• Title, Summary, Keyword: affine

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GENERALIZED AFFINE DEVELOPMENTS

  • Park, Joon-Sik
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.1
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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.

An approximated implementation of affine projection algorithm using Gram-Scheme orthogonalization (Gram-Schmidt 직교화를 이용한 affine projection 알고리즘의 근사적 구현)

  • 김은숙;정양원;박선준;박영철;윤대희
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.24 no.9B
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    • pp.1785-1794
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    • 1999
  • The affine projection algorithm has known t require less computational complexity than RLS but have much faster convergence than NLMS for speech-like input signals. But the affine projection algorithm is still much more computationally demanding than the LMS algorithm because it requires the matrix inversion. In this paper, we show that the affine projection algorithm can be realized with the Gram-Schmidt orthogonalizaion of input vectors. Using the derived relation, we propose an approximate but much more efficient implementation of the affine projection algorithm. Simulation results show that the proposed algorithm has the convergence speed that is comparable to the affine projection algorithm with only a slight extra calculation complexity beyond that of NLMS.

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INVARIANT OPEN SETS UNDER COCOMPACT AFFINE ACTIONS

  • Park, Kyeong-Su
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.1
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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.

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Controller Design and Stability Analysis of Affine System with Dead-Time (불감시간을 갖는 Affine 시스템의 안정도 해석과 제어기 설계)

  • Yang Hai-Won;Byun Hwang-Woo
    • Journal of Institute of Control, Robotics and Systems
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    • v.11 no.2
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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.

Viewpoint Unconstrained Face Recognition Based on Affine Local Descriptors and Probabilistic Similarity

  • Gao, Yongbin;Lee, Hyo Jong
    • Journal of Information Processing Systems
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    • v.11 no.4
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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.

Robust Multiloop Controller Design of Uncertain Affine TFM(Transfer Function Matrix) System (불확실한 Affine TFM(Transfer Function Matrix) 시스템의 강인한 다중 루프 제어기 설계)

  • Byun Hwang-Woo;Yang Hai-Won
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.54 no.1
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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.

Affine Local Descriptors for Viewpoint Invariant Face Recognition

  • Gao, Yongbin;Lee, Hyo Jong
    • Proceedings of the Korea Information Processing Society Conference
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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.

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SOME PROPERTIES OF VERMA MODULES OVER AFFINE LIE ALGEBRAS

  • Kim, Wan-Soon
    • Communications of the Korean Mathematical Society
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    • v.10 no.4
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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.

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Survey Analysis of Regional Name, Use and Availability of Gnaphalium affine at Jeonnam Province

  • Park, Yun Jum;Ku, Yang Gyu;Kim, Ho Cheol;Cho, Ja Yong;Heo, Buk Gu
    • Journal of People, Plants, and Environment
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    • v.20 no.2
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    • pp.185-193
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    • 2017
  • In order to establish basic data for the succession and development of use culture of Gnaphalium affine, a traditional rice cake plant resource, this study was carried out with a survey on 259 women aged 60 or over living 18 city and county in Jeonnam province. The results are summarized as follows. All respondents in the survey did not know the standard name of Gnaphalium affine. 178 repondents (68.7%) knew the plant name called in the local area. The frequency was higher in the order of Jebissuk (37.5%) > Gaessuk (21.2%) > Seorissuk (19.7%) > Gyessuk (4.3%) > Goissuk (1.9%), including duplicate responses. Of the 178 respondents who responded that they could distinguish it, 82.6% knew only one species, and 17.4% knew two in Gnaphalium affine. 62.3% of respondents said they ate dishes made from Gnaphalium affine, and 62.3% had experience cooking Gnaphalium affine. 61.8% of respondents said they ate rice cake made from Gnaphalium affine, and 40.2% had experience making rice cake with Gnaphalium affine. Edible taste of Gnaphalium affine was evaluated as 'delicious and sticy taste (4.75)'and 'above sticky (4.89)'according to criterion level 5.0. The final eating period was followed from 1951-1970 (33.1%) > 1971-1990 (29.4%) > 1991-2010 (17.5%) > after 2011 (13.8%) > before 1950 (10.0%), respectively. As a result, it is very necessary that the standard name of Gnaphalium affine is spread widely and the use culture is succeeded and active.