• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.103-109
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• 2000

In this paper, we present the proof of generalized Fenchel's theorem by estimating the Gauss-Kronecker curvature of the tube of a nondegenerate closed curve in R$^{n}$ .

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.537-544
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• 1996

Crofton's formula on Euclidean plane $E^2$ states: Let $\Gamma$ be a rectifiable curve of length L and let G be a straight line. Then $$ \int_{G \cap \Gamma \neq \phi} n dG = 2L $$ where n is the number of the intersection points of G with the curve $\Gamma$.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.713-718
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• 1994

Voronoi diagrams for closed shapes have many practical applications, ranging from numerical control machining to mesh generation. Shape offset based on Voronoi diagram avoids the topological problems encountered in traditional offsetting algorithms. In this paper, we propose a procedure for generating a Voronoi diagram and an exact offset for planar curve. A planer curve can be defined by free-form curve segements. The procedure consists of three steps : 1) segmentation by minimum curvature, 2) construction of Voronoi diagram, and 2) generation of the exact offset.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.209-223
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• 2024

In this paper, we investigate the spatial quaternionic expressions of the ruled surfaces whose base curves are formed by the Smarandache curve. Moreover, we formulate the striction curves and dralls of these surfaces. If the quaternionic Smarandache ruled surfaces are closed, the pitches and angle of pitches are interpreted. Finally, we calculate the integral invariants of these surfaces using quaternionic formulas.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.1
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• pp.188-196
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• 2007

In this paper we propose an efficient offset curve generation algorithm for open and closed 2D point sequence curve(PS curve) with line segments in the plane. One of the most difficult problems of offset generation is the loop intersection problem caused by the interference of offset curve segments. We propose an algorithm which removes global as well as local intersection loop without making an intermediate offset curve by forward tracing of tangential circle. Experiment in computer sewing machine shows that proposed method is very useful and simple.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.7
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• pp.525-536
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• 2014

In this paper, GUI program for microspeaker system simulation program was developed and verified through closed box, vent box and 6th order bandpass enclosure system. By using the pseudo loudspeaker model concept, TS parameters and rear volume of microspeaker were identified. Their suitabilities were proved by comparing test results with simulations of electrical impedance and sound pressure response curves for the three box types; closed box, vent box and 6th order bandpass box. Also, MSSP was found to be effective regardless of the microspeaker's shape, either circular or rectangular shape. MSSP can be used for the microspeaker system simulation, and can give a general prediction of such as; sound pressure level curve, electrical impedance, diaphragm velocity and displacement curve according to multiple design parameters; diaphragm mass, compliance, force factor, front and rear volume, front and rear port's diameter and length.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1557-1571
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• 2017

The L-curve method is a parametric plot of interrelation between the residual norm of the least squares problem and the solution norm. However, the L-curve method may be hard to apply to the total least squares problem due to its no closed form solution of the regularized total least squares problems. Thus the sequence of the solution norm under the fixed regularization parameter and its corresponding residual need to be found with an efficient manner. In this paper, we suggest an efficient algorithm to find the sequence of the solutions and its residual in order to plot the L-curve for the total least squares problems. In the numerical experiments, we present that the proposed algorithm successfully and efficiently plots fairly 'L' like shape for some practical regularized total least squares problems.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.695-706
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• 2014

Various properties of digital covering spaces have been substantially used in studying digital homotopic properties of digital images. In particular, these are so related to the study of a digital fundamental group, a classification of digital images, an automorphism group of a digital covering space and so forth. The goal of the present paper, as a survey article, to speak out utility of digital covering theory. Besides, the present paper recalls that the papers [1, 4, 30] took their own approaches into the study of a digital fundamental group. For instance, they consider the digital fundamental group of the special digital image (X, 4), where X := $SC^{2,8}_4$ which is a simple closed 4-curve with eight elements in $Z^2$, as a group which is isomorphic to an infinite cyclic group such as (Z, +). In spite of this approach, they could not propose any digital topological tools to get the result. Namely, the papers [4, 30] consider a simple closed 4 or 8-curve to be a kind of simple closed curve from the viewpoint of a Hausdorff topological structure, i.e. a continuous analogue induced by an algebraic topological approach. However, in digital topology we need to develop a digital topological tool to calculate a digital fundamental group of a given digital space. Finally, the paper [9] firstly developed the notion of a digital covering space and further, the advanced and simplified version was proposed in [21]. Thus the present paper refers the history and the process of calculating a digital fundamental group by using various tools and some utilities of digital covering spaces. Furthermore, we deal with some parts of the preprint [11] which were not published in a journal (see Theorems 4.3 and 4.4). Finally, the paper suggests an efficient process of the calculation of digital fundamental groups of digital images.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2000.04a
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• pp.475-478
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• 2000

Recently encryption algorithms based on difficulties of factorization have been used with popularization. Prime number factorizations are progressed rapidly. In this paper, characteristics of elliptic curve are analyzed and generation of elliptic curves suitable for prime number factorization is discussed.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.4
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• pp.590-597
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• 1990

To represent shape characteristics of digital closed curve, many algorithms, mainly based on local properties, have been proposed. In this paper, we propose a new algorithm for detecting local curvature maxima which reflects context, i.e., structural or surrounding regional characteristics. The algorithm does not require the value of k as an input parameter which is the major problem in k-curvature method in digital curve, but calculates it at each point depening on the context. The algorithm has been applied to two dimensional image boundaries. The efficiency of the algorithm is addressed by comparing the result of existing contest dependent algorithm.