• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.135-139
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• 1998

The hodograph, which are usually defined as the derivative of parametric curve or surface, is useful far various geometric operations. It is known that the hodographs of Bezier curves and surfaces can be represented in the closed form. However, the counterparts of rational Bezier curves and surface have not been discussed yet. In this paper, the equations are derived, which are the closed form of rational Bezier curves and surfaces. The hodograph of rational Bezier curves of degree n can be represented in another rational Bezier curve of degree 2n. The hodograph of a rational Hazier surface of degree m×n with respect to a parameter can be also represented in rational Bezier surface of degree 2m×2n. The control points and corresponding weight of the hodographs are directly computed using the control points and weights of the given rational curves or surfaces.

• Earthquakes and Structures
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• v.3 no.3_4
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• pp.473-494
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• 2012

The capacity of pipelines to resist collapse under external pressure and bending moment is a major aspect of deepwater pipeline design. Existing design codes present interaction equations that quantify pipeline capacities under such loadings, although reasonably accurate, are based on empirical data fitting of the bending strain, and assumed simplistic interaction with external pressure collapse. The rational model for collapse of deepwater pipelines, which are relatively thick with a diameter-to-thickness ratio less than 40, provides a unique theoretical basis since it is derived from first principles such as force equilibrium and compatibility equations. This paper presents the rational model methodology and compares predicted results and recently published full scale experimental data on the subject. Predictive capabilities of the rational model are shown to be excellent. The methodology is extended for the problem of pipeline collapse under point load, longitudinal bending and external pressure. Due to its rational derivation and excellent prediction capabilities, it is recommended that design codes adopt the rational model methodology.

• 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.312-317
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• 1999

An inflection point on a curve is a point where the curvature vanishes. An inflection point is useful for various geometric operations such as the approximation of curves and intersection points between curves or curve approximations. An inflection point on planar Bezier curves can be easily detected using a hodograph and a derivative of hodograph, since the closed from of hodograph is known. In the case of rational Bezier curves, for the detection of inflection point, it is needed to use the first and the second derivatives have higher degree and are more complex than those of non-rational Bezier curvet. This paper presents three methods to detect inflection points of rational Bezier curves. Since the algorithms avoid explicit derivations of the first and the second derivatives of rational Bezier curve to generate polynomial of relatively lower degree, they turn out to be rather efficient. Presented also in this paper is the theoretical analysis of the performances of the algorithms as well as the experimental result.

• Journal of electromagnetic engineering and science
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• v.6 no.3
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• pp.155-159
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• 2006

An efficient method is presented to design filters without the similarity transform of their coupling coefficient matrix as circuit parameters, which is very tedious due to pivoting and deciding rotation angles needed during the iterations. The transfer function of a filter is directly used for the design and its desired form is derived by the optimized rational-function fitting technique. A 3rd order coaxial lowpass filter is taken as an example to validate the proposed method.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.771-771
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• 1999

• Journal of the Korean Home Economics Association
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• v.33 no.5
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• pp.75-88
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• 1995

The objectives of this study were to classify the contents of clothing shopping orientation, to group women into shopper types, and to examine the differences in clothing purchase criteria according to the shopper types. Samples were 335 women(20-49 years of age) in Seoul, Korea. The data were analyzed using factor analysis, cluster analysis, one-way ANOVA, Duncan's multiple range test, X2 test, paired t-test, multiple regression analysis. The results of the study were the followings. 1. Five factors of clothing shopping orientation derived by factor analysis : F.1 'impulsive shopping' ; F.2 'rational shopping' ; F.3 'independent shopping' ; F.4 'economic shopping' ; F.5 'convenient shopping'. Three shopper types were classified by cluster analysis of the 5 factors : T.1 'convenient shopper' ; T.2 'impulsive shopper' ; T.3 'rational shopper'. 2. Significant differences were found among the 3 shopper types in all clothing purchase criteria. Rational shopper perceived all purchase criteria as more important than did the other 2 types. Impulsive shopper perceived 'fashion', 'attractiveness', 'style', and 'bland' as more important than did convenient shopper. 3. Married women and unemployed women were more distributed in rational shopper, while the unmarried and the employed more in impulsive shopper. Impulsive shopper used more credit care, purchased suits and blouses at department store and brand specialty store more than did rational shopper. Rational shopper purchased at discount store and wholesale store more than did impulsive shopper. 4. Women assessed 'color and fabric design' as most important in suit and blouse purchase criteria. 'Care' was perceived more important in blouses than in suits, and the other 9 purchase criteria(fashion, attractiveness, style, color and fabric design, fabric, durability, costruction, comfort, and brand) were perceived more important in suits than in blouses. 5. Rational and economic shopping orientation scores were higher in suit purchase than in blouse, while impulsive, independent, and convenient shopping orientation scores were higher in blouse purchase. 6. Post-purchase suit satisfaction was influenced by rational shopping orientation, educational level, style, income, and comfort. The explanatory power of the 5 variables was 17.2%. Post-purchase blouse satisfaction was influenced by style, care, rational shopping orientation, and independent shopping orientation. The explanatory power of the 4 variables was 10.2%.

• Journal of Korea Water Resources Association
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• v.52 no.6
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• pp.411-420
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• 2019

The objective of this study is to evaluate the appropriateness of methodology for designing urban sewer system using a rational method-based model, Makesw and an urban runoff model, SWMM. The Gunja basin was selected as a study area and precipitation, runoff, vegetation, soil, imperviousness data were used to estimate floods. The appropriateness of methodology was evaluated based on comparison analysis between floods estimated from Makesw and SWMM. The comparison analysis was conducted between floods estimated from Makesw and SWMM, which were simulated using design rainfall and measured rainfall from past inundation events. The comparison results showed that in the case of design rainfall, the rational method-based floods were larger than that based on SWMM in all main lines. However in several branch lines, the rational method-based floods were smaller than thoes based on SWMM. In addition, for the case of measured rainfall from past inundation events, it was easily to find the main and branch lines where the rational method-based floods were smaller than SWMM based ones. Especially, the lines where rational method-based floods were underestimated, were mostly main, $1^{st}$, $2^{nd}$ lines. It was concluded that the rational method-based results were not conservative. Based on rational method (steady flow analysis) and SWMM (unsteady flow analysis), the more conservative results the method provides, the more highly it is recommended to use in designing an urban sewer system.

• Proceedings of the Korea Concrete Institute Conference
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• 1990.10a
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• pp.35-40
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• 1990

Because of the inherent random nature of most manmade and environmental loadings and materials as well as the emperfect structural analysis, the reliability-based structural design has been recognized as a rational approach and the probability-based design criteria has been successfully developed for many standards. In order to do this it is necessary to establish target reliability levels, for which the reliability levels inherent in present design practice will be used as a rational guide. In this study the reliability levels implied in current practices, therefore, are investigated using the load and resistance models developed for domestic uses.

• 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.