• Journal of the Korea institute for structural maintenance and inspection
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• 제3권4호
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• pp.155-162
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• 1999

This paper presents a generation of analytical fragility curves for bridge. The analytical fragility curves are constructed on the basis of nonlinear dynamic analysis. Two-parameter lognormal distribution functions are used to represent the fragility curves with the parameters estimated by the maximum likelihood method. To demonstrate the development of analytical fragility curves, two of representative bridges with a precast prestressed continuous deck in the Memphis. Tennessee area are used.

• ETRI Journal
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• 제33권4호
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• pp.656-659
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• 2011

In ICISC 2007, Comuta and others showed that among the methods for constructing pairing-friendly curves, those using cyclotomic polynomials, that is, the Brezing-Weng method and the Freeman-Scott-Teske method, are affected by Cheon's algorithm. This paper proposes a method for searching parameters of pairing-friendly elliptic curves that induces minimal security loss by Cheon's algorithm. We also provide a sample set of parameters of BN-curves, FST-curves, and KSS-curves for pairing-based cryptography.

• Bulletin of the Korean Mathematical Society
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• 제49권1호
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• pp.75-88
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• 2012

A new algorithm is proposed for the construction of Brezing-Weng-like elliptic curves such that polynomials defining the CM discriminant are linear. Using this construction, new families of curves with variable discriminants and embedding degrees of $k{\in}\{8,16,20,24\}$, which were not covered by Freeman, Scott, and Teske [9], are presented. Our result is useful for constructing elliptic curves with larger and more flexible discriminants.

• Honam Mathematical Journal
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• 제45권1호
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• pp.130-145
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• 2023

In this paper, we define some integral curves connected with a framed curve in Euclidean 3-space. These curves include framed generalized principal-direction curve, framed generalized binormal-direction curve, framed principal-donor curve and framed Darboux-direction curve. We obtain some relations between the framed curvatures of new defined framed curves and framed curvatures of given framed curve. By using the obtained relationships we give some characterizations for such curves. We also give methods for constructing framed helix and framed slant helix from planar curves.

• Journal of the Korean Society for Nondestructive Testing
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• 제23권6호
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• pp.605-615
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• 2003

In practice, it is common to manufacture reference blocks containing simple reflectors to obtain distance-amplitude correction (DAC) curves. However, the construction or DAC curves in this manner requires the use of a large number of specimens with appropriate curvatures and reference reflectors located at various depths. Therefore, less costly and quantitative procedures are strongly needed. To address such a need, in this study, we have developed model-based transfer curves to relate a DAC curve obtained in a particular reference configuration with that for a completely different configuration. An example of transferring DAC curves, using the proposed transfer curves, is given.

• Journal of Korean Institute of Industrial Engineers
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• 제20권2호
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• pp.77-90
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• 1994

Curve-net interpolation surface is one of the most popular method in engineering design. Therefore it is supported with many commercial CAD/CAM system. However, construction algorithm of curve-net interpolation surfaces is rarely opened to the public because of its copy-right. In this paper we establish a construction algorithm of curve-net interpolation surface so called sweeping surface which especially concentrates on trajectory of cross-section curve. We also show the method which can construct sweeping surfaces as NURB or Bezier mathematical models. Surfaces having the form of standard mathematical models are very useful for the application of joining, trimming, blending etc. The proposed surface interpolation scheme consists of four steps; (1) preparation of guide curves and section curves, (2) remeshing guide curves and section curves, (3) blending section curves after deformation, and (4) determination of control points for sweeping surface using gordon method. The proposed method guarantee $G^1$-continuety, and construct the surface salifying given section curves and trajectory of section curves.

• Honam Mathematical Journal
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• 제40권3호
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• pp.561-576
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• 2018

In this paper, we define null Cartan and pseudo null Bertrand curves in Minkowski space ${\mathbb{E}}^3_1$ according to their Bishop frames. We obtain the necessary and sufficient conditions for pseudo null curves to be Bertand B-curves in terms of their Bishop curvatures. We prove that there are no null Cartan curves in Minkowski 3-space which are Bertrand B-curves, by considering the cases when their Bertrand B-mate curves are spacelike, timelike, null Cartan and pseudo null curves. Finally, we give some examples of pseudo null Bertrand B-curve pairs.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.451-455
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• 2008

In this paper we give some results on the points of elliptic curves which have application to elliptic curve cryptography.

• Bulletin of the Korean Mathematical Society
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• 제50권4호
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• pp.1109-1126
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• 2013

Let $\mathbb{M}^3_q(c)$ denote the 3-dimensional space form of index $q=0,1$, and constant curvature $c{\neq}0$. A curve ${\alpha}$ immersed in $\mathbb{M}^3_q(c)$ is said to be a Bertrand curve if there exists another curve ${\beta}$ and a one-to-one correspondence between ${\alpha}$ and ${\beta}$ such that both curves have common principal normal geodesics at corresponding points. We obtain characterizations for both the cases of non-null curves and null curves. For non-null curves our theorem formally agrees with the classical one: non-null Bertrand curves in $\mathbb{M}^3_q(c)$ correspond with curves for which there exist two constants ${\lambda}{\neq}0$ and ${\mu}$ such that ${\lambda}{\kappa}+{\mu}{\tau}=1$, where ${\kappa}$ and ${\tau}$ stand for the curvature and torsion of the curve. As a consequence, non-null helices in $\mathbb{M}^3_q(c)$ are the only twisted curves in $\mathbb{M}^3_q(c)$ having infinite non-null Bertrand conjugate curves. In the case of null curves in the 3-dimensional Lorentzian space forms, we show that a null curve is a Bertrand curve if and only if it has non-zero constant second Frenet curvature. In the particular case where null curves are parametrized by the pseudo-arc length parameter, null helices are the only null Bertrand curves.

• Water for future
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• 제21권2호
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• pp.193-201
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• 1988

A simplified model for higher order scanning curves in the soil water characteristic function is suggested. The conceptual hysteresis models developed by $Mualem_{8,9}$ are simplied for higher order scanning curves. Higher order drying curves are regarded as primary drying curves and the last wetting reversal point is assumed to be on the main wetting curve by moving that point vertically downward. For the higher order wetting curves, it is assumed that these curves can be regarded as primary curves and the last wetting reversal point sits on the imaginary main drying curve which passes through the last wetting reversal point. The water content computed from the simplified model are compared with those obtained from Mualem's original model for second order scanning curves. It is found that absolute differences between the two methods aree relatively small and the simplified model always underestimates for higher order drying curves while it overestimates for higher order wetting curves. Hence, those two tend to compensate each other for repeated drying-wetting processes. The simplified model approximates higher order scanning curves well and reduces computation considerably.