• 한국CDE학회논문집
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• 제3권2호
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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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• 제3권3_4호
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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.

• 한국수학사학회지
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• 제27권5호
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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.

• 한국CDE학회논문집
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• 제4권4호
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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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• 제6권3호
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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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• 제6권3호
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• pp.771-771
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• 1999

• 대한가정학회지
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• 제33권5호
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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%.

• 한국수자원학회논문집
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• 제52권6호
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• pp.411-420
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• 2019

본 연구의 목적은 합리식 기반의 하수관거 설계모델 Makesw와 도시유출해석모델 SWMM을 활용한 국내 하수관거 설계 방법의 적정성 평가를 수행하는 것이다. 대상유역으로는 군자배수구역을 선정하였으며, 강수량, 유량, 토지피복도, 토양도, 불투수도, 수치지형도의 자료를 수집하여 홍수량 산정에 활용하였다. 적정성 평가는 SWMM 기반 홍수량을 기초로 Makesw 기반 홍수량과 비교하여 수행하였다. 홍수량 비교분석은 설계강우와 실제 침수강우사상 기반의 Makesw와 SWMM의 홍수량에 대하여 수행하였다. 설계강우 기반 홍수량 비교 결과 유역의 간선에서는 합리식 설계홍수량이 SWMM 설계홍수량보다 과대모의 하였으나, 유역 내 지선에서는 합리식 설계홍수량이 과소모의되는 관거가 다수 나타났다. 또한 실제 침수사상 적용 결과, 간선 및 지선에서 합리식 모델의 홍수량이 SWMM의 홍수량보다 과소모의되는 관거가 다수 발견되었다. 특히, 유역 중심에 위치하는 간선, 1차 2차지선에서 유량 차이가 큰 관거가 집중되었다. 따라서 합리식 설계방법은 보수적인 설계방법이라고 말하기 어려우며, 하수관거 설계시 정상류해석 방법인 합리식과 부정류 해석방법인 SWMM을 활용한 설계를 병행하고 안정적인 해석결과를 활용하여 설계를 할 필요가 있다.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1990년도 가을 학술발표회 논문집
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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.

• 한국CDE학회논문집
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• 제4권4호
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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.