IndarKness « Leading the way

Kane vs Alex

Aug 22nd

Kane Hsieh is an amazing guy. He is using Intel X25-18M SSD as same as mine. He is a definitely computer geek. And he is a cyclist,too. It’s really fabulous to find a guy you have so many things to share with. After the cyclists’ exchange, I was thinking the paragraph on the feedback…OK, it’s just joking. The point is, I will get the world’s most special cycling jersey.

OK, it’s late, leave the headquarter and grab a pillow for sleep.

Kane

Summer Note 2-The Adjoint Method

Aug 11th

Posted by IndarKness in Others

No comments

The outline can be listed below:
1. The bounded linear operator, and the continuity definition of a linear operator, which is equivalent to: bounded or continuous at the origin.
2. The dual space, which is defined as a real bounded linear function. The adjoint operator definition:
Let $T:X \to Y$ be a bounded linear operator between Banach spaces X and Y. The adjoint operator $T^{*} : X^{*} \to Y^{*}$ can be constructed as: $T^{*} (F)(x)=F(T(x))$ for all $x\in X, F\in Y^*$
Because every bounded linear operator over a Banach space X can be reconsidered as inner product:
$F(x)=<x,y>$ for all $x\in X$ and $||F||=||y||$ Here y is only linked with F.
So it is a comparatively simple step to define the inner product form of an adjoint operator $y^*$ instead of the function form $T^*$ :
$F_T(x):=<T(x),y>=<x,y^*>$ for all $x\in H$
3. The differentiability definition in a Banach Space:

Gateaux differentiable at $x_0$

$DT(x_0;h):=\lim_{\epsilon \to 0} \frac{T(x_0+\epsilon h)-T(x_0)}{\epsilon}$

Frechet differentiable:

$\lim_{||\delta x||\to 0}\frac{||T(x_0+\delta x)-T(x)-T'(x_0)\delta x||}{||\delta x||}=0$

They are equal when the two equations exist on all $x,\delta x \in X$

The partial Frechet derivative $D_x(x_0,y)$ of an operator:

$\lim_{||\delta x|| \to 0}\frac{||U(x_0+\delta x,y)-U(x_0,y)-D_x(x_0,y)(\delta x)||}{||\delta x||}=0$

Because the differentiability is defined by limit equations, the notion of the chain rule applies to operators that are continuously Frechet differentiable.

Then it comes the optimal question, I had the problem on figuring out the two functions given: $J(\rho,\lambda),E(\rho,\lambda)$ . $J(\rho,\lambda)$ is the cost function and $E(\rho,\lambda)=0$ is the solution of $\frac{\partial \rho(x,t)}{\partial t}+\frac{\partial}{\partial x}(v(\rho)\rho(x,t))=0$ with conditions.

Because $\rho$ is a function of $\lambda$ , $J(\rho,\lambda)$ can be seen as $j(\lambda)$ . Then the book gives 3 conditions assumed, which assume everything is continuously Frechet differentiable. I have some problems here. I can’t understand how he find these 3 assumptions. Hope it will be clear when I reading the calculation part.

I should look up the details on Lagrangian operator. The only thing I know in calculating minimum is Lagrange multipliers. Which is said not work during the semiconductor factory problem. I will update the Algorithm For Solving when I am ready.

Summer Note 1 – Mathematical Models for Control Systems

Aug 1st

Posted by IndarKness in Path to the Truth

1 comment

It has become a problem that nowadays control system is getting complex. To describe, calculate, and optimize production, 3 classical mathematical models are introduced.

1.Discrete event simulation: very accurate but hard to calculate complex models. Probability distribution calculation needed. Distribution functions calculability limited by sample accessibility.

2.Queueing networks: fairly accurate (using average data) but hard to calculate complex models. Only works with steady models (time infinite).

3.Fluid Models (ODE): $\frac{dq(t)}{dt}=\lambda(t)-\sigma(t)$
It describes queue change rate is influx rate minus outflux rate.
It is easy to calculate. But it uses average data (no possibility included), which may lead to trivial results. And $\lambda(t)$ and $\sigma(t)$ are not easy to find.

So the author introduced a new model: Continuum Model
It uses a totally new view. The model doesn’t put too much attention on the physical position. A new attribute is introduced for each item, stage x, from 0% to 100%. Then the completion of a item can be involved into mathematical calculation.
The core equation is:
$\frac{\partial \rho (x,t)}{\partial t}+\frac{\partial}{\partial t}(v(\rho)\rho (x,t))=0$
The function $\rho (x,t)$ is the density, when the stage is x and time is t.

It took me some time to understand the equation. I think it is just like the flood in Yangtze River now. The height of water is the function $\rho (x,t)$ , over position x and time t.
The equation is setup up like this because the change of $\rho (x,t)$ over time(x fixed) is just like the change of the height of water. It is caused by the different velocity of water over position x. The different velocity is describe as the $-\frac{\partial}{\partial t}(v(\rho)\rho (x,t))$ .
Here the author uses $v(\rho)$ , which describe moving speed of 1 item (just like 1 water molecule in Yangtze River).

