• Honam Mathematical Journal
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• v.35 no.1
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• pp.37-49
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• 2013

Consider a non-degenerate open convex cone C with vertex the origin in the $n$2-dimensional Euclidean space $E^n$. We study volume properties of strictly convex hypersurfaces in the cone C. As a result, for example, if the volume of the region of an elliptic cone C cut off by the tangent hyperplane P of M at $p$ is independent of the point $p{\in}M$, then it is shown that the hypersurface M is part of an elliptic hyperboloid.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.44 no.2
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• pp.120-128
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• 2008

Estimation of the gear shape and cross section of sweep at mouth of a bottom trawl net was described and applied to the field experiments obtained with the Scanmar system. The shape of the trawl net from wingend to the beginning of codend was assumed to be part of an elliptic cone of which the cross section was ellipse, and that of the float rope be of form $y_f=a_fx^{bf}$. In case of a bottom trawl with warp 180m long, the radius of ellipse, the cross section of sweep at mouth, the eccentricity of the ellipse, the inclination angle of float rope and the contribution of the side panel to net height were estimated in accordance with towing speed. The horizontal radius of the upper ellipse increased with increasing towing speed, the eccentricity of it became slightly bigger as increasing the towing speed which meant the shape of it being flat. And the inclination angle of the float rope was about between 7 and 12 degrees in case of the above bottom trawl.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.643-655
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• 2001

We discuss the existence of positive solutions to a certain nonlinear elliptic system representing a competition interaction with self-diffusion. The method used here is a fixed point index theory in a positive cone. We give a sufficient condition for the existence of positive solutions.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.485-498
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• 2005

In this article we show that every quasi-homogeneous convex affine domain whose boundary is everywhere differentiable except possibly at a finite number of points is either homogeneous or covers a compact affine manifold. Actually we show that such a domain must be a non-elliptic strictly convex cone if it is not homogeneous.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.701-717
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• 2006

The positive coexistence of a simple food chain model with ratio-dependent functional response and cross-diffusion is discussed. Especially, when a cross-diffusion is small enough, the existence of positive solutions of the system concerned can be expected. The extinction conditions for all three interacting species and for one or two of three species are studied. Moreover, when a cross-diffusion is sufficiently large, the extinction of prey species with cross-diffusion interaction to predator occurs. The method employed is the comparison argument for elliptic problem and fixed point theory in a positive cone on a Banach space.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.11
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• pp.1102-1110
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• 2006

This paper addresses the problem of computing grasp stability of the object for two-fingered robots in two dimensions. The concepts of force-closure and dual space are introduced and discussed in novel point of view, and we transform friction cones in a robot work space to line segments in a dual space. We newly define a grasp stability index by calculating intersection condition between line segments in dual space. Moreover, we propose a method to find the optimal grasp points of the given object by comparing the defined grasp stability index. Its validity and effectiveness are investigated and verified by simulations for quadrangle object and elliptic objects.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.28 no.2
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• pp.194-201
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• 1995

In order to make clear the resistance of bag nets, the resistance R of bag nets with wall area S designed in pyramid shape was measured in a circulating water tank with control of flow velocity v and the coefficient k in $R=kSv^2$ was investigated. The coefficient k showed no change In the nets designed in regular pyramid shape when their mouths were attached alternately to the circular and square frames, because their shape in water became a circular cone in the circular frame and equal to the cone with the exception of the vicinity of frame in the square one. On the other hand, a net designed in right pyramid shape and then attached to a rectangular frame showed an elliptic cone with the exception of the vicinity of frame in water, but produced no significant difference in value of k in comparison with that making a circular cone in water. In the nets making a circular cone in water, k was higher in nets with larger d/l, ratio of diameter d to length I of bars, and decreased as the ratio S/S_m$ of S to the area $S_m$ of net mouth was increased or as the attack angle 9 of net to the water flow was decreased. But the value of ks15m was almost constant in the region of S/S_m=1-4$ or $\theta=15-90^{\circ}$ and in creased linearly in S/S_m>4 or in $\theta<15^{\circ}$ However, these variation of k could be summarized by the equation obtained in the previous paper. That is, the coefficient $k(kg\;\cdot\;sec^2/m^4)$ of bag nets was expressed as $$k=160R_e\;^{-01}(\frac{S_n}{S_m})^{1.2}\;(\frac{S_m}{S})^{1.6}$$ for the condition of $R_e<100$ and $$k=100(\frac{S_n}{S_m})^{1.2}\;(\frac{S_m}{S})^{1.6}$$ for $R_e\geq100$, where $S_n$ is their total area projected to the plane perpendicular to the water flow and $R_e$ the Reynolds' number on which the representative size was taken by the value of $\lambda$ defined as $$\lambda={\frac{\pi d^2}{21\;sin\;2\varphi}$$ where If is the angle between two adjacent bars, d the diameter of bars, and 21 the mesh size. Conclusively, it is clarified that the coefficient k obtained in the previous paper agrees with the experimental results for bag nets.