查询词典 bounded function

The definition of the absolute value for a fuzzy number is obtained.Furthermore,a lot ofproblems,such as absolute integrability,bounded variation and absolute continuity,arepresented and discussed.The representation theorem of the absolute values of fuzzy num-bers is established.It plays an important role in discussing the problems conceming theabsolute value.The relation between the absolute integrability and integrabili-ty is discussed,and the following result is obtained:aintegrable fuzzy-number-valued function is absolutely integrable iff it is integrable.The relation between theabsolute integrability and the absolute continuity of the primitive for fuzzy-number-valuedfunctions is dealt with.It is also pointed out that a fuzzy number valued function is ab-solutelyintegrable if and only if its integral primitive is fuzzy absolutely continuous.

提出了模糊数绝对值的概念并讨论了与绝对值相关的一系列问题，如绝对可积性、有界变差性、绝对连续性等，给出了模糊数绝对值的定义以及表示定理，该表示定理在涉及绝对值问题的讨论中起非常重要的作用；讨论了绝对可积与可积之间的关系，得到了结论：可积的模糊数值函数绝对可积的充要条件是该模糊数值函数可积；给出了模糊数值函数绝对可积与其积分原函数绝对连续性之间的关系，指出模糊数值函数绝对可积的充要条件是其原函数模糊绝对连续。

This research method is independent of Green"s function and variational structure. So it can tackle with the BVP for non self-adjoint and self-adjoint difference equations and overcome the difficulties brought about by the establishment of Green"s function, a study of the sign and the estimate of below and above bounded for Greens function.

本章的研究方法既不依赖于Green函数又不依赖于变分结构，因而能解决非自共轭的差分方程边值问题，且克服了Green函数的建立、其符号的判断及其上下界的估计给研究带来的困难，该方法同样适用于研究自共轭的差分方程边值问题。

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。

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。

The relation between general one-way function and bounded one way function is given by authors previously.

该文的作者在以前的文章中，对有界单向函数与一般单向函数的关系进行了探讨，从而得到一般单向函数的一个刻画。

It also gets a unified condition which has a wider range than regulated function and comes to the conclusion that the function of bounded variation is the integrable function of Riemann.

通过定义多维零测度集将可积函数的特征扩展到多维情形，同样统一了多维情形的充分条件，建立了多维情形的可积性理论。

On the basis of the coincident relation between a radar signal and a radar ambiguity function, an arbitrary bounded two-dimensional function of intergrable square is presented as a necessary and sufficient condition for radar ambiguity function.

本文基于雷达信号和雷达模糊度函数间的一致关系，提出了任意平方可积的二维有界函数是雷达模糊度函数的充要条件，并且指出它包括了Wilcox提出的离散的可实现条件。

The growth of functions in these spaces depends on a weighted function ρ. We investigate the relation between growth and boundary values of the functions, and prove that a function or its radial derivative is in one of the spaces if and only if the p'integral average of the difference of its boundary value function is integrable or bounded.

研究这些函数空间中函数的增长性与边界值的关系，得到了函数或其径向导数属于相应空间的充分必要条件是其边界值差分的p次积分平均应具备一定的可积性或有界性。

In the study of the stochastic chaos in simple pendulum, the random Melnikov process is derived and the mean-square criterion is used to determine the threshold amplitude of the bounded noise excitation for the onset of the chaos or random chaos in the system. For the coupled simple pendulum and harmonic oscillator, the Melnikov function is used to determine the condition for the onset of chaos in the case of Hamiltonian perturbations. In the case of non-Hamiltonian perturbation, the generalized random Melnikov process and mean-square criterion are used to determine the threshold amplitude of the bounded noise for the onset of random chaos.

在随机混沌研究中，应用随机Melnikov过程的均方准则研究了单摆在有界噪声激励下发生混沌或随机混沌时有界噪声激励的临界幅值；对于耦合的单摆-谐振子系统，先用Melnikov函数研究了在哈密顿扰动下发生混沌的必要条件；然后用推广的随机Melnikov过程方法研究了在非哈密顿扰动下发生随机混沌的必要条件；用最大Lyapunov指数及Poincaré截面方法结果与上述理论结果作了对比。

However, for the collision processes in He target, a large discrepacy between the CTMC results and experimental measurement is found. As is well known, the microcanonical distributions of bounded electrons in CTMC method is quite different from quantal distributions, we modified the initial microcanonical distribution by using eleven different ionization thresholds of electron bounded in target. With modification, we calculated the collisional process of O~(3+) with He, and the total cross sections of all processess are calculated as a function of the incident energies. The agreement with experiments is improved by the modified distributions.

但由于靶电子的微正则分布与量子分布有很大不同，在计算离子与He靶碰撞时发现结果与实验差距很大，我们基于使用多个系统总能量U值，对初始电子的微正则分布进行了优化，使其更接近于量子力学的径向空间分布，然后计算了O~(3+)与氦原子随入射离子能量变化的各种反应过程截面，发现优化极大地提高了计算精度，特别是我们的模型对于描述单电子、双电子丢失过程非常成功。

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。