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In this paper,we give the error expressions of piecewise linear Lagrange polynomial interpolation and piecewise cubic polynomial interpolation using the Taylor expansions.

中文摘要：本文利用Taylor展开得到三角形上线性Lagrange插值和三次Lagrange插值的导数余项公式，对这些余项公式进行分析，给出了两类能以四阶精度逼近被插函数在对称点的导数值的格式，一种是在均匀剖分时其分片线性插值的相邻单元的导数值的后处理格式，一种是在六片强正规剖分时的三次插值在对称点上的导数值的后处理格式，使得在已知原函数在各节点的值后，通过一个简单的线性计算就可得到原函数在对称点的导数的一个超逼近值，将以往提出的平均导数的二阶精度提高到四阶。

For, now, the last of the fleet of ships was round the last low point we had headed; and the last green barge, straw-laden, with a brown sail, had followed; and some ballast-lighters, shaped like a child's first rude imitation of a boat, lay low in the mud; and a little squat shoal-lighthouse on open piles, stood crippled in the mud on stilts and crutches; and slimy stakes stuck out of the mud, and slimy stones stuck out of the mud, and red landmarks and tidemarks stuck out of the mud, and an old landing –stage and an old roofless building slipped into the the mud, and all about us was stagnation and mud.

现在，那些急飞的舰队中的最后一支正绕过我们来时已经过的的低水湾，很快便不见了踪影；最后一艘满载稻草的绿色游艇、扬着棕褐色的风帆尾随其后，也很快消失了；只见几只装运沙石的驳船，形状粗糙得如同小孩们第一次学做的船舶模型，一艘艘低陷在泥浆里；一座支在桩上略显矮小的灯塔，像是踩着高跷、拄着拐杖的瘸子踏在泥浆里；泥滑的木桩立在泥浆里，泥滑的石头躺在泥浆里，红色的地标和潮标露出在泥浆里，一个破旧的码头和一座没有了屋顶的房子滑倒在泥浆里。

The father of dying appearance forgot the affair few days ago, the Will took the love of comprehension and drewed up the story of the other day for father, that story related according to the logic of the father's comprehension life of, in the story, the Will embraced the father rushed this was used to imprison the patient's hospital, they arrived at the by the lake of outskirts, father once in this by the lake met by chance famous big fish in that another cause matter, in that lake near the bank, all in the father whole life he met and once helped of the late lament all at-witch, connect body beauty, giant, the residents of the host of the circus troupe, mother, barefoot small town and bank hijacker ……, at public send off of vision in, the father was put by the Will to go into water and became the big fish that a tail gave birth to Long Huo Hu and by leap and bound roved around and disappeared at people's visual field in.

弥留状态的父亲忘记了数天前的事情，威尔带着理解的爱，为父亲编造了前几天的故事，那个故事按照父亲的理解人生的逻辑讲述的，在故事里，威尔抱着父亲奔跑出了这个只用来囚禁病人的医院，他们来到郊外的湖边，父亲曾在这个湖边邂逅那条他故事里著名的大鱼，在那个湖岸边，父亲一生中所有他遇见和帮助过的故人都在--女巫、连体美女、巨人，马戏团主人、母亲、光脚小镇的居民、银行劫匪……，在众人送别的目光里，父亲被威尔放入了水中，成为了一尾生龙活虎的大鱼，飞快地游走，消失在人们的视野里。父亲的眼睛因为威尔的讲述而湿润，父亲与儿子之间的理解，在他人生的最后时刻终于和谐。父亲含笑而去。

