• 충청수학회지
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• 제28권1호
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• pp.65-72
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• 2015

The (affine) development of a smooth curve in a smooth manifold M with respect to an arbitrarily given affine connection in the bundle of affine frames over M is well known (cf. S.Kobayashi and K.Nomizu, Foundations of Differential Geometry, Vol.1). In this paper, we get the generalized affine development of a smooth curve $x_t$ ($t{\in}[0,1]$) in M into the affine tangent space at $x_0$ (${\in}M$) with respect to a given generalized affine connection in the bundle of affine frames over M.

• 한국통신학회논문지
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• 제24권9B호
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• pp.1785-1794
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• 1999

Affine projection 알고리즘은 RLS보다 적은 계산량으로 LMS보다 우수한 수렴성능을 나타낸다. 그러나 affine projection 알고리즘은 역행렬 연산을 필요로 하기 때문에 여전히 LMS에 비해 과중한 계산을 필요로 한다. 본 논문에서는 affine projection 알고리즘을 분석하여 이 알고리즘이 Gram-Scheme 구조로 해석될 수 있음을 보이고 이를 이용하여 NLMS와 비슷한 계산량으로 affine projection 알고리즘을 근사적으로 구현할 수 있는 새로운 알고리즘을 제안하였다. 제안한 방법은 NLMS와 비슷한 계산량을 가지면서 기존의 affine projection 알고리즘과 비슷한 수렴성능을 나타내었다.

• Korean Journal of Mathematics
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• 제30권4호
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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.

• 대한수학회보
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• 제36권1호
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• pp.203-207
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• 1999

In this paper, we find a condition of an open subset of the affine space which admits a cocompact affine action. To do it, the asymptotic flag of an open convex subset is introduced and some applications to affine manifolds are presented.

• Journal of Information Processing Systems
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• 제11권4호
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• pp.643-654
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• 2015

Face recognition under controlled settings, such as limited viewpoint and illumination change, can achieve good performance nowadays. However, real world application for face recognition is still challenging. In this paper, we propose using the combination of Affine Scale Invariant Feature Transform (SIFT) and Probabilistic Similarity for face recognition under a large viewpoint change. Affine SIFT is an extension of SIFT algorithm to detect affine invariant local descriptors. Affine SIFT generates a series of different viewpoints using affine transformation. In this way, it allows for a viewpoint difference between the gallery face and probe face. However, the human face is not planar as it contains significant 3D depth. Affine SIFT does not work well for significant change in pose. To complement this, we combined it with probabilistic similarity, which gets the log likelihood between the probe and gallery face based on sum of squared difference (SSD) distribution in an offline learning process. Our experiment results show that our framework achieves impressive better recognition accuracy than other algorithms compared on the FERET database.

• 제어로봇시스템학회논문지
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• 제11권2호
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• pp.93-102
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• 2005

The Nyquist robust stability margin is proposed as a measure of robust stability for systems with Affine TFM(Transfer Function Matrix) parametric uncertainty. The parametric uncertainty is modeled through a Affine TFM MIMO (Multi-Input Multi-Output) description with dead-time, and the unstructured uncertainty through a bounded perturbation of Affine polynomials. Gershgorin's theorem and concepts of diagonal dominance and GB(Gershgorin Bands) are extended to include model uncertainty. Multiloop PI/PID controllers can be tuned by using a modified version of the Ziegler-Nichols (ZN) relations. Consequently, this paper provides sufficient conditions for the robustness of Affine TFM MIMO uncertain systems with dead-time based on Rosenbrock's DNA. Simulation examples show the performance and efficiency of the proposed multiloop design method for Affine uncertain systems with dead-time.

• 대한전기학회논문지:시스템및제어부문D
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• 제54권1호
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• pp.17-25
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• 2005

This paper provides sufficient conditions for the robustness of Affine linear TFM(Transfer Function Matrix) MIMO (Multi-Input Multi-Output) uncertain systems based on Rosenbrock's DNA (Direct Nyquist Array). The parametric uncertainty is modeled through a Affine TFM MIMO description, and the unstructured uncertainty through a bounded perturbation of Affine polynomials. Gershgorin's theorem and concepts of diagonal dominance and GB(Gershgorin Bands) are extended to include model uncertainty. For this type of parametric robust performance we show robustness of the Affine TFM systems using Nyquist diagram and GB, DNA(Direct Nyquist Array). Multiloop PI/PB controllers can be tuned by using a modified version of the Ziegler-Nickels (ZN) relations. Simulation examples show the performance and efficiency of the proposed multiloop design method.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2014년도 춘계학술발표대회
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• pp.781-784
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• 2014

Face recognition under controlled settings, such as limited viewpoint and illumination change, can achieve good performance nowadays. However, real world application for face recognition is still challenging. In this paper, we use Affine SIFT to detect affine invariant local descriptors for face recognition under large viewpoint change. Affine SIFT is an extension of SIFT algorithm. SIFT algorithm is scale and rotation invariant, which is powerful for small viewpoint changes in face recognition, but it fails when large viewpoint change exists. In our scheme, Affine SIFT is used for both gallery face and probe face, which generates a series of different viewpoints using affine transformation. Therefore, Affine SIFT allows viewpoint difference between gallery face and probe face. Experiment results show our framework achieves better recognition accuracy than SIFT algorithm on FERET database.

• 호남수학학술지
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• 제37권1호
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• pp.53-63
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• 2015

We get a necessary and sufficient condition for a generalized affine connection in the affine orthonormal frame bundle over a smooth manifold (M, g) to be a Yang-Mills connection.

• 대한수학회논문집
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• 제10권4호
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• pp.789-795
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• 1995

For nonintegrable weight $-\rho$, some weight multiplicities of the irreducible module $L(-\rho)$ over $A^{(1)}_{(1)}$ affine Lie algebras are expressed in terms of the colored partition functions. Also we find the multiplicity of $L(-\rho)$ in ther Verma module $M(-\rho)$ for any affine Lie algebras.