• 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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.4
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• pp.562-565
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• 2013

A new variable rate speech coding technique is proposed. The method is based on the observation that the speech signal approximately looks linear for a very short period of time. The information transmitted is the location and data value of inflection points. If the distance between the inflection points is large, the mid point location and its data value are also delivered. Thus, the encoder transmits both the location and the data value for the inflection samples, but the location only for the non-inflection points. The location information is expressed using one bit for each sample, 0 for non-inflection and 1 for inflection point. At the receiver, using the interpolation, the decoder estimates the untransmitted sample values for non-inflection locations from the received sample values for the inflection samples. With 50 % of computational cost of the existing CVSD delta modulation, the proposed method is expected to achieve the data rate of 36 to 38 kbps and the SNR of 10 to 13 dB.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.11a
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• pp.681-688
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• 2000

This study presented the new method for evaluating the coefficient of consolidation by using inflection point method which was based on the fact that time factor, T corresponding to the inflection point of a semilogarithmic plot of a time curve is fixed and equals to T ＝ 0.405 at 70% consolidation. In the proposed method, the next load increment is applied as soon as the necessary time required to identify the inflection point. Thus, the coefficient of consolidation may be easily evaluated. The time required to complete the testing using this rapid consolidation method could be as low as 1.5-3 hours compared with 1 or 2 weeks in the case of the conventional consolidation test.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.353-368
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• 2022

In the previous paper [4], we classified the Weierstrass semigroups at a pair of inflection points of multiplicities d and d - 1 on a smooth plane curve of degree d. In this paper, as a continuation of those results, we classify all semigroups each of which arises as a Weierstrass semigroup at a pair of inflection points of multiplicities d, d - 1 and d - 2 on a smooth plane curve of degree d.

• Journal of the Korean Geotechnical Society
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• v.18 no.4
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• pp.85-93
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• 2002

This study presented a new method for evaluating the coefficient of consolidation by using inflection point method which was based on the fact that time factor, T corresponding to the inflection point of a semi-logarithmic plot of a time curve is fixed and equals to T = 0.405 at 70.03% consolidation. In the proposed method, as the next load increment is applied as soon as the inflection point is confirmed, the time required to identify the inflection point can be shortened. Thus, the coefficient of consolidation may be easily evaluated. The time required to complete the testing using this rapid consolidation method could be as low as 0.5~9 hours compared with 1 or 2 weeks in the case of the conventional consolidation test. For this study, we designed settlement equipment for normalization of test samples. In test results, the factors of consolidation agreed with undisturbed samples results.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.369-378
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• 2007

We classify all semigroups each of which arises as a Weierstrass semigroup at a pair of inflection points of multiplicities d or d-1 on a smooth plane curve of degree d.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.12
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• pp.1750-1754
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• 2013

A variable bit rate speech coder is presented. The coder is based on the observation that a speech signal can be viewed as a combination of piecewise linear signals in a short time period. The encoder detects the sample points where the slope of the signal changes, which are called the inflection points in this paper. The coder transmits the location and value for the detected inflection sample, but only the location information for the noninflection samples. In the decoder, the noninflection samples are estimated with interpolation of the received information. Several factors affecting the performance of the coder have been tested through simulation. Simulation results show that the linear interpolation produces 1 ~ 5 dB improvement over the cubic spline interpolation. And the -law companding does not provide any benefit when it is applied before the inflection detection. With low threshold values in the inflection point detection, the coder shows better MOS and more than 16 dB improvement in SNR compared to the continuously variable slope delta modulation (CVSDM).

• Journal of the Korean Society for Precision Engineering
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• v.20 no.11
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• pp.166-170
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• 2003

Contouring errors are important especially for high speed and precision machining. In this study, contouring errors along contours having inflection points are studied. When a table of a machine tool moves along a circular path, acceleration acts toward the center of the circle. Thus, at inflection points, acceleration as well as inertia force changes its direction abruptly. The effect of inertia force on the contouring error is investigated in this study. It is found that the contouring error at an inflection point is proportional to the acceleration. This result can be useful in determining contouring errors along general paths.

• Fashion & Textile Research Journal
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• v.11 no.5
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• pp.788-798
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• 2009

This study aims to develop a highly reproducible, optimal frame design algorithm using variations in the curvature of armscye circumference, which will provide the basics for remodeling the 3D human body shape with the concept of reverse design used to develop total contents for the apparel industry. 1. The results of the experiment proved that ratio value was significantly efficient than absolute value of curvature variation to extract feature points in the armscye circumference 2. For the shoulder(1st and 2nd quadrant) and front armhole(3rd quadrant) parts of the armscye circumference, frame remodeling with the positive point of inflection led to the completion of a highly reproducible frame. 3. Similarly, even for the rear armhole part(4th quadrant) in the armscye circumference, it was found that frame remodeling using the positive maximum point of inflection resulted in highly reproducible body shape with the maximum point of inflection situated within the range of split angles $305^{\circ}{\sim}330^{\circ}$, while frame remodeling using simultaneously the two largest points of inflection including maximum point of inflection led to highly reproducible body shape with the maximum point of inflection out of the range $305^{\circ}{\sim}330^{\circ}$. 4. Based upon the optimal frame design algorithm developed in this study, section-specific feature points in the armscye circumference were extracted depending on the rate of curvature variation and remodeling with spline curves was conducted. The results indicate a remarkably high reproducibility(98.6%) and suggest that the algorithm developed in this study is suitable for human body modeling.

• Journal of Ocean Engineering and Technology
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• v.22 no.5
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• pp.39-43
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• 2008

For a partially filled and deeply submersed membrane container, an analytic solution for similarity shape was studied. The static shape of a membrane container can be expressed as a set of nonlinear ordinary differential equations. These equations are combined into an integrable equation. The solution of the equation is derived in terms of elliptic integrals, the arguments of which contain an unknown at the point of inflection. The point of inflection is determined by using the boundary condition at a separating point. Some characteristic values of the similarity shape were evaluated and the shapes are illustrated.