以下为句子列表：
英文: Abstract: This paper discusses the different differential methods of Alternating Direction Implicit Method with initial condition and boundary conditions in detail.
中文: 文摘:详细地研究了各种情形的求解二维抛物型方程初边值问题的交替方向隐式差分法。
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英文: The above remark is very important in considering any type of transient operation because of the initial condition problem.
中文: 鉴于初始条件的重要性，任何类型的冷凝非稳态操作中，上述论述都是非常重要的。
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英文: The fundamental solution of the mixed problem with the third kind homogeneous boundary condition and that with the zero initial condition are given respectively.
中文: 分别给出具有第三类齐次边条件的混合问题基本解以及具有零初始条件的混合问题基本解。
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英文: The initial condition is one of an absolute ruler who can confiscate any assets his subjects may own or any future income but, because policing and monitoring costs are positive, the ruler stands to gain by exchanging with his subjects.
中文: 初始的状况是一个完全的统治者，它能够没收他的臣民所拥有的任何财产和未来的收入，但是由于监管和维持治安的费用很高，统治者就决定通过与臣民交易来获益。
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