孤立的

The road through the forest one of those wagon-tracks that were being opened from the clearings of the settlers, and that wound along beneath trees of which those now seen in Kentucky are the unworthy survivors--oaks and walnuts, maples and elms, centuries old, gnarled, massive, drooping, majestic, through whose arches the sun hurled down only some solitary spear of gold, and over whose gray-mossed roots some cold brook crept in silence; with here and there billowy open spaces of wild rye, buffalo grass, and clover on which the light fell in sheets of radiance; with other spots so dim that for ages no shoot had sprung from the deep black mould; blown to and fro across this wagon-road, odours of ivy, pennyroyal and mint, mingled with the fragrance of the wild grape; flitting to and fro across it, as low as the violet-beds, as high as the sycamores, unnumbered kinds of birds, some of which like the paroquet are long since vanished.

通过这些车皮了正在从定居者的结算开首曲目森林一条道路，并沿下树木的伤口现在看见的，在肯塔基州是不值得的幸存者-橡树和胡桃，枫树和榆树，百年老，格纳尔德，大规模，下垂，庄严，通过投掷下来的拱门只有一些孤立的金矛的太阳，而超过其灰mossed基层一些冷布鲁克在沉默中悄悄地，与在这里和那里的野生黑麦，水牛汹涌的休憩用地草，三叶草上的光板下跌的光芒；与其他景点，非常昏暗，对于没有拍摄了从深黑模具；被炸来回穿越这车，路，常春藤气味，薄荷油，薄荷涌现年龄，夹杂着的野生葡萄香味，飞来飞去往返境而过，像紫床低，高的桑树，种鸟类的一间，其中一些像paroquet是早已消失了。

In chapter 3,we study the Zakharov-Kuznetsov-Modified Equal-Width equation by employing the extended Jacobi elliptic function expansion method and obtain some new solutions of Jacobi elliptic function type of the ZK-MEW equation.;Secondly,using sn-cn method,we study K(m,n,1) equation and obtained some new exact solutions when k=s=3,especially obtained abundand solitary solutions and trigonometric function solutions when m→0 and m→1;In chapter 4,Painleve singular analysis was applied to nonlinear PDE with variable coefficients.

第四章将Painleve奇性分析方法应用到带阻尼项的变系数Burgers方程中，并得到了该类Burgers方程具有Painleve性质的条件，给出了该类Burgers方程的Backlund变换，用所得Backlund变换得到了若干精确孤立波解，包括奇异孤立波解，这些解不等同于行波型孤立波解；用齐次平衡法得到了对数型DBM方程的Backlund变换，并获得了DBM方程的各种孤立波解，包括尖峰孤立波解和奇异尖峰孤立波解。

In 2000, F. LUCA proved that Fermat number are anti-sociable numbers, and in 2005, M. H. LE proved all powers of 2 are anti-sociable numbers. We have used the method of M. H. LE to obtain some new results of the anti-sociable numbers. For every integer n containing prime divisors that are 1 mod 4, let p mod 4 be an arbitrary prime divisor of n. There is at least one anti-sociable number in n^2, p^2n^2, p^4n^2, and p^6n^2. Therefore we can prove that anti-sociable numbers have positive density in perfect square numbers. We also give a method to find the exact anti-sociable numbers.

LUCA证明了Fermat数都是孤立数；2005年，乐茂华教授证明了2的方幂都是孤立数，用乐茂华教授的方法给出孤立数的一些新的结果：对于任意含有4w+1型素因子的正整数n，设p为n的任意一个4w+1型素因子，则在n^2，p^2n^2，p^4n^2，p^6n^2里至少有一个是孤立数，因此可以证明孤立数在完全平方数里有正密度，另外也给出求解确定孤立数的方法。

The solitary wave can be generated considering Goring and Raichlen's movement of a paddle. The proposed original linear solution for the solitary wave generation is expressed in the hypergeometric function. Two disadvantages of the original solution with large trailing wave and skewed wave profile are found by comparing with the theory of solitary wave derived from Boussinesq's equation.

本文并以弱非线性的孤立波造波问题做为解析之对象，由於孤立波造波板速度为一超越函数，造成解析上的困难；本文以 hypergeometric 函数推求常微分方程式之全解，并与理论波形解比较后，发现由於未考虑非线性及分散性过强等问题，使得线性暂态解较理论波形拉长与歪斜，可能无法有效描述孤立波造波问题，故针对线性之分散关系做出修正。

The solitary wave can be generated considering Goring and Raichlen's movement of a paddle. The proposed original linear solution for the solitary wave generation is expressed in the hypergeometric function. Two disadvantages of the original solution with large trailing wave and skewed wave profile are found by comparing with the theory of solitary wave derived from Boussinesq's equation. The difference between the original linear solution and the solitary wave theory results from the nonlinearity and dispersion of generated waves in the flume.

