无穷

With the idea and the technique of the newly constructed basitheoryology ~ [1] , this article discusses two different concepts of infinite set existing in present set theory: potential infinity and actual infinity.

从新构建的基础理论学的角度，以全新的基础理论学的方法[1]，讨论同时存在于现有集合论中两种性质上截然不同的"无穷集合"概念：潜无穷式的与实无穷式的无穷集合。

If we hope to use a sequence of finite objects to approximate infinite objects, then we should know what kinds of infinite objects are approximable and how to approximate them effectively.

无穷形式对象可逼近的充分条件为了研究哪一类无穷对象可以逼近以及如何有效地逼近它们，我们用过程模式作为无穷对象上的计算的模型，用以刻画接受无穷输入、生成无穷输出的无穷对象上的计算。

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we define δ-fine partitions for infinite interval and integral of vector-valued functions on infinite interval, and discuss the properties of integral, and characterize its primitives...

主要包括以下五部分内容：在第一部分中，我们介绍了本文所用到的基本概念和引理；在第二部分中，通过定义无穷区间上δ-精细的分法，我们给出了无穷区间上向量值函数的积分的定义，并讨论其性质，还给出了原函数的刻划；在本文的第三部分中，我们着重讨论了无穷区间上向量值函数积分的收敛定理；在本文的在第四部分中，我们首先应用无穷区间上向量值函数积分的收敛定理给出了常微分方程整体广义解的存在性定理，其次应用强积分对Banach空间常微分方程广义解进行了讨论；最后，在第五部分中，我们将模糊积分推广到无穷区间上并给出了其数值计算方法。

In this paper,after the concept of infinite interval estimating and its utmost goodness are built,the optimal relation between infinite interval estimating and relevant hypothesis testing is proved.

在提出无穷区间估计以及其上的最优性概念之后，证明了无穷区间估计与相应假设检验的最优性之间的关系，及推演了若干重要的无穷区间估计的最优性。

For the analysis properties of infinite matrix,first,it establishes the automatic conti-nuity theorems on the sequence spaces with 0-GHP or WGHP,and the automaticboundedness theorem on the sequence spaces with 0-GHP.

在无穷矩阵的分析性质方面，建立了具有0-GHP或具有WGHP的矢值序列空间上无穷矩阵算子的自连续性定理，以及具有0-GHP矢值序列空间上无穷矩阵算子的自有界性定理。

To seek new infinite sequence exact solutions to nonlinear evolution equationsNEE(s, the formula of nonlinear superposition of the solutions of the second kind of elliptic equation are given, infinite sequence exact solutions to combined KdV with varible coefficients and forcible term is constructed with the aid of symbolic computation system Mathematica, which include Jacobi-like elliptic function solutions, infinite sequence soliton-like solutions and infinite sequence triangular function solutions.

为了获得变系数非线性发展方程的无穷序列精确解，给出第二种椭圆方程解的非线性叠加公式，借助符号计算系统Mathematica构造了带强迫项变系数组合KdV方程的无穷序列精确解。这里包括无穷序列类Jacobi椭圆函数解、无穷序列类孤子解和无穷序列三角函数解。

At last, the isochronous center of infinity of a class of quintic systems is studied and all conditions of center and isochronous center are obtained for infinity of this system, which is the first time for the research on the isochronous center of infinity.

最后，研究了一类实平面五次系统的无穷远点的等时中心，给出了系统无穷远点为中心和等时中心的全部条件。这是迄今对无穷远点等时中心进行的首次研究。

Using the recursive formula and computer algebra system-Mathematica, the first six singular point values at infinity of the system are given.

对一类三次系统给出了计算无穷远点奇点量的递推公式，并在计算机上用计算机代数系统Mathematica推导出该系统无穷远点的前6个奇点量，进而导出了无穷远点成为中心和最高阶细焦点的条件，在此基础上得到了一个三次系统在无穷远点分支出6个极限环的实例，指出了极限环的精确位置。

It investigates mainly infinite matrix conver-gence、infinite matrix transformations、the automatic continuity and boundedness of infinitematrix operators、infinite matrix topological algebras、invariant theory、infinite matrix meth-ods、compact operators series and Eberlein-Smulian theorem,etc.

主要研究了无穷矩阵收敛、无穷矩阵变换、无穷矩阵算子的自连续性和自有界性、无穷矩阵拓扑代数、不变性理论、无穷矩阵方法、紧算子级数与Eberlein-Smulian定理等。

Aristotle distinguished between the potential infinite and the actual infinite, and concluded there is in general no actual infinite object because the infinite is the unfinished, the indefinite, the unrealizable, which cannot be completed and actualized.

亚里士多德把潜无穷和实无穷区别开来，得出结论：一般不存在实无穷的对象，无穷是没有结束的、非确定的、没有实现的，并且是不能完善和实在化的东西。

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。