查询词典 infinite interval

The paper studies the asymptotic behavior of "interior point" on the second mean value theorem for integrals when the length of integral interval tends to be infinite,and the asymptotic estimation formulas under very weak conditions are given.

讨论当积分区间长度趋于无穷大时，积分第二中值定理的"中间点"的渐近性态，在较弱的条件下，获得积分第二中值定理的"中间点"当积分区间长度趋于无穷大时的渐近估计式。

As I said,many of us were old,and most of us were indoor men,and I was amused to see how close to the head some of us held our hats,the merest barleycorn of interval being maintained for reverence sake,wheras the sexton and the clergymanb had slipped on those black velvt skull-caps which God,in his infinite mercy,either completely overlooks,or seeing,smiles at.

我已经说过，我们之中许多人都上了年纪，大部分平时又是深居简出，这时候他们手里拿着的帽子贴着脑瓜那么近，为了对死者表示敬意才挪开一颗大麦粒那么大的距离，我看着心里不禁感到好笑，与此同时，教堂的工役和牧师却早已悄悄带上他们那黑天鹅绒的小帽，对此，无限仁慈的上帝若非一时没有瞅清，定是看了而一笑置之。

Based on the flaw of the probability reliability model in the case of small amount of information,non-probability and mixed probability/non-probability reliability models are presented. When the uncertainty of the basic random variable is described by convex, analytical and numerical methods are constructed to calculate the convex of response variable. The infinite norm index, which is the minimal infinite norm distance from original coordinate point to the surface of the limit state in the standard interval space, is presented to measure the safety of the structure.

针对概率可靠性模型在小子样信息下的缺陷，建立了非概率可靠性模型及概率—非概率混合可靠性模型；给出了用集合来描述变量不确定性时，极限状态变量变化集合的解析解和数值迭代解法；提出了物理概念明确且十分易于工程应用的度量结构、机构安全程度的无穷范数指标，它是标准区间空间中坐标原点到极限状态表面的最小无穷范数距离。

Under some moderate conditions, the prior estimate of the solutions of the system is obtained. Making use of constructing Picard iterative sequence, Doob martingale inequality, Gronwall inequality, Borel-Cantelli lemma and some fundamental inequalities, together with the uniform Lipschitz conditions, the existence and uniqueness of the solution for stochastic functional differential equations with infinite delay is derived on the interval t0,∞.

在适当的条件下，得到了随机泛函微分方程的解的先验估计；再结合一致Lipschitz条件，通过构造Picard迭代序列，利用Doob较不等式、Gronwall不等式、Borel-Cantelli引理及一些基本不等式，得到该方程的解在区间[t0，∞]上是存在且唯一的。

However, due to the oscillation and singularity of the integrand of Green's function and that integral interval is infinite, it is difficult to compute the function and to control the accuracy.

而格林函数中被积函数的振荡性，奇异性和积分区间为无穷使得该函数的计算较为困难，精度不易控制。

Using minimum upper bound and matrix Riccati equation, a robust lower guaranteed cost fault tolerant controller is designed for interval matrix systems with performance index in a finite or infinite time interval. The systems under consideration have uncertainties both in system matrix and input matrix.

利用最小上界及矩阵Riccati方程，给出了系统矩阵和输入矩阵均含有不确定性时，区间矩阵系统有限时间及无限时间保低成本鲁棒容错控制器设计方法。

Be called the infinite series of functions on the interval ,where

称为定义在区间上的无穷级数，简称级数。

First, the interval algebra of James Allen is modified to introduce intervals of infinite length.

我们首先讨论James Allen的时区代数结构，并对其进行了扩充。

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先，在一致Lipschitz条件，线性增长条件和压缩性条件下，直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性，并给出了解的矩估计，近似解与精确解之间的误差估计；将一致Lipschitz条件替换为局部Lipschitz条件，也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性，同时，也给出了在整个区间0，+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理；其次，也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计；最后，在局部Lipschitz条件和压缩性条件下，建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

The Generalized Kolmogorov Probability generalized the 1st Kolmogorov's axiom and allows the probability values to be within the whole open real interval of (-infinite,+infinite).

广义的柯尔莫果洛夫概率(Generalized Kolmogorov Probability)推广了柯尔莫果洛夫概率三公理的第一公理：概率可在开区间范围内取值。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。