把光学软件啊什么的地址全都删掉了~ sorry~

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Category Archives: study

Powers of Ten - Units - Dimensions - Measurements - Uncertainties - Dimensional Analysis - Scaling Arguments

2013.05.8 , , Powers of Ten - Units - Dimensions - Measurements - Uncertainties - Dimensional Analysis - Scaling Arguments已关闭评论 , 2,116 views

首先是一个小视频,从1e+24到1e-16,

测量,误差精度很重要!误差永远存在!

假设动物的尺寸是S,质量是M,骨骼长度为L,骨骼的横截面是A

{l \propto s}

{m \propto {s^3} \propto {l^3}}

{preause \propto \frac{{weight}}{A} \propto \frac{m}{{{d^2}}}}

Now follow me closely.

If the pressure is higher than a certain level the bones will break.

Therefore, for an animal not to break its bones when the mass goes up by a certain factor let's say a factor of four in order for the bones not to break d squared must also go up by a factor of four.

That's a key argument in the scaling here.

You really have to think that through carefully.

Therefore, I would argue that the mass must be proportional to d squared.

This is the breaking argument.

Now compare these two.

{m \propto {d^2}}

{{d^2} \propto {l^3} \Rightarrow d \propto {l^{\frac{3}{2}}}}

这里就是推导出来的长度以及骨骼的厚度的关系了(尽管事实上是不正确的。。。)

然后是单位的匹配。纲量分析。

假设苹果质量m,从高度h落下,时间为t,

{t \propto {h^\alpha }{m^\beta }{g^\gamma }}

{{{[T]}^1} = {{[L]}^\alpha }{{[M]}^\beta }\frac{{{{[L]}^\gamma }}}{{{{[T]}^{2\gamma }}}}}

{\beta = 0}

{\alpha + \gamma = 0}

{1 = - 2\gamma }

{t = C\sqrt {\frac{h}{g}}\propto\sqrt h }

不确定度的计算

Technology and Invention in Finance

2013.04.21 , , Technology and Invention in Finance已关闭评论 , 1,835 views
Overview:

Technology and innovation underlie finance. In order to manage risks successfully, particularly long-term, we must pool large amounts of risk among many, diverse people and overcome barriers such as moral hazard and erroneous framing. Inventions such as insurance contracts and social security, and information technology all the way from such simple things as paper, and the postal service to modern computers have helped to manage risks and to encourage financial systems to address issues pertaining to risk. The tax and welfare system is one of the most important risk management systems.

这节课开始讲的一些保险方面的问题,这就是一个风险分摊这样的意思,就是比如很多人买了一个保险,可是真的出事的并不会所有人都出事是吧,那么出事的那个人所遭受的灾难在得到补偿的时候平分到所有买保险的人身上。。。(这个浅显的道理我好像以前没有注意到。。。)然后这里还讲到的一个重要的词就是道德危险,就是说保险这个事上很多在有嫌似诈骗或者说故意为了保险金的事。以及后续的保险的判断上(判断标准确实很难,很多时候。)

后面还有提到的是一个轮子的故事,还有邮票啊什么的,网络。

The Universal Principle of Risk Management: Pooling and the Hedging of Risks

2013.04.21 , , The Universal Principle of Risk Management: Pooling and the Hedging of Risks已关闭评论 , 1,906 views
Overview:

Statistics and mathematics underlie the theories of finance. Probability Theory and various distribution types are important to understanding finance. Risk management, for instance, depends on tools such as variance, standard deviation, correlation, and regression analysis. Financial analysis methods such as present values and valuing streams of payments are fundamental to understanding the time value of money and have been in practice for centuries.

 

我记下这些就像课程笔记一样,或者说我不想看过了然后过了几天就忘了,想要记起一些东西来还得去重看那么一段视频。

这节课主要讲的是高数里面的概率这个东西,如果你是学数学或者比较了解的话会好懂很多。这里截取一些课程pdf里面的公式,其实我是比较懒,虽然wordpress我也有装一些能显示公式的插件,但还是截屏比较方便。然后,WLW确实是一个好东西,离线博客编辑,谁用谁知道。哈哈~

这节课的后面有些忘记了。前几天看的没想写下来,现在想记起来有些难。。。所以说,好记性不如烂笔头。。。是这么说的么。

Probability P, 0<P<1
• Multiplication rule for independent events: Prob(A and B) = Prob(A)*Prob(B)
• Probability of n independent accidents = P^n
• Probability of x accidents in n policies (Binomial Distributon):    

f(x) = {P^x}{(1 - P)^{(n - x)}}n!/(x!(n - x)!)

Expected Value, Mean, Average

9674609

Variance and Standard Deviation

• Variance (^2)is a measure of dispersion
• Standard deviation is square root of variance

9867062

Covariance
• A Measure of how much two variables move together

9921000

Correlation
• A scaled measure of how much two variables move together

10003640

Present Discounted Value (PDV)
• PDV of a dollar in one year = 1/(1+r)
• PDV of a dollar in n years = 1/(1+r)^n
• PDV of a stream of payments x1,..,xn

10137890

Consol and Annuity Formulas
• Consol pays constant quantity x forever
• Growing consol pays x(1+g)^(t-1) in t 
• Annuity pays x from time 1 to T

10206656