The velocity $v(\rho)$ is defined by: $v(\rho)=\frac{v_{max}}{1+\int_0^{1}\rho (s, t) ds}$

or by $v(\rho)=v_{max}(1-\frac{\int_0^{1}\rho (s,t) ds}{L_{max}})$ . Here $L_{max}$ is the max load.

I haven’t looking up the article where these two definition come from. But it can be concluded from experience I think.

In this model, the changing chain: influx–WIP–velocity–outflux

mathematics, Note, paper

Lost&Found

Jul 24th

Posted by IndarKness in Way to My Heart

2 comments

It is a blog written in Chinese.

思绪很乱很杂，我各种语言又不好，没有条理请见谅。

引子

这几天事情很多，3天前林说了新加坡现在的状态，让我很无奈。2天前N说了下现在的英国状态，让我更无奈。客观上某个国家的状况会直接影响我的判断，因为我并没有想好我到底要读什么，我只是想着，只要一个比上海平静的地方，过着比民工高级的生活，享受着比屁民更好的福利，就行了。当强烈经济衰退和华人歧视摆在眼前的时候，我就会退缩，因为这些决定不是灵魂决定的，是物质取向的。

今天牛又有一篇老长的文章对数学系的抱怨。的确，三年了，我根本不知道自己要什么，也不知道自己该怎么做。N暑假在家，每天早晨5点起床，就是为了多读一本书，那么OK，我明天也5点起床好了，那么我该读哪本书呢？真的，想不出来，我该读哪本书。除了GRE和Toefl摆在眼前，我必须要背单词，除了这个，我真不知道，自己该读什么，该看什么，该学什么。

More >

Finally it is all over.

Jul 12th

Posted by IndarKness in Way to My Heart

No comments

I can proudly announced that I almost finish all the courses required by Fudan Mathematic School now. After the final exam passed(hope I won’t get an ‘F’) I have to find a new place to put myself in, a college, a workyard or something else.

I am now the oldest student in my school(Compared with other pre-bachelor). How is the passed three years, I don’t know. But I will be informed by the world, in the following months.

lessons

PPP Using Freeradius and Mysql, Controled in Daloradius

Jul 2nd

Posted by IndarKness in Route of Joy

1 comment

There exists PPP VPN on my server. I used auth-file to manage user account before, but it was not efficient. Now, after radius established, almost everything can be done in WEB!!!

PPP can be used as a NAS of Radius, but it is not fully functioned. I cannot send packet of disconnection to PPP from Radius and terminate a user’s connection. But other functions work fine.

I am using ppp, freeradius, mysql and daloradius. It took me a long time on debug. And now it works fine.

Let me pick some pics.

Here is the sql.conf I am using. Hope it helps.

Linux, Radius, Toy, VPN

Maybe the Last Harmonica Video

Jun 14th

Posted by IndarKness in Way to My Heart

2 comments

This is from the youtube video on benq channel.

I am included. Maybe it is the last video I was in with harmonica. It is maybe an end, or a fresh start. Anyway, I should come to life.

harmonica

Refresh

Jun 12th

Posted by IndarKness in Way to My Heart

1 comment

GRE, which can be interpreted as Great Renpin Examination, finally, came to a stop. I didn’t mention the word “end” not only because I am determined to take the GRE test this October again, but also for my endless study life. In the days following, I will live in a new life. Since tomorrow, every ideal time-consuming entry will be on my schedule.
It is a refresh. Hope it for best. Avoiding flooding I will create a new page in my blog. Listing everyday aim and life. Alex IndarKness reloaded.

diary, GRE

Got PhD

Jun 4th

Posted by IndarKness in Others

1 comment

It is such a burden that I have to recite 3000 words in a week. My head is burning now, just as the same feeling as a comet towards the sun. I think I have got PhD already, not the PhD in university, but Permanent head Damage.

GRE, Study

Major Decided

Jun 3rd

Posted by IndarKness in Flight to the Future

No comments

Thanks Great Benny, who helps me to made the major decision. I will pay a lot of money on Studying Actuary for one year, which will become the first step of the flight to my future.
These days GRE really freaks me out. I will, meet the 3 conditions Neal told me, and reclaim. I will make efforts. Just wait and see.

Actuary, Study

IndarKness

Kane vs Alex

Summer Note 2-The Adjoint Method

Summer Note 1 – Mathematical Models for Control Systems

Lost&Found

Finally it is all over.

PPP Using Freeradius and Mysql, Controled in Daloradius

Maybe the Last Harmonica Video

Refresh

Got PhD

Major Decided

Call Me with a US phone

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