• Title/Summary/Keyword: representation groups

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MATRIX REALIZATION AND ITS APPLICATION OF THE LIE ALGEBRA OF TYPE F4

  • CHOI, SEUNGIL
    • Honam Mathematical Journal
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    • v.28 no.2
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    • pp.205-212
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    • 2006
  • The Lie algebra of type $F_4$ has the 26 dimensional representation. Its matrix realization can be obtained via 26 by 26 matrices and has a direct useful application to degenerate principal series for p-adic groups of type $F_4$.

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On the History and the Irreducible Characters in Group Representations (군표현의 역사와 기약지표들)

  • Wang Moon-ok;Lee Kwang-suk
    • Journal for History of Mathematics
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    • v.18 no.1
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    • pp.75-84
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    • 2005
  • In this paper, we know the historical background in group representations and prove the properties such that a finite group G has non-trivial abelian normal subgroup in some condition for the irreducible character G and prove the properties of product of irreducible characters of finite groups.

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VECTOR GENERATORS OF THE REAL CLIFFORD ALGEBRA Cℓ0,n

  • Song, Youngkwon;Lee, Doohann
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.4
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    • pp.571-579
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    • 2014
  • In this paper, we present new vector generators of a matrix subalgebra $L_{0,n}$, which is isomorphic to the Clifford algebra $C{\ell}_{0,n}$, and we obtain the matrix form of inverse of a vector in $L_{0,n}$. Moreover, we consider the solution of a linear equation $xg_2=g_2x$, where $g_2$ is a vector generator of $L_{0,n}$.

ON REGULARITY OF SOME FINITE GROUPS IN THE THEORY OF REPRESENTATION

  • Park, Eun-Mi
    • Communications of the Korean Mathematical Society
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    • v.9 no.4
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    • pp.773-782
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    • 1994
  • Investigation of the number of representations as well as of projective representations of a finite group has been important object since the early of this century. The numbers are very related to the number of conjugacy classes of G, so that this gives some informations on finite groups and on group characters. A generally well-known fact is that the number of non-equivlaent irreducible representations, which we shall write as n.i.r. of G is less than or equal to the number of conjugacy classes of G, and the equality holds over an algebraically closed field of characteristic not dividing $\mid$G$\mid$. A remarkable result on the numbers due to Reynolds can be stated as follows.

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Content-Based Image Retrieval System using Feature Extraction of Image Objects (영상 객체의 특징 추출을 이용한 내용 기반 영상 검색 시스템)

  • Jung Seh-Hwan;Seo Kwang-Kyu
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.27 no.3
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    • pp.59-65
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    • 2004
  • This paper explores an image segmentation and representation method using Vector Quantization(VQ) on color and texture for content-based image retrieval system. The basic idea is a transformation from the raw pixel data to a small set of image regions which are coherent in color and texture space. These schemes are used for object-based image retrieval. Features for image retrieval are three color features from HSV color model and five texture features from Gray-level co-occurrence matrices. Once the feature extraction scheme is performed in the image, 8-dimensional feature vectors represent each pixel in the image. VQ algorithm is used to cluster each pixel data into groups. A representative feature table based on the dominant groups is obtained and used to retrieve similar images according to object within the image. The proposed method can retrieve similar images even in the case that the objects are translated, scaled, and rotated.

HILBERT'S THEOREM 90 FOR NON-COMPACT GROUPS

  • Rovinsky, Marat
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.5
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    • pp.1757-1771
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    • 2017
  • Let K be a field and G be a group of its automorphisms. It follows from Speiser's generalization of Hilbert's Theorem 90, [10] that any K-semilinear representation of the group G is isomorphic to a direct sum of copies of K, if G is finite. In this note three examples of pairs (K, G) are presented such that certain irreducible K-semilinear representations of G admit a simple description: (i) with precompact G, (ii) K is a field of rational functions and G permutes the variables, (iii) K is a universal domain over field of characteristic zero and G its automorphism group. The example (iii) is new and it generalizes the principal result of [7].

Development of Gap Searching System for Car Body Assembly by Decomposition Model Representation (분해 모델을 이용한 자동차 차체의 틈새 탐색 시스템 개발)

  • Bae, Won-Jung;Lee, Sung-Hoon;Park, Sung-Bae;Jung, Yoong-Ho
    • Transactions of the Korean Society of Automotive Engineers
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    • v.20 no.4
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    • pp.109-118
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    • 2012
  • Large number of part design for aircraft and automobile is preceded by functional or sectional design groups for efficiency. However, interferences and gaps can be found when the parts and sub-assemblies by those design groups are to be assembled. These interferences and gaps cause design changes and additional repair processes. While interference problem has been resolved by digital mockup and concurrent engineering methodology, gap problem has been covered by temporary treatment of filling gap with sealant. This kind of fast fix causes fatal problem of leakage when the gap is too big for filling or the treatment gets old. With this research, we have developed a program to find the gap automatically among parts of assembly so that users can find them to correct their design before manufacturing stage. By using decomposition model representation method, the developed program can search the gap among complex car body parts to be visualized with volumetric information. It can also define the boundary between the gap and exterior empty space automatically. Though we have proved the efficiency of the developed program by applying to automobile assembly, application of the program is not limited to car body only, but also can be extended to aircraft and ship design of large number of parts.

Numerical Calculation Method for Paraxial Zoom Loci of Complicated Zoom Lenses with Infinite Object Distance by Using Gaussian Bracket Method (가우스 괄호법을 이용한 무한 물점을 갖는 복잡한 줌 렌즈의 수치해석적인 근축광선 줌 궤적 추적법)

  • Yoo, Nam-Jun;Kim, Won-Seob;Jo, Jae-Heung;Ryu, Jae-Myung;Lee, Hae-Jin;Kang, Geon-Mo
    • Korean Journal of Optics and Photonics
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    • v.18 no.6
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    • pp.410-420
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    • 2007
  • We theoretically derive the set of utilizable paraxial zoom locus equations for all complicated zoom lens systems with infinite object distance, such as a camera zoom lens, by using the Gaussian bracket method and the matrix representation of paraxial ray tracing. And we make the zoom locus program according to these equations in Visual Basic. Since we have applied the paraxial ray tracing equations into Gaussian bracket representation, the resultant program systematically simplifies various constraints of the zoom loci of various N group types. Consequently, the solutions of this method can be consistently used in all types of zoom lens in the step of initial design about zoom loci. Finally, in order to verify the usefulness of this method, we show that one example among 4 groups and that among 5 groups, which are very complex zoom lens systems, can be rapidly and with versatility traced through various interpolations by using this program.