以下为句子列表：
英文: A class of exact solutions of the Dirac equation are obtained for an electron in the electromagnetic field of a wave guide formed by two pairs of hyperbolic cylinders.
中文: 摘要研究了位于由两对双曲柱面构成的波导管电磁场里的单电子的性质，得到了单电子在场中狄拉克方程的新一类精确解；计算了极化算符的本征函数。
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英文: A class of nonconforming finite elements are applied to hyperbolic equation with semidiscretization on anisotropic meshes, the optimal error estimates are derived.
中文: 摘要在各向异性条件下，讨论了双曲型方程的一类非协调有限元逼近，给出了半离散格式下的最优误差佑计。
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英文: A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engin
中文: 本课程讲授求解不同线性及非线性椭圆、抛物线及双曲线偏微分方程式与积分方程式等之现代数值技巧基础，并强调在许多科学、工程及相关领域上的应用。
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英文: Abstract: The boundary-value problem of an ultra-hyperbolic equation with an integral condition is studied and existence and uniqueness of the solution are proved.
中文: 文摘:本文研究一类超双曲型方程的极限问题，提出并证明了具一积分条件的超双曲型方程的边值问题解的存在性和唯一性。
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英文: According to the analysis, the 3D interference images are hyperboloidal beams and the 2D interference images are hyperbolic beams.
中文: 同时也分析出三维干涉图像为双曲面族，以及二维干涉图像为双曲线族的图像特征。
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