• 충청수학회지
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• 제36권2호
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• pp.125-133
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• 2023

We establish a characterization theorem of elliptic paraboloids in the (n+1)-dimensional Euclidean space 𝔼ⁿ⁺¹ with extrinsic properties such as the (n+1)-dimensional volumes of regions enclosed by the hyperplanes and hypersurfaces, and the n-dimensional areas of projections of the sections of hypersurfaces cut off by hyperplanes.

• 한국정밀공학회지
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• 제17권11호
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• pp.206-212
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• 2000

This paper presents a hybrid actuator scheme to actively control the end-point position and vibration of a two-link flexible robot arm. Control scheme consists of four different actuators; two servo-motors at the hubs and two piezoceramics bonded to the surfaces of the flexible links. Two sliding hyperplanes are designed for two servo-motors which have time varying parameters to maintain control performance in any configuration. The surface gradients of the hyperplanes are determined by pole assignment technique to guarantee the stability on the hyperplanes themselves. During the motion, undesirable oscillations caused by the torques based on the rigid link dynamics are actively suppressed by applying feedback control voltages to the piezoceramic actuators. Consequently, desired tip motion is achieved. In order to demonstrate the effectiveness of the proposed methodology, experiments are performed for the regulating and tracking control problems.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2004년도 가을 학술발표논문집 Vol.31 No.2 (2)
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• pp.703-705
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• 2004

Conventional support vector machines (SVMs) find optimal hyperplanes that have maximal margins by treating all data equivalently. In the real world, however, the data within a data set may differ in degree of uncertainty or importance due to noise, inaccuracies or missing values in the data. Hence, if all data are treated as equivalent, without considering such differences, the optimal hyperplanes identified are likely to be less optimal. In this paper, to more accurately identify the optimal hyperplane in a given uncertain data set, we propose a membership-induced distance from a hyperplane using membership values, and formulate three kinds of membership-induced SVMs.

• 대한수학회보
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• 제48권2호
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• pp.335-342
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• 2011

In this paper, we prove that minimal hypersurfaces when n $\geq$ 3 and nonzero constant mean curvature hypersurfaces when n $\geq$ 2 foliated by spheres in parallel horizontal hyperplanes in $\mathbb{H}^n{\times}\mathbb{R}$ must be rotationally symmetric.

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

• 충청수학회지
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• 제20권2호
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• pp.109-115
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• 2007

In this paper, we obtain the general solution and the stability of the multi-dimensional Cauchy's functional equation $f(x_1+y_1,{\cdots},x_n+y_n)=f(x_1,{\cdots},x_n)+f(y_1,{\cdots},y_n)$. The function f given by $f(x_1,{\cdots},x_n)=a_1x_1+{\cdots}+a_nx_n$ is a solution of the above functional equation.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.634-639
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• 1998

A methodology based on the concept of variable string length GA(VGA) is developed for determining automatically the number of hyperplanes and their appropriate arrangement for modeling the class boundaries of a given training data set in RN. The genetic operators and fitness functionare newly defined to take care of the variability in chromosome length. Experimental results on different artificial and real life data sets are provided.

• 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 $x_i+x_j=1$, $x_k=0$, $x_l=1$, $1{\leq}i,j,k,l{\leq}n$.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.1213-1218
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• 1993

Variable structure control is applied to the robust output tracking control problem of general nonlinear multi-input multi-output (MIMO) systems. Using the concept of relative degree and minimum phase, input/output(I/O) linearization is undertaken. For I/O the linearized system, a new sliding hyperplanes design method is proposed. In this procedure, we can construct very robust and efficient sliding mode controller for general nonlinear systems of relative degree higher than two. The control results are illustrated by adopting a numerical example.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.505-510
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• 1994

To prevent the stable states from the complex dynamics, the global behavior of the overall system must be considered. Thus, indirect adaptive scheme might result in needless responses. Discrete-time variable structure controllers for a well-known logistic map are designed for two deferent sliding hyperplanes. Impulse disturbances are fully rejected by tile virtue of discrete-time variable structure control(DVSC). A numerical example is given to illustrate the effectless of the DVSC.