有限维的

When A is a non-trivial,cohomologically finite dimensional regular DG al-gebra,His not bounded above.

当A是非平凡的，同调局部有限维的正则DG代数时，A的同调没有上界。

At last, it is proved for the two systems that when the control domain U is a bounded, closed set, the reachable set is the same as that when the control domain is the convex of U.It is an advancement for original results.

最后证明了当控制区域U是有界闭集时上述两个系统的等时区域与控制区域是U的凸包时的等时区域相同，推广了有限维的结论。

Secondly, a finite element method is used to approximate the constrained minimization problem, both existence of minimizer for cost functional in finite demensional space and the convergence of minimizer are proven.

然后利用有限元方法对上述定解问题进行离散，并证明了有限维空间上泛函的极小元存在以及有限维空间上的极小元收敛到无限维空间上的极小元。

The entanglement of formation and the Peres condition have good correspondence, and if the mixed-state deviates the similar pure state slightly, its maximum entanglement drops suddenly. The conclusion of the entanglement of the infinite dimension mixed-state in J-C model never losing is demonstrated besides finding the necessary condition of disentanglement of the finite dimension mixed-state in J-C model.

通过研究有限维混合态光场与二能级原子相互作用系统中的纠缠，发现形成纠缠理论与Peres判据有着良好的对应，同时看到偏离纯态很小的混合态，其最大纠缠度急剧减小；找到了有限维混合态J-C模型在演化过程中出现消纠缠的必要条件，论证了在无限维情况总存在纠缠的结论。

College of Guandong Business, Guanzhou 510320, China）Abstract: Since large-scale vertical quench furnace is voluminous, whose working condition is a typically complex process with distributed parameter, nonlinear, multi-inputs/multi-outputs, close coupled variables, etc, dynamically decoupling control algorithm of temperature distributed parameter system in the furnace was presented, by which the whole system was decoupled to several subsystems and the implementation of controller was simplified. With finite difference approximation, the space and time step size was solved to ensure the convergency of finite difference approximation. After decoupling, the subsystems were controlled with self-learning PID control algorithm. The results show that the temperature control precision and homogeneity are improved; the overshoot and process in temperature rising period are reduced simultaneity.

摘 要：针对大型立式淬火炉体积庞大，工况复杂，炉内温度分布呈本征非均匀性，具有多输入/多输出、非线性、强耦合等特性，难以实现炉内温度高精度高均匀性控制目标等问题，提出一种温度分布参数系统动态解耦控制算法，其原理是：采用有限维逼近方法将对象解耦为多个独立的子系统，简化控制器的实现过程；通过分析有限维逼近方法的收敛性，获得保证收敛性的空间和时间步长应满足的条件；解耦后的子系统采用自学习PID控制算法，实现炉内温度高精度和高均匀性控制以及升温过程的快速性和小超调。

Assume the underlying vector space is finite dimensional (therefore issues such as continuity of a projection need not be considered).

假定底层的向量空间是有限维的(因此问题如投影的连续性不需要考虑)。

The problem is researched that under what conditions the - resolvent operator of - subdifferential mapping of a proper functional is aLipschitz continuous single-valued mapping on whole space.

利用冲一预解算子分析了有限维欧氏空间中的广义参数集值变分包含问题唯一解的灵敏性；利用预解算子分析了有限维欧氏空间中的一般参数集值变分包含问题解集的灵敏性。

Based on the surjection of maximal monotone operators, we prove that some semilinear heat equations with weak Lipschitz nonlinear terms are exactly controllable by L〓 0, T: H〓(Ω control; Based on the critical point theorem of coercive convex functionals, we prove that some parabolic equations with Lipschitz nonlinear terms are globally approximately controllable and finite-dimensional exactly controllable by controls acting on mobile supports, and finally, we extend the results to parabolic equations in R〓.

首先利用极大单调算子的满射原理证明了半线性热方程在较弱Lipschitz条件下可通过L〓0.T；H〓(Ω控制实现精确能控。然后通过构造强制凸泛函并利用其临界点理论证明了带Lipschitz非线性项的抛物型方程可通过作用在在移动支集上的控制来实现整体近似能控与有限维精确能控，最后将整体近似能控与有限维精确能控结论推广到无界区域R〓上。

In 1997,Their infinite-dimensional dissipativity wasfurther studied by Hill,who also studied the finite-dimensional and infinite-dimensionaldissipativity of one-leg methods.However,up to now,no papers have been concernedwith the dissipativity of delay dynamical systems and their numerical solutions.Thethird part of the thesis is devoted to discussing it.

当用数值方法求解这些系统时，自然希望数值方法能保持系统的该重要特性。1994年，Humphries和Stuart首次研究了Runge-Kutta方法对有限维系统的散逸性。1997年Hill进一步研究了Runge-Kutta方法的无穷维散逸性和单支方法的有限维和无穷维散逸性。

It is clear that A restricted on ker T is : identity, which is compact, it must hold that ker T is finite-dimensional.

虽然ker T的有限维可以直接用反证法得出。利用ker T的有限维性质也应该是最简单的证法了吧多谢解答！

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。