Never Say Goodbye Bon Jovi Crossroad As I sit in this smokey room The night about to end I pass my time with strangers But this bottle's my only friend Remember when we used to park On Butler Street out in the dark Remember when we lost the keys And you lost more than that in my backseat baby Remember how we used to talk About busting out - we'd break their hearts Together - forever Never say goodbye, never say goodbye You and me and my old friends Hoping it would never end Never say goodbye, never say goodbye Holdin' on - we got to try Holdin' on to never say goodbye Remember days of skipping school Racing cars and being cool With a six pack and the radio We didn't need no place to go Remember at the prom that night You and me we had a fight But the band they played our favorite song And I held you in my arms so strong We danced so close We danced so slow And I swore I'd never let you go Together - forever Never say goodbye, never say goodbye You and me and my old friends Hoping it would never end Never say goodbye, never say goodbye Holdin' on - we got to try Holdin' on to never say goodbye I guess you'd say we used to talk About busting out We'd break their hearts Together - forever THE END by lune

不要说再见邦乔维十字路口正如我坐在这个熊室夜晚即将结束传递我的时间与陌生人但是，这瓶是我唯一的朋友请记住，当我们用公园对巴特勒街在黑暗请记住，当我们失去了钥匙和你失去了，在我的后座婴儿还记得我们用来谈论关于破坏了-我们要打破他们的心在一起-永远从来没有说再见，从来没有说再见你和我和我的老朋友希望它会永远不会结束从来没有说再见，从来没有说再见握住'的-我们得尝试握住就永远不会说再见记住天逃学赛车酷六包和电台我们不需要没有地方可去记得那天晚上的舞会你和我，我们进行了斗争但是，带他们打我们最喜爱的歌曲举行你和我在我的武器如此强大我们跳舞如此接近我们跳舞如此缓慢，我发誓我从未让你去在一起-永远从来没有说再见，从来没有说再见你和我和我的老朋友希望它会永远不会结束从来没有说再见，从来没有说再见握住的-我们得尝试握住就永远不会说再见我猜你会说我们用来谈论关于破坏了我们想打破他们的心在一起-永远再见 LUNE

"That the doctrine of the Reformed churches concerning predestination, and the points annexed to it, by its own genius and necessary tendency, leads off the minds of men from all piety and religion; that it is an opiate administered by the flesh and by the devil, and the stronghold of Satan, where he lies in wait for all; and from which he wounds multitudes, and mortally strikes through many with the darts both of despair and security; that it makes God the author of sin, unjust, tyrannical, hypocritical; that it is nothing more than interpolated Stoicism, Manicheism, Libertinism, Turcism; that it renders men carnally secure, since they are persuaded by it that nothing can hinder the salvation of the elect, let them live as they please; and therefore, that they may safely perpetrate every species of the most atrocious crimes; and that, if the reprobate should even perform truly all the works of the saints, their obedience would not in the least contribute to their salvation; that the same doctrine teaches, that God, by a mere arbitrary act of his will, without the least respect or view to sin, has predestinated the greatest part of the world to eternal damnation; and, has created them for this very purpose; that in the same manner in which the election is the fountain and cause of faith and good works, reprobation is the cause of unbelief and impiety; that many children of the faithful are torn, guiltless, from their mothers' breasts, and tyrannically plunged into hell; so that, neither baptism, nor the prayers of the Church at their baptism, can at all profit by them;" and many other things of the same kind, which the Reformed Churches not only do not acknowledge, but even detest with their whole soul.

"该学说的革新教会联谊会关于宿命，并分附在它，由它自己的天才和必要的倾向，导致起飞的头脑男子从所有虔诚与宗教；这是一个鸦片类由血肉所魔鬼和据点撒旦，在那里他是在等待所有；从他的伤口众多，而致命打击，通过许多与飞镖都绝望与安全；因为它使上帝的作者单，不公正，专横，虚伪的，即它只不过是多插生活俭朴，摩尼教，放纵， turcism ；这使得男性的肉体关系稳固，因为它们是说服它说，没有任何东西可以阻碍救赎的选举，让他们住，因为他们请；因此，他们可以安全地胡作非为，每一个物种的最残暴的罪行，并认为，如果reprobate甚至应该真正履行全部工程的圣人，他们的服从，将不会在至少贡献出他们的救恩，即同一教义教导说，上帝，由一个单纯的任意行为，他的意志，如果没有起码的尊重，或以单，有predestinated最大的是世界的一部分，以永恒damnation ，并且创造了，他们为了这个目的，即在同一何种方式选举是喷泉和事业的信念和良好的工程， reprobation ，是导致不信者和不虔诚；说，许多儿童的教友们被拆除，无罪，从他们的母亲的乳房，并tyrannically陷入地狱，因此，既不洗礼，也没有祷告的教会，在他们的洗礼，能在所有利润由他们来主宰；"和许多其他东西的同类，而改革教会不仅不承认，但即使是讨厌自己的整个灵魂。

