分类 🌻微语&随笔 下的文章 - 我的学记|刘航宇的博客

【概率论】自由度为n的卡方分布，t分布，F(m,n)分布的期望和方差 卡方分布：E(X)=n，D(X)=2nt分布：E(X)=0(n>1)，D(X)=n/(n-2)(n>2)F(m,n)分布：E(X)=n/(n-2)(n>2)D(X)=[2n^2*(m+n-2)]/m(n-2)^2*(n-4)

【双语美文】心灵鸡汤学学自信的人都是怎么做的 Anyone can adopt the habits confident people practice on a regular basis. Below are just some of the ways those with extra self-possession approach life differently than everyone else.每个人都能培养自信的人每天做事的习惯，以下就是那些特别镇定自若的人生活中一些与他人不同的做事方法。They're more productive.他们效率更高。Confidence = hustle. Research suggests that confident people may be more productive because their can-do thoughts inspire real action. It's no wonder confident people seem to own the office.信心=抓紧时间。研究显示自信的人可能做事效率更高，因为“我能搞定”的想法鼓励着他们真正行动起来。难怪自信的人看起来好像掌管着整个办公室一样。Their body language helps boost their confidence.他们的肢体语言有助于提高自信。Studies show that how a person carries him or herself influences how he or she feels on the inside. A tall posture and even stretching can help people feel a surge of power -- and confident people take advantage of those little adjustments.研究显示，一个人表达想法的方式影响着其内心的感受。挺拔的姿态、甚至舒展身体都有助于激发力量，自信的人会利用好这一切。They aren't self-assured all the time.他们并不总是自信。All people have their flaws. The difference lies in recognizing those insecurities and carrying on with life despite them. Research shows self-acceptance is paramount to a happier life, but it's a habit many people rarely practice. Confident people aren't superhuman -- they just accept their imperfections wholeheartedly and live a happy life regardless.所有人都有缺点，区别就在于要认清不安全的因素，并且继续生活。研究显示，自我接受是生活更幸福的关键，但这也是很多人所缺少的习惯。自信的人不是超人——他们只是真正接受自己的不完美并过着幸福生活，而不去考虑那些。They actively pursue success.他们真的在追求成功。"No" is simply not in a confident person's vocabulary, at least when it comes to success. Confidence is crucial when pursing a career, according to a study published in the journal Basic and Applied Social Psychology. The research found that the more likely someone is able to picture themselves achieving their goal, the more likely they're going to be able to do it.对于自信的人来说，他们的字典里真的没有“不”这个字，至少在谈及成功时如此。发表在《基础与应用社会心理学》杂志上的研究表明，信心在追求事业时起到决定性作用。这项研究发现，一个人越能幻想自己达成目标，就越有可能获得成功。They channel their inner celebrity.他们引导自己向内心的名人看齐。A confident person's mantra is "I am Beyonce." OK, maybe that's just this author's, but regardless, there's power in celebrity. Research published in the journal Personal Relationships found that when people wrote down qualities they shared with their favorite celebrities of the same gender, they felt much more compelled to become their best selves.自信之人的咒语是“我是碧昂斯（美国女歌手）”。好吧，可能那只是本作者的想法，但不管怎样，名人效应总是有的。发表在《人际关系》杂志上的研究发现，当人们写下与自己最喜欢的同性别名人所共有的品格时，他们会迫使自己做到最好。They stick to their convictions.他们坚持自己的信念。Confident people place trust in their own opinions -- but not without listening to others, of course. As confidence coach Susie Moore explained in a HuffPost blog, confident people hear all sides of an argument, but ultimately, they stick to what they feel is best.自信的人信赖自己的想法——当然也不是不听人劝。正如自信导师苏西•摩尔在赫芬顿邮报博客中写道：自信的人会倾听辩论双方的观点，但最终他们会坚持自己看来最好的想法。"Confident people listen to other people but do not let their difference of perspective take them off track," she wrote.她写道：“自信的人听别人的说法，但不会让他们观点之间的不同带自己偏离轨道。”They don't fear failure.他们不害怕失败。All people have their setbacks. Confidence isn't doing everything right, it's pushing on even after being wrong. Research suggests that people who appear more self-assured are also seem more intelligent.所有人都会遇到挫折，自信不是做对每件事，而是在做错后仍能勇往直前，研究表明看起来自信的人也似乎更聪明。They're not afraid of being confident.他们不害怕自信。Confident individuals don't shy away from asserting themselves, whether they're actually feeling comfortable or just faking it until they make it. As singer Demi Lovato's recent single so poignantly asks, "What's wrong with being confident?" The answer: Nothing at all.自信的人不会羞于坚持自己的主张，无论他们是真自信还是假装自信，他们都会坚持如此直到成功。正如歌手黛米•洛瓦特最近的单曲中寓意深刻地问道的那样：“自信有错吗？”答案就是：“何错之有”。

