• Korean Journal of Computational Design and Engineering
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• v.5 no.3
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• pp.276-284
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• 2000

Usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves in a power form is done by either a knot refinement followed by basis conversions or applying a Taylor expansion on the B-spline curve for each knot span. Presented in this paper is a new algorithm, called a direct expansion algorithm, for the problem. The algorithm first locates the coefficients of all the linear terms that make up the basis functions in a knot span, and then the algorithm directly obtains the power form representation of basis functions by expanding the summation of products of appropriate linear terms. Then, a polynomial segment of a knot span can be easily obtained by the summation of products of the basis functions within the knot span with corresponding control points. Repeating this operation for each knot span, all of the polynomials of the B-spline curve can be transformed into a power form. The algorithm has been applied to both static and dynamic curves. It turns out that the proposed algorithm outperforms the existing algorithms for the conversion for both types of curves. Especially, the proposed algorithm shows significantly fast performance for the dynamic curves.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.265-278
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• 1996

This paper is composed of the complete representation of two dimensional single layer potentials with linear strength on a straight line segment and its far field behavior which is closely related to the pose of this line segment. The far field behavior of a single layer potential on a given curve has informations of the shape of the curve.

• Journal of the Ergonomics Society of Korea
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• v.11 no.2
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• pp.47-56
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• 1992

In this paper, a mathematical model of learning curve is proposed to study the fi- nger's reaction time. The model is a logarithmic linear type which represents a lear- ning curve appropriately, and parameters are estimated by the linear. The learning coefficient and percentage of a reaction time can easily computed in the mathematical model. This quantitative approach provieds an important information to be used fot the working capqbility qualification of re-employment as well as the adaptability estimation of aged workers.

• Journal of Integrative Natural Science
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• v.5 no.1
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• pp.38-41
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• 2012

In this paper we show that for any triangle and any point on the circumcircle the envelope of the Wallace-Simson lines with signed angle ${\alpha}$ is a parabola. The proof is obtained naturally using polar coordinates. We also present the reparametrization of the envelope which is a linear normal curve.

• Proceedings of the ESK Conference
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• 1992.10a
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• pp.113-120
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• 1992

In this paper, a mathematical model of learning curve is proposed to study the finger's reaction time. The model is a logarithmic linear type which represents a learning curve appropriately, and parameters are estimated by the linear. The learning coefficient and percentage of a reaction time can be easily computed in the mathematical model. This quantitative approach provides an important information to be used for the working capability qualification for re-employment as well as for the adaptability estimation of aged workers.

• Journal of KSNVE
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• v.10 no.3
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• pp.531-535
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• 2000

A three-parameter model of viscoelastic damper which has a non-linear spring as an element is incorporated into an oscillator. The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by get analytic solutions of the system. The frequency-response curves show that multiple solutions co-exist and that the jump phenomena can occur. In addition it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurences of such non-linear phenomena. A direct time intergration of the original equation of motion validifies the use of the harmonic balance method to this sort of problem.

• Corrosion Science and Technology
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• v.19 no.6
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• pp.302-309
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• 2020

This study aimed to predict the pitting corrosion characteristics of AL-6XN super-austenitic steel using multiple linear regression. The variables used in the model are degree of sensitization, temperature, and pH. Experiments were designed and cyclic polarization curve tests were conducted accordingly. The data obtained from the cyclic polarization curve tests were used as training data for the multiple linear regression model. The significance of each factor in the response (critical pitting potential, repassivation potential) was analyzed. The multiple linear regression model was validated using experimental conditions that were not included in the training data. As a result, the degree of sensitization showed a greater effect than the other variables. Multiple linear regression showed poor performance for prediction of repassivation potential. On the other hand, the model showed a considerable degree of predictive performance for critical pitting potential. The coefficient of determination (R2) was 0.7745. The possibility for pitting potential prediction was confirmed using multiple linear regression.

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.229-241
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• 2018

In the present study, we derive the problem of constructing a hypersurface family from a given isogeodesic curve in the 4D Galilean space $G_4$. We obtain the hypersurface as a linear combination of the Frenet frame in $G_4$ and examine the necessary and sufficient conditions for the curve as a geodesic curve. Finally, some examples related to our method are given for the sake of clarity.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.13-29
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• 2007

In this paper, we first present a method for finding the implicit equation of the curve given by rational parametric equations. The method is based on the computation of $Gr\"{o}bner$ bases. Then, another method for implicitization of curve and surface is given. In the case of rational curves, the method proceeds via giving the implicit polynomial f with indeterminate coefficients, substituting the rational expressions for the given curve and surface into the implicit polynomial to yield a rational expression $\frac{g}{h}$ in the parameters. Equating coefficients of g in terms of parameters to 0 to get a system of linear equations in the indeterminate coefficients of polynomial f, and finally solving the linear system, we get all the coefficients of f, and thus we obtain the corresponding implicit equation. In the case of polynomial surfaces, we can similarly as in the case of rational curves obtain its implicit equation. This method is based on characteristic set theory. Some examples will show that our methods are efficient.

• Journal of The Korean Society of Agricultural Engineers
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• v.62 no.1
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• pp.61-70
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• 2020

To estimate the ventilation volume of mechanically ventilated swine farms, various regression models were applied, and errors were compared to select the regression model that can best simulate actual data. Linear regression, linear spline, polynomial regression (degrees 2 and 3), logistic curve, generalized additive model (GAM), and gompertz curve were compared. Overfitting models were excluded even when the error rate was small. The evaluation criteria were root mean square error (RMSE) and mean absolute percentage error (MAPE). The evaluation results indicated that degree 3 exhibited the lowest error rate; however, an overestimation contradiction was observed in a certain section. The logistic curve was the most stable and superior to all the models. In the estimation of ventilation volume by all of the models, the estimated ventilation volume of the logistic curve was the smallest except for the model with a large error rate and the overestimated model.