无穷区间

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。

In the thesis, the author firstly clears up some basic theories of wavelet analysis, revises some formulae and proves and deduces some theorems and formulae in detail and gives a counter example and paradox.

本文首先对小波分析的理论部分进行整理，对部分公式进行修正，同时给出了部分定理和公式详细的推导和证明，并且给出无穷区间积分的一个反例和悖论。

We say that the corresponding improper integral converges.Otherwise ,the integral is siad to diverge.

这时也称反常积分收敛；如果上述极限不存在，函数在无穷区间上的反常积分就没有意义，习惯上称为反常积分发散。

The integral on infinite interval is an indispensable part of the theory of integral.

中文摘要：无穷区间上积分的讨论是积分理论中不可缺少的一部分。

Thus we available defined a fuzzy Henstock integral on infinite interval.

基于这种考虑，定义了无穷区间上的模糊Henstock积分。

By means of traditional criterions of generalized integral's convergence and divergence, this paper, from the analysis of integrated function's nature, discovers a series of new criterions, which are briefer and more suitable: on the aspect of generalized integral for functions of a single variable, through the investigation of integrated function, together with the inner relationship between positive series and generalized integral in infinite interval under the condition of positive function, it gives several criterions of generalized integral's convergence and divergence, which are similar to positive series' criterions of convergence and divergence.

本文从分析被积函数本身所具的性质出发，借助传统的广义积分敛散性判别方法，发现1系列更简捷适用的新判别方法：单变量函数广义积分方面，通过考察被积函数，结合正项级数与正函数情形下无穷区间上广义积分的内在联系，给出了几个与正项级数敛散性判别法相类似的广义积分敛散性判别方法；多变量函数广义积分方面，着重讨论了广义2重积分和广义3重积分，结合被积函数的特点，运用比较判别法和柯西判别法，本文给出了判别广义2重积分收敛的1种新方法。

-integrals of vector valued functions on infinite interval

无穷区间上n维模糊数值函数的积分：背景，定义及刻划

In this paper, we will introduce the weighted modulus of smoothness and the weighted K-functional to discuss the direct and the converse theorems, the local saturation results on the simultaneous approximation on an infinite interval with Jacobi-weight by the integral operator, the lin...

本文利用带权光滑模与带权K--泛函讨论定义在无穷区间上的积分型算子Gamma算子线性组合对空间L_∞(0，∞)中函数的带Jacobi权同时逼近的正逆定理以及局部饱和结果，还讨论了Gamma算子的强逆不等式。

But , when we changeour trainofthought , we can find that sometimes using mathematical Analysis is a better solution to the linear algebraic problems.In thispaper, use the propertyofcontinuous function andimproper integralof infinite interval and to solve some matrix and quadratic form problems.Algebraic ideas andmethodstosolvemathematical analysisproblems are indicated by several specific examples. Close contactof differentmathematical analysis fields is shown.

该文探讨运用数学分析的有关知识（如：函数连续性、无穷区间的广义积分）和方法解决高等代数中的某些复杂、繁琐的问题；通过具体的实例，阐述高等代数的思想和方法在解决数学分析问题中的作用，揭示不同的数学领域之间的密切联系，例如：二次型与正交变换是代数学的基本内容，其用途十分广泛，而重积分的计算往往存在技术性的困难，若利用"二次型"与"正交变换"的有关理论去解决某些重积分的计算问题是颇有功效的。

Under the conclusion of this, we prove the exponential asymptotical stability of the solution.

本文主要研究了一类无穷区间正倒向随机微分方程，利用连续性方法证明了此类方程在M~(2，k)(0，∞；R~n)空间中解的存在唯一性，并指出了k的范围，通过所得到的结论，进一步证明了FBSDE解的指数渐进稳定性。

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。