• The KIPS Transactions:PartA
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• v.9A no.1
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• pp.99-104
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• 2002

The goal of this paper is to generalize the concept of Bezier curves and surfaces defined on the vector space $R_n$ to Lie groups, which is a new generation method of curves (called Bezier curves) on Lie groups. The defined Bezier curves and surfaces are alsways smooth because of the properties of Lie groups. We apply this method to smooth motion interpolation or smooth trajectory generation for moving rigid body in space.

• Honam Mathematical Journal
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• v.2 no.1
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• pp.1-8
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• 1980

논문(論文)[3] (본(本) 논문(論文) 제1부(第1部))에서 미분가능다양체(微分可能多樣體) M 위의 (n-1)차(次) 미분형식(微分型式) ${\beta}^{(n-1)}$이 Compact인 Carrier를 가지면 ${\int}d{\beta}^{(n-1)}=0$이며, (p-1)차(次) 미분형식(微分型式) ${\beta}^{(p-1)}$과 p차(次) 미분가능쇄(微分可能쇄鎖) $C^{(p)}=\Sigma\limits_ik_iS_i{^{(p)}}$에 대(對)하여 ${\int\limits_{c^{(p)}}}d{\beta}^{(p-1)}={\int\limits_{{\partial}{c}^{(p)}}}{\beta}^{(p-1)}$이 성립(成立) (Stokes 정리(定理)의 일반화(一般化))⋯등(等) M위의 적분(積分)에 관한 여러 가지 성질(性質)들을 구명(究明)하였다. 이 성질(性質)들을 토태(土台)로 하여 본(本) 논문(論文)에서는; 제2절(第2節)에서 미분가능다양체(微分可能多樣體) M위의 Lie 도함수(導函數)의 정의(定義)와 Lie적분(微分)에 관(關)한 여러가지 성질(性質)들을 고찰(考察)하고, 제3절(第3節)에서 div X와 Laplace 작용소(作用素) ${\Delta}f$의 정의(定義) 및 실(實) n차원(次元) 가부호미분가능(可符號微分可能) 다양체(多樣體) M 위에서의 divX와 ${\Delta}f$의 적분(積分)에 관(關)한 성질(性質), 즉(卽) $V=\sqrt{{\mid}g{\mid}}dx^1{\Lambda}{\cdots}{\Lambda}dx^n{\in}A^n(M)$에 대(對)하여 $$\int_MdivXV\limits=\int_M{\Delta}fv=0$$인 관계(關係)가 성립(成立)함을 구명(究明)한다. (정리(定理) 3.3)

• Journal for History of Mathematics
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• v.29 no.3
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• pp.157-172
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• 2016

Sophus Lie's research is regarded as one of the most important mathematical advancements in the $19^{th}$ century. His pioneering research in the field of differential equations resulted in an invaluable consolidation of calculus and group theory. Lie's group theory has been investigated and constantly modified by various mathematicians which resulted in a beautifully abstract yet concrete theory. However Lie's early intentions and ideas are lost in the mists of modern transfiguration. In this paper we explore Lie's early academic years and his object of studies which clarify the ground breaking ideas behind his theory.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.13-26
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• 2009

Elie Cartan is one of the mathematicians whose works marked the development of geometry and algebra of 20th century. We illuminate his mathematical contributions which is familiar to the experts but is alien to most of the mathematicians in general. Also we elucidate some of his influences.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.5
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• pp.850-856
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• 2001

Even though the hydraulic servo system has been widely used in industrial and military equipments since it has a lot of advantages, it is not easy to design controller due to the high nonlinearities and the parametric uncertainties. The dynamic behavior of the real process in the hydraulic servo system differs from that described by its model because the model is linearized. Another reason of the difference is caused by the variety of parameters, since the system parameters of the dynamic equation are affected by the operating conditions such as temperature and pressure. In this study, the designing process of the MRNC with a PID compensator is introduced and applied to the load sensing hydraulic servo system. The results show that the designed controller guarantees the robust control performance despite of both the nonlinearities and the parametric uncertainties.

