• 대한수학회보
• /
• 제54권2호
• /
• pp.375-382
• /
• 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.

• 대한수학회보
• /
• 제58권1호
• /
• pp.21-30
• /
• 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.

• 대한수학회보
• /
• 제53권5호
• /
• pp.1281-1289
• /
• 2016

Richard Stanley suggested the problem of finding combinatorial proofs of formulas for counting regions of certain hyperplane arrangements defined by hyperplanes of the form $x_i=0$, $x_i=x_j$, and $x_i=2x_j$ that were found using the finite field method. We give such proofs, using embroidered permutations and linear extensions of posets.

• 대한수학회보
• /
• 제26권2호
• /
• pp.185-190
• /
• 1989

In [4], J. Leray introduced the notion of partial hyperbolicity to characterize the operators for which the non-characteristic Cauchy problem is solvable in the Geverey class for any data which are holomorphic in a part of variables x"=(x$_{2}$,..,x$_{l}$ ) in the initial hyperplane x$_{1}$=0. A linear partial differential operator is called partially hyperbolic modulo the linear subvarieties S:x"=constant if the equation P$_{m}$(x, .zeta.$_{1}$, .xi.')=0 for .zeta.$_{1}$ has only real roots when .xi.'is real and .xi."=0, where P$_{m}$ is the principal symbol of pp. Limiting to the case of operators with constant coefficients, A. Kaneko proposed a new sharper condition when S is a hyperplane [3]. In this paper, we generalize this condition to the case of general linear subvariety S and show that it is sufficient for the solvability of Cauchy problem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.blem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.

• East Asian mathematical journal
• /
• 제16권2호
• /
• pp.205-214
• /
• 2000

In this paper, we shall give new characterizations of best approximation element in linear 2-normed spaces in terms of bounded linear 2-functionals and 2-hyperplanes.

• 대한수학회보
• /
• 제30권1호
• /
• pp.29-34
• /
• 1993

J. Leray [7] proposed a sufficient condition ofr the solvability of the Cauchy problem on the initial hyperplane x$_{1}$=0 with Cauchy data which are holomorphic with respect to the variables parallel to some analytic subvariety S of the initial hyperplane. Limiting the problem to the case of operators with constant coefficients, A. Kaneko [2] proposed a new sharper sufficient condition. Later we generalized this condition and showed that it is necessary and sufficient for the solvability of the Cauchy problem for the hyperfunction Cauchy data and the distribution Cauchy data which contain variables parallel to S as holomorphic parameters in [5, 6]. In this paper, we extend the results in [6] to the case of operators with variable coefficients and show that it is sufficient for the solvability of the Cauchy problem for the hyperfunction Cauchy data. Our main theorem can be considered as an example of a deep theorem on micro-hyperbolic systems by Kashiwara-Schapira [4] and we give a direct proof based on an elementary sweeping out procedure developed in Kaneko [3].

• 대한수학회지
• /
• 제58권6호
• /
• pp.1485-1500
• /
• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• 한국정보과학회논문지:소프트웨어및응용
• /
• 제27권4호
• /
• pp.422-431
• /
• 2000

본 논문에서는 주성분 해석 기법에 기반한 새로운 벡터 양자화 코드북 설계 방법을 제안한다. 주성분 해석 알고리즘은 입력 영상벡터를 더 작은 차원의 특징 벡터로 변환시키는데 사용되며, 변환된 영역에서 특징 벡터의 군집을 최적으로 결정된 분할 초평면을 이용하여 두 군집으로 분할하는 과정을 반복 함으로써 코드북을 생성한다. 본 논문에서는 연산 시간이 오래 걸리는 최적 분할 초평면 탐색을 (1) 분할 초평면은 특징 벡터의 주축에 수직이며, (2) 좌우측 부군집의 오차의 균형점과 일치하며, (3) 좌우측 부군집의 오차를 점진적으로 조정함으로서 연산 수행 시간을 크게 단축시켰다. 제안한 주축 연속 분할은 분할전후의 오차의 감축이 가장 큰 군집에 대해, 전체 군집의 오차가 설정한 수준보다 작을 때까지 연속적으로 수행된다. 실험 결과 제안한 주성분 해석 기반 벡터 양자화 방법은 SOFM을 이용한 방법보다 수행시간이 빠르며 K-mean 알고리즘을 이용한 방법보다 복원 성능이 뛰어남을 볼 수 있다.

• 전기전자학회논문지
• /
• 제13권2호
• /
• pp.140-149
• /
• 2009

최근 인터넷을 통한 각종 침해사고 및 트래픽 폭주와 같은 현상이 급격하게 증가함에 따라 네트워크의 비정상적 상황을 조기에 탐지하기 위한 보다 능동적이고 진보적인 기술이 요구되고 있다. 본 논문에서는 캠퍼스 네트워크와 같이 트래픽이 주기적인 특성을 띠는 환경에서 Fisher 선형 분류법(FLD)을 사용하여 트래픽을 두 개의 그룹으로 분류하고, 네트워크에 유입되는 트래픽이 어떤 그룹에 속하는지를 판별하는 기법을 제안한다. 이를 위해 WISE-Mon이라 불리는 트래픽 분석 시스템을 개발하여 캠퍼스 네트워크의 트래픽을 수집하고 이를 모니터링해서 분석을 수행한다. 생성된 트래픽의 training set을 이용하여 비정상 트래픽의 범위를 판단하기 위한 chi-square distribution을 유도하고, FLD를 적용하여 유입되는 트래픽을 두 그룹으로 분리하기 위한 초평면 (hyperplane)을 만든다. 또한 네트워크 내의 트래픽 패턴이 시간이 지남에 따라 계속적으로 변하는 상황을 반영하기 위하여 self-learning 알고리즘을 적용한다. 캠퍼스 네트워크의 트래픽을 적용한 수학적 결과를 통하여 제안하는 기법의 정확성과 신뢰도를 보여준다.

• 대한수학회보
• /
• 제59권2호
• /
• pp.361-373
• /
• 2022

We study the factoriality of a nodal quartic hypersurface V₄ in ℙ⁴ when there is a hyperplane in ℙ⁴ containing all the nodes of V₄. As an application, we obtain new examples of irrational quartic 3-folds.