有界集合

We have proposed the switching adaptive control law for the systems and designed the Lyapunov function in this thesis. It is proved that the proposed switching adaptive control law guarantees the solutions of the nonlinear systems boundedness and convergence of the tracking error to a residual set based on the Lyapunovs stability theory. The residual set can be made arbitrarily small by choosing a certain design parameters.

文中设计出了这类系统的切换自适应控制律，并构造出相应的Lyapunov函数，基于Lyapunov稳定性理论证明了系统在所设计的控制律作用下，闭环信号都有界并且跟踪误差收敛到一个集合，通过选择适当的参数可使这个集合任意小。

The proposed method has the merit that the numerical characteristics of stochastic temperature field response can be obtained by analyzing the random temperature field just in one time.3. Perturbed numerical algorithm of nonprobabilistic convex set theoretical models on the temperature fieldThe uncertain parameters of physical parameters and initial boundary conditions of heat conduction are described by the convex model. The perturbation formulas of the upper and lower bounds of temperature field response with unknown-but-bounded parameters are given via the combination of matrix perturbation theory and the convex set theory model.4. Numerical analysis for transient temperature field with interval parametersConsidering the uncertainties of the transient heat transfer, the physical parameters and initial boundary conditions are regarded as interval variables.

该方法具有只进行一次随机温度场分析便可以获得其响应的数字特征的优点。3、温度场的非概率凸集合理论模型的摄动数值解法将结构导热的物理参数、温度场的初始和边界条件等不确定性参数以凸模型加以描述，基于矩阵摄动理论和处理不确定问题的凸集合理论模型的结合，导出有界不确定参数瞬态温度场响应所在集合的上、下界摄动计算公式。4、具有区间参数的瞬态温度场数值分析考虑结构瞬态热传导问题的不确定性，将结构各物理参数和温度的初、边值条件均视为区间变量。

Let A" denote the commutant of a bounded linear operator S on H and R denote the collection of all operators in A" which are compact and upper triangular operators with diagonal sequence being zeros. In this paper, we show that if A"= CI + R, the K_0-group of A" is isomorphic to the integer group.

本文指出若H上的有界线性算子S的换位代数A′=CI+R，其中C是复数域，I是H上的单位算子，R是所有与S可交换的对角线为0的紧上三角有界线性算子的集合，则K_0A′

By using the integral equation and the Schauder fixed point theorem, through considering the height of nonlinear term on some bounded set, a new existence theorem is established.

利用积分方程和Schauder不动点定理，通过考察非线性项在某些有界集合上的高度建立了一个新的存在定理。

We focus on a particular class of subsets in the above topological space which is named support-bounded constructible subset as an analogue of constructible subsets in module variety and is invariant under derived equivalence.

我们研究了复形拓扑空间的一类特殊的子集合，称为支撑有界可构集，它是普通模簇上可构集在导出范畴上的类比并且是导出不变的。

The converse does not hold, since any infinite set can be given the discrete metric under which it is bounded and yet not totally bounded.

但逆命题不成立，因为任何无限集合可以用离散度量给出，在其下它是有界但非完全有界的。

Chapter 3 is devoted to equistability and equiboundedness of matrix differential equations by making use of the symbol property of the matrix Liapunov function and its Dini derivate on specific set.

第三章研究了矩阵微分方程的渐近行为，给出了直接运用矩阵Liapunov函数在某特定集合上的符号与其广义Dini导数符号的性质研究矩阵微分方程的稳定性和有界性。

Since the set of the centres of these balls is finite, it has finite diameter, from which it follows that every totally bounded space is bounded.

因为这些球的中心的集合是有限的，它有有限半径，从而得出所有完全有界空间是有界的。

Assuming that there is a plural Z and , with the following iterative calculation : Z = Z2 +, because the value of different , after several iteration number Z after the amplitude may tend to infinity. May also maintained sector, Mandebo Lott who is set to make Z maintained sector pool put on the complex plane make the distribution of images, as demonstrated above in the extremely complex structure.

假设有复数Z和μ，用下式迭代计算：Z=Z2＋μ，由于μ的取值不同，经过若干次数迭代以后Z的幅值可能趋向无穷，也可能保持有界，曼德勃罗特集就是那些使Z保持有界的μ的集合，把μ在复平面上的分布作成图像，就像上面演示的那样具有极其复杂的结构。

In aim at the complicity and high-dimensional state-space for the controlled system, it simplifies the calculation of geometric polytope by optimize with ellipsoidal approximate techniques, and the robust control effectiveness near to the optimal.

本论文所提示的基于几何理论的约束非线性控制算法是建立在最大输出允许集合的基础上，运用状态空间的有界子集表达鲁棒时优离散时间控制问题的价值函数，通过逆序计算该价值函数的水平集合，求得其所需的控制量，针对被控系统的复杂性及高维状态空间问题，运用椭球近似技术予以优化，使得几何多面体的计算得以简化，且鲁棒控制效果接近最优。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。