合同矩阵、二次型满足C^TAC=B求可逆矩阵C一种简单求法 合同矩阵、二次型满足C^TAC=B求可逆矩阵C一种简单求法例题：设A=[0 1 1;1 2 1;1 1 0],B=[2 1 1;1 0 1;1 1 0]求可逆矩阵C使得C^TAC=B?解答：观察A =0 1 11 2 11 1 0B =2 1 11 0 11 1 0A交换1,2行, 交换1,2列即得B左乘变行右乘变列所以将单位阵进行对应变化 C =0 1 01 0 00 0 1满足C^TAC=B

爱要及时说出口【双语美文】 There was once a guy who suffered from cancer, a cancer that can't be cured. He was 18 years old and he could die anytime. All his life, he was stuck in his house being taken cared by his mother. He never went outside but he was sick of staying home and wanted to go out for once. So he asked his mother and she gave him permission.曾有一男孩，患了不治之癌。他才18岁，但生命随时会结束。一直以来，男孩都被困在屋子里，由他的母亲照料。男孩从未出去过，但他厌倦了一直窝在家里，想出去走一走。男孩因此询问他的母亲，并得到了母亲的同意。He walked down his block and found a lot of stores. He passed a CD store and looked through the front door for a second as he walked. He stopped and went back to look into the store. He saw a beautiful girl about his age and he knew it was love at first sight. He opened the door and walked in, not looking at anything else but her. He walked closer and closer until he was finally at the front desk where she sat.男孩出了门，路过了许多家店。经过一家卖CD的音像店时他看了眼前门。男孩停了下来，并走回去又往店里看了看。他看见一个漂亮的女孩，年龄大约和他一般大。男孩意识到他一眼就爱上了这女孩。他打开了这家店的门，走了进去，什么也不看，就只看着她。男孩越走越近，直到来到这女孩坐着的前台。She looked up and asked, "Can I help you?"女孩抬起头来问道：“有什么需要帮忙的吗？”She smiled and he thought it was the most beautiful smile he has ever seen before and wanted to kiss her right there.女孩笑了笑，男孩认为这是他见过的最美丽的笑容，他甚至想当场就亲吻这女孩。He said, "Uh... Yeah... Umm... I would like to buy a CD."他说道：“呃…是的…嗯…我想买张CD。”He picked one out and gave her money for it.男孩随便挑了一张出来并把钱递给女孩。"Would you like me to wrap it for you?" she asked, smiling her cute smile again.“需要我帮你把它包起来吗？”女孩问，脸上又露出可爱的微笑。He nodded and she went to the back. She came back with the wrapped CD and gave it to him. He took it and walked out of the store.男孩点了点头，女孩走到前台的后面。回来的时候女孩拿着包装好了的CD，交给了男孩。他拿了过来，然后走出了这家店。He went home and from then on, he went to that store every day and bought a CD, and she wrapped it for him. He took the CD home and put it in his closet. He was still too shy to ask her out and he really wanted to but he couldn't. His mother found out about this and told him to just ask her. So the next day, he took all his courage and went to the store as usual. He bought a CD like he did every day and once again she went to the back of the store and came back with it wrapped. He took it and when she wasn't looking, he left his phone number on the desk and ran out...