• Proceedings of the KIEE Conference
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• 2009.07a
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• pp.1921_1922
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• 2009

According to recent researches, apparent power in non-sinusoidal single phase system can be represented with geometric algebra. In this paper, the geometric algebra is applied to apparent power defined in a multi-line system having transmission lines with frequency-dependent resistances under non-sinusoidal conditions.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.10
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• pp.2064-2070
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• 2009

According to recent researches, apparent power in a non-sinusoidal single phase system can be represented with geometric algebra. In this paper, the geometric algebra is applied to apparent power defined in a multi-line system having transmission lines with frequency-dependency under non-sinusoidal conditions.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.05a
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• pp.359-360
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• 2010

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.327-335
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• 2022

Let R be a commutative ring with identity. We call the ring R to be an almost weakly finite conductor if for any two elements a and b in R, there exists a positive integer n such that aⁿR ∩ bⁿR is finitely generated. In this article, we give some conditions for the trivial ring extensions and the amalgamated algebras to be almost weakly finite conductor rings. We investigate the transfer of these properties to trivial ring extensions and amalgamation of rings. Our results generate examples which enrich the current literature with new families of examples of nonfinite conductor weakly finite conductor rings.

• East Asian mathematical journal
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• v.37 no.4
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• pp.401-426
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• 2021

In order to propose ways to implement mathematical connection between algebra and geometry, this study reinterpreted and visualized the Khayyam's geometric method solving the cubic equations using two conic sections and the Al-Kāshi's method of constructing of angle trisection using a cubic equation. Khayyam's method is an example of a geometric solution to an algebraic problem, while Al-Kāshi's method is an example of an algebraic a solution to a geometric problem. The construction and property of conics were presented deductively by the theorem of "Stoicheia" and the Apollonius' symptoms contained in "Conics". In addition, I consider connections that emerged in the alternating process of algebra and geometry and present meaningful Implications for instruction method on mathematical connection.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.05a
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• pp.279-280
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• 2012

• Journal of the Korean Society for Precision Engineering
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• v.29 no.10
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• pp.1119-1127
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• 2012

In this paper, we present an inverse kinematics of a 7-dof Anthropomorphic robot arm using conformal geometric algebra. The inverse kinematics of a 7-dof Anthropomorphic robot arm using CGA can be computed in an easy way. The geometrically intuitive operations of CGA make it easy to compute the joint angles of a 7-dof Anthropomorphic robot arm which need to be set in order for the robot to reach its goal or the positions of a redundant robot arm's end-effector. In order to choose the best solution of the elbow position at an inverse kinematics, optimization techniques have been proposed to minimize an objective function while satisfying the euler-lagrange equation.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.715-730
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• 2016

The purpose of this study is to analyze Descartes's point of view on the mathematical connection of algebra and geometry which help comprehend the traditional frame with a new perspective in order to access to unsolved problems and provide useful pedagogical implications in school mathematics. To achieve the goal, researchers have historically reviewed the fundamental principle and development method's feature of analytic geometry, which stands on the basis of mathematical connection between algebra and geometry. In addition we have considered the significance of geometric solving of equations in terms of analytic geometry by analyzing related preceding researches and modern trends of mathematics education curriculum. These efforts could allow us to have discussed on some opportunities to get insight about mathematical connection of algebra and geometry via geometric approaches for solving equations using the intersection of curves represented on coordinates plane. Furthermore, we could finally provide the method and its pedagogical implications for interpreting geometric approaches to cubic equations utilizing intersection of conic sections in the process of inquiring, solving and reflecting stages.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.635-647
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• 1995

Let $H$ denote a separable, infinite dimensional complex Hilbert space and let $L(H)$ denote the algebra of all bounded linear operators on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $1_H$ and is closed in the $weak^*$ operator topology on $L(H)$. For $T \in L(H)$, let $A_T$ denote the smallest subalgebra of $L(H)$ that contains T and $1_H$ and is closed in the $weak^*$ operator topology.

• Journal of the Korean Society for Precision Engineering
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• v.32 no.3
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• pp.253-261
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• 2015

A parallel mechanism with redundancy can be regarded as a means for not only maximizing the benefits of parallel mechanisms but also overcoming their drawbacks. We proposed a novel parallel mechanism by eliminating an unnecessary degree of freedom of the configuration space. Because of redundancy, however, the solution for the inverse kinematics of the developed parallel mechanism is infinite. Therefore, we defined a cost function that can minimize the movement time to the target orientation and found the solution for the inverse kinematics by using a numerical method. In addition, we proposed a method for determining the boundary of the geometric singularity in order to avoid singularities.