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In this paper the aberrations of a sort of sphere lens with spherical Symmetrical gradient index have ben analysied.

本文分析了一种折射率为球对称梯度分布的球形透镜的像差，得到了该透镜对无限远物点的纵、横向球基及其焦距的精确表达式。

The characteristics of pressure fluctuation in a standpipe at negative pressure gradient were investigated based on measurement in the gas-solid two-phase circulating fluidized bed.

通过对气固循环流化床负压差下料立管的压力测量，分析了立管下料过程的压脉动特性。

The gas-phase flow characteristics of gas-solid two-phase flow in standpipe were investigated under negative pressure gradient.

对负压差立管内气固两相流的气相流动特性进行了分析，并基于滑落速度与空隙率的线性关系，建立了立管内气相速度的计算模型，给出了气体流量与相关参数的关联式。

While with the increase of the circulating amount of the system,negative pressure gradient and slip velocity in the standpipe increase too.

循环流化床燃烧/热解双应器中灰流动性研究可为热态过程操作条件的选取、立管内流动状态的预测等提供参考。

Results show that with the increase of the apparent gas velocity in the riser,there is little change in negative pressure gradient in the standpipe.

结果表明：随着提升管内表观气速的增加，立管内的负压差梯度变化不大；而随着系统循环量的增加，立管内的负压差梯度以及滑移速度均增大；随着加入热解室内松动气量的增加，立管内尤其是立管上部的压力也随之增大，热解室内无论是移动床流动还是流态化流动均对立管的稳定性影响不大；但当热解室内的压力超过某一值时，立管内的料封很快被破坏，导致系统无法运行。

During the period of dry, raw material is effected by stirring-up rake with gradient and hot air, it can be moved and passed through the dry region and to star valve and then discharge the finished product.

在干燥过程中，物料在带有倾斜度的抄板和热气流的作用下，可调控地运动至干燥机另一段星型卸料阀排出成品。

Then, in a second interval, the voltage is raised to a second voltage no less than the starting voltage and with an absolute gradient smaller than that for the voltage rise in the first interval.

然后，在第二区间中，电压上升至不小于启动电压的第二电压，并且电压上升的绝对斜率小于在第一区间中电压上升的绝对斜率。

An on-line blind source separation algorithm of non-stationary mixed signals is presented. The algorithm uses the multiple time-delayed decorrelation and natural gradient rule to obtain the stationary point of the cost function, only a small number of observed samples is needed to minimize the Frobenius norm of the correlation matrices, so the computing cost is low and continuous separation calculation could be realized by on-line operation.

利用一种基于多时延解相关准则的代价函数和自然梯度原则，分别推导出非平稳信号在瞬态线性混合及卷积混合情况下的在线盲分离算法，仅通过对有限个时延样本的相关矩阵进行Frobenius范数最小化运算得到分离矩阵，计算工作量小，无需对样本进行分块处理，可实现对信号的连续跟踪操作。

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

Steepest gradient descent method had been mostly used in the iteration process of the error energy function during conventional programming problems.

传统的规划问题中，一般使用最陡梯度算法进行误差能量函数的迭代过程。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。