下界

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

Finally, we proved that the absolute and asymptotic competitive ratio for FAC are 19/9 and 2, respectively.

最后，在FAC中，我们分别证明了解决这个问题在线算法的绝对竞争比和渐进竞争比的下界分别是19／9和2。

Apsu underworld ocean; begetter of the skies and earth

阿卜苏，下界的海洋；天与地的生产者

For the linear model with aggregated data, this paper proposed one kinds of the relative efficiency of Peter-Karsten estimator compare to the best linear unbiased estimator.

对于聚集数据的线性模型，本文给出了Peter-Karsten估计相对于最佳线性无偏估计的一个相对效率，得到了相对效率的下界，讨论了该相对效率与广义相关系数的关系。

Two methods are presented to calculate the lower bound and upper bound on the bisection width of H-Torus topology.

针对H-Torus拓扑结构，给出两种确定该拓扑结构等分带宽上、下界的方法。

But we can prove that the corresponding Eulur\'s function is bounded from below in a proper set S of W_0~(1,p)× W_0~(1,q), and then a minimizer of Eulur\'s function in S gives rise to a solution of the problem.

但是，我们可以证明欧拉泛函在合适的集合S中有下界，因此在该集合中利用变分方法寻找泛函的极小就可以得到原问题的解。

In this thesis,we mainly study complete noncompact Riemannian manifolds with Ricci curvature bounded from below. We study the topology of these manifolds via comparisonal geometry methods.In chapter 1 ,we will make a general description on the recent researches in our field.

在本文中，我们主要研究了Ricci曲率有下界完备非紧的Riemann流形的拓扑问题，在比较几何的基础上研究了有特定曲率条件的Riemann流形的拓扑，得到了有关其拓扑结构的一些结果。

The composite nonsmooth optimization problem is defined as follows:〓where h is a convex function defined on〓and is bounded from below,and〓〓is a mapping from〓to〓and〓are twicecontinuously differentiable function on〓.

复合NDO问题被定义如下：〓这里h是一个定义在〓上的凸函数，并且有下界，〓，〓是一个从〓到〓上的映照。

Moreover, the lower bounder we will improve is at the least ((33)~(1/2)+2/6 for m machine case .

特别地，对于m台机的情况，我们给出了此问题的一个下界为(33~(1/2)+3/6。

In this paper, we first study the game chromatic number on graphs, and then we give some examples for the lower bound about the game chromatic number of the planar graphs.

首先全面分析了图的点对策着色问题，对某些定理的下界，给出了具体的例子。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