男孩回到了家。从那以后，他每天都会来这家店，买一张CD，然后女孩就给他包装起来。男孩把CD带回家，放进他的衣橱里。他还是很害羞，不敢把她约出来。他真的很想，但是他做不到。男孩的母亲知道了此事后，就告诉他，只管把她约出来就好了。于是第二天，男孩鼓起了全部的勇气，像往常一样来到了店里。像过去那样，他还是买了一张CD，而女孩也还是走到后面，回来的时候再把包装好的CD交给他。男孩接了过来，趁女孩不注意，他把他的电话号码留在了桌子上，然后跑了出去…RRRRRING!!!“铃铃铃铃铃铃…”One day the phone rang, and the mother picked it up and said, "Hello?"一天，电话响了起来。男孩的母亲接起电话说道，“你好？”It was the girl!!! The mother started to cry and said, "You don’t know? He passed away yesterday..."是那个女孩！！！男孩的母亲开始哭了起来，说道：“你不知道吗？他昨天就去世了…”The line was quiet except for the cries of the boy's mother. Later in the day, the mother went into the boy's room because she wanted to remember him. She thought she would start by looking at his clothes. So she opened the closet.电话里安静了下来，只听到男孩母亲啜泣的声音。之后，男孩的母亲来到了他的房间，缅怀她的儿子。男孩的母亲想先看一看男孩的衣物。于是她打开了男孩的衣柜。She was face to face with piles and piles and piles of unopened CDs. She was surprised to find all these CDs and she picked one up and sat down on the bed and she started to open one. Inside, there was a CD and as she took it out of the wrapper, out fell a piece of paper. The mother picked it up and started to read it. It said: Hi... I think U R really cute. Do u wanna go out with me? Love, Jocelyn.在她的面前，是一摞又一摞的CD。看到这么多的CD，男孩的母亲感到很惊讶。她随手拿出一张，坐在了男孩床上。她拆开了包装，把CD拿了出来。一张纸条掉了出来。男孩的母亲捡起了纸条，开始读起来。上面写着：你好…我觉得你真的很可爱。你想和我出去约会吗？爱你的，乔瑟琳。The mother was deeply moved and opened another CD...男孩的母亲被深深打动了，拆开了另一张CD…Again there was a piece of paper. It said: Hi... I think U R really cute. Do u wanna go out with me? Love, Jocelyn.又发现了另一张纸条。上面写着：你好…我觉得你真的很可爱。你想和我出去约会吗？爱你的，乔瑟琳。Love is... when you've had a huge fight but then decide to put aside your egos, hold hands and say, "I Love You." 爱就是…当你万般挣扎过后，把自我放到一边，握住对方的手，说：“我爱你。”

向量组的线性相关性及其判断 1．N维向量的定义(注：向量实际上就是特殊的矩阵——行矩阵和列矩阵；默认向量a为列向量)。2．向量的运算： 3．线性组合4．向量组的线性相关性（1）线性相关与线性无关的定义　设 ，若k1,k2,…,kn不全为0，称线性相关；若全为0，称线性无关。（2）判别方法：① r(α1，α 2，…，αn)<n，线性相关； r(α1，α 2，…，αn)=n，线性无关。②若有n个n维向量，可用行列式判别：　n阶行列式||＝0，线性相关（≠0无关）5．极大无关组与向量组的秩（1）定义：最大无关组所含向量个数称为向量组的秩（2）求法：设A＝( a1，a2，…，an )，将A化为阶梯阵，则A的秩即为向量组的秩，而每行的第一个非零元所在列的向量就构成了极大无关组。（3）矩阵的秩等于它的行向量组的秩也等于它的列向量组的秩。

