以美丽心灵,幸福校园为主线,自拟题目可以写什么文章.老师突然叫我写一点头绪都没

　　其实这个答案是不统一的.这个答案带有很多的个人色彩的含义在里面.
　　我认为美丽心灵指的是人内心的那个希望,当初在看a beautiful mind的时候,令我最感动的莫过于纳什妻子对纳什那份爱,这种爱超乎了夫妻之间的感情,超乎了亲人之间的情感.对于纳什得病了,却依旧很耐心的守候着他、陪伴着他.感动观众的不光光是纳什的那份毅力,还有妻子对他的那份守望与忠诚.曾经看过纳什的一段采访,看的出纳什对妻子很依赖!
　　I wasn't actually planning on going to see "A Beautiful Mind" in the first place,but as it was,I was convinced by the friend that accompanied me that it was truly something to see.And now,after seeing it,I thank her for that.Instead of spending two and a half hours watching George Clooney and Matt Damon rob casinos or Kevin Spacey and Julianne Moore dealing with their problems in New Foundland,I found myself pulled into another kind of story,a powerful,emotional story of how one man learned to battle his own demons and dazzle the world.
　　"A Beautiful Mind",based on the novel by Sylvia Nasar,is the story of John Forbes Nash Jr.,the genius mathematician,whose life suddenly takes a turn for the worse when he is diagnosed with paranoid schizophrenia.After fierce battles with his inner self,he overcomes this and returns to win the Nobel Prize in 1994 for his brakethrough game theory in economics that he had been working on during his years in Princeton University in the 1950s.
　　John Nash,portrayed very well by the versatile and brilliant Russell Crowe,is a partly shy,yet ironic and sometimes even arrogant,gifted young student studying in Princeton University in the late 1940s.He dedicates his time to numbers and equations,set on to solving every problem at hand,rather than mingling with co-students on the football field or in the pub.
　　Nash is later on introduced to Sylvia (played by the lovely Jennifer Connely),a physics student attending his classes.She helps Nash to open up and eventually discover love.
　　Enter William Parcher (played by Ed Harris),a shadowy and mysterious agent working for the Department of Defense.Parcher,after realizing Nash's ability to see mathematical and geometrical patterns everywhere,approaches Nash with a mission that involves national security.
　　Now,amidst his work and relationship,Nash is suddenly thrown into a whirlwind of emotions and disbeliefs as he is diagnosed with paranoid schizophrenia.And this is the part where "A Beautiful Mind" truly shines:in portraying the disorder from Nash's own point of view.In a powerful and emotional way,it shows the viewer how difficult an illness like this can be to not only face,but overcome,something that people today may not always realize.
　　Before seeing this movie,I must admit that I was a bit afraid that casting such a well-known actor as Russell Crowe as the main character would ruin the image of John Nash,forcing the viewer to see Crowe,rather than Nash.This is a common problem when dealing with famous actors,but to my surprise,it didn't much bother me much.And the same goes for Ed Harris.
　　As a movie,"A Beautiful Mind" is absolutely great (It is so much more,but I cannot find the words to praise it enough,so I will simply go with "great" =).Not only does it have a strong point and an importaint message to the viewer,but it delivers it in a touching and sensitive,partly even humourous kind of way,with the help of powerful actors,a great screenplay and even a few special effects to boost it up.So for anyone whose grown tired of the consant pointless action-movies out there,and instead want to immerse themselves into a character-driven story that might actually bring a tear to your eyes,I sincerily recommend "A Beautiful Mind".

Nash:"Terrified,Mortified petrified,stupefied by you."
被你吓呆了,惊呆了,窘呆了,而且目瞪口呆了.

