• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1111-1117
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• 2011

Using the moving plane method, we establish the radial symmetry of topological one-vortex solutions of a semilinear elliptic system arising from the self-dual Maxwell-Chern-Simons O(3) model.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.133-135
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• 1995

In this note, we will investigate the radial symmetry of some kind of solutions of nonlinear ellipitic equations $$ \Delta U = f(U) $$ $$ (1.1) U = 0 in B $$ $$ U \in C^2 (\bar{B}) on \partial B$$ Here f is $C^1$ and B denotes a n-dimensional unit ball in $R^n$.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.283-291
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• 2004

In this paper we show the radial symmetry of topological one-vortex solutions in the Maxwell-Chern-Simons-Higgs Model.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.751-761
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• 2000

Symmetry properties of positive solutions for semilinear elliptic problems in n are considered. We give a symmetry result for the problem in the feneral case, and then derive various results for certain classes of demilinear elliptic equations. We employ the moving plane method based on the maximum principle on unbounded domains to obtain the result on symmetry.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.305-313
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• 2016

In this paper, we give several sufficient conditions ensuring that any positive radial solution (u, v) of the following ${\gamma}$-Laplacian systems in the whole space ${\mathbb{R}}^n$ has the components symmetry property $u{\equiv}v$ $$\{\array{-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u,v)\text{ in }{\mathbb{R}}^n,\\-div({\mid}{\nabla}v{\mid}^{{\gamma}-2}{\nabla}v)=g(u,v)\text{ in }{\mathbb{R}}^n.}$$ Here n > ${\gamma}$, ${\gamma}$ > 1. Thus, the systems will be reduced to a single ${\gamma}$-Laplacian equation: $$-div({\mid}{\nabla}u{\mid}^{{\gamma}-2}{\nabla}u)=f(u)\text{ in }{\mathbb{R}}^n$$. Our proofs are based on suitable comparation principle arguments, combined with properties of radial solutions.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.4
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• pp.36-44
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• 1997

An efficient context-free multiple-object segmentation using attention operator based on modified generalized symmetry transform is proposed and implemented by modifying a radial basis function network. By using the difference of intensity gradient, instead of te intensity gradient itself, in generalized symmetry tranform so as to make the attention operator to preserve the edges of the objects shape, an efficient context-free multiple-object segementation is proposed in which no a priori shape informtion on the objects is requried. The attention operator is implemented by using a modified radial basis function network which can reflect symmetry, and by using te edge pyramid of the input image, both of the local and the global symmetry of the objects are reflected simultaneously to make the multiple-object with different sizes be segmented with a singel fixed-size $n\timesm$ can be done with O(n) complexity. The simulaton results show that the proposed algorithm can efficiently be used in context-free multiple-object segmentation even for the low contrast IR images as well as for the images from the camera.

• Journal of architectural history
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• v.33 no.1
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• pp.19-31
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• 2024

Jinhae is the oldest Western-style radial and grid city on the Korean Peninsula, and it also has the most defined structure to date, remaining largely unchanged and unlike any other in Korea. The Jinhae town plan was completed immediately after the signing of the Japan-Korea Treaty. Although the city of Jinhae was built by the Japanese, its overall organizational principle is clearly a radial-grid form that was established in the West. The Jinhae radial-grid planning was elaborately constructed with multiple layers of overlapping structures. It is the result of the application of geometry that creates symmetry and hierarchy in European countries, and the simultaneous consideration of road hierarchy and land form in the process of combining radial and grid forms. To reveal these points, four analyses are performed. First, the formation process of Western radial and grid streets is reviewed and compared to derive review points for Jinhae City. Second, the layout and geometric characteristics of radial streets are discussed. Third, the hierarchical characteristics and connections of grid streets are analyzed. The last part is a comparative analysis of the plan and the final realization.

• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.445-459
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• 2024

In this paper, by establishing the direct method of moving planes for the fractional Laplacian system with positive-negative mixed powers, we obtain the radial symmetry and monotonicity of the positive solutions for the fractional Laplacian systems with positive-negative mixed powers in the whole space. We also give two special cases.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.10 s.103
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• pp.1186-1194
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• 2005

In this paper, we have systematically formulated the equations concerned to the in-plane and out-of-plane motions and deformations of a thick circular beam by using the kinetic and strain energies in order to analyse natural frequencies of a thick ring. The effects of variation of radius of curvature across the cross-section and also the effects of bending shear, extension and twist are considered. The equations of motion for natural vibration analysis of a ring are obtained utilizing the cyclic symmetry of vibration modes of the ring. The frequencies calculated using thick ring model and thin ring model are compared and discussed with the ones obtained from finite element analysis using the method of cyclic symmetry with 20-node hexahedral solid elements for rings with the different ratio of radial thickness to mean radius.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.38 no.1
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• pp.89-96
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• 2001

In this paper, a noise-tolerant generalized symmetry transform(NTGST) is proposed and implemented as a context-free attention operator for efficient detection of multi-object. In contrast to the conventional context-free attention operator based on the GST in which only the magnitude and the symmetry of the pixel pairs are taken into account, the proposed NTGST additionally takes into account the convergence and the divergence of the radial orientation of the intensity gradient of the pixel pair. Thus, the proposed attention operator can easily detect multiple objects out of the noisy and complex backgrounded image. Experiments are conducted on various synthetic and real images, and the proposed NTGST is proved to be effective in multi-object detection from the noisy and complex backgrounds.