判断曲线渐近线 水平、垂直渐近线斜渐近线y=kx+b

间断点判断 1.找出无定义的点，就是间断点。2.用左右极限判断是第一类间断点还是第二类间断点，第一类间断点包括第一类可去间断点和第一类不可去间断点，如果该点左右极限都存在，则是第一类间断点，其中如果左右极限相等，则是第一类可去间断点，如果左右极限不相等，则是第一类不可去间断点，即第一类跳跃间断点。如果左右极限中有一个不存在，则第二类间断点。间断点可以分为无穷间断点和非无穷间断点，在非无穷间断点中，还分可去间断点和跳跃间断点。如果极限存在就是可去间断点，不存在就是跳跃间断点

博客中动态背景线条跟随鼠标移动，吸附鼠标效果代码 添加方法：将下方代码复制到网站想添加线条跟随鼠标移动效果的页面上方or下方或添加到网站底部模板文件 foot.htm 里面<!--代码放置于</body>上or下方--> <script> !function(){ function n(n,e,t){ return n.getAttribute(e)||t } function e(n){ return document.getElementsByTagName(n) } function t(){ var t=e("script"),o=t.length,i=t[o-1]; return{ l:o,z:n(i,"zIndex",-1),o:n(i,"opacity",.5),c:n(i,"color","0,0,0"),n:n(i,"count",99) } } function o(){ a=m.width=window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth, c=m.height=window.innerHeight||document.documentElement.clientHeight||document.body.clientHeight } function i(){ r.clearRect(0,0,a,c); var n,e,t,o,m,l; s.forEach(function(i,x){ for(i.x+=i.xa,i.y+=i.ya,i.xa*=i.x>a||i.x<0?-1:1,i.ya*=i.y>c||i.y<0?-1:1,r.fillRect(i.x-.5,i.y-.5,1,1),e=x+1;e<u.length;e++)n=u[e], null!==n.x&&null!==n.y&&(o=i.x-n.x,m=i.y-n.y, l=o*o+m*m,l<n.max&&(n===y&&l>=n.max/2&&(i.x-=.03*o,i.y-=.03*m), t=(n.max-l)/n.max,r.beginPath(),r.lineWidth=t/2,r.strokeStyle="rgba("+d.c+","+(t+.2)+")",r.moveTo(i.x,i.y),r.lineTo(n.x,n.y),r.stroke())) }), x(i) } var a,c,u,m=document.createElement("canvas"), d=t(),l="c_n"+d.l,r=m.getContext("2d"), x=window.requestAnimationFrame||window.webkitRequestAnimationFrame||window.mozRequestAnimationFrame||window.oRequestAnimationFrame||window.msRequestAnimationFrame|| function(n){ window.setTimeout(n,1e3/45) }, w=Math.random,y=;m.id=l,m.style.cssText="position:fixed;top:0;left:0;z-index:"+d.z+";opacity:"+d.o,e("body")[0].appendChild(m),o(),window.onresize=o, window.onmousemove=function(n){ n=n||window.event,y.x=n.clientX,y.y=n.clientY }, window.onmouseout=function(){ y.x=null,y.y=null }; for(var s=[],f=0;d.n>f;f++){ var h=w()*a,g=w()*c,v=2*w()-1,p=2*w()-1;s.push() } u=s.concat([y]), setTimeout(function(),100) }(); </script>

常用级数展开式 常用级数展开式

∑(-1)^n/n^p和∑1/n^p收敛发散讨论 暂无简介

ds和dx,dy,cos(τ,y),cos(τ,x)的关系及其cos(n,x)=cos(t,y)，cos(n,y)=-cos(t,x)证明 对向量求偏导，不妨对其求方向导数。 关系证明例题：

第二型曲面积分 第二型曲面积分