这个问题大致上还是清楚的,只是有三点疑问.
1.没写明X是什么,可能性比较大的是X为R³中的一个点.
如果把X换为R³的其它子集,问题的结果需要代数拓扑里的概念.
2.没说明F和g的可微性.
比较省事的要求是F,g都光滑(无穷次可微),降低可微性会带来非常技术性的问题.
虽然也可以讨论,但我想不会是题目的本意.
3.不清楚最后一个符号是什么.
最可能的是问号"?",即这是一个计算题.
按照最省事的理解,问题的严格叙述是这样:
设X是R³中的一个单点集,定义线性空间:
V = {F:R³X → R³ | F光滑,且∇×F = 0},
W = {F:R³X → R³ | 存在R³X上的光滑函数g,使F = ∇g},
求dim(V/W) = (注:由∇×∇g = 0,可知W是V的子空间,由此可讨论商空间V/W.)
答案是0,即V = W.
换句话说就是:R³X上旋度为0的光滑向量场一定是某个光滑函数的梯度场.
证明大意如下:
任意取定R³X中一点p.对R³X中任意一点x,取L为R³X中由p到x的光滑曲线.
考虑F沿L的第二类曲线积分∫{L} F,可以证明其不依赖L的选取:
若L1,L2是p到x的两条光滑曲线,不妨设二者没有端点以外的公共点.
考虑闭曲线C:由p经L1到x再反向经L2回到p,则C是R³X中分段光滑的简单闭曲线,
存在R³X中的曲面D以C为边界.
由Stokes公式,∫{C} F = ∫{D} ∇×F = 0,即得∫{L1} F = ∫{L2} F.
若L1与L2相交(有端点以外的公共点),可取L3与L1,L2都不相交,
可得∫{L1} F = ∫{L3} F = ∫{L2} F,即∫{L} F不依赖L的选取.
取g(x) = ∫{L} F,可以证明g(x)光滑,且∇g = F (细节略).
即F是光滑函数g的梯度场.
这个问题有比较深刻的背景,即de Rham上同调理论,不过就说来话长了.

安琪既是一位美丽的天使又是一位全能的才女。她最受男生欢迎，却不受女生欢迎，原因无它，这一切都是安琪自己的智慧和美貌惹的祸。美貌遭到嫉妒，智慧遭到排斥，这使她原本曲曲折折的命运变得更加坎坷多变，比如安琪只有成群的仰慕者，却没有一个知心朋友。没有哪一个女生愿意和她同桌，没有哪一个女生愿意和她做朋友，没有哪一个女生愿意和她一起吃饭，评“三好学生”的时候更没有女生选她，她在人群中像一只既高贵又优雅而且孤独的白天鹅。可她对这些并不介意，也不为此沮丧而是更加发奋学习。而这又促进了她和女生们之间的矛盾深化了。学校要把报送名额送给安琪，可事情来了一个一百八十度的大转弯，报送名额给了王云。这些都是女生忌妒的结果。然而谁会想到这给美丽的天使背后隐藏着一个不为人知的秘密：安琪得了心脏病。直道她住院治疗，秘密才被揭开。女生们改变了对安琪的看法，而且去医院探望了安琪。不幸的是，安琪不久就离开了！ 我读后，不仅被主人公对命运的抗争所感动，同时也感到了作者失去同学的悲痛之情，惋惜之心，还有悔恨之痛。主人公十几年来与病魔抗争，从不向病魔屈服，顽强的活了下来，并争分夺秒地努力学习，不在意自己是个病人，力求当一个正常人。她那种乐观的态度，横溢的才华以及令人痛惜的病逝，给人一种凄厉之美。这种美德毁灭给人们心灵上造成了极大的震撼，可以说是人物命运和人物精神的两重矛盾冲突。安琪一个人自小面对死亡的威胁还是那样豁达，足见其坚韧难道。这在我们日常生活是一种非常少见的精神。 这篇作品的主题不仅仅是歌颂安琪那种与病魔抗争到底，心灵美的高尚品德以及豁达态度，同时赞扬了母爱的伟大。

