• 대한수학회보
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• 제56권1호
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• pp.201-217
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• 2019

Ricci curvature for locally finite graphs, as proposed by Lin, Lu and Yau, provides a useful isomorphism invariant. A Matching Condition was introduced as a key tool for computation of this Ricci curvature. The scope of the Matching Condition is quite broad, but it does not cover all cases. Thus the current paper introduces extended versions of the Matching Condition, and applies them to the computation of the Ricci curvature of a class of circulants determined by certain number-theoretic data. The classical Matching Condition is also applied to determine the Ricci curvature for other families of circulants, along with Cayley graphs of abelian groups that are generated by the complements of (unions of) subgroups.

• 대한수학회지
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• 제49권6호
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• pp.1111-1121
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• 2012

A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we classify tetravalent symmetric graphs of order $9p$ for each prime $p$.

• 대한수학회보
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• 제51권6호
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• pp.1689-1696
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• 2014

Recently, it was proved that every p-Schur ring over an abelian group of order $p^3$ is Schurian. In this paper, we prove that every commutative p-Schur ring over a non-abelian group of order $p^3$ is Schurian.

• Kyungpook Mathematical Journal
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• 제45권3호
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• pp.363-394
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• 2005

In this expository paper we survey basic results on isotropic immersions.

• 호남수학학술지
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• 제41권3호
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• pp.505-514
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• 2019

In this paper, some results are obtained from studying convolution on the spectrum of full transformation semigroup and some of its subsemigroups using Cayley's table. The shift of ${\alpha}$ determines its eigenvalues and one-dimensional linear convolution is complex in Symmetric group.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.471-471
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• 2000

This paper presents a new kurtosis-based algorithm for blind separation of convolutively mixed source signals. The algorithm whitens the signals not only spatially but also temporally beforehand. A separator is built for the whitened signals and it exists in the set of para-unitary matrices. Since the set forms a curved manifold, it is hard to treat its elements. In order to avoid the difficulty, this paper introduces the Cayley transformation for the para-unitary matrices. The transformed matrix is referred to as para-skew-Hermitian matrix and the set of such matrices forms a linear space. In the set of all para-skew-Hermitian matrices, the kurtosis-based algorithm obtains a desired separator. This paper also shows the algorithm's application to electrogastrogram datum which are observed by 4 electrodes on subjects' abdomen around their stomachs. An electrogastrogram contains signals from a stomach and other organs. This paper obtains independent components by the algorithm and then extracts the signal corresponding to the stomach from the data.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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• pp.269-280
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• 2006

Recently $L_{\delta}$-groups were introduced in the study of geometric group theory. Three levels of $L_{\delta}$-groups are difined and discussed. It is shown that each of these levels of $L_{\delta}$-groups is closed under taking a direct product.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2008년도 한국컴퓨터종합학술대회논문집 Vol.35 No.1 (B)
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• pp.584-587
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• 2008

매크로-스타그래프와 전위그래프는 Cayley 그래프로 널리 알려지니 상호연결망이다. 본 논문에서는 매크로-스타그래프와 전위그래프에 연장을 5, 확장률 1에 임베딩 가능함을 보인다. 또한, 전위그래프를 매크로-스타 그래프에 임베딩하는 연장율이 O(n)이지만, 평균 연장율이 2이하임을 보인다. n은 전위 그래프의 차원이다.

• Korean Journal of Mathematics
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• 제31권3호
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• pp.295-303
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• 2023

This paper introduces a novel method for obtaining umbrella matrices, which are defined as orthogonal matrices with row sums of one, using skew-symmetric matrices and Cayley's Formula. This method is presented for the first time in this paper. We also investigate the kinematic properties and applications of umbrella matrices, demonstrating their usefulness as a tool in geometry and kinematics. Our findings provide new insights into the connections between matrix theory and geometric applications.

• 대한기계학회논문집B
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• 제20권8호
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• pp.2572-2592
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• 1996

A low-Reynolds-number second moment turbulence closure was developed with the aid of DNS data. Model coefficients of nonlinear return to isotropy term were derived by use of Cayley-Hamilton theorem and two component turbulence limit condition as the functions of invariances of anisotropy and turbulent Reynolds number. Launder and Tselepidakis' cubic mean pressure strain model was modified to fit the predicted pressure-strain components to the DNS data. Two component turbulence limit condition was the precondition to be satisfied in developing the second moment turbulence closure for the realizable Reynolds stress prediction. But the satisfactions of Reynolds stress level and pressure-strain level of each component were compromised because the satisfaction of both levels was impossible.