下降函数

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

It also is the function of age and the coefficient of moisture diffusion reduces non-linearlyas age increases.

水分扩散系数是水灰比的函数，同时又是龄期的函数，随龄期增长而呈非线性下降。

It"s considered that the algae blooms control function in the algae"s growth dynamics model is influenced mostly by the water temperature, sun illumination, water flow speed and the concentration of the nutriment in water. A function including the four elements was built. By using cell mapping algorithm and contacting with the practical water condition of the Wujiang river and the Hanjiang river we analyzed and computed the algae blooms in the two areas and found the result was very near to the practical result. And we found that the ascend of water temperature and the descend of the water flow speed will contribute to the growth of algae and the nutriment is the substance basis of the algae blooms but not the only element. It must be under the condition of condign water temperature, enough sun illumination, slow water flow and abundant nutriment that algae blooms may break out unexpectedly.

本文认为藻类生长营养动力学模型中的水华爆发控制函数主要受水温、光照强度、水流速和营养盐浓度的影响，构建了包含水温、光照强度、水流速和营养盐浓度的水华爆发控制函数，通过对乌江、汉江的水华爆发进行胞映射分析，得到的计算结果与实际监测非常吻合，并认为水温升高和水流速下降将有利于藻类生长，营养盐是水华爆发的物质基础，但不是唯一因素，必须在适宜的水温、光照、缓慢的水流和充足的营养盐条件下，藻类才可能出现突发式的"疯长"，即水华爆发。

It transforms the image based on the cumulative distribution function of histogram. However, there is a caveat to over-enhance the contrast when the auto-generated transform curve is too sharp due to some high peaks in the histogram.

但是当直方图的分布函数中某一个值特别大的时候，则会使产生的转换函数斜率过大，换句话说就是使影像过度增强，这会使输出影像太亮，清晰度反而下降。

During the process of learning, a new kind of empirical risk function is proposed which is differentiable and can be minimized by gradient descent strategy.

对于参数的学习，提出了一种适用于分类器的可微经验风险函数，该函数能够有效地利用梯度下降法进行最小化。

At the end of the function, this class instance will be out of scope so the destructor of the class will be called and the level will decrease.

在该函数的末尾，这个类实例将进行范围如此类的析构函数将被调用，该水平会下降。"/页"

Analysis and simulation results show that tail distribution is very different from Gaussian; the effects of passive intermodulation interference on communication systems are mainly in the region of low bit error rates.

分析和数值结果表明：互调产物的幅度一般来说随阶数的增加而下降；高阶互调产物的下降行为本质上与传递函数的类型有关。

By the least common denominator of all denominators in the equation to transform it into an integral equation;（2）Solve the integral equation

一次函数y=kx+b有下列性质：当k＞0时，y随x的增大而增大，这时函数的图象从左到右上升：当k＜0时，y随x的增大而减小，这时函数的图象从左到右下降。

In this paper, by using some characteristic quantities such as value function, trust region radius, etc. in trust region method, we present a global error bound for the distance between a feasible solution and the optimal solution under the condition that the gradient vector of the objective function is strongly monotone.

本文利用信赖域方法中的几个特征量（由预测下降量给出的价值函数与信赖域半径等），在目标函数的梯度向量是强单调的条件下，为约束最优化问题的可行解与最优解之间的距离提供了一个全局误差界。

In Chapter 2, a nonmonotone trust region method with a line search technique is presented. Unlike traditional trust region methods, our method does not restrict a monotonic decrease of the objective function value at each iteration, but only requires an average of the successive objective function values decreasing.

第二章，我们提出了一类带线搜索的非单调信赖域算法，与传统的信赖域方法不同的是：我们的算法不要求目标函数值在每一步都有充分下降，而是要求目标函数的连续平均值充分下降。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。