A BEAUTIFUL MIND (2001)
A Beautiful Mind's greatest achievement,in my humble opinion,is the way it makes schizophrenia accessible to "sane" people.The general public knows schizophrenics tend to talk to themselves,repeat certain actions and do things generally at odds with the norm.But why?It's nearly impossible for a "sane" individual to understand why this happens...and more importantly,what that feels like.Without this essential empathy,many people become frustrated with the mentally ill,asking why patients can't pull themselves together and just bear up.We express this same impatience with the criminally insane who act upon delusions with disastrous results.It is incomprehensible.
A Beautiful Mind does all it can to change that,and it succeeds.Unless you are familiar with John Nash's story,you probably won't guess he's schizophrenic until part-way into the movie.He's eccentric,abrupt,and highly intelligent,but doesn't seem crazy.His delusions are as real as reality to Nash,and likewise,they are real to the audience,who cannot tell the difference between truth and delusion.
Incidentally,I came across a review from a "professional critic" who blasted A Beautiful Mind for including "all that spying stuff that had nothing to do with Nash's work that was thrown in for Hollywood thrill." I feel bad for that chap,since he missed the entire point of the film.But that just proves Ron Howard's genius in creating a picture of insanity indistinguishable from reality.
There are some truly shocking moments in A Beautiful Mind.When Alicia finds her husband's secret cache of newspaper clippings behind their house,I was eerily reminded of Jack Nicholson's wife in The Shining discovering his endless,typewritten pages of the same phrase.The scene that follows,culminating with Nash's realization that his delusions are indeed a false reality is brilliant.In a moment,remembering Marcee,Nash has a flash of insight,and he finally accepts his illness -- ironically,through his intellect.When Nash imagines that someone is going to harm Alicia,he lunges at her -- and only through his eyes do we see how a seemingly senseless act of violence is a gesture of love,filtered through the smog of delusion.
Now my take on the acting:Superb in every sense of the word.Russell Crowe is incredible.I can't stress that enough.There's never any question about the authenticity of his character.Crowe doesn't rely on his elaborate makeup to age Nash -- his walk,words,and voice do that elegantly in the movie's end.Crowe will get at least another Oscar nomination out of this one.And,he better win.Jennifer Connelly is amazing as well.And when Crowe and Connelly are put together,extraordinary chemistry erupts,they just gel together,they really belong with one another.Some people have had problems with the romance part of the movie,saying that the way John and Alicia even started seeing each other wasn't very realistic and why Alicia would stay with John after he becomes distant.But,I think that maybe it started out as just a crush,you know,and the math question she showed him was just her excuse for going to his office and she already knew she was going to ask him out before hand.Maybe she's just attracted to the kind of person Nash is?Who knows?A lot of people are attracted to the "weirdest" things sometimes.The crush took over the fact that he sort of insulted her work and she still asked him anyway.When you're around someone you like so much you can't help but be fooled by them.I can't really explain it,but I can understand why she still asked him to dinner.And I guess if you love someone as much as Alicia loved John,then you would stick with them through anything.Even how distant he became,she still stuck with him.
Moving on,I think Ed Harris is,as always,great.Harris continues to prove that,simply because he's flawless.With delusions like these,no wonder Nash was torn between treatment and "spying."
Simply put,A Beautiful Mind is a film which extends far beyond the 2 hours and 15 minutes that you will spend viewing it in the theater.The characters continued to haunt me after the movie (and still do),thanks to the Oscar-inducing performances by Russell Crowe,Jennifer Connelly and all of the supporting players.They are not merely acting,yet are transformed into the characters,leaving no trace of a line between their part and reality.
Of course a film is only as good as a screenplay would allow,and the story contained within is written in a way that compliments everything that is truly great about A Beautiful Mind.Ron Howard contributes truly inspiring work to this film,and I hope that the critics remember him when awards are being given out.
All I can tell you now is that if you're looking for an emotionally-charged movie that will make you cry,but still filters in some very funny moments as to lighten things up every now and then,with near perfect acting,cinematography,directing,editing and a screenplay which will cause the story of John Nash to inspire you,then consider A Beautiful Mind.
I hope a lot of people see this film.Not just because Russell Crowe is a hunk or because it's a Ron Howard piece,but because you will learn something important.You will learn why compassion is an absolute must when dealing with the mentally ill.You won't glare at the next person you see muttering to themselves.And when someone you love is dealing with a disorder,be it schizophrenia or depression,you won't ask them to "pull themselves together." You will understand why they need your love -- because they are just as confused as you are.
In closing,if Russell Crowe isn't awarded the Best Actor Oscar this year,then my faith in movies and its rewards system will be seriously tarnished.

Nash:"Terrified,Mortified petrified,stupefied by you."
被你吓呆了,惊呆了,窘呆了,而且目瞪口呆了.