查询词典 bounded

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

This result can best be viewed as a quantum black hole version of the third law of thermodynamics. As a result of this area spectrum, the spectrum of M is discrete, bounded below, and can be made positive. Prom the physical point of view, the semiboundedness and positivity of the spectrum are very satisfying results: The semi-boundedness of the spectrum implies that one cannot extract an infinite amount of energy from the system, whereas the positivity of the spectrum is in agreement with the well-known positive-energy theorems of general relativity.

同时根据EMDA黑洞动力学，存在与面积谱对应的大于零且有下界的质量离散谱，从物理上来看，质量谱的半有界性意味着不可能从系统吸取无限的能量，而正定性则与广义相对论中的正能定理一致，也就说稳态轴对称EMDA时空的ADM能量总是大于零。

F where S is a bounded closed set and f is continuous over S.

f此处S为R〓中的一个有界的闭集，f为S上的连续函数。

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。

This method is based on the work of reference [1]. By using the Riesz present theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using the Schauder fixed point theory, we construct a numerical verification method with high efficiency that through numerical computation generates a bounded, closed, convex set in which the approximate solution is included.

通过Hilbert空间中的Riesz表示定理，首先将变分不等式问题的迭代过程转化为一种不动点形式，再利用Schauder不动点定理构造了一个高效率的数值证明过程，即通过数值计算产生一个包含近似解的有界闭凸子集。

Only Lake, is the most suitable for human habitation bounded domain; only lake, is the best human beings to inhabit.

唯有湖，才是最适宜人类居住的界域；唯有湖，才是人类最优质的栖居地。

Transitivity determines whether the trust is bounded by the domain and the realm in the trust relationship.

传递决定信任是否被信任关系里的域和领域绑定。

Let f be defined for all nonnegative x, and suppose that it is continuous, strictly increasing and bounded on its domain.

令f定义在一切非负的x 上，并在定义域内连续、严格递增和有界。

We prove that a bounded hyperconvex domain D is Bergman complete if the pluricoinplex Green function is symmetric.

我们证明了若一个有界超凸域的多复变量Green函数是对称的，则其是Bergman完备的。

Next, we concern with the famous problem of Kobayashi as follows: Which bounded pseudoconvex domain is complete w.r.t.

第二部分，我们研究Kobayashi提出的一个著名问题：什么样的拟凸域是Bergman完备的？

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。