Yall already know what it is and if you don't Then the great Mannie Fresh will enlighten you Ladies and gentlemen, pimps and playas Half ass rappers and true rhyme sayers This is the Carter, so hold onto your teenage daughter Because this is the Carter, a lot more rich and a whole lot smarter Wayne in ya brain young Carter Wayne in ya brain young Carter Who am I, young wizzle fa shizzle Flow sicker than a third floor in hospitals My charm starburst, my watch skittles I'm hot sizzle, what up hot bizzle Holla at a playa, I'm sorta like BD Yall can't stop my dribble, or block the lay-ups Soft top the Coupe, mami pop her too Don't chase the feelin baby girl let it come to you Remove the ceiling on the girl now she comfortable I'ma world class G mami fuck wit dude I got Lazy-Boy bank that's comfort low I'ma offense coordinator run the shoe You watch your grill what you ought to do Fore' your ribs get barbecued And my ribs is showin I say I'm starving dude This, this, this, this, this is the Carter dude What up Reel, c'mon I'm the Birdman Birdman Jr. bitch I be high in the sky shit on you and yo bitch I be flyer than your guy nigga lose the prick Now if ya follow everything just grab a wing And we could sssssshhhhhhhh All the way down to the mall and bet I buy it all Young Mar' picture the broad lick All the way down to the balls then she wipe it off If getting money is wrong I ain't right at all I young money a car I just write it off I'm the boss of my own shit, I'm my own click I would say fuck ya but go and get ya own dick Get ya game up boy hustle harder This, this, this, this, this, this, this, this, this Get ya game up boy hustle harder This, this, this, this, this, this is the Carter, yea And yall better blame Baby Cuz he the muthufucka that made me, and I'm crazy And yall ask why I never left the navy Cuz he the muthufucka that pay me, is you crazy Young, young, young wizzle baby Give you yo issue, me don't wanna kiss you No, no, no me no want no bullshit So, so stop baller blockin cuz a nigga hood rich And I floss everyday because I could bitch So holla at ya boy cuz I'm still on some hood shit Like, like, like whats really good wit ya mom or your lil boy And your sister lookin good shit, shit I'm still Apple Eagle weasel 1-7 Hollygrove never ever ever leave you I got yall waitin on my sequel This, this, this, this, this, this is the Carter people

