• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.473-484
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• 2015

Archimedes determined the center of gravity of a parabolic section as follows. For a parabolic section between a parabola and any chord AB on the parabola, let us denote by P the point on the parabola where the tangent is parallel to AB and by V the point where the line through P parallel to the axis of the parabola meets the chord AB. Then the center G of gravity of the section lies on PV called the axis of the parabolic section with $PG=\frac{3}{5}PV$. In this paper, we study strictly locally convex plane curves satisfying the above center of gravity properties. As a result, we prove that among strictly locally convex plane curves, those properties characterize parabolas.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.407-417
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• 2022

Archimedes proved that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area of the region bounded by the parabola X and the chord AB is four thirds of the area of the triangle ∆ABP. This property was proved to be a characteristic of parabolas, so called the Archimedean characterization of parabolas. In this article, we study strictly convex curves in the plane ℝ². As a result, first using a functional equation we establish a characterization theorem for quadrics. With the help of this characterization we give another proof of the Archimedean characterization of parabolas. Finally, we present two related conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open arc of a parabola.

• The Transactions of the Korea Information Processing Society
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• v.1 no.4
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• pp.531-540
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• 1994

Spline curve scheme is the most valuable tool for the CAD of industrial products. Hence, the development of a new, effective curve scheme can have immediate impact on the current design industries. This paper develops and implements a new methodology for the implementation of the visually continuous class of splines which can produce a more flexible and diverse curve shapes. This class of splines has advantaged over existing splines in that it can accommodate wider range of shapes while maintaining the interpolators property of the ordinary cardinal splines. Most importantly, we avoid using the previous method of implementing G$^1$ curves, where users must specify scalar values for the control of curve shapes. We derive and implement an easy-to -use transformation between the user-specified graphical tangent vectors and the actual parameters for the resulting curve. Since the resulting curve shape reflects original tangential direction faithfully, CAD users can simply represent approximate curve shapes with proper tangents. Consequently, a simple user interface device such as a mouse can effectively produce a various spline curves using the proposed spline tool.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.583-595
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• 2016

Archimedes showed that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area S of the region bounded by the parabola X and chord AB is four thirds of the area T of triangle ${\Delta}ABP$. It is well known that the area U formed by three tangents to a parabola is half of the area T of the triangle formed by joining their points of contact. Recently, the first and third authors of the present paper and others proved that among strictly locally convex curves in the plane ${\mathbb{R}}^2$, these two properties are characteristic ones of parabolas. In this article, in order to generalize the above mentioned property $S={\frac{4}{3}}T$ for parabolas we study strictly locally convex curves in the plane ${\mathbb{R}}^2$ satisfying $S={\lambda}T+{\nu}U$, where ${\lambda}$ and ${\nu}$ are some functions on the curves. As a result, we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be an open arc of a parabola.

• Journal of Korean Society of Steel Construction
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• v.22 no.6
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• pp.609-616
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• 2010

The objective of this study is to investigate the structural character of the buckling strength of 600MPa-class high-strength steel compression members. The buckling strength of circular hollow-section columns is evaluated by a numerical analysis of the stress-strain curves of the tension test results. The numerical analysis was based on the beam-column theory and the tangent modulus theory. It was considered possible to enlarge the nominal yield strength of the 600MPa-class steel.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.1
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• pp.73-80
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• 2008

An improved method to measure the dynamic viscoelastic properties of elastomers is proposed. The method is based on the analysis of forced oscillation of a cylindrical sample loaded with inertial mass. No special equipment or instrumentation other than the ordinary vibration measurement apparatus is required. Typical measurement of the viscoelastic properties of a silicone rubber $Silastic^{(R)}$ S2 were measured over the wide frequency range from 10 Hz to 3 kHz under the action of wide region of deformation from $10^{-4}%$ to 5%. It was shown that modulus of elasticity and loss tangent fall on the single curves when the ratio of load mass to sample mass changed from 1 to 20.

• International Journal of Highway Engineering
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• v.14 no.4
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• pp.149-162
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• 2012

PURPOSES : The causes of traffic accidents can be classified into the factors of highway users, vehicles, and driving environments. Traffic accidents result from the deficiency in single or combination of these three factors. The objective of this study is to define the "potentially hazardous sections of highway" in terms of traffic safety considering these three factors. METHODS : The test drivers performed repeated driving on these highway sections. The drivers and passengers recorded the sections on which the driving was uncomfortable, and the speeds on the sections excluding the uncomfortable sections were used for the development of the model. RESULTS : The model is composed of three sub-models for each of the horizontal curve, tangent, and the section where the curve starts/ends. The safe driving behavior coefficients by the horizontal curvature were derived by comparing the maximum operating speeds at which the vehicle may slide or deviate and the speeds at which the drivers feel comfort. The safety speeds on tangent were derived by the length of tangent section considering the driver's desired speeds under the traffic condition on which the drivers hardly influenced by the other vehicles. For the sections where the curve starts/ends, the driving behaviors were classified by the distances between the curves, and the safe acceleration/deceleration speeds were derived on which the drivers enter/exit the curve sections safely. CONCLUSIONS : Safety speed could then be regarded that the model suggested in this study may be useful to define the potentially hazardous highway section and contribute the improvement of highway safety.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.1
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• pp.3-10
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• 1990

Hull form can be described numerically by two approaches, one is to describe a hull form with a set of curves("curve approach"), and the other is to describe it with surfaces directly("surface approach"). This paper describes the numerical definition scheme of hull form using curve approach method which defines the hull form by a set of curves consisting of 2-dimensional transverse section curves and 3-dimensional longitudinal curves. A set of curves in the hull form definition scheme is described by the modified cubic spline which modified the general parametric cubic spline in order to ensure a very smooth curvature distribution within the curve segment even though a curve segment has large tangent angle at its end points. Illustrative examples are given showing the application of the method to represent the hull form of SWATH ship and oceanographic research vessel. Also, examples for hull form transformation are shown by using this method connected with transformation technique.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.911-921
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• 2009

Receiver Operating Characteristic(ROC) and Cumulative Accuracy Profile(CAP) curves are two methods used to assess the discriminatory power of different credit-rating approaches. The points of optimal classification accuracy on an ROC curve and of maximal profit on a CAP curve can be found by using iso-performance tangent lines, which are based on the standard notion of accuracy. In this paper, we offer an alternative accuracy measure called the true rate. Using this rate, one can obtain alternative optimal threshold points on both ROC and CAP curves. For most real populations of borrowers, the number of the defaults is much less than that of the non-defaults, and in such cases the true rate may be more efficient than the accuracy rate in terms of cost functions. Moreover, it is shown that both alternative scores of optimal classification accuracy and maximal profit are the identical, and this single score coincides with the score corresponding to Kolmogorov-Smirnov statistic used to test the homogeneous distribution functions of the defaults and non-defaults.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.7 s.250
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• pp.757-764
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• 2006

Isothermal cyclic stress-strain deformation and thermomechanical deformation (TMD) of 429EM stainless steel were analyzed using a rheological model employing a bi-linear model. The proposed model was composed of three parameters: elastic modulus, yield stress and tangent modulus. Monotonic stress-strain curves at various temperatures were used to construct the model. The yield stress in the model was nearly same as 0.2% offset yield stress. Hardening relation factor, m, was proposed to relate cyclic hardening to kinematic hardening. Isothermal cyclic stress-strain deformation could be described well by the proposed model. The model was extended to describe TMD. The results revealed that the hi-linear thermomechanical model overestimates the experimental data under both in-phase and out-of-phase conditions in the temperature range of $350-500^{\circ}C$ and it was due to the enhanced dynamic recovery effect.