by the center manifold theorem under the some conditions. With this result, we can lead the hyperplane of the n-dimensional cyclic Lotka-Volterra equaions. In other section, we study the 3- or 4-dimensional Hamiltonian Lotka-Volterra equations which satisfy the Jacobi identity. We analyze the solution of the Hamiltonian Lotka- Volterra equations with the functions called the split Liapunov functions by [4], [5] since they provide the Liapunov functions for each region separated by the invariant hyperplane. In the cyclic Lotka-Volterra equations, the role of the Liapunov functions is the same in the odd and even dimension. However, in the Hamiltonian Lotka-Volterra equations, we can show the difference of the role of the Liapunov function between the odd and the even dimension by the numerical calculation. In this paper, we regard the invariant hyperplane as the important item to analyze the motion of Lotka-Volterra equations and occur the chaotic orbit. Furtheremore, an example of the asymptoticaly stable and stable solution of the 3-dimensional cyclic Lotka-Volterra equations, 3- and 4-dimensional Hamiltonian equations are shown.

• 대한수학회논문집
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• 제33권3호
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• pp.759-765
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• 2018

We use the finite method developed by C. Athanasiadis based on Crapo-Rota's theorem to give a complete formula for the characteristic polynomial of hyperplane arrangements ${\mathcal{J}}_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $1{\leq}i,j,k,l{\leq}n$.

• 대한수학회논문집
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• 제30권3호
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• pp.253-267
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• 2015

Given a complex submanifoldM of the projective space $\mathbb{P}$(T), the hyperplane system R on M characterizes the projective embedding of M into $\mathbb{P}$(T) in the following sense: for any two nondegenerate complex submanifolds $M{\subset}\mathbb{P}$(T) and $M^{\prime}{\subset}\mathbb{P}$(T'), there is a projective linear transformation that sends an open subset of M onto an open subset of M' if and only if (M,R) is locally equivalent to (M', R'). Se-ashi developed a theory for the differential invariants of these types of systems of linear differential equations. In particular, the theory applies to systems of linear differential equations that have symbols equivalent to the hyperplane systems on nondegenerate equivariant embeddings of compact Hermitian symmetric spaces. In this paper, we extend this result to hyperplane systems on nondegenerate equivariant embeddings of homogeneous spaces of the first kind.

• 대한수학회보
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• 제58권1호
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• pp.21-30
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• 2021

In this paper, we prove some rigidity results about embedded minimal hypersurface M ⊂ ℝn+1 with compact ∂M that has one end which is regular at infinity. We first show that if M ⊂ ℝn+1 meets a hyperplane in a constant angle ≥ ��/2, then M is part of an n-dimensional catenoid. We show that if M meets a sphere in a constant angle and ∂M lies in a hemisphere determined by the hyperplane through the center of the sphere and perpendicular to the limit normal vector nM of the end, then M is part of either a hyperplane or an n-dimensional catenoid. We also show that if M is tangent to a C2 convex hypersurface S, which is symmetric about a hyperplane P and nM is parallel to P, then M is also symmetric about P. In special, if S is rotationally symmetric about the xn+1-axis and nM = en+1, then M is also rotationally symmetric about the xn+1-axis.

• 한국통신학회논문지
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• 제30권1C호
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• pp.82-91
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• 2005

본 논문은 iterative hyperplane projection 을 이용한 효율적인 APA(affine projection algorithm)을 소개한다. 다양한 적응 알고리즘들 중 APA는 랭크 부족 문제를 해결하며 고속 수렴의 특성 때문에 다양한 응용분야에 적용되고 있다. SIMO(Single-Input-Multiple-Output) 시스템을 위한 STDE(Space-Time Decision- directed Equalizer) 적용 시 흔히 단일 채널 환경에서 발생하는 "shifting invariance property"를 이용할 수 없으므로 인해 FTF(Fast Transversal Filter)와 같이 저 복잡도를 갖는 고속 적응 알고리즘을 사용할 수 없다. 따라서 APA 기반의 STDE 기능을 수행하는 과정에서 SMI(Sample Matrix Inversion) 처리가 불가피하며, 계산상의 복잡도가 증가하게 된다. 이러한 문제점을 해결하고자 본 논문에서는 APA 기법 고유의 우수한 추적 특성 및 고속 수렴 성질을 유지하면서, 낮은 복잡도를 갖는 IHP(Iterative Hyperplane Projection) 알고리즘 기반의 효율적인 수정 APA 기법을 소개한다. 제안된 IHP 기반 APA 기법의 성능을 확인하기 위하여, 무선 SIMO 채널 환경 하에서 제안된 IHP-APA 알고리즘을 적용한 STED에 대한 비트 에러 오률 (BER) 특성과 계산량 분석을 통해서 우수성을 입증하였다.