算子的指数

By fixed point index theory, multiplicity question of solutions to superlinear operator equations in ordered Banach space is discussed.

通过不动点指数理论，讨论了一类超线性算子方程的多重解问题。

Three methods for the computation of the isotropic tensor function,spectral decomposition method,eigenprojection operator method and representation theorem method,are compared.Different approaches to calculate the eigenvalues and their corresponding eigenvectors are also discussed.As an example,the exponent tensor function is calculated.

对计算各向同性对称张量函数的3种方法(谱分解法、特征投影算子法和表示定理法)进行了分析比较，同时也对如何计算特征根与特征向量的技巧进行了探讨，并利用3种方法对指数张量函数进行了实例计算。

The example shows that the exponential change has tremendous influences on iterative number, Lagrange multiplier value and initial value. An appropriate value selected can make the algorithm have a good convergence property.

算例结果表明，指数的变化对迭代次数、拉格朗日乘子的取值及初值的选取都有较大影响，通过合适的取值可使算法具有更好的收敛性。

In Chapter 2,we firstly study the super-stability of the exponential operator equation f= ff in some special spaces.

第二章首先研究了指数算子方程f=ff在一些特殊空间中的超稳定性问题。

Then we consider the stability of the exponential operator equation under the definition which Ger first defined.

接着我们又讨论了在Get提出的稳定性意义下，指数算子方程稳定性的一些情况。

In fifth chapter,as applications of the existence theorem of〓-optimalcoupling operator for the jump processes,the estimate of the varied expontialconvergence rate for the jump processes and the existence of an order-preservingMarkov coupling for the jump processes are investigated,where,the obtained theexistence theorem of an order-preserving Markov coupling is a general theorem onPolish space endowed with semiorder,it includes the results that existence theoremon countable state apace endowed with total order or finite state space endow withsemiorder have been obtained by the internal and external mathematicians in recentten years.

第五章作为跳过程〓最优耦合算子存在性定理的应用，讨论了跳过程各种指数收敛速度的估计和保序Markov耦合的存在性。其中保序Markov耦合存在定理是具有偏序关系波兰空间上的跳过程最一般的定理，它包括了近10年来国内外对具有全序关系可数状态空间或具有偏序关系有限状态空间上的跳过程关于保序Markov耦合存在定理的研究成果。

The steady-state solution is known to be the positive eigenfuction corresponding to the simple eigenvalue 0 of the system operator.

于是作为半群拟紧性和不可约性的直接结果，得到了系统的时间依赖解指数收敛到其静态解，并且该静态解即为系统算子简单特征值0对应的正的特征向量。

Russell([17]) has showed that, a compact perturbation, generated from unitary operator groups in infinite-dimensional linear Hilbert spaces, is unable to make the perturbed semigroup exponentially stable.

Russell([17])曾指出，无限维Hilbert空间中的酉算子群对生成的紧扰动不能使被扰动半群具有指数稳定性。

In Chapter 3, by establishing a L-operator inequality and using the properties of M-matrix and stochastic analysis techniques, some sufficient conditions ensuring the exponential dissipativity in mean square of impulsive stochastic functional differential equations of Ito-type are obtained.

第三章，通过建立L-算子不等式，运用M-矩阵的理论和随机分析技巧，获得了一类脉冲随机泛函微分方程均方指数耗散的充分条件。

We prove that when mutation is independent, it may be performed either before or after multi-point crossover, the consequences of schema in EA are probabilistically the same.

通过引入模式进化、模式进化能力、适度模式等概念，以标准遗传算法为例，证明了在变异算子独立的条件下，进化算法中模式的构成与多点交叉和变异的顺序无关，然后证明了具有强进化能力的模式，将以指数阶增长。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。