无穷

The coast forest onion onion, in green grass cushion cushion, the lake the blue water is clear, near the lake alley, the pebbles shoal, the stair slope protection, the countless changes, causes the lake shore smoothly to stand erect from time to time, the edges and corners are distinct, from time to time the mountain riddlings fold, completely relaxed.

沿岸林木葱葱、绿草茵茵、湖中碧水粼粼，临湖小路，卵石浅滩，台阶护坡，变化无穷，使湖岸时而平滑直立，棱角分明，时而山石层叠，令人心旷神怡。

That which ends in exhau stion is death, but the perfect ending is

终止于衰竭是&死亡&，但&圆满&却终止于无穷。

Then we deal with the new system with a method similar to the one we have applied to the sublinear equation. At last, we can get infinitely many subharmonic bouncing solutions for the old impact system.

然后采用与讨论次线性Duffing方程类似的思想来处理新的碰撞系统，从而得到原碰撞振子的无穷多次调和弹性解的存在性。

In this article, We consider two important models for second order sublinear differential equations: the existence of infinitely many subharmonic solutions for Duffing equation with bounded restore force and for the sublinear impact oscillator.

本文考虑被数学和其他科学、工程领域的研究人员广为关注的两个重要的二阶次线性微分方程模型：具有有界恢复力的Duffing方程和次线性碰撞振子的无穷多个次调和解的存在性。

In this article, We consider two important models for second order sublinear differential equations: the existence of infinitely many subharmonic solutions for Duffing equation with bounded restore force and for the sublinear impact oscillator. They have attracted lots of researchers attention in mathematical, other scientific and engineering fields.

本文考虑被数学和其他科学、工程领域的研究人员广为关注的两个重要的二阶次线性微分方程模型：具有有界恢复力的Duffing方程和次线性碰撞振子的无穷多个次调和解的存在性。

For m-modal maps with m turning points C1,C2,…,Cm, by defining equivalent scaling factors α_e as the geometric average of all scaling factors α_Ci (i=1,2,…,m),|α_e|=|α_C1α_C2…α_Cm|1/m, global superuniversal relationship between equivalent scaling factors α_e and fractal dimensions d of Feigenbaum-type attractors on all the infinitely many critical points of transitions to chaos is obtained: dlog_|α_e|=β~, where|W| is the basic period of the m-tuply superstable sequences W, and β~ is not only independent of the concrete sequences W, but also independent of the concrete maps.

对于具有m个转变点C_1，C_2，…，C_m的m峰映射，通过定义等效标度因子α_e为所有标度因子α_(i=1，2，…，m)的几何平均，|α_e|=|α_(C_1)α_(C_2)…α_|~(1/m)，得到了等效标度因子α_e与所有无穷多个转变至混沌的临界点上Feigenbaum型吸引子的分维d之间的一个整体性的超普适关系：dlog_|α_e|=β~(e，其中|W|是m超稳序列W的基本周期，超普适常数β~(e不仅不依赖于具体的序列W，而且也不依赖于具体的映射。

For m-modal maps with m turning points C1,C2,…,Cm, by defining equivalent scalingfactors α_e as the geometric average of all scaling factors α_Ci (i=1,2,…,m),|α_e|=|α_C1α_C2…α_Cm|1/m, global superuniversal relationship between equivalent scaling factors α_e and fractal dimensions d of Feigenbaum-type attractors on all the infinitely many critical points of transitions to chaos is obtained: dlog_|α_e|=β~, where|W| is the basic period of the m-tuply superstablesequences W, and β~ is not only independent of the concrete sequences W, but also independent of the concrete maps.

对于具有m个转变点C_1，C_2，…，C_m的m峰映射，通过定义等效标度因子α_e为所有标度因子α_(i=1，2，…，m)的几何平均，|α_e|=|α_(C_1)α_(C_2)…α_|~(1/m)，得到了等效标度因子α_e与所有无穷多个转变至混沌的临界点上Feigenbaum型吸引子的分维d之间的一个整体性的超普适关系：dlog_|α_e|=β~(e，其中|W|是m超稳序列W的基本周期，超普适常数β~(e不仅不依赖于具体的序列W，而且也不依赖于具体的映射。

It was my faith in Infinite Intelligence that that tided me over these

而使我坚持信念和理想，并且帮助我度过难关的就是我从无穷智慧所获得的信。

It was my faith in Infinite Intelligence that that tided me over these rough ots and saw me through.

而使我坚持信念和理想，并且帮助我度过难关的就是我从无穷智慧所获得的信。

Sometimes,when the flames of hope dwindled to a flicker, i had to fan them with everything i possessed to keep them from going out.it was my faith in infinite intelligence that that tided me over these rough spots and saw me through.

有时候，当心中出现希望的火苗时，我必须运用我手边所能运用的资源把它再煽大一点以免熄灭。而使我坚持信念和理想，并且帮助我度过难关的就是我从无穷智慧所获得的信。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。