• Korean Journal of Mathematics
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• v.30 no.4
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• pp.643-652
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• 2022

In this paper, we will describe affine homogeneous domains in the complex plane. For this study, we deal with the Lie algebra of infinitesimal affine transformations, a structure of the hyperbolic metric involved with affine automorphisms. As a consequence, an affine homogeneous domain is affine equivalent to the complex plane, the punctured plane or the half plane.

• The Transactions of the Korea Information Processing Society
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• v.3 no.7
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• pp.1894-1905
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• 1996

Delauuany triangulation which is the dual of Dirichlet tessellation is not affine invariant. In other words, the triangulation is dependent upon the choice of the coordinate axes used to represent the vertices. In the same reason, Delahanty tetrahedrization does not have an affine iveariant transformation property. In this paper, we present a new type of tetrahedrization of spacial points sets which is unaffected by translations, scalings, shearings and rotations. An affine invariant tetrahedrization is discussed as a means of affine invariant 2 -D triangulation extended to three-dimensional tetrahedrization. A new associate norm between two points in 3-D space is defined. The visualization of the structure of tetrahedrization can discriminate between Delaunay tetrahedrization and affine invariant tetrahedrization.

• The Journal of the Acoustical Society of Korea
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• v.23 no.3
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• pp.221-227
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• 2004

This paper presents the subband affine projection algorithm(SAPA). The improved performance of SAPA is achieved by applying the affine projection algorithm to the subband adaptive structure. In this algorithm, the weight updating formula of adaptive filter is simply derived by using the orthogonal quadrature filter(OQF) as an analysis filter bank for subband filtering. The derived SAPA has the fast convergence speed and small computational complexity. The efficiency of the proposed algorithm for colored input signal is evaluated through some experiments.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.6
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• pp.1173-1178
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• 2010

In this note, a systematic design of a new robust nonlinear integral variable structure controller based on state dependent nonlinear form is presented for the control of uncertain more affine nonlinear systems with mismatched uncertainties and matched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear integral variable structure controller is presented. To be linear in the closed loop resultant dynamics and remove the reaching phase problems, the linear integral sliding surface is suggested. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the linear integral sliding surface, which will be investigated in Theorem 1. Through a design example and simulation studies, the usefulness of the proposed controller is verified.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.5
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• pp.945-949
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• 2010

In this paper, a systematic design of a new robust nonlinear variable structure controller based on state dependent nonlinear form is presented for the control of uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.7
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• pp.1295-1301
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• 2010

In this note, a systematic general design of a new robust nonlinear variable structure controller based on state dependent nonlinear form is presented for the control of uncertain affine nonlinear systems with mismatched uncertainties and mismatched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the nonlinear integral-type sliding surface is applied. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the nonlinear integral-type sliding surface, which will be investigated in Theorem 1. Through a design example and simulation studies, the usefulness of the proposed controller is verified.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1754-1760
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• 2011

In this paper, a systematic design of a robust nonlinear multivariable variable structure controller based on state dependent nonlinear form is presented for the control of MIMO uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After a MIMO uncertain affine nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding diagonalized control input is proposed to satisfy the closed loop global exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.183-201
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• 1999

Let M be an 0-minimal structure on the standard structure :=( , +, ,<) of the field of real numbers. We study Cr -G manifolds (0$\leq$r$\leq$w) which are generalizations of Nash manifolds and Nash G manifolds. We prove that if M is polynomially bounded, then every Cr -G (0$\leq$r<$\infty$) manifold is Cr -G imbeddable into some n, and that if M is exponential and G is a compact affine Cw -G group, then each compact $C\infty$ -G imbeddable into some representation of G.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1301-1324
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• 2006

The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.165-167
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• 2005

Let M = (R, +, $\cdot$, <, ... ) be an o-minimal expansion of the standard structure R = (R, +, $\cdot$, >) of the field of real numbers. We prove that if 2 $\le$ r < $\infty$, then every n-dimensional definable $C^r$ manifold is definably $C^r$ imbeddable into $R^{2n+l}$. Moreover we prove that if 1 < s < r < $\infty$, then every definable $C^s$ manifold admits a unique definable $C^r$ manifold structure up to definable $C^r$ diffeomorphism.