以下为句子列表：
英文: A new computational formula to nonlinear adjustment by parameters, in consideration of the second-order terms, is derived in this paper from the precise orthogonality condition equations to nonlinear least squares by analyzing the direct solving process a
中文: 在分析线性化的非线性参数平差的近似直接解法与迭代解法基础上，利用非线性最小二乘的精确正交性条件方程，推导出顾及到二次项的非线性参数平差的一种新的计算公式。
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英文: Based on the previous screenhouse study and field experiment, fertilization , plant variety and plant density were studied on two selected cropping systems: rape-rice-rice and wheat-rice, using an orthogonality design.
中文: 在过去网室研究和大田试验的基础上，在油菜-水稻-水稻和小麦-水稻两种供试种植制度上研究了施肥、作物品种和种植密度，采用正交设计。
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英文: By using new dual vectors, dual differential matrix and orthogonality relationship, a new solution method by igenfunction expansion for an elastic system with one continuous coordinate is establishen based on the theory of ordinary differential eguations.
中文: 摘要以常微分方程的理论为基础，利用新的对偶变量、对偶微分矩阵和正交关系，以单连续座标弹性体系为例，建立了与弹性力学求解新体系平行的特徵函数展开解法。
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英文: The orthogonality relationship is applied to the treatment of boundary conditions to decouple the coefficient equations, and the explicit solutions are obtained.
中文: 并将正交关系应用于可对角化边界条件的处理，实现了求解待定系数方程组的解耦，求得问题的显式封闭解。
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