• 제목/요약/키워드: radial symmetry

검색결과 37건 처리시간 0.022초

RADIAL SYMMETRY OF POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS IN $R^n$

  • Naito, Yuki
    • 대한수학회지
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    • 제37권5호
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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.

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SYMMETRY OF COMPONENTS FOR RADIAL SOLUTIONS OF γ-LAPLACIAN SYSTEMS

  • Wang, Yun
    • 대한수학회지
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    • 제53권2호
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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.

일반화 대칭변환을 변형한 관심 연산자에 의한 사전 정보없는 다중 물체 분할 (Context-free multiple-object segmentation using attention operator based on modified generalized symmetry transform)

  • 구태모;전준형;최흥문
    • 전자공학회논문지C
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    • 제34C권4호
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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.

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진해 시가지의 방사-격자 도시 형태에 관한 연구 (A Study on Urban form of Jinhae Radial-Grid Planning)

  • 신건수
    • 건축역사연구
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    • 제33권1호
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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.

PROPERTIES OF POSITIVE SOLUTIONS FOR THE FRACTIONAL LAPLACIAN SYSTEMS WITH POSITIVE-NEGATIVE MIXED POWERS

  • Zhongxue Lu;Mengjia Niu;Yuanyuan Shen;Anjie Yuan
    • 대한수학회지
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    • 제61권3호
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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.

두꺼운 링의 고유진동 해석 (Natural Vibration Analysis of Thick Rings)

  • 박정우;김세희;김창부
    • 한국소음진동공학회논문집
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    • 제15권10호
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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.

잡음에 강건한 주목 연산자의 구현과 효과적인 다중 물체 검출 (An Implementation of Noise-Tolerant Context-free Attention Operator and its Application to Efficient Multi-Object Detection)

  • 박창준;조상현;최흥문
    • 대한전자공학회논문지SP
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    • 제38권1호
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    • pp.89-96
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    • 2001
  • 본 논문에서는 잡음에 강건한 일반화 대칭 변환을 주목 연산자로 제안하고 이를 이용하여 크기와 형태가 다양한 물체들을 효과적으로 검출하였다. 기존의 주목 연산자와는 달리 두 화소의 명도변화의 크기와 대칭성뿐만 아니라 방사(radial)방향 명도변화의 수렴 및 발산을 누적 대칭도에 반영시킴으로써 명도변화 방향의 일관된 수렴이나 발산이 없는 잡음 영역에 의한 대칭 기여도가 누적되지 않도록 하였다. 따라서 제안한 주목 연산자를 사용하면 잡음이 많고 복잡한 배경으로부터 물체만을 쉽게 검출할 수 있도록 하였다. 다양한 합성영상(synthetic images)과 실영상(real images)에 대해 실험하여 잡음의 영향을 적게 받으며 효과적으로 다중 물체를 검출함을 확인하였다.

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