定理

It always takes longer than you expect, even when you take into account Hofstadter's Law.

Hofstadter 定理："一件事情总是会花费比你预期更多的时间，就算是你已经考虑过本条Hofstadter 定理"。

Always takes longer than you expect, even when you take into account Hofstadter's Law.- Hofstadter's Law

Hofstadter 定理："一件事情总是会花费比你预期更多的时间，就算是你已经考虑过本条Hofstadter 定理"。

From the famous Gabriel's theorem ,a basic connected finite dimensional associative algebra A over an algebraically closed field can be looked as a quotient of a path algebra decided by a connected finite quiver Q.

由Gabriel 定理，代数闭域上基的，连通的有限维结合代数A 同构于一个由连通有限箭图Q 确定的路代数的商代数。

Theorem The arc length of a plane curve which is smooth can be calculated.

定理 光滑曲线弧是可以求长的。

Theorem 2 The product of a bounded function and an infinitesimal is an infinitesimal.

定理 2 有界函数与无穷小的乘积是无穷小。

Let a =∈〓. Then corresponding to 62 equivalence classes in χ for ～, we have 144polynomial elements in one variable in canonical basis, each of them also cor-responds to a region which consists of six independent inequalities.

定理。设a=∈〓。那么与χ关于～的62个等价类对应，在典范基中有144个单变量多项式元素，每个单变量多项式元素也对应一个由六个独立不等式构成的区域。

The Fary-Milnor theorem states that the total curvature of a knotted simple closed curve in R^3 is greater than 4π.

Fary-Milnor 定理：一条空间中的简单封闭扭结其总曲率必大於4π。

Theorem 1 (Boundedness and max-min theorem) If is a continuous function on a closed interval, then has an absolute maximum and an absolute minimum on the interval.

定理 1 (有界性与最大值最小值定理)在闭区间上连续的函数在该区间上有界且一定能取得它的最大值和最小值。

Theorem Let be continuous on a bounded closed region in the -plane.(1) If is given by and , where are continuous functions of on, then

定理 设在xy平面上的有界闭区域 D 上连续，(1)若区域由和所给出，其中是上的连续函数，则。

Next, we provide some basal definitions and theories in the second section, such as the maximum principle, Holder continuity, Schauder theory and so on, which are foundation of the later work.

第二节主要给出一些相关的基本概念，定理。主要包括极值原理，Hlder连续性，Schauder理论，这些都是解决后面问题必要的基础知识。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。