• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1535-1547
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• 2015

A vector field on a Riemannian manifold (M, g) is called concircular if it satisfies ${\nabla}X^v={\mu}X$ for any vector X tangent to M, where ${\nabla}$ is the Levi-Civita connection and ${\mu}$ is a non-trivial function on M. A smooth vector field ${\xi}$ on a Riemannian manifold (M, g) is said to define a Ricci soliton if it satisfies the following Ricci soliton equation: $$\frac{1}{2}L_{\xi}g+Ric={\lambda}g$$, where $L_{\xi}g$ is the Lie-derivative of the metric tensor g with respect to ${\xi}$, Ric is the Ricci tensor of (M, g) and ${\lambda}$ is a constant. A Ricci soliton (M, g, ${\xi}$, ${\lambda}$) on a Riemannian manifold (M, g) is said to have concircular potential field if its potential field is a concircular vector field. In the first part of this paper we determine Riemannian manifolds which admit a concircular vector field. In the second part we classify Ricci solitons with concircular potential field. In the last part we prove some important properties of Ricci solitons on submanifolds of a Riemannian manifold equipped with a concircular vector field.

• Journal of Korean Ophthalmic Optics Society
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• v.15 no.3
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• pp.235-240
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• 2010

Purpose: In this study, we proposed a simple accommodation-dependent crystalline lens with a constant volume and homogeneous refractive index. Methods: We proposed a human crystalline lens with two aspheric surfaces. Two surfaces intersect in two points and straight line between two points was equator(2b). It assumed that the derivative in axial direction was zero at the equator and the radial derivative was zero at the vertex. Proposed human crystalline lens was divided by the equator into the anterior and posterior parts. It was assume that the volume of each part and refractive index of the human crystalline lens were constant during accommodation. Results: For the changes during accommodation, geometrical parameters were determined by different objective distances. Considering the constant volume of each part with the small decrement of the equator, we obtained the paraxial parameters, such as the anterior and posterior vertex radius of curvature and lens thickness. Compared with the experimental data published in the literature, calculated values using simple approximation showed similar change per accommodative stimulus. Conclusions: These results showed that proposed simple approximation using assumption of constant volume and refractive index of the human crystalline lens made it possible to predict changes of geometrical parameters during accommodation.

• Journal of Biosystems Engineering
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• v.31 no.6 s.119
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• pp.514-523
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• 2006

Production of green pepper has been increased due to customer's preference and a projected ten-year boom in the industry in Korea. This study was carried out to develop an automatic grading and sorting system for green pepper using machine vision. The system consisted of a feeding mechanism, segregation section, an image inspection chamber, image processing section, system control section, grading section, and discharging section. Green peppers were separated and transported using a bowl feeder with a vibrator and a belt conveyor, respectively. Images were taken using color CCD cameras and a color frame grabber. An on-line grading algorithm was developed using Visual C/C++. The green peppers could be graded into four classes by activating air nozzles located at the discharging section. Length and curvature of each green pepper were measured while removing a stem of it. The first derivative of thickness profile was used to remove a stem area of segmented image of the pepper. While pepper is moving at 0.45 m/s, the accuracy of grading sorting for large, medium and small pepper are 86.0%, 81.3% and 90.6% respectively. Sorting performance was 121 kg/hour, and about five times better than manual sorting. The developed system was also economically feasible to grade and sort green peppers showing the cost about 40% lower than that of manual operations.

• The Korean Journal of Ecology
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• v.19 no.2
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• pp.151-163
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• 1996

To investigate the early symptoms of light-chilling, alterations of chlorophyll fluorescence transients were monitored in cucumber (Cucumis sativus L. cv. Ilmichungjang) leaves. During 24 h chilling, decreases in (Fv)m/Fm, qE and qQ, and an increase in Fo were observed. The chilling effects were not recovered at room temperature, and a significant increase in Fo was observed during the recovery period. After 6 h chilling, ‘dip’(D) level of the transients became obscure, and the negative slope after ‘peak’(P) disappeared. The first derivative (dFv/dt) of the fast fluorescence rise curve was used to obtain more accurate information about the changes in the transients. The maximal rate of the fluorescence increase in the D-p rise curve (Fr) has been the most frequently used chilling stress indicator. However, a correct value of Fr could not be measured when the D level became obscure. This problem was overcome by introducing a new indicator, HFr (dFv/dt at Fv = 1/2 (Fv)m), and HFr gave very similar values to Fr. To monitor the changes in curvature around D level, another new parameter, ${\Delta}S$(D-Fr), was also introduced. These three parameters decreased very sensitively during light-chilling. In addition, increases in these parameters were observed during the first 2 h chilling, but this increase in Fr was also observed in pea leaf discs dark-chilled for 15 min, suggesting that this very early change is a common response to chilling in both pea and cucumber leaves. Quenching coefficients were also very sensitive to chilling, especially qE. Discussion on the usage of these parameters as chilling stress indicators is given in the text.