以下为句子列表：
英文: In this paper, we consider mixed boundary problem of P-laplacian equations in a bounded domain of RN.
中文: 摘要研究空间中有界区域混合边值问题的正解存在唯一性。
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英文: It has two characteristics: new filters enhance input image edges by using Laplacian operation; designing filters is based on targets enhanced rather than their original.
中文: 它有两个特点：（1）采用拉普拉斯算子增强输入图像边缘；（2）滤波器的设计是基于增强后的目标而不是原始目标。
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英文: In Chapter , the polar coordinates for the Koranyi unit sphere on H-type group are introduced . Then we prove an expression between the sub-Laplacian and the radial function, and construct a compact operator T;
中文: 在第二章,我们引入了H型群中Koranyi球上的极坐标表示,证明了H型群中次Laplace算子对径向函数的一个公式,构造并证明了算子T是一个紧算子;
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