The Android SDK Tools

Posted on December 12, 2018 by rpflee

EQL5-Android | Common Lisp for Android App Development 2018

After installing Qt, check whether its version is 5.9 or later.

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If so, install the Android SDK Tools by installing Android Studio.

If you use Ubuntu 18.04 or later, you can use the snap command to install Android Studio.

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Besides installing Android Studio, it also automatically updates Android Studio regularly.

— Me@2018-12-12 02:21:45 PM

Slope parameter

Posted on December 11, 2018 by rpflee

Problem 14.5c4 | Counting states in heterotic SO(32) string theory

c) Are there tachyonic states in heterotic string theory?

Write out the massless states of the theory (bosons and fermions) …

~~~

What is the meaning of $\displaystyle{\alpha'}$ ?

How come $\displaystyle{\alpha' = \frac{1}{2}}$ ?

— Me@2018-12-07 10:43:10 PM

If we consider a rigidly rotating open string, $\alpha'$ is the proportionality constant that relates the angular momentum $J$ of the string, measured in units of $\hbar$ , to the square of its energy $E$ . More explicitly,

$\displaystyle{ \frac{J}{\hbar} = \alpha' E^2 }$

— p.68

$\displaystyle{ J = \frac{1}{ 2 \pi T_0 c} E^2 }$

As anticipated, the angular momentum is proportional to the square of the energy of the string. Comparing with equation (8.69) we deduce that

$\displaystyle{ \begin{aligned} \alpha' &= \frac{1}{2 \pi T_0 \hbar c} \\ T_0 &= \frac{1}{2 \pi \alpha' \hbar c} \end{aligned}}$

These equations relate the slope parameter $\alpha'$ to the string tension $T_0$ .

— p.69

— A First Course in String Theory

The problem of induction 3.2

Posted on December 10, 2018 by rpflee

The meaning of induction is that

we regard, for example, that

“AAAAA –> the sixth is also A”

is more likely than

“AA –> the second is also A”

We use induction to find “patterns”. However, the induced results might not be true. Then, why do we use induction at all?

There is everything to win but nothing to lose.

— Hans Reichenbach

If the universe has some patterns, we can use induction to find those patterns.

But if the universe has no patterns at all, then we cannot use any methods, induction or else, to find any patterns.

However, to find patterns, besides induction, what are the other methods?

What is meaning of “pattern-finding methods other than induction”?

— Me@2012.11.05

— Me@2018.12.10

Miserable in comfort

Posted on December 9, 2018 by rpflee

Money, if it does not bring you happiness, will at least help you be miserable in comfort.

– Helen Gurley Brown

2018.12.09 Sunday ACHK

迷宮直昇機 5.2

Posted on December 9, 2018 by rpflee

Ken Chan 時光機 1.4.2

…

但是，他的學校不正常——在中四和中五的校內考試測驗中，不斷地考核高考課程。所以，他在中四時代開始，已經要鑽研，高考程度和大學程度的物理。

結果，到真正會考時，由於「只會」考核中五程度的東西，他會突然覺得十分容易。

其實，那種快感不難體會。

假設，你現在是中學四年級。

你想像，如果突然之間，那份中四的數學卷，換成中一程度的數學卷。你會有什麼感受？

你不單會覺得如釋重負，而且會有信心，有機會取滿分；即使，那份中一測驗卷的課題，在中一以後，從來未刻意溫習過。

（問：我又不敢說，我一定會滿分。）

我沒有說「一定」。我只是說「覺得有機會」。

試想想，現為中四的你，面對一份中四的數學卷，你夠不夠膽說「有機會取滿分」？

（問：不太敢，因為，那幾乎沒有可能。但是，我明白你的意思。現在要我做回中一的測驗卷，又真的會覺得，一定會高分，可能會滿分。）

其實，那種情形，對現為中四的你而言，並不只是一個「假設」，因為，你現正修讀， G.Maths（核心數學）和 A.Maths（附加數學）。

「附加數」比「基礎數」而言，艱深非常，大部分人也覺得十分辛苦。但是，亦正正是因為「附加數艱深非常」，你才會覺得「核心數容易萬分」。

那又為什麼，會有這個現象呢？

— Me@2018-12-09 09:03:02 PM

EQL5-Android

Posted on December 8, 2018 by rpflee

Common Lisp for Android App Development 2018

The first step to set up EQL5-Android is to install Qt.

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In Ubuntu, if you do not need the most updated Qt, you can just install the Qt-Creator using apt-get.

— Me@2018-12-08 09:18:19 PM

Problem 14.5c3

Posted on December 7, 2018 by rpflee

Counting states in heterotic SO(32) string theory | A First Course in String Theory

At any mass level $\displaystyle{\alpha' M^2 = 4k}$ of the heterotic string, the spacetime bosons are obtained by “tensoring” all the left states (NS’+ and R’+) with $\displaystyle{\alpha' M_L^2 = k}$ with the right-moving NS+ states with $\displaystyle{\alpha' M_R^2 = k}$ .

Similarly, the spacetime fermions are obtained by tensoring all the left states (NS’+ and R’+) with $\displaystyle{\alpha' M_L^2 = k}$ with the right-moving R- states with $\displaystyle{\alpha' M_R^2 = k}$ .

c) Are there tachyonic states in heterotic string theory?

Write out the massless states of the theory (bosons and fermions) …

~~~

Open String:

$\displaystyle{ \begin{aligned} N^\perp &= \sum_{p=1}^{\infty} \alpha_{-p}^I \alpha_p^I \\ L_n^{\perp} &= \frac{1}{2} \sum_{-\infty}^{\infty} \alpha_{n-p}^I \alpha_{p}^I~~~(n \ne 0) \\ L_0^{\perp} &= \alpha' p^I p^I + N^\perp \end{aligned} }$

Closed String:

$\displaystyle{ \begin{aligned} N^\perp &= \sum_{p=1}^{\infty} \alpha_{-p}^I \alpha_p^I \\ \bar N^\perp &= \sum_{p=1}^{\infty} \bar \alpha_{-p}^I \bar \alpha_p^I \\ L_0^\perp &= \frac{\alpha'}{4} p^I p^I + N^\perp \\ \bar L_0^\perp &= \frac{\alpha'}{4} p^I p^I + \bar N^\perp \end{aligned} }$

— A First Course in String Theory

We have the following well-known bosonic string mass formulae $\displaystyle{\alpha' = \frac{1}{2}}$ :

open string:

$\displaystyle{\frac{1}{2} M^2 = N - a}$

closed string:

$\displaystyle{\frac{1}{8} M^2 = N_L - a}$
$\displaystyle{\frac{1}{8} M^2 = N_R - a}$

p.55

— Solutions to K. Becker, M. Becker, J. Schwarz String Theory And M-theory

— Mikhail Goykhman