最小

This paper overviews the various algorithms for least square collocation, discusses the matrix QR decomposition, derives the relationship between QR decomposition and generalized inverse matrix, and obtains least square inverse used for calculating matrix. In addition, the estimation formula for least square collocation by QR decomposition and its accuracy formula are derived. A case study is conducted using gravity anomaly test and calculation to demonstrate that the QR method is correct and valid in least-square collocation calculation.

分析了目前采用的最小二乘配置法解算方法，在讨论了矩阵的QR分解方法的基础上，推导得出了矩阵QR分解与广义逆矩阵的关系，得出了可以直接利用QR分解求解矩阵的最小二乘逆，并推导了应用QR分解求解最小二乘配置的估值计算公式和精度估算公式，最后通过重力异常实例进行了计算，得出矩阵的QR分解用于最小二乘配置解算的正确性和可行性。

First of all, studies the structural characteristic of the controllable region by means of the support hyperplane of the.convex set,then the synthesis problem of minimum step and minimum energy control sc.quence ...

利用凸集的支撑超平面等方法首先研究了能控域的结构特性，然后定义控制能量受限下的最小拍最小能量控制序列的综合问题。最后还给出了求解最小拍最小能量控制综合序列的计算方法。

The necessary and sufficient condition for the existence of 2-dimensional minimal realization is given, which is described by the relation of elements of the infinite sequence and is easy to check.

给出了存在2维最小实现的充要条件，该条件是用无穷序列｛g｝(上标∞下标 0)元素之间的关系描述的，因而容易判断；同时，用涂奉生提出的结构标准形和最小实现算法给出了2维最小实现的构造方法，从而完全解决了2维最小实现问题。

The simulation results also find that the Quasi-Aitken weighted least squares estimator has a smaller asymptotic variance than least squares estimator.

研究结果显示机率加权最小平方法与Quasi-Aitken机率加权最小平方法的回归参数估计式皆具有不偏性，其中Quasi-Aitken机率加权最小平方法的回归参数估计式的变异最小。

The simulation results show that probability weighted least squares estimator and Quasi-Aitken weighted least squares estimator are unbiased estimators of regression coefficients.

研究方法系采用Monte Carlo模拟方式模拟比较最小平方法、分层加权最小平方法、机率加权最小平方法及Quasi-Aitken机率加权最小平方法在分层不等机率抽样下的表现。

By the minimum risk Bayes decision theory, this paper develops a new way of image segmentation: establish the mathematics model of image segmentation; estimate the probability density of grey scales and figure out its math-expectation and square difference that accord with normal distribution and the loss function; and judge the every pixel dot in the image according to the minimum risk Bayes decision theory and determine whether it is of target or non-target images, thereby realizing the extraction of the target image.

依据最小风险贝叶斯决策理论，提出了一种基于最小风险贝叶斯决策的图像分割方法。首先建立图像分割的最小风险贝叶斯决策模型，对灰度级类条件概率密度估计出其符合正态分布的数学期望和方差以及损失函数，再依据最小风险贝叶斯决策理论对图像中的每一像素点进行目标图像和非目标图像的类别判断，从而实现目标图像的提取。

Chapter 7,discusses some unresolved problems about minimum genus and genus distribution of orientable embeddings for a graph,such as based on the joint tree model,calculation of minimum genus of complete graphs,determination of minimum genera for further types of graphs or even arbitrary graphs,etc.

第七章介绍了图的最小亏格及亏格分布领域中一些需要更进一步研究的问题，如如何利用联树模型计算完全图的最小亏格，以及如何通过刻画最小亏格关联曲面的特性来确定更广泛图类，乃至任意图类的最小亏格问题等等。

Finally, the programme of design for routing protocols is chose in the thesis. Secondly, improved algorithms are introduced in detail. In order to achieve to reduce duplication of data sent in, save energy, prolong the network lifetime and balance the network load, improved algorithms are based on the minimum hops algorithm which is one of the energy-aware routing, When the characters of the minimum hops algorithm are analysed in detail,multi-path routing, adaptive dynamic routing, routing reliability are designed.Then a new algorithm based on minimum hops in plane routing protocol and a new algorithm based on minimum hops in clustering routing protocol are designed in the thesis.

接著详细介绍了本文的改进路由算法，为实现减少数据的重复发送量、节约能量、延长网络寿命、平衡网络负载的目标，本文以能量感知路由之一的最小跳数算法为基础，详细分析了最小跳数算法的特点，设计了多路径修正路由，自适应动态路由，路由可靠性机制三方面的改进方案，并且结合改进方案设计了基于最小跳数的改进平面路由协议和基于最小跳数的改进分簇路由协议，将两种类型算法的优点相结合，提高网络的健壮性与可扩展性。

The minimum fluidization velocity has a minimum value when the frequency of sound waves is 120Hz and it will decrease as the sound pressure level increases. The degree of sound attenuation will increase while bed material is higher and the fluidization quality of fine particles will become poor and the minimum fluidization velocity will increase. Compared with TiO2, the SiO2 fine particles have a better quality of fluidization at the same fluidized conditions.The cluster/subcluster model and oscillators model are used to describe the fluidization characteristics of fine particles in a sound-assisted fluidized bed. The theoretical calculations show that the minimum fluidization velocity umf is decreased with the SPL increased at the same frequency of sound and the quality of fluidization is better.

论文还系统的考察了声压和频率对纳米SiO2和TiO2颗粒流化特性的影响，结果表明：在频率一定的情况下，声压越高，流化床中形成的聚团尺寸越小，最小流化速度越低，流化质量越好；当声压低于120dB时，声场对超细颗粒流化特性的影响减小，当声压大于130dB时，则能显著改善流化效果，使流化床内的颗粒聚团明显减小，最小流化速度明显降低，粉体带出减小；声压一定，频率为120Hz左右时，最小流化速度最低，此时流化床中形成的聚团尺寸最小，流化效果最好；超细颗粒达到较好的流化状态存在一个最佳频率范围，随着声压增高，这个频率范围将增大。

The amount of drainage in 1998-1999 was caudated by the equation, the average was 149.4mm, the maximum value was 197.5mm and the minimum was 93.1mm, coefficient variability was 2.9%. The average amount of drainage in 1999-2000 was 286.4 mm, the maximum value was 391.9 mm and the minimum was 193.9 mm, the maximum value was two times than minimum value, and CV was 6.4%.

通过上面建立的关系式，计算得到了1998-1999年10个小区的渗漏量，其平均值为149.4mm，最大值为197.5mm，最小值为93.1mm，变异系数为2.9％。1999-2000年的渗漏量平均值为286.4mm，最大值为391.9mm，最小值为193.9mm，最大值约是最小值的2倍，变异系数为6.4％。

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。