• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.393-404
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• 2003

In general, a differential operator can be used as a tool of treating the local properties of given function. However, when the given function is varied with high frequency and has irregular form with non-stationary evolution it may not act its role sufficiently as in case of nowhere differentiable curves. In this paper we introduce a multi-scale derivative as a form of weakened global derivative so that it may explain its semi global diffusion properties as well as local ones for the various irregular diffusion phenomena.

• Journal of KIISE
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• v.42 no.6
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• pp.764-768
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• 2015

Requirement of effective image handling methods such as image retrieval has been increasing with the rising production and consumption of multimedia data. In this paper, a method of constructing more effective descriptor is proposed for robust keypoint based image retrieval. The proposed method uses information embedded in the first order and second order derivative images, in addition to the scale space image, for the descriptor construction. The performance of multi-image descriptor is evaluated in terms of the similarities in keypoints with a public domain image database that contains various image transformations. The proposed descriptor shows significant improvement in keypoint matching with minor increase of the length.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.33-50
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• 2023

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.37-53
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• 2021

In this paper we define scaled visual curvature and visual Frenet frame that can be visually accepted for discrete space curves. Scaled visual curvature is relatively simple compared to multi-scale visual curvature and easy to control the influence of noise. We adopt scaled minimizing directions of height functions on each neighborhood. Minimizing direction at a point of a curve is a direction that makes the point a local minimum. Minimizing direction can be given by a small noise around the point. To reduce this kind of influence of noise we exmine the direction whether it makes the point minimum in a neighborhood of some size. If this happens we call the direction scaled minimizing direction of C at p ∈ C in a neighborhood Br(p). Normal vector of a space curve is a second derivative of the curve but we characterize the normal vector of a curve by an integration of minimizing directions. Since integration is more robust to noise, we can find more robust definition of discrete normal vector, visual normal vector. On the other hand, the set of minimizing directions span the normal plane in the case of smooth curve. So we can find the tangent vector from minimizing directions. This lead to the definition of visual tangent vector which is orthogonal to the visual normal vector. By the cross product of visual tangent vector and visual normal vector, we can define visual binormal vector and form a Frenet frame. We examine these concepts to some discrete curve with noise and can see that the scaled visual curvature and visual Frenet frame approximate the original geometric invariants.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.1
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• pp.75-81
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• 2002

In the re-entry comtrol system, errors apt to induce because the time deriviative of drag acceleration is analytically estimated. Still more, the difficulty of estimation of th exact drag coefficient in hypersonic velocity and the non-reality of the scale height cause a steady-state drag errer. In the Space-Shuttle, a steady-state drag error is reduced by the addition of the integral term of drag acceleation error into the control system. This method, however, induces a difficulties in respect to the modern controller composition due to the multi-poles in a closed-loop system. Thus, this paper proposes the additional method of the disturbance observer. This reduces the steady-state drag error according to the following by the analytic calculation, and then creates the new drag acceleration time derivative using the estimated error. The performance of the re-entry control system is verified about 32 refernce trajectories.