• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.849-866
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• 2024

In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1485-1500
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• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.67-83
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• 2014

The notion of rectifying curve in the Euclidean space is introduced by Chen as a curve whose position vector always lies in its rectifying plane spanned by the tangent and the binormal vector field t and $n_2$ of the curve, [1]. In this study, we have obtained some characterizations of semi-real spatial quaternionic rectifying curves in $\mathbb{R}^3_1$. Moreover, by the aid of these characterizations, we have investigated semi real quaternionic rectifying curves in semi-quaternionic space $\mathbb{Q}_v$.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.301-319
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• 2019

The aim of the paper is to characterize some curves with the help of their harmonic curvature functions. First of all, we have defined harmonic curvature function of an arbitrary curve and have re-determined the position vectors of helices in terms of their harmonic curvature functions in Galilean 3-space. Then, we have investigated the relation between rectifying curves and Salkowski (or anti-Salkowski) curves in Galilean 3-space. Furthermore, the position vectors of them are obtained via the serial approach of the curves. Finally, we have given some illustrated examples of helices and rectifying curves with some assumptions.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.603-616
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• 2017

In this paper, we give some relations related with a spacelike principal-direction curve and a spacelike binormal-direction curve of a timelike Frenet curve. The Darboux-direction curve and the Darboux-rectifying curve of a timelike Frenet curve in Minkowski 3-space $E^3_1$ are introduced and some characterizations related with these associated curves are given. Later we define the spacelike V-direction curve which is associated with a timelike curve lying on a timelike oriented surface in $E^3_1$ and present some results together with the relationships between the curvatures of this associated curve.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.967-978
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• 2009

In this work, we give some characterizations of rectifying curves in dual Lorentzian space. Also, we show that rectifying dual Lorentzian curves can be stated by the aid of dual unit spherical curves.

• Proceedings of the Safety Management and Science Conference
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• 2011.11a
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• pp.205-211
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• 2011

The papaer reviews four theoretical acceptance sampling plans as OC(Operating Characteristics) curve based inspection, rectifying inspection, switching inspection, and continuous inspection. In addition, the study presents practical limitations of theoretical acceptance sampling by attribute and by variable. Finally, following research also recommends the sampling inspection based on production technology. However, the inspection method requires quality expertise with various experience and implicit knowledge of the field.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.383-390
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• 2019

We consider special curves (rectifying-type curves) in the simplest Myller configuration and study their properties, in order to compare these properties in both cases, Myller and Euclidean settings.

• Journal of Korean Society for Quality Management
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• v.19 no.2
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• pp.63-77
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• 1991

Currently the problem of air pollution caused by the motor vehicle emission is one of the most serious problems to be solved. Thus we needed the inspection method and technical innovation constraining the motor vehicle emission. In order to establish the more reasonable certified test, the multivariate sequential rectifying inspection plan designed in this paper has been applied to the domestic vehicles by analyzing the statistic characteristics of the emission distribution. This inspection method is designed to satisfy the evaluation measure constraining domestic vehicle emission, and it serves the defect rectifying system and performance certification of catalytic converts. As the prior parameter for the domestic vehicles, we used the data for the catalytic converts which passed the certified test excuted by the EPK. For the case of engine test, we used those data which passed the certified test of domestic vehicles. The multivariate sequential rectifying inspection plan of the vector parameter is able to minimize the average sample number and increase the pass probability of operating characteristic curve.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.113-129
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• 2014

In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space $\mathbb{E}_3$ also is any Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.