采用近似等价的方法，将含有混合密度的恢复方程简化为单一密度求解。
An approximate equivalence method is used to simplify the recovery equation with mixture densities into single density.
如果把这两个看做等价的，实际上，就是用函数的线性近似式来代替原函数。
And, if we set these things equal, what we get is actually, we are replacing the function by its linear approximation.
其中的一些术语进行了近似的分类——比如“主要开发者”和“维护者”是等价的。
For some terms, I have made a closest-approximation categorisation — for example equating "lead developer" with "maintainer."
用集合的近似凸性研究函数的拟凸性。在较弱假设下，获得了拟凸性的一些等价条件。
Quasiconvex functions are studied by applying nearly convexity of sets. Under weaker assumptions, some equivalent conditions for quasiconvexity are derived.
用集合的近似凸性研究函数的预不变凸性，在较弱的假设下获得了预不变凸性的一些等价条件。
Preconvex functions are studied by applying nearly convexity of sets in this paper. Under weaker assumptions, some equivalent conditions for preconvexity are derived.
阐述了剪刀带的形成机制，并论证了在半经典近似和平均场近似下，倾斜轴推转模型与粒子转子模型等价。
It is proved that the tilted axis cranking (TAC) model is equivalence to the particle rotor model (PRM) under the semi classical and mean field approximations.
加权等价线性化方法是研究非线性随机振动的一种有效近似方法。
The weighted equivalent linearization technique is an effective approximation for nonlinear random vibration analysis.
利用这种等价性，构造了一些新的扰动近似点算法，并证明了由此算法所产生的迭代序列的收敛性。
Using this equivalence, we construct some new perturbed proximal point algorithms and prove the convergence of iterative sequences generated by the algorithms.
研究发现，阻尼比为5%时的地震动总输入能量谱和最大瞬时输入能量谱的等价速度谱可以分别用阻尼比为0.5%和10%下的拟速度谱来近似获得；
It is found that the input energy and momentary input energy spectra with a damping factor of 5% can be estimated from the pseudo-velocity spectra with damping factors of 0.5% and 10%.
接着对分布约简的可辨识矩阵中等价类的区分关系进行改进，提出一种新的近似约简算法。
Secondly, it introduces an improved algorithm which revises the discernibility relation of similarity sets on the basis of the Discernibility Matrix of distribution reduction.
证明了模式i与模式III也是等价的，从而得出三种近似推理模式是等价关系。
Thus the three different types of approximate reasoning patterns are equivalent to each other.
证明了模式i与模式III也是等价的，从而得出三种近似推理模式是等价关系。
Thus the three different types of approximate reasoning patterns are equivalent to each other.
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