• 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 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.

• Korean Journal of Agricultural Science
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• v.43 no.4
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• pp.623-633
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• 2016

A total of 6,973 steer growth records of Hanwoo breeding bull's progeny test data collected from 1989 to 2015 were analyzed to identify the most appropriate growth curve among three growth curve models (Gompertz, Logistic and von Bertalanffy). The Gompertz growth curve model equation was $W_t=990.5e^{{-2.7479e}^{-0.00241t}}$, the Logistic growth curve model equation was $W_t=772(1+8.3314e^{-0.00475t})^{-1}$, and the von Bertalanffy growth curve model equation was $W_t=1,196.4(1-0.646e^{-0.00162t})^3$. The Gompertz model parameters A, b, and k were estimated to be $990.5{\pm}10.27$, $2.7479{\pm}0.0068$, and $0.00241{\pm}0.000028$, respectively. The inflection point age was estimated to be 421 days and the weight of inflection point was 365.3 kg. The Logistic model parameters A, b, and k were estimated to be $772.0{\pm}4.12$, $8.3314{\pm}0.0453$, and $0.00475{\pm}0.000033$, respectively. The inflection point age was estimated to be 445 days and the weight of inflection point was 385.0 kg. The von Bertalanffy model parameters A, b, and k were estimated to be $1196.4{\pm}18.39$, $0.646{\pm}0.0010$, and $0.00162{\pm}0.000027$, respectively. The inflection point age was estimated to be 405 days and the weight of inflection point was 352.0 kg. Mature body weight of the von Bertalanffy model was 1196.4 kg, the Gompertz model was 990.5 kg, and the Logistic model was 772.0 kg. The difference between actual and estimated weights was similar in the Logistic model and the von Bertalanffy model. The difference between market weight and estimated market weight was the lowest in the Gompertz model. The growth curve using the von Bertalanffy model showed the lowest mean square error.

• 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.

• 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.

• Journal of Animal Science and Technology
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• v.46 no.4
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• pp.503-508
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• 2004

This study was conducted to estimate the growth curve parameters of crossbreds between Korean native boars and Landrace sows and their relationships with meat qualities. The data used were weight-age data and carcass data from 131 males and 122 females raised at N.L.R.I in Korea. Growth curve parameters were estimated from nonlinear regression using Gompertz model individually. Average mature weight(A), average maturing rate(k), and average inflection point(u) showing maximum growth rate estimated were 179.54${\pm}$6.06kg, 0.3154${\pm}$0.0059, and 5.50${\pm}$0.11 months in females, and 179.84${\pm}$6.33kg, 0.3049${\pm}$0.0061, and 5.24${\pm}$0.13 months in males, respectively. For the growth curve parameters and derived statistics, the phenotypic correlations of maturing rate with gain rate at inflection, mature weight, and inflection point were - .30, - .77, and - .93 in male, and - .31, - .78 and - .94 in female, respectively. Matrure weight was positively correlated to the inflection point as + .89 in both male and female, indicating that late maturing pigs with lower k had longer maturing period with increasing gain rate and reached point of inflection later than early maturing pigs with higher k, and grew to larger mature weight. Backfat thickness and erode fat contents were correlated with mature weight positively in male and negatively in female, and correlated with gain rate at inflection point positively in both male and female, of which coefficients were as high as .42 and .50 in male, respectively.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.4 s.304
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• pp.127-132
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• 2005

The curve of motion indicated to waveform of the fast movement of human extracted using virtual reality or the quantity of time fluctuation of the electromagnetic signal as the quantity of electric fluctuation of the atmosphere is complex. It is important to decide exactly the signal property as the inflection point for the observation signal. When the signal is mixed by noise signal, the traditional method is difficult to detect the inflection point. In this paper the noisy signal is eliminated by wavelet thresholding method and the filter using natural observation theorem is applied. It shows that the inflection point of the signal waveform can be detected exactly.

• 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.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.309-317
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• 2016

As a generalization of an inflection point, we consider a point P on a smooth plane curve C of degree m at which another curve C' of degree n meets C with high intersection multiplicity. Especially, we deal with the existence of two curves of degree m and n meeting at the unique point.

• Advances in environmental research
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• v.1 no.4
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• pp.237-255
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• 2012

We review the research literature on relationship between environmental regulation and industrial development in three aspects of environmental regulation and investment, environmental regulation and efficiency, environmental regulation and trade. Indeed, the linkage between environmental regulation and material consumption of industrial system is absent. Environmental regulation is measured as the expenditure share for industrial pollutants abatement, and effluent charge intensity. Using panel-level data from 31 provinces, municipalities and autonomous regions in China, we build correlation models between material consumption and environmental regulation, results show that: (1) there are significant quadratic function relationship between material consumption and environmental regulation. And there is the fact that inflection point exists. (2) On basis of inflection points, we make two remarkable reflections. Firstly, the inflection points are the most important scale to judge reasonability and performance of regulations. Secondly, a Pareto improvement may occur when the regulations achieve a certain target. (3) Both intensities of industrial pollutants abatement expenditure and effluent charge have not yet achieved the expected target in most regions of mainland China at present. And most of regions of material consumption decreasing are distributed in western China. Main reasons lie in the impacts of industrial features as well as the regulations.