• Journal for History of Mathematics
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• v.27 no.5
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• pp.329-345
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• 2014

CAGD(Computer Aided Geometric Design) is a branch of applied mathematics concerned with algorithms for the design of smooth curves and surfaces and for their efficient mathematical representation. The representation is used for the computation of the curves and surfaces, as well as geometrical quantities of importance such as curvatures, intersection curves between two surfaces and offset surfaces. The $B\acute{e}zier$ curves, B-spline, rational $B\acute{e}zier$ curves and NURBS(Non-Uniform Rational B-Spline) are basically and widely used in CAGD. The definitions and properties of these curves are presented in this paper. And a brief history of study on the bound for derivative of rational curves in CAGD is also presented.

• Korean Journal of Computational Design and Engineering
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• v.4 no.4
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• pp.350-354
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• 1999

The problem of the computation of derivatives arises in various applications of rational Bezier curves. These applications sometimes require the computation of derivative on numerous points. Therefore, many researches have dealt with the representation for the computation of derivatives with the small computation error. This paper compares the performances of the representations for the derivative of rational Bezier curves in the performances. The performance is measured as computation requirements at the pre-processing stage and at the computation stage based on the theoretical derivation of computational bound as well as the experimental verification. Based on this measurement, this paper discusses which representation is preferable in different situations.

• Journal of Korean Society of Steel Construction
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• v.12 no.4 s.47
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• pp.417-428
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• 2000

In recent years, composite materials have been used in civil engineering as well as architecture, automobile, aerospace, shipping industries. Composite materials are composed of two or more different materials to produce desirable properties for structural strength. The shell structures have the advantage of more efficient load resistance due to its curved shape as compared to the plate structures. And the shell structures with composite materials have many advantages in strength, corrosion resistance, and weight reduction. The objective of this study is to analyze circular conical shells with shear deformation effects and to prove the advantage of composite materials. To solve differential equations of conical shells, this paper used finite difference method.

• Journal of the wind engineering institute of Korea
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• v.22 no.4
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• pp.155-161
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• 2018

In modern society, damage caused by strong winds such as typhoons is expected to increase due to urbanization and global warming. In order to test the reinforcement performance of the newly developed window protection device, two-point force test and uniformly distributed load test were carried out on non-reinforced plate glass. It reinforcement performance of the window protection device was evaluated based on the flexural performance improvement. The analytical performance of the window protection device was evaluated by analysis using differential equations of elastic loading method and deflection curve and Midas-Gen. First, the analytical window protection device was evaluated by formulae derived using differential equations of elastic loading and deflection curve. The validity of the derived formulae investigated by comparing the maximum deflection of the central part of the plate with the experimental value and the theoretical value at maximum load. Then the results were compared with those by finite element FE method using Midas-Gen. Under the experimental conditions, with the window protection device, stress reduction effect up to 40% and deflection reduction up to 71.4% under the same load were obtained. It was also found that it is advantageous to perform the FE analysis using the plate element when the performance is evaluated because the error of FE analysis result using plate elements is far less than that using beam elements.

• Progress in Medical Physics
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• v.11 no.2
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• pp.157-165
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• 2000

Purpose: For estimation of yields of l)NA damages induced by radiation and enhanced by oxygen, a mathematical model was used and tested. Materials and Methods: Reactions of the products of water radiolysis were modeled as an ordinary time dependant equations. These reactions include formation of radicals, DNA damage, damage repair, restitution, and damage fixation by oxygen and H-radical. Several rate constants were obtained from literature while others were calculated by fitting an experimental data. Sensitivity studies were performed changing the chemical rate constant at a constant oxygen number density and varying the oxygen concentration. The effects of oxygen concentration as well as the damage fixation mechanism by oxygen were investigated. Oxygen enhancement ratio(OER) was calculated to compare the simulated data with experimental data. Results: Sensitivity studies with oxygen showed that DNA survival was a function of both oxygen concentration and the magnitude of chemical rate constants. There were no change in survival fraction as a function of dose while the oxygen concentration change from 0 to 1.0 x 10$^{7}$ . When the oxygen concentration change from 1.0 $\times$ 107 to 1.0 $\times$ 101o, there was significant decrease in cell survival. The OER values obtained from the simulation study were 2.32 at 10% cell survival level and 1.9 at 45% cell survival level. Conclusion: Sensitivity studies with oxygen demonstrated that the experimental data were reproduced with the effects being enhanced for the cases where the oxygen rate constants are largest and the oxygen concentration is increased. OER values obtained from the simulation study showed good agreement for a low level of cell survival. This indicated that the use of the semi-empirical model could predict the effect of oxygen in cell killing.