很打瞌睡，就此寫下： ? Having to be proud and brave in front of everybody. ? I think I'm only staying alive to satisfying you. ? Yes, you can sift the flour, if that's what makes you happy. ? 中午去做了個(gè)家教，數(shù)學(xué)的，高一的，我真是太有才了。中午回來也沒睡，就到崢嶸這玩起來了。看了個(gè)那個(gè)"Alex"的"The Hours"，一個(gè)小時(shí)過去了，郁悶死了，摘了上面幾句，就算完事吧。一點(diǎn)勁都沒有。還是更喜歡看那個(gè)"My commitment"。那里有很多的東西，好句子一個(gè)接一個(gè)，天天早上都要讀好些會(huì)兒，也寫幾個(gè)： ? We've arrived at these and various rules through a process of trial and error over the course of our four-year relationship. ? She(Mother) must hold the world's record for being the world's most optimistic mother. ? She believed in marriage with a strength and a vigor that I've never equalled. ? My mum was the only person in the world who still called Dan. ? It was nice to be fussed over like this.To know that there was someone in the world who,no matter you were a convicted homicidal maniac, a porn baron or crack addict,?would love you unconditionally... ? 關(guān)于英語說到這，我這人生也太單調(diào)了monotone，不過那樣的話，有很好的性質(zhì)，比如最多只有可數(shù)個(gè)不連續(xù)點(diǎn)，可積的，有界變差的，可以逼近很多的東西。對(duì)，就說數(shù)學(xué)了： ? 現(xiàn)代偏微分方程：現(xiàn)在感覺入門了，正在往前走，當(dāng)然還有許多的證明細(xì)節(jié)未能一一羅列，但最起碼基本方向知道了，而且也能自己做些推倒。回顧下： ????第二章是橢圓型方程的$L^2$理論，通過積分把強(qiáng)解換成弱解，而后通過正則化又得強(qiáng)解，中間這個(gè)過渡就是現(xiàn)代的意思了。弱解的存在性是通過函數(shù)空間和Riesz表示定理，Lax-Milgram定理來的，那是些很好的定理，順便也把Gilbarg-Trudinger的第五章關(guān)于泛函分析的內(nèi)容結(jié)束了。弱解的正則性是通過差分（是這個(gè)詞么）來達(dá)到的，差分有很好的性質(zhì)，而Sobolev空間中差分的定理就成了正則性的基本事實(shí)。那個(gè)test function取得是那樣的好，以致$L^2$范數(shù)有界，可以導(dǎo)出二階弱導(dǎo)數(shù)。弱解的唯一性那是很好的了。最后還有個(gè)Fredolm Alternative，說的是B^*空間中的緊線性算子的性質(zhì)，把齊邊界條件和非齊邊界條件分開了。 ???第三章還沒看完，是關(guān)于拋物型方程的$L^2$理論，也一樣，先構(gòu)造弱解，還有好幾個(gè)等價(jià)的定義，那是數(shù)學(xué)分析的純形式推導(dǎo)。我們的存在性因?yàn)槌踹呏禇l件的不同而選用了不同的方法，對(duì)于拋物邊界上為零的情形，用Lax-Milgram的個(gè)變體，及其Hilbert空間的個(gè)定理，很好的證明。對(duì)于初值不為零的情形，用Rothe方法，昨天用了整整一上午才看完，看完了又到外面整整想了半個(gè)小時(shí)。于是有“詩”如下： ? 其中奧妙； 著實(shí)難料。 科學(xué)陡峭； 需你常笑。 ? 方法其實(shí)都很類似，與數(shù)學(xué)分析的沒什么兩樣。對(duì)t進(jìn)行等距分割，對(duì)這些分割點(diǎn)t，我們有橢圓型方程了，而后構(gòu)造對(duì)所有的t都有的逼近解，那是相當(dāng)不錯(cuò)的方法，在中間就是個(gè)線性函數(shù)。之后因?yàn)橐菇庥惺諗孔恿?#xff08;列緊），做相當(dāng)?shù)墓烙?jì)，那個(gè)也是相當(dāng)精妙的，之后對(duì)極限看是否滿足弱解的定義咯。還有后面的Galerkin方法，是泛函分析威力的場(chǎng)所，就到這里，還沒看完。可分的Hilbert空間中的有界線性自伴緊算子有特征值，他們的特征向量構(gòu)成一組正規(guī)正交基。一個(gè)一個(gè)做組合，是的每個(gè)組合都有弱解的樣式，而后去逼近。 ? 泛函分析，那是個(gè)很長(zhǎng)的學(xué)問。Lars Harmonder的Linear Functional Analysis是很不錯(cuò)的，可惜自己資質(zhì)太低，看了點(diǎn)就不想看，也只弄懂皮毛，上課時(shí)瀏覽吧。張恭慶的泛函分析，現(xiàn)在重讀，發(fā)現(xiàn)能作出相當(dāng)多的題目了，那種感覺真是妙不可言，有的讓人吃驚，有的讓人勢(shì)不可擋。今天晚上開始，學(xué)Rudin的Functional Analsyis吧，那個(gè)可能更容易點(diǎn)，沒關(guān)系，反正也是個(gè)所謂的famous吧，別虧待了自己。 ? 下面就用英文寫了，那樣的話，就沒什么不好意思了，希望很多的人看不懂，而自己卻能聊以自慰： ? I'm destined to be a mathematician...I'm almost blind, and I've no other choice but mathematics...And I'm eager of knowledge and the truth of nature. I was born on Jan,23th,1987...What a fabulous day! Since 987 is the reverse of 789,and 0123 is the only consequent?number which can be occured in month and day...And I can introduce my birthday like this: after exactly 5/4 centuries, another mathematician like David Hilbert was born...I've the same birthday as him, and I've the same first name as him...My first name is David, which came from the big stomach I have when I was an undergraduate...Surely, I don't even mention it, since I can bear it...But when I write down these in English words fluently, I'm confident....and a little proud...Also, Lars?Hormander has only one day which differ with my birthday, that is, his birthday is on Jan,24th...Fantastic...and I've the same birthday as Newton in lunar canlendar...we were both born on the "small" spring festival in each other's country...And Einstein, his born year is 1879....change a little,it is me...Aha...I'm a fun of astrology and numerology...I like this sometimes,this gives me confidence and pleasure, relief of the tiredness...regain the strength to go on...

轉(zhuǎn)載于:https://www.cnblogs.com/zhangzujin/p/3826331.html

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