In this paper , we have proved that an anti - bounded c _ ( 0 ) - group in infinite - dimensional reflexive banach spaces is not exponentially stable under generating compact perturbation , and that a c _ ( 0 ) - isometric semigroup in infinite - dimensional hilbert spaces has the same property . so , we have extended and improved russell theorem 在本文中，我们分别证明了无限维自反banach空间中的反有界c _ 0 -群和无限维hilbert空间中的c _ 0 -等距半群在生成的紧扰动下一定不具指数稳定性，从而推广和改进了russell定理。
The existence conditions of unique solutions are discussed by using - reslovent operators for set - valued mixed quasi - variational - like inequality and generalized set - valued variational inclusion problems on finite dimensional euclidean spaces ; respectively . the problem that under what conditions the solution set is nonempty ( not necessarily unique solution ) is ?利用-预解算子在有限维空间中探讨了集值混合拟类变分不等式问题和广义集值变分包含问题存在唯一解的条件；利用分析的方法在实hilbert空间中讨论了集值混合拟类变分不等式问题解集的非空性(不一定只有唯一解) 。
And by far , most theories of wavelet analysis are established in , but this method is rare to be known and exists defects in the reproducing kernel space with good properties . then in the reproducing kernel space , isometric isomorphism of relation is founded between and by differential operator . and starting from the haar basis , multi - resolution analysis inis gived by folding method ; then multi - resolution analysis and orthonormal wavelet in are obtained through integral transform from to . then the reproducing kernel space can be expressed by wavelet spaces 于是，在再生核空间中，利用积分算子建立了空间与hilbert空间的等距同构关系；并且从haar小波出发，由折叠法实现的空间中多尺度分析通过积分变换得到中多尺度分析和正交小波，使得再生核空间可以由小波空间来刻划；从而对空间中的函数，给出了小波逼近具体表达式和相应的采样公式，形式简单易于数值分析。
It comes up with a new notion , d - solution , which is applied to the distance estimation , by virtue of hilbert space ; furthermore , the dissertation has gained a necessary condition which is identity of minimum mean - square value in linear function classes , so that d - solution extends minimum mean - square value within the domain of nonlinear function equation or equation system ; and , the dissertation studies in detail the classical moment estimation and maximal likelihood estimation on the parameters of ar ( p ) , a series of theorems in the estimation section shows the moment estimators are consistent on the ground of large samples jikewise , those distribution functions of the estimated parameters accord to maximum likelihood estimation converge gauss distribution if the white noise is gaussan 首先，借助hilbert空间理论，提出了距离估计的d -解，给出了d -解的必要条件，这个条件在线性函数类里即是极小二乘估计法， d -解的必要条件满足的方程实质上将极小二乘估计法推广到多函数及非线性函数类。再而，详细地研究了多元弱平稳序列自回归模型ar ( p )的参数经典的矩的替代估计和极大似然估计，获得矩的替代估计的一致性的结果。对基于gauss白噪声假设多元弱平稳序列自回归模型的均值、白噪声的协方差阵的极大似然估计都有依分布收敛到多元正态分布的统计性质。
