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Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

At first I did all my jobs twice, first in Houdini - then I would try to get Glassworks to buy it, they would say no - then I would have to redo it in XSI.

在最开始的时候我把我的工作都做了两遍，首先在 houdini 中，然后我试着去说服 Glassworks 来买这个软件，他们说：不。然后我就不得不在 xsi 中从新做一遍。

Blame it on SimX and DoriftoKids, they're painful to judge, simply because both of these two teams have done great in some aspects, but made some mistakes at other aspects of their run, after concluding their scores, I keep getting the same score between them, no if you watch the replay, you'll notice their runs aren't similar, but they both made a fair share of mistakes in order to share that same score over and over again , I have been reviewing my scores of all teams for 3 times, and reviewed the scores between SimX and DoriftoKids for 5 times, trying desperately to find the little details in which I can deduct the points on, but failed I was, so I thought to myself... why not just let the two teams in....

只能怪SimX和DoriftoKids，这两支车队太难分出优劣了，因为他们在比赛中都在一些环节发挥出色，也在一些环节犯了错误，每次为两队评分后，我总是得到相同的分数，但是如果你看了录像，你会发现他们的跑法是不同的，但是他们犯了差不多的错误以致于每次的评分都相同，所有车队的成绩我都检查了三遍，并且这两支队的成绩检查了五遍，尽全力寻找可以扣分的细节，但是失败了，所以我对自己说，两支队为什么不能都进决赛呢。。。

As a child that has fallen happily asleep in its nurse's arms, and wakes to find itself alone and laid in a strange place, and searches corners and cupboards, and runs from room to room, despair growing silently in its heart, even so Portly searched the island and searched, dogged and unwearying, till at last the black moment came for giving it up, and sitting down and crying bitterly.

他像一个在奶妈怀里甜甜入睡的小孩，醒来时，发现自己孤零零呆在一个陌生的地方，就到处寻觅。找遍了所有的屋角和柜橱，跑遍了所有的房间，心里越来越失望。胖胖坚持不懈地搜遍了整个小岛，最后他完全绝望了，坐在地上伤心地大哭起来。

In Figure 1 storage structure to achieve depth-first search traversal and breadth-first search traversal, and gives Ergodic results.

在图1 存储结构上实现深度优先搜索遍历和广度优先搜索遍历，并给出遍历结果。

And then when I went up to bed she come up with me and fetched her candle, and tucked me in, and mothered me so good I felt mean, and like I couldn't look her in the face; and she set down on the bed and talked with me a long time, and said what a splendid boy Sid was, and didn't seem to want to ever stop talking about him; and kept asking me every now and then if I reckoned he could a got lost, or hurt, or maybe drownded, and might be laying at this minute somewheres suffering or dead, and she not by him to help him, and so the tears would drip down silent, and I would tell her that Sid was all right, and would be home in the morning, sure; and she would squeeze my hand, or maybe kiss me, and tell me to say it again, and keep on saying it, because it done her good, and she was in so much trouble.

随后我上楼睡觉时，她跟着我上来，替我掖好被子，象母亲一般亲热，这叫我觉得自己太卑鄙了，连她的脸我都不敢正视一下。她在床边上坐了下来，和我说了好一阵子的话。还说西特是一个多么了不起的孩子。她仿佛说到西特时就是爱说得没有个完。她再三再四问我，要我说说，认为西特会不会死了，或者受了伤，或者落水了，这会儿说不定躺在什么个地方，或者受了伤，或者死了，可她却不能在边上照看他。说着说着，眼泪暗暗淌了下来。我就对她说，西特是平安无事的，准定会在早上回家来的。她呢，会紧紧握着我的手，或者亲亲我，要我把这话再说一遍，还不停地要我把这话再说一遍，因为说了她就好受一些。

I not only thought these the pure Productions of Providence for my Support, but not doubting, but that there was more in the Place, I went all over that Part of the Island, where I had been before, peering in every Corner, and under every Rock, to see for more of it, but I could not find any; at last it occur'd to my Thoughts, that I had shook a Bag of Chickens Meat out in that Place, and then the Wonder began to cease; and I must confess, my religious Thankfulness to God's Providence began to abate too upon the Discovering that all this was nothing but what was common; tho' I ought to have been as thankful for so strange and unforseen Providence, as if it had been miraculous; for it was really the Work of Providence as to me, that should order or appoint, that 10 or 12 Grains of Corn should remain unspoil'd,(when the Rats had destroy'd all the rest,) as if it had been dropt from Heaven; as also, that I should throw it out in that particular Place, where it being in the Shade of a high Rock, it sprang up immediately; whereas, if I had thrown it anywhere else, at that Time, it had been burnt up and destroy'd.

当时，我不仅认为这些谷类都是老天为了让我活命而赐给我的，并且还相信岛上其他地方一定还有。于是，我在岛上搜遍了我曾经到过的地方，每个角落，每块岩石边我都查看了一遍，想找到麦穗和稻秆，可是，再也找不到了。最后，我终于想起，我曾经有一只放鸡饲料的袋子，我把里面剩下的谷壳抖到了岩壁下。这一想，我惊异的心情一扫而光。老实说，我认为这一切都是极其平常的事，所以我对上帝的感恩之情也随之减退了。然而，对发生这样的奇迹，对意料之外的天意，我还是应该感恩戴德的。老鼠吃掉了绝大部分谷粒，而仅存的十几颗竟然没有坏掉，仿佛从天上掉下来似的，发生这样的奇迹难道不是天意又是什么呢？再说，我把这十几颗谷粒不扔在其他地方，恰恰扔在岩壁下，因而遮住了太阳，使其很快长了出来；如果丢在别处，肯定早就给太阳晒死了，这难道不是天意吗？

Data mining for traversal patterns has been found useful in several applications. However, traditional model of traversal patterns mining only considered unweighted traversals.

遍历模式数据挖掘方法已经在多种应用中被提出，传统的遍历模式挖掘仅仅考虑了非加权遍历。

In most cases is 3 times I am in Beijing all the time to look at the flag-raising ceremony on Tiananmen Square to know when the speakers usually take 3 times of major festivals and special time for the scene, where a military band played 1 times.

大多数情况是3遍我就在北京大家有空早上去天安门广场看看升旗就知道了平时的时候喇叭放3遍重要节日和特殊时间现场有军乐队演奏1遍。

This paper proposed a transformable model of EWDG (edge-weighted directed graph) and VWDG (vertex-weighted directed graph) to resolve the problem of weighted traversal patterns mining. Based on the model, developed a new algorithm, called LGTWFPMiner (local graph traversals-based weighted frequent patterns miner), and its local estimation of support/weight-hound to discover weighted frequent patterns from the traversals on graph with a level property.

为解决加权遍历模式挖掘问题，首先提出了一种从EWDG到VWDG的变换模型；基于这种模型，提出了在具有层次特性的局部图遍历中，挖掘加权频繁模式的LCTWFPMiner（局部图遍历加权频繁模式挖掘法）及其支持度／权值界的局部评枯方法。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失