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The major breakthrough from a physically point of view occurred in 1985 when Halsey et al. introduced the function f . In 1995, Olsen gave a strict mathematical Multifractal Formulism. Meanwhile, Cawley, Mauldin, Arbeiter and Patzschke et cetera published articles on these topics.

之后，Frish和Benz等人将此概念推广到动力系统中吸引子的分形结构。1985年，Halsey等人从物理和直观的意义上作了突破性的工作，在测度的谱和集合的分形维数之间建立了联系。1995年，Olsen提出了严格的重分形形式体系的数学框架。

Fortis occurred in the past two days, some new changes seem to favor China Ping'an direction.

富通集团在过去两天发生的，一些新的变化，似乎有利于中国平安的方向。

The I-V characteristics of the diodes with 100μm diameter indicated that as the densities of V-defects on GaN films increased from 4.1×105cm-2 to 1.03×107cm-2, the Schottky barrier height decreased from 1.44eV to 1.19eV and the reverse bias leakage current at -1V is increased sharply from 10-10A to 10-7A . Further studies on a single V-defect using conductive atomic force microscope demonstrated that the value of forward current biased at 8V at V-defect side-walls appears to be one order higher than that of plain region, indicating that the conductivity mainly occurred at the side-walls of V-defect.

实验结果发现，随著V型缺陷密度由4.1×105cm-2增加至1.03×107cm-2，在氮化镓表面蒸镀镍金属所制成直径为100μm的萧基元件之所属能障从1.44eV下降至1.19eV，而且在-1V的操作下反向偏压漏电流从10-10A急遽的攀升至10-7A；为了了解V型缺陷对厘米尺寸n-GaN萧基元件电流传导机制之影响，我们进一步的利用导电原子力显微镜(Conductive Atomic Force Microscopy， C-AFM)，特别针对单一个V型缺陷进行微观电性之量测。

A schematic model was proposed to illustrate the occurrences of various lithologies and lithofacies associations. The erosional surfaces on siliciclastic mudstones, funnel-shaped structure, and the exhuming of massive cold-seep carbonates exposed might have been occurred concurrently during a tectonic unstable time in SW Taiwan. The deposition of fossiliferous mudstone interfingered with the conglomerate lithofacies, and represented the rapid facies transition from siliciclastic (non-carbonate) into carbonate environment.

综合岩相观察结果，建构一个符合台湾西南部更新世珊瑚礁与基底泥岩接触关系的沉积相模式；其中，基底泥岩顶部的不规则冲蚀面、充填碳酸盐胶结泥岩砾与碳酸岩烟柱的漏斗状沉积，以及块状冷泉碳酸盐岩的出露，可能均为区域地质构造活动时期所造成；至於与含化石泥岩同时沉积的砾岩相，可能均为基底泥岩在快速浅化的过程中所沉积，标志古环境由矽质碎屑快速转变为碳酸盐环境的过程。

Also as reported to the PADEP, on September 22, 2009 a release of frac fluid occurred on the same location of approximately 420 gallons.

另外，作为报告的PADEP于2009年9月22日压裂液的释放，发生在约四百二加仑相同的位置。

It occurred to Byron that he could go back to the fraternity house through Claremont Avenue.

拜伦突然想起，他蛮可以取道克莱蒙特大街返回兄弟会。

These phenomena occurred due to the increased free volume and chain mobility of polymers, and the decreased energy barrier for crystal form transition by the plasticization effect of scCO2 and other supercritical fluids.

这些现象的发生，是由于超临界二氧化碳及其它超临界流体增大了聚合物的自由体积和链活动性，降低了相转变的能垒。

The article first introduces the slide problem that occurred for testing the friction drive capacity of traction wheel after the lift is installed, then analyzes reasons for the problem, and also puts forward a solution to solve the problem.

结合电梯安装后的曳引轮摩擦传动能力检查时所出现的滑移现象，分析了产生这种现象的原因，提出了解决办法，且对解决所出现问题的施工可行性进行了探讨。

When I decided to quit my full time employment it never occurred to me that I might become a part of a new international trend.

在我决定放弃全职工作的时候，我怎么也没有想到我会成为一个国际流行趋势的一部分。

And Erin tells us, I'm in Fullerton, and I was just sitting at my desk when the quake occurred.

而伊润告诉我们：我在 Fullerton，我在地震发生时坐在桌子旁。

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。