• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1525-1537
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• 2019

Let ${\tilde{M}}$ be a Riemannian manifold equipped with a concircular vector field ${\tilde{X}}$ and M a submanifold (with its induced metric) of ${\tilde{M}}$. Denote by X the restriction of ${\tilde{X}}$ on M and by $X^T$ the tangential component of X, called the canonical field of M. In this article we study submanifolds of ${\tilde{M}}$ whose canonical field $X^T$ is also concircular. Several characterizations and classification results in this respect are obtained.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1823-1834
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• 2018

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold M. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component $x^T$ of the position vector field is the most natural vector field tangent to the Euclidean submanifold M. We simply call the vector field $x^T$ the canonical vector field of the Euclidean submanifold M. In earlier articles [4,5,9,11,12], we investigated Euclidean submanifolds whose canonical vector fields are concurrent, concircular, torse-forming, conservative or incompressible. In this article we study Euclidean submanifolds with conformal canonical vector field. In particular, we characterize such submanifolds. Several applications are also given. In the last section we present three global results on complete Euclidean submanifolds with conformal canonical vector field.

• The Journal of Society for e-Business Studies
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• v.8 no.1
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• pp.113-119
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• 2003

This paper proposes a new multiplicative inverse algorithm for the Galois field GF (2/sup m/) whose elements are represented by optimal normal basis type Ⅱ. One advantage of the normal basis is that the squaring of an element is computed by a cyclic shift of the binary representation. A normal basis element is always possible to rewrite canonical basis form. The proposed algorithm combines normal basis and canonical basis. The new algorithm is more suitable for implementation than conventional algorithm.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.709-715
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• 2008

We construct certain ring class fields over an imaginary quadratic field by making use of Shimura's canonical models and extend the result of Chen-Yui ([1] Theorem 3.7.5(2)) to the case where (a, b, N) $\neq$ N or (a/N, N) $\neq$ 1 for a positive integer N > 1.

• Bulletin of the Korean Mathematical Society
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• v.24 no.1
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• pp.47-47
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• 1987

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.2
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• pp.18-24
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• 2010

A correct and accurate model of optical data storage systems is very important in development and performance evaluation of various data detection algorithms. In this paper, we present an nonlinear modeling scheme of a super-resolution near-field structure (Super-RENS) read-out signal using the canonical piecewise-linear (PWL) and the second-order Volterra models. Nonlinear equalizers may be developed on the basis of the information obtained from this nonlinear modeling. To mitigate the nonlinear inter-symbol interference (ISI), we proposed a new nonlinear equalizer for Super-RENS discs. Its validity is tested with the RF signal samples obtained from a Super-RENS disc. The experiment results verified the possibility that the canonical PWL and the second-older Volterra models can be utilized for nonlinear modeling of Super-RENS systems. The proposed equalizers are superior to the one without equalization in terms of bit error rate (BER).

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1077-1100
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• 2016

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.939-942
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• 1988

In order to construct a nonlinear observer, change of coordinate system is necessary. However, as in the case of feedback linearizable system it is not easy to obtain a coordinate transformation map. ln this paper, a canonical structure is proposed for observable systems with an objective of finding a vector field which is necessary for the generation of a new coordinate system.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.763-770
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• 2006

Let X be a four-dimensional projective variety defined over the field of complex numbers with only terminal singularities. We prove that if the intersection number of the canonical divisor K with every very general curve is positive (K is almost numerically positive) then every very general proper subvariety of X is of general type in ';he viewpoint of geometric Kodaira dimension. We note that the converse does not hold for simple abelian varieties.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.45 no.4
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• pp.267-271
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• 2000

A total of 1,830 soybean collections were grown in the field and characterized for 10 morphological traits to determine the diversity and relationship within and among geographical regions. Phenotypic variation was found within all regions for most characters. The Shannon-Weaver diversity index ranged from 0.49 to 0.62 across regions, and 0.09 to 1.00 across characters. Canonical discriminant analysis and clustering of the canonical means delineated 3 regional clusters: (ⅰ) Kyunggi, Chungchong, Kangwon, Chulla, and Kyungsang; (ⅱ) Heilongjiang; and (ⅲ) Jilin, Manchuria, central China, south China, Others (China), Hokkaido, Honshu, and Others (Japan).