• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.23-38
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• 2012

The purpose of this paper is to describe the true meaning of smooth curve and to let people understand the smooth curve by way of velocity. It is true that it is not easy for us to perceive smooth curve because when there are no cups in the curve and the shape of the curve looks smooth, we often perceive it is smooth curve. However, even when the shape of curve looks smooth, it happens that it is not smooth curve. When the particle moves on the curve, depending on the velocity, it can be smooth curve or not. That is, even though the shape looks smooth, when the velocity is discontinuous or it is 0, it is not smooth curve. Therefore, this paper shows that it is important to understand and to teach smooth curve by way of velocity. In other words, when parameter of path for the smooth curve is taught in the calculus of high school, it needs to be understood by way of velocity. Finally, this paper tries to suggest that we need to shift our paradigm in teaching of smooth curve from fixed curve to dynamic curve.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.399-411
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• 2021

We consider a Weierstrass semigroup at a generalized flex on a smooth plane curve. We find the candidates of a Weierstrass semigroup at a 2-flex of higher multiplicity on a smooth plane curve of degree d ≥ 5, and give some examples to show the existence of them.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.251-267
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• 2020

We classify all semigroups each of which arises as a Weierstrass semigroup at a pair of non-Weierstrass points on a smooth plane curve of degree 5. First we find the candidates of semigroups by computing the dimensions of linear series on the curve. Then, by constructing examples of smooth plane curves of degree 5, we prove that each of the candidates is actually a Weierstrass semigroup at some pair of points on the curve. We need to study the systems of quadratic curves, which cut out the canonical series on the plane curve of degree 5.

• Korean Journal of Computational Design and Engineering
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• v.9 no.3
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• pp.183-191
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• 2004

This paper deals with smooth curve fitting of data corrupt by noise. Most research efforts have been concentrated on employing the smoothness penalty function with the estimation of its optimal parameter in order to avoid the 'overfilling and underfitting' dilemma in noisy data fitting problems. Our approach, called DBSF(Differentiation-Based Smooth Fitting), is different from the above-mentioned method. The main idea is that optimal functions approximately estimating the derivative of noisy curve data are generated first using genetic programming, and then their integral values are evaluated and used to recover the original curve form. To show the effectiveness of this approach, DBSP is demonstrated by presenting two illustrative examples and the application of estimating the principal dimensions of bulk cargo ships in the conceptual design stage.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.4
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• pp.803-808
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• 2010

We propose a smooth path planning method for autonomous mobile robots. Due to nonholonomic constraints by obstacle avoidance, the smooth path planning is a complicated one. We generate smooth path that is considered orientation of robot under nonholonomic constraints. The proposed smooth planning method consists of two steps. Firstly, the initial path composed of straight lines is obtained from V-graph by Dijkstra's algorithm. Then the initial path is transformed by changing the curve. We apply the cardinal spline into the stage of curve generation. Simulation results show a performance of proposed smooth path planning method.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.699-725
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• 2015

In this paper, we study the estimation for algebraic polynomials in the bounded and unbounded regions bounded by piecewise Dini smooth curve having interior and exterior zero angles.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.539-541
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• 1997

Let X be a smooth projective threefold. Let C be a smooth projective curve and let $f : X \to C$ be a fiber space with connected fiber S. Assume that $q_1(S) = 0$. Then we have $-X(O_C)X(O_S) \leq -X(O_X)$.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.65-72
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• 2015

The (affine) development of a smooth curve in a smooth manifold M with respect to an arbitrarily given affine connection in the bundle of affine frames over M is well known (cf. S.Kobayashi and K.Nomizu, Foundations of Differential Geometry, Vol.1). In this paper, we get the generalized affine development of a smooth curve $x_t$ ($t{\in}[0,1]$) in M into the affine tangent space at $x_0$ (${\in}M$) with respect to a given generalized affine connection in the bundle of affine frames over M.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.567-580
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• 1999

We prove two variants of a base-point-free pencil trick, which are similar in the spirit of the proof, and apply them to the study of special divisors on a smooth plane curve involving a theorem of Max Noether.

• Journal of Power System Engineering
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• v.11 no.1
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• pp.127-133
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• 2007

SG-365 steel is an important material and used for manufacturing a pressure vessel which the gas piping. In this investigation, the elastic plastic fracture toughness of this material is evaluated by the unloading compliance method according to the ASTM E813-97 and E1152-97 method on the smooth and side groove 1CT specimens. The effect of smooth and side groove is studied on the elastic plastic fracture toughness. The side grooved specimen is very useful in estimation of the $J_{IC}$. It is much easier than the smooth specimen to the onset of the ductile tearing by the R curve method. Besides, it improves the accuracy of toughness values, decreases a phenomenon of the tunneling and shear lip by the side groove.