• Honam Mathematical Journal
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• v.29 no.4
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• pp.617-630
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• 2007

In this paper, we'll introduce infinitesimal Finsler metrics induced by the higher order Kobayashi pseudometric and then prove some properties related to these as compared with the usual Kobayashi metric.

• Journal of The Korean Astronomical Society
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• v.29 no.1
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• pp.1-8
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• 1996

When we follow the lines of the trajectory of photons which intersect the circle, the circle may suffer some deformation as approaching to the observer. We consider an infinitesimal light bundle suffering gravitational bending. We examine the deformation of the deflected light bundle due to the gravitational lens. The size of the deformation is expressed in terms of the focal length of the gravitational lens.

• Journal for History of Mathematics
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• v.15 no.2
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• pp.1-14
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• 2002

The paper is analyzed the crisis of mathematics for paradoxes in mathematics, also its process of conquest in the history of mathematics. We have found that various views of the infinity and infinitesimal in the history of mathematics. This study be tried to find out the process development of mathematics on passing through a crisis conquest of mathematics for contradictions in the hi story of mathematics.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.2 s.233
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• pp.333-340
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• 2005

Feedrate is one of the factors that have the significant effects on the productivity, qualify and tool life in the cutting mechanism as well as cutting velocity, depth of cut and width of cut. In this study, in order to realize the high-efficient machining, a new feedrate optimization method is proposed based on the concept that the optimum feedrate can be derived from the allowable cutting power since the cutting power can be predicted from the cutting parameters as feedrate, depth of cut, width of cut, chip thickness, engagement angle, rake angle, specific cutting force and so on. Tool paths are extracted from the original NC program via the reverse post-processing process and converted into the infinitesimal tool paths via the interpolation process. And the novel NC program is reconstructed by optimizing the feedrate of infinitesimal tool paths. Especially, the fast feedrate optimization is realized by using the Boolean operation based on the Goldfeather CSG rendering algorithm, and the simulation results reveal the availability of the proposed optimization method dramatically reducing the cutting time and/or the optimization time. As a result, the proposed optimization method will go far toward improving the productivity and qualify.

• Journal of Institute of Control, Robotics and Systems
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• v.2 no.1
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• pp.26-34
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• 1996

One of the challenging tasks in visual inspection using CCD camera is to identify surface defects in an image with complex textured backgeound. In microscopic view, the surface of real objects shows regular or random textured patterns. In this paper, we present a visual inspection algorithm to extract abnormal surface defects in an image with textured background. The algorithm uses the space and frequency information at the same time by introducing the Dominant Frequency Map(DFM) which can describe the frequency characteristics of every small local region of an input image. We demonstrate the feasibility and effectiveness of the method through a series of real experiments for a 14" TV CRT mold. The method successfully identifies a variety of infinitesimal defects, whose size is larger than $50\mu\textrm{m}$, of the mold. The experimental results show that the DFM based method is less sensitive to the environmental changes, such as illumination and defocusing, than conventional vision techniques.ques.

• Advances in biomechanics and applications
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• v.1 no.2
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• pp.85-93
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• 2014

In this paper, two procedures of enumerating the axial rotation are proposed using the unit sphere of the spherical rotation coordinate system specifying 3D rotation. If the trajectory of the movement is known, the integration of the axial component of the angular velocity plus the geometric effect equal to the enclosed area subtended by the geodesic path on the surface of the unit sphere. If the postures of the initial and final positions are known, the axial rotation is determined by the angular difference from the parallel transport along the geodesic path. The path dependency of the axial rotation of the three dimensional rigid body motion is due to the geometric effect corresponding to the closed loop discontinuity. Firstly, the closed loop discontinuity is examined for the infinitesimal region. The general closed loop discontinuity can be evaluated by the summation of those discontinuities of the infinitesimal regions forming the whole loop. This general loop discontinuity is equal to the surface area enclosed by the closed loop on the surface of the unit sphere. Using this quantification of the closed loop discontinuity of the axial rotation, the geometric effect is determined in enumerating the axial rotation. As an example, the axial rotation of the arm by the Codman's movement is evaluated, which other methods of enumerating the axial rotations failed.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.459-468
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• 1997

The purpose of this paper is to give some characterizations of homogeneous real hypersurfaces of type A in complex space forms $M_n(c), c \neq 0$, in terms of Lie derivatives.

• Honam Mathematical Journal
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• v.19 no.1
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• pp.81-86
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• 1997

The aim of this paper is to prove the boundary behavior between the Caratheodory and Kobayashi-Royden metrics in a strongly pseudoconvex bounded domain with $C^2$-boundary in $\mathbb{C}^n$ and to show that the converse does not holds. S. Venturini([Ven]) proved the corresponding result with distances in place of the infinitesimal metrics.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.793-802
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• 1998

We apply the generalization of Levy's infinitesimal equation $\delta$X(t) = $\psi$(X(s), s $\leq$ t, $Y_{t}$, t, dt), $t\in R^1$, for a random field X (C) indexed by a contour C or by a more general set. Assume that the X(C) is homogeneous in x, say of degree n, then we can appeal to the classical theory of variational calculus and to the modern theory of white noise analysis in order to discuss the innovation for the X (C.)

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.401-411
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• 2007

In this paper we propose an influence measure for detecting potentially influential observations using the infinitesimal perturbation and the local influence in the log-linear regression model. Also, we propose a goodness-of-fit measure for variable selection. A real data set are used for illustration.