I understand that quantum tunneling is a pure example of the uncertainty principle but clearly transistor had to be powered to work properly, anyhow I like to know if it is true that particle must borrow energy to quantum tunnel then quickly pay it back? I thought this is supposed to be probabilistic phenomenon so how does energy come into play?
If we allow that the energy to allow quantum tunnelling through a potential barrier has been borrowed by the Heisenberg energy-time uncertainty relation, from the vacuum energy. How is the borrowed energy paid back?
If I attempt to change my password to nothing by opening "User Accounts", the "Change" button remains greyed out:    How do I change my password to be empty? I know you can set Ubuntu to automatically log you in, but I want my password to be empty, I never want to type in a password to authenticate myself as that user.  I know that there are reasons why this might not be a good idea, but I want to know if it is even possible. I'm using Ubuntu 12.10. Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$ How to prove this for positive real numbers? $$a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$$  I tried AM-GM, CS inequality but all failed. Most games build on other games' successes and many are downright clones. Where is the limit of imitation before legal issues come into play? Is it down to literary or graphic work like characters and storyline that cause legal problems, or can someone actually claim to own gameplay mechanics?  There are so many similar clone games out there that the rules are probably very slack or nonexistent, but I'd like to hear the views of more experienced developers / designers. Why should a CTE start with a semi-colon? A closed form of $\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$ This integral has been bugging me since yesterday:     $$\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$$   I've tried substitution $y={1}/{x}$ and $e^y={1}/{x}$, but those didn't help much. Wolfram Alpha gives me result: $-0.67172$. Could anyone here please help me to obtain the closed form of the integral preferably (if possible) with elementary ways (high school methods)? Any help would be greatly appreciated. Thank you. Delete all files except specified files/folders using command line? I have a folder containing a lot of folders and different files with the following structures :  NASA │ ├── a │   ├── doc1 │   ├── doc2 │   ├── doc3 │   ├── folder1 │   └── folder2 │ ├── b │   ├── doc1 │   ├── doc2 │   ├── doc3 │   ├── folder1 │   └── folder2 │ ├── c │   ├── doc1 │   ├── doc2 │   ├── doc3 │   ├── folder1 │   └── folder2 │ ├─ x ├─ y └─ z          I want to delete the content of the folder (NASA/) except specified folders and files.   For example I want to keep a folder, b folder and x file.     I tried   :   rm !(a/) -r NASA/   And (as explained in the answer ):  find NASA/ -type f ! -iname "x" -delete   But this is not very straight forward and I have to use a bash script.    Am I missing a more easy way ? How can I do this in a single command? My office is going to buy a bulk number of desktop PCs (for developmental purposes).  I encouraged them to buy PCs without a pre-installed OS and then install Linux. My colleagues agree with me but they are not regular users of any Linux-based OS, so they want to choose a Linux OS which is best for our purposes and user-friendly and I suggested Ubuntu.  Now I want some data to support my position, what's so good about Linux and specifically Ubuntu? Show that some monomial ideal is primary Show that $I=(X_{k_1}^{a_1},...,X_{k_s}^{a_s})$ is $(X_{k_1},...,X_{k_s})$-primary.   I noticed  that $$\sqrt{({X_{i_1}}^{a_1},...,{X_{i_k}}^{a_k})}=\sqrt{({X_{i_1}}^{a_1})+\cdots+({X_{i_k}}^{a_k})}=\sqrt{\sqrt{(X_{i_1})^{a_1}}+\cdots+\sqrt{(X_{i_k})^{a_k}}}=\sqrt{(X_{i_1})+\cdots+(X_{i_k})}=\sqrt{(X_{i_1},...,X_{i_k})}=(X_{i_1},...,X_{i_k}).$$ I have to show that $I$ is $P$-primary (where $P=(X_{k_1},...,X_{k_s})$), i.e., if $u v\in I$ then $u\in I$ or $v\in P$. I tried to prove that if $u\notin I$ and $v\notin P$ then $uv\notin I$. (There is a similar question, but the answer is too hard for me.) How can I strike through an expression (e.g. "2x") obliquely, e.g. from bottom left to top right, so as to indicate cancellation? With the \sout command from the ulem package, I can only strike horizontally. Suppose $\sqrt6 = \frac pq$ where $p$ and $q$ have no common factors.  $$6 = \frac {p^2}{q^2}$$  $$6p^2 = q^2$$  So $q^2$ and therefore $q$ is divisible by $6$.   $$p^2 = \frac {q^2}{6}$$  So $p^2$ and therefore $p$ is divisible by $6$.   S0, $p$ and $q$ have a common factor $6$. Contradiction.  Therefore $\sqrt6$ is irrational.  Does the proof work? Access a glyph on fontspec using a GID (Glyph ID) I