以下为句子列表：
英文: Abstract: Direct limit and inverse limit are the methods producing new algebra in universal algebra.In order to further study the production of the new algebra, authors define the family of duplicate set and duplicate limit,discuss the algebraic duplicate
中文: 文摘:直极限和逆极限是泛代数中生成新代数的方法，为了进一步研究新代数的生成，笔者给出了重集族和重极限的定义，讨论了代数的重极限；其次研究了二重直集族和二重直极限及相应性质，讨论了二重直代数族和二重直代数族的极限.
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英文: An algebraic compiler adapted from the MAD(Michigan Algorithmic Decoder) language. It is a high-speed compiler that allows a wide latitude of generality in expressions.
中文: 一种代数编译语言，由密执安算法翻译语言（MAD）修改而成，是一种高速的编译语言，在表达式方面具有很广的一般性。
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英文: An algebraic expression is one or more algebraic terms in a phrase.
中文: 一个代数式是由一个或多个代数项构成的短语。
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英文: As 2-D 3-T heat conduct equations are discretized in a fully implicit method, it is very difficult to solve the nonlinear algebraic equations obtained due to strong nonlinearity.
中文: 摘要由于二维三温热传导方程具有很强的非线性特性，因此采用全隐格式对该方程离散后，所得非线性代数方程组的求解将变得非常困难。
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英文: Based on the algebraic transformation and the frame of KMM algorithm, a self-adjusting factor was embedded into Newton equations for P0 linear complementarity problem, a new infeasible interior point algorithm for P0 linear complementarity problem (P0-LCP
中文: 摘要基于代数变换和KMM算法的框架，通过在牛顿方程中嵌入一种自调节功能，提出了一种新的求解P0阵线性互补问题的不可行内点算法，并证明了该算法的全局收敛性。
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