In chapter two , we first give the condition of generalized wavelets on l2 ( x ) by using the gelfand transform , where x = r + r denotes the underlying manifold of square integrable polyradial functions on the heisenberg group hn . then , we establish the theory of generalized wavelet transform and generalized wavelet packet transform on it 在第二章中，我们利用gelfand变换刻画了海森堡群h _ n上平方可积柱径向函数空间的基础流形laguerre超群x = r _ + ~ n r上的广义小波，讨论了该超群上的广义小波变换与广义小波包变换
By introduction of derivative rule , derivative formula can be found ; through defining multi - dimension function space and reorganizing the function rules , the inaccuracy rules , and the end rules , the scope of formula finding is broadened ; by introduction of three - dimension expand rule and multidimensional expand rule , multi - dimension formulas can be discovered ; through improvement of flow of algorithm , more complete traverse has been achieved 通过引入导数规则，可以发现导数公式；通过定义函数空间，重新组织函数规则，误差规则，终止规则等知识，扩大了公式发现的广度；引入多维扩展规则，可以发现多维函数公式；针对公式发现流程进行了改进，使得对搜索树的遍历更加完备。
Abstract : in the way of adjustment with the first and second order term of expanded nonlinear function in consideration and the way of nonlinear adjustment in the fields of nonlinear to do the same adjustment , by comparison of its ' results , stressed on the necessity of constructing theory of adjustment & data processing in the space of nonliear functions 文摘:用顾及一阶泰勒项的线性平差方法，顾及二阶泰勒项的线性平差方法及非线性函数空间的平差方法对同一平差问题进行研究，在比较其平差效果的基础上论述了建立非线性函数空间测量平差与数据处理理论的必要性。
Under certain requisitions , the estimations of pointwise nonsquare constant in orlicz sequence space and orlicz functional space endowed with luxemburg norm are given . the values of pointwise nonsquare constant in lp and lp also are given . these estimations and values will provide helpful conditions for the research , testification and guess of big space 同时，本文的第三部分给出了点态非方常数在满足一定条件下的赋luxemburg范数orlicz函数空间与orlicz序列空间中的估计，以及点态非方常数在l ~ p和l ~ p空间中的计算值，为对大空间的研究、证明、猜想提供了条件。
This thesis presents the feasibility of nonlinear model predictive control implemented in spacecraft control and the optimality of increasing the control precision and decreasing the fuels expenditure . and the discussions are then focused on the simulation of spacecraft control using function - space model predictive control algorithm as mentioned below : 1 本文的主要研究工作是探讨非线性模型预测控制( nmpc )应用于空间飞行器自适应控制的可行性及对提高控制精度和减少燃料使用方面的优越性，同时利用函数空间模型预测控制算法( f - mpc )对空间飞行器的位置和姿态控制进行仿真，具体内容如下：一
We can show the existence of solutions to the differential inclusions problem by baire category method , and so the formal problem . the main steps of using baire category method are as follows . first we construct a complete metric space v . then with the help of the likelihood functional , we obtain a series of open and dense subset vs in v . finally , by baire category theorem , we know that the subset vs is dense in v 本文指出在适当的条件下，可以将原问题转化为一个微分包含问题：对于此微分包含问题运用baire稠密性方法，构造一个完备的度量空间，也就是容许函数空间，再利用似然泛函构造出它的一列稠密开子集(实际上是逼近解集) ，从而由baire稠密性定理可以得到解的存在性。
