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. ? 中午去做了個家教，數學的，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。看了個那個"Alex"的"The Hours"，一個小時過去了，郁悶死了，摘了上面幾句，就算完事吧。一點勁都沒有。還是更喜歡看那個"My commitment"。那里有很多的東西，好句子一個接一個，天天早上都要讀好些會兒，也寫幾個： ? 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... ? 關于英語說到這，我這人生也太單調了monotone，不過那樣的話，有很好的性質，比如最多只有可數個不連續點，可積的，有界變差的，可以逼近很多的東西。對，就說數學了： ? 現代偏微分方程：現在感覺入門了，正在往前走，當然還有許多的證明細節未能一一羅列，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，通過積分把強解換成弱解，而后通過正則化又得強解，中間這個過渡就是現代的意思了。弱解的存在性是通過函數空間和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的第五章關于泛函分析的內容結束了。弱解的正則性是通過差分（是這個詞么）來達到的，差分有很好的性質，而Sobolev空間中差分的定理就成了正則性的基本事實。那個test function取得是那樣的好，以致$L^2$范數有界，可以導出二階弱導數。弱解的唯一性那是很好的了。最后還有個Fredolm Alternative，說的是B^*空間中的緊線性算子的性質，把齊邊界條件和非齊邊界條件分開了。 ???第三章還沒看完，是關于拋物型方程的$L^2$理論，也一樣，先構造弱解，還有好幾個等價的定義，那是數學分析的純形式推導。我們的存在性因為初邊值條件的不同而選用了不同的方法，對于拋物邊界上為零的情形，用Lax-Milgram的個變體，及其Hilbert空間的個定理，很好的證明。對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小時。于是有“詩”如下： ? 其中奧妙； 著實難料。 科學陡峭； 需你常笑。 ? 方法其實都很類似，與數學分析的沒什么兩樣。對t進行等距分割，對這些分割點t，我們有橢圓型方程了，而后構造對所有的t都有的逼近解，那是相當不錯的方法，在中間就是個線性函數。之后因為要使解有收斂子列（列緊），做相當的估計，那個也是相當精妙的，之后對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，他們的特征向量構成一組正規正交基。一個一個做組合，是的每個組合都有弱解的樣式，而后去逼近。 ? 泛函分析，那是個很長的學問。Lars Harmonder的Linear Functional Analysis是很不錯的，可惜自己資質太低，看了點就不想看，也只弄懂皮毛，上課時瀏覽吧。張恭慶的泛函分析，現在重讀，發現能作出相當多的題目了，那種感覺真是妙不可言，有的讓人吃驚，有的讓人勢不可擋。今天晚上開始，學Rudin的Functional Analsyis吧，那個可能更容易點，沒關系，反正也是個所謂的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...

轉載于:https://www.cnblogs.com/zhangzujin/p/3826331.html

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