yall已经知道它是什么，以及如果你不然后伟大mannie新鲜会启发你女士们，先生们，皮条客和普拉亚斯半驴说唱和真正的押韵sayers 这是卡特，所以举行到您的十几岁的女儿因为这是卡特，有很多更丰富的和整体堑，长一智韦恩在亚脑青少年卡特韦恩在亚脑青少年卡特我是谁，年轻wizzle发shizzle 流病加重了超过三分之一的楼在医院我的魅力starburst ，我的观赏skittles 我的热点sizzle ，有什么了热bizzle holla在playa ，我sorta一样，屋宇署 yall不能阻止我的运球，或阻止裁员的UPS 软顶的跑车， mami弹出她太不追赶feelin女婴，让它到你们这里来删除的上限，该名女童，现在她舒适我是世界一流的克mami他妈的束手无策dude 我懒惰-男童银行的舒适度低我的进攻协调员运行擦鞋您看您的烧烤什么，你应该做的前列'你的肋骨，获得烧烤和我的肋骨是showin我说我挨饿， dude 这，这，这，这，这是卡特dude 什么了轴， c'mon 我是birdman birdman小荡妇我高，在天空中shit外围对你和摇摇荡妇我比你的传单家伙nigga失去刺现在，如果亚后续的一切只是抢到的一翼我们可以sssssshhhhhhhh 所有的方式到商场和打赌，我买它的所有年轻三月'图片广大舔所有的方式到球，然后她擦拭它关闭如果得到的钱是错误的I是不正确的，在所有 i年轻的钱买车，我只是将它写小康我的老板，我自己的shit外围，我自己的点击我会说他妈的亚，但去获得亚自己的迪克获得亚的游戏了男童hustle更难这，这，这，这，这，这，这，这，这获得亚的游戏了男童hustle更难这，这，这，这，这，这是卡特，雅和yall更好地归咎于婴儿 cuz他该muthufucka使我，我疯了和yall问，为什么我从来没有离开海军 cuz他该muthufucka薪酬，我是你疯了青少年，青少年，青年wizzle婴儿给你呦问题，我不想亲吻你不，不，不，我没有想没有布尔什特所以，所以停止球员blockin cuz一nigga遮光罩丰富我每天用牙线，因为我可以荡妇因此， holla在亚男童cuz我仍然对一些遮光罩shit外围像，像，像什么真正好的束手无策亚妈妈或您的莉儿男童和您的妹妹来查找良好shit外围， shit外围我还是苹果鹰weasel 1月7日hollygrove以往任何时候都从未离开你我得到yall waitin对我的续集这，这，这，这，这，这是卡特人

In midlatitude, the ionospheric response to southward turnings in summer and equinox and by night is stronger, which fades out with latitude decreases. During the recovery phase the irregular fluctuation in the ionosphere comes forth. In low-latitude, the disturbance caused by the turnings is strong in summer and equinox and weak in winter, although it tends to be immersing into the background disturbances.

在中纬，发生在夏分季和夜间的翻转能造成较强的电离层负响应，其幅度随纬度的降低而变弱，在恢复过程中存在不规则振荡；在低纬，南向翻转引起的电离层响应在夏分季较强，在冬季则较弱，且易被淹没在电离层自身的扰动中。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

If you would attain that Truth, if you would become perfect in the knowledge of that Truth, you must go through this process of renunciation, setting aside those things which have no value, putting aside your little knowledge in order to acquire greater knowledge, putting aside your little wisdom in order to acquire greater wisdom; and so when you reach the abode where there is no cloud of doubt, of misjudgement, where there is no question of perverting judgment, or of false thoughts, of false emotions, of fleeting affections, then you are truly in possession of the Truth, then truly are you like myself -the Beloved.

其他人也许鼓励，其他人也许阻挠，但是在只有在你内才有去行走的力量，只有在你内才有决心，只有在你内才有智慧，如果你想获得那真理，如果你想在真理的知识方面变的完美，你必须走过这个弃绝的过程，把那些没有价值的事情放在一旁，把你的小知识放在一旁为了获得更伟大的知识，把你的小智慧放在一旁为了获得那更大的智慧；并且因此当你到达那住所，在那里没有怀疑的，错误判断的乌云，在那里没有滥用判断的，或者错误的想法的，错误的情感的，暂时的喜爱的问题的时候，那么你就真正地拥有了真理，那么你真正地像你自己——挚爱者。

This Summer, when Neves takes on Taunton native Mike Varner for the second time in three months at the Mohegan Sun Arena (Varner won the "Last Man Standing" MMA title in Fall River last December) Hawes and Harnois will have ringside seats, and in an upcoming episode of Ghost Hunters, so will Neves.

今年夏天，内韦斯时，需对风景如画的本土麦克varner为第二次在3个月内，在舞台上的莫黑根湖畔孙（ varner赢得了"最后的男子站在"甲基丙烯酸甲酯的标题在秋季河在去年12月）霍斯和阿尔努瓦将有ringside议席，并在在即将举行的插曲鬼猎人，所以将韦斯。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。