本文并以弱非线性的孤立波造波问题做为解析之对象，由於孤立波造波板速度为一超越函数，造成解析上的困难；本文以 hypergeometric 函数推求常微分方程式之全解，并与理论波形解比较后，发现由於未考虑非线性及分散性过强等问题，使得线性暂态解较理论波形拉长与歪斜，可能无法有效描述孤立波造波问题，故针对线性之分散关系做出修正。

In chapter 1, we introduce the development of module theory and it s applications in the development of algebra,and present conditions of development of prime submodule s,prime radicals,isolated submodules.

本文讨论了环与模范畴中一个重要的子模类—孤立子模的一些性质以及它与强不可约子模等之间的一些联系，并引入了强孤立子模和局部孤立子模的概念，探讨了它们的一系列性质，在第一章中，介绍了模论的发展，模论在代数的发展中所起的重要作用以及素子模，素根和孤立子模的发展现状；在第二章中，给出了与本课题有关的重要概念及其结论。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

For contrast experiments, k-means and DBSCAN algorithms are also implemented using Visual C++ 6. 0. We conducted a series of experiments, including the experiment of the correctness of clustering and outlier detection, the experiment of the precision of clustering and outlier detection. The experiment of the runtime, the experiment of the effect of clustering and outlier detection on parameters, the experiment of the impact of clustering and outlier detection precision by the order of data input, and the experiment of the effect of the algorithm validness by the density character of dataset.

本文使用Visual C++ 6.0实现了基于距离的聚类和孤立点检测算法、k-means算法和DBSCAN算法，做了大量的对比实验，包括聚类算法和孤立点检测正确性实验；聚类算法和孤立点检测精度实验；算法执行时间实验；参数对聚类和孤立点检测结果的影响实验；数据输入顺序对算法聚类和孤立点精度的影响实验；数据集密度对算法有效性的影响等。

And when the evening mist clothes the riverside with poetry, as with a veil, and the poor buildings lose themselves in the dim sky, and the tall chimneys become campanili, and the warehouses are palaces in the night, and the whole city hangs in the heavens, and fairy-land is before us——then the wayfarer hastens home; the working man and the cultured one, the wise man and the one of pleasure, cease to understand, as they have ceased to see, and Nature, who, for once, has sung in tune, sings her exquisite song to the artist alone, her son and her master——her son in that he loves her, her master in that he knows her.

当傍晚的迷雾用它薄纱般的诗意笼罩着河岸，古老的建筑迷失在朦胧的天空，高耸的烟囱幻化成一座座孤立的钟楼，林林总总的仓库就像夜里的宫殿整个城市都悬挂在了天空中，宛如仙境展现在我们眼前，在那时，路上的行人匆匆地赶回家；劳动者和文人，智者和浪子，他们视而不见，自然也就不能理解，而只在此时才开始歌唱的大自然便把自己美妙的歌曲献给了艺术家们——她的儿子和她的主人；说他是儿子是因为他爱她，说他是主人是因为他理解她。

There remained the generic conditions imposed by natural, as distinct from human law, as integral parts of the human whole: the necessity of destruction to procure alimentary sustenance: the painful character of the ultimate functions of separate existence, the agonies of birth and death: the monotonous menstruation of simian and human females extending from the age of puberty to the menopause: inevitable accidents at sea, in mines and factories: certain very painful maladies and their resultant surgical operations, innate lunacy and congenital criminality, decimating epidemics: catastrophic cataclysms which make terror the basis of human mentality: seismic upheavals the epicentres of which are located in densely populated regions: the fact of vital growth, through convulsions of metamorphosis, from infancy through maturity to decay.

324截然不同于人为的法则，这里依然存在着按照自然的法则作为对维持整个人类的生存不可分割的部分加诸于人的生物学之基本条件。为了获得有营养的食品，就不得不进行破坏性的杀戮。孤立的个人生存中终极机能那充满了苦恼的性质。生与死的痛苦。类人猿和人类女性那单调的月经，自初潮期一直延续到闭经期。海洋上、矿山和工厂里那些不可避免的事故；某些非常痛苦的疾病以及伴随而来的外科手术；生来的疯颠，先天性犯罪癖；导致人口大批死亡的传染病；在人类心灵深处种下恐怖种子的灾难性特大洪水；震中位于人口密集地区的大地震；历经剧烈变形，自幼年经过成熟期进入衰退期的生命成长的事实。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！