• Journal for History of Mathematics
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• v.30 no.2
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• pp.53-69
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• 2017

This paper demonstrates how a nineteenth century Japanese votive temple problem known as sangaku from Okayama prefecture can be solved using traditional mathematical methods of the Japanese Edo (1603-1868 CE). We compare a modern solution to a sangaku problem from Sacred Geometry: Japanese Temple Problems of Tony Rothman and Hidetoshi Fukagawa with a traditional solution of ${\bar{O}}hara$ Toshiaki (?-1828). Our investigation into the solution of ${\bar{O}}hara$ provides an example of traditional Edo period mathematics using the tenzan jutsu symbolic manipulation method, as well as producing new insights regarding the contextual nature of the rules of this technique.

• Architectural research
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• v.13 no.3
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• pp.41-47
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• 2011

A study on the free vibration analysis of elastic bar is described in this paper. In order to determine the natural frequencies of bars, a bar element is developed by using isogeometric formulation. The B-spline is introduced to represent the geometry of bar and the same geometric definition is also used to define its unknown displacement field in isogeometric formulation. Therefore, the stiffness and mass matrices are derived by the order-free B-spline basis function. The efficiency and accuracy of the present isogeometric bar elementis demonstrated by using several numerical tests. From numerical results, it is found to be that the present isogeometric element produces very accurate natural frequencies of bars. Finally, the present isogeometric solutions are provided as future reference solutions.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.894-895
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• 2007

This paper presents coupled analysis between finite element method and analytic technique for predicting temperature rise of 25.8kV 25kA three-phase GIS bus bar. The power losses and temperature distribution of three-phase GIS bus bar model are analyzed by magneto-thermal finite element method. The heat transfer coefficients on the boundaries are analytically calculated by applying Nusselt number considering material constant and model geometry for the natural convection. And these are used as the input data to predict the temperature rise of three-phase GIS bus bar model by coupled magneto-thermal F.E.A. The predicted temperature of 25.8kV 25kA three-phase GIS bus bar model shows good agreement with the experimental data.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.08a
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• pp.88-97
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• 1999

In this study, a systematic approach for roll pass design in bar rolling was studied. To minimize the trial and errors in the process design, a roll CAD system and a FE analysis system were combined. Based on the system, a methodology for roll pass design by FEM was studied. At first, designed process was compared with the FE analysis results and process redesign based on the FEM results was performed to obtain the specified final geometry. Then, empirical formula for roll speed set-up was compared with the FE analysis results. Further study on various simulations for bar rolling will help in making up for the inaccuracy in the currently used empirical roll speed rules. In addition, verification of the accuracy of the FE analysis system must be performed using experimental data in the industry.

• Proceedings of the KIEE Conference
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• 2005.07b
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• pp.990-992
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• 2005

This paper presents a new magneto-thermal finite element analysis for predicting the temperature rise of the EHV GIS bus bar. The power losses of a bus bar calculated by the magnetic field analysis are used as the input data to predict the temperature rise for the thermal analysis. The heat-transfer coefficients on the boundaries are analytically calculated by applying the Nusselt number considering material constant and model geometry for the natural convection. The temperature distribution in a bus bar by coupled magneto-thermal finite element analysis shows good agreement with the experimental data.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.451-461
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• 2014

We study the geometry of indefinite trans-Sasakian manifold $\bar{M}$, of type (${\alpha},{\beta}$), admitting a half lightlike submanifold M such that the structure vector field of $\bar{M}$ does not belong to the screen and coscreen distributions of M. The purpose of this paper is to prove several classification theorems of such an indefinite trans-Sasakian manifold.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.635-647
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• 2011

In this paper, we study the geometry of real half lightlike submanifolds of an indefinite Kaehler manifold $\bar{M}$. We provide several new results on such a real half lightlike submanifold M by using the F-structure of M induced by the almost complex structure J of $\bar{M}$.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.25-35
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• 2013

In this paper, we study lightlike hypersurfaces of an indefinite Sasakian manifold $\bar{M}$. First, we construct a type of lightlike hypersurface according to the form of the structure vector field of $\bar{M}$, named by ascreen lightlike hypersurface. Next, we characterize the geometry of such ascreen lightlike hypersurfaces.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1711-1726
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• 2014

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a generic lightlike submanifold M subject such that the structure vector field of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. The purpose of this paper is to prove a classification theorem of such an indefinite generalized Sasakian space form.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.1097-1104
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• 2015

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a lightlike hypersurface M subject such that the almost contact structure vector field ${\zeta}$ of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. We prove a classification theorem of such an indefinite generalized Sasakian space form.