• Journal of the Korea Concrete Institute
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• v.15 no.6
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• pp.785-793
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• 2003

This study is intended to analyze the effectiveness of expansive additive, shrinkage reducing agent and combination of the two to reduce the autogenous and drying shrinkage of high performance concrete using mineral admixture such as fly ash, blast furnace slag powder and silica fume. According to results, when expansive additive and shrinkage reducing agent are mixed within an appropriate mixing ratio, fluidity and air content are not influenced, and the enhancement of compressive strength is favorable at the age of 91 and 180days. At the mixing ratio of expansive additive of 5% and 10%, the autogenous and drying shrinkage is reduced by 32∼68% and 25∼49% respectively in comparison with plain concrete. And they are reduced by 18∼34% and 16∼26% respectively at the mixing ratio of shrinkage reducing agent of 0.5% and 1.0%, compared with plain concrete. The mixture of EA-SR combined with expansive additive and shrinkage reducing agent is most effective for reduction of shrinkage. Therefore, it is considered that the using method in combination with expansive additive and shrinkage reducing agent is effective to reduce the shrinkage of high performance concrete using mineral admixture such as fly ash, blast slag powder and silica fume.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.225-233
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• 1995

This paper presents an efficient numerical method for computation of eigenpair derivatives for the real symmetric eigenvalue problem with distinct and multiple eigenvalues. The method has very simple algorithm and gives an exact solution. Furthermore, it saves computer storage and CPU time. The algorithm preserves the symmetry and band of the matrices, allowing efficient computer storage and solution techniques. Thus, the algorithm of the proposed method will be inserted easily in the commercial FEM codes. Results of the proposed method for calculating the eigenpair derivatives are compared with those of Rudisill and Chu's method and Nelson's method which is efficient one in the case of distinct natural frequencies. As an example to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The design parameter of the cantilever plate is its thickness. For the eigenvalue problem with multiple natural frequencies, the adjacent eigenvectors are used in the algebraic equation as side conditions, they lie adjacent to the m (multiplicity of multiple natural frequency) distinct eigenvalues, which appear when design parameter varies. As an example to demonstrate the efficiency of the proposed method in the case of multiple natural frequencies, a cantilever beam is considered. Results of the proposed method fDr calculating the eigenpair derivatives are compared with those of Bailey's method (an amendation of Ojalvo's work) which finds the exact eigenvector derivatives. The design parameter of the cantilever beam is its height. Data is persented showing the amount of CPU time used to compute the first ten eigenpair derivatives by each method. It is important to note that the numerical stability of the proposed method is proved.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.4
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• pp.383-389
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• 2011

In this paper, a statistical calibration method is proposed in order to identify the variability of complex modulus for a rubber material due to operational temperature and experimental/model errors. To describe temperature- and frequency-dependent material properties, a fractional derivative model and a shift factor relationship are used. A likelihood function is defined as a product of the probability density functions where experimental values lie on the model. The variation of the fractional derivative model parameters is obtained by maximizing the likelihood function. Using the proposed method, the variability of a synthetic rubber material is estimated and applied to a rubber mount problem. The dynamic characteristics of the rubber mount are calculated using a finite element model of which material properties are sampled from Monte Carlo simulation. The calculated dynamic stiffnesses show very large variation.

• The Transactions of the Korea Information Processing Society
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• v.7 no.2
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• pp.477-487
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• 2000

When volume data is visualized by the ray casting method, the color value of each pixel in the image is obtained by composing the color contributions of the sample points that lie on the ray cast from the pixel point. In most ray tracing methods including Levoy's classical method, the color composition is formulated as a summation of the color contributions of the discrete sample points. However, the more precise color composition is formulated as differential equations over the color contributions of the continuous sample points. The discrete formulation is used, because analytical solutions to the continuous formulations are hard to find. In this paper, however, we have discovered a semi-analytical solution to the continuous formulation of a typical ray tracing of volume data. We have applied both Levoy's method and ours to the same set of data, and compared the visual quality of both results. The comparison shows that our method produces a more fine-grained visualization of volume data.

• Investigative Magnetic Resonance Imaging
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• v.2 no.1
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• pp.58-66
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• 1998

Purpose : This paper introduces a new three dimensional magnetic Resonance Image classification which is based on Mar kov Random Field-Gibbs Random Field with a line model. Material and Methods : The performance of the Gibbs Classifier over a statistically heterogeneous image can be improved if the local stationary regions in the image are disassociated from each other through the mechanism of the interaction parameters defined at the local neighborhood level. This usually involves the construction of a line model for the image. In this paper we construct a line model for multisignature images based on the differential of the image which can provide an a priori estimate of the unobservable line field, which may lie in regions with significantly different statistics. the line model estimated from the original image data can in turn be used to alter the values of the interaction parameters of the Gibbs Classifier. Results : MRF-Gibbs classifier for volumetric MR images is developed under the condition that the domain of the image classification is $E^{3}$ space rather thatn the conventional $E^{2}$ space. Compared to context free classification, MRF-Gibbs classifier performed better in homogeneous and along boundaries since contextual information is used during the classification. Conclusion : We construct a line model for multisignature, multidimensional image and derive the interaction parameter for determining the energy function of MRF-Gibbs classifier.