正则性条件

In the last chapter,we study the control problems of the distributedparameter system governed by a class of higher order pseudohyperbolicequation related to the symmetric regularized long wave equation.we havediscussed the controllability and optimal control problems.we have obtainedcompatibility condition of the constraint when the state is controllable,therepresentation of the optimal control for both the time optimal control problemand the optimal control problem of minimum energy type,and the equationsatisfied by the minimum time.we have shown that the optimal control belongsto the boundary of the admissible control set.

在第六章中，我们研究了与对称正则长波方程相关的一类高阶拟双曲型方程支配的分布参数系统的控制问题。讨论了系统的状态能控性问题和最优控制问题，给出了状态能控时的约束相容性条件，给出了最速控制问题、最小能量型最优控制问题的最优控制表达式和最速时间所满足的方程式，证明了最优控制属于控制集合的边界。

These algorithms contain rich information of system structure, especially, the information of coupling and structure at infinity.

给出非正则反馈线性化问题有解的一系列构造性的充分条件以及必要条件，以及求解线性化反馈变换的递推算法。

Necessary and sufficient conditions of the robust positively invariant sets are established for the linear discrete-time system family specified by matrix convex polyhedron and additive interval disturbances.

对由矩阵凸多面体和加性区间扰动描述的线性时变离散系统族，得到了鲁棒正不变集的充分必要条件；对非线性系统族则得到有关充分条件。

The model in this paper takes the form as belowThe main contents and results in this paper are as follows:In section 1, we state our main analytical results on equilibria of the above system. First, several sufficient conditions for coexistence of the steady-state are given by the standard fixed-point index theory in cone. Second, the global structure of the coexistence solutions and their local stability are established by using bifurcation theory. Third, the multiplicity, uniqueness and stability of positive steady-state solutions to this system are derived by means of perturbation theory of eigenvalues, standard regularity theory, Sobolev embedding theorem and fixed-point index theory.

本文主要有两章内容：第一章研究了该模型正平衡解的性质，可分为三部分：第一部分运用极值原理、上下解方法和锥映射不动点指标理论得到正平衡解存在的充分条件；第二部分利用分歧理论给出了平衡态系统正分歧解的结构，并讨论了局部分歧解的稳定性；第三部分利用特征值扰动理论、标准椭圆正则化理论、Sobolev嵌入定理及指标理论讨论了正平衡解的多重性、唯一性及稳定性，并讨论了参数对解的影响。

According to the result, the confidence region of unknown parameters in single-index models is constructed. Finally, we consider the test of correlation and heterogeneity for hierarchical nonlinear mixed-effects models. According to Laplace approximation expansion of integrated log-quasilikelihood, a class of score test statistics is proposed. Under some very mild conditions, we prove the asymptotic distribution of the test statistics is a standard X~2-distribution. Through a Monte Carlo simulation study, the finite sample performance is examined.

最后，我们研究的第四个问题是分层非线性随机混合效应模型的相关性与异方差性检验问题，依据对数拟积分似然的Laplace近似展开提出了检验统计量，在一些正则条件下，得到了检验统计量的渐近分布是一个标准的χ~2-(来源：d7d7A65BC论文网www.abclunwen.com)分布，通过Monte Carlo模拟研究了其小样本的表现，实例验证了其实际应用。

Under the assumption that the splitting function satisfies a Lipschitz condition, some convergence conditions of the discrete waveform relaxation schemes are given.

在假定分裂函数满足Lipschitz条件的前提下，通过矩阵正则分裂和特殊矩阵相关性质的运用，获得离散波形松弛迭代的收敛性条件，拓展和改进了相关文献中的一些结果。

The penalty optimal brain surgeon is a post-training algorithm and it has extreme high complexity. The OBS oriented compute model implemented neural network training and OBS pruning simultaneously, by taking the OBS pruning case as a penalty term of neural network objective functions based on optimized structure of the regularization method included in the neural network training process. It both maintained the OBS's accuracy and had regularization method's high efficiency. Raised the generalization of neural network model.

最优脑外科过程是一种训练后网络剪枝算法，计算的复杂度非常高，通过把剪枝条件以惩罚项的形式纳入神经网络的训练目标函数中，把正则化方法的结构优化蕴涵于网络训练过程，构建面向最优脑外科过程的计算模型，实现网络训练过程和最优脑外科过程并行剪枝，既保持了最优脑外科过程的准确性，又具有正则化的高效性，提高了神经网络模型的泛化性能。

We know that asymptotically linear operator equations have negative solutions and sign-changing solutions besides positive solutions, in this chapter, we obtain the existence of this three kind of solutions in Banach space, and we can know the concrete place of these solutions.

第三章的目的就在于借助于不动点指数理论利用一致正条件讨论非线性算子方程变号解的存在性，同时研究了变号解与一对正负解之间的关系，在一定条件下我们证明了：若算子方程x=Ax存在一个变号解，则它的正解和负解必定成对出现。

The algorithm has following properties: Although the merit function has the form of least squares of a system of overdetermined equations, in the Newton equation of our algorithm, only the coefficient matrix of the system of overdetermined equations is used instead of its product as in Guass-Newton method for solving the least squares problems. That is, our Newton method is more like that for the system of nonlinear equations rather than that for LSPs. The global convergence is obtained for VLCP with vertical block P_0 + R_0 matrix; The local quadratic convergence rate is proved under the condition that the solution is BD-regular; Although there is only a Newton equation in our algorithm, the finite convergence property can be shown if matrix is vertical block P— matrix (without the hypotheses of strict complementarity).

该算法具有下列特点：所构造的价值函数虽然具有超定方程组的最小二乘问题的形式，但在基此建立的Newton算法中，其Newton方程的形式更象非线性方程组的Newton法中的Newton方程，仅利用了超定方程组的系数矩阵本身的信息，避免了一般最小二乘问题的Guass-Newton法中必须计算系数矩阵的乘积的工作量；对竖块P_0+R_0矩阵的垂直线性互补问题，算法具有全局收敛性；在解是BD-正则条件下，证明了算法的局部二次收敛性；虽然算法只含一个Newton方程，但对竖块P-矩阵垂直线性互补问题，算法具有有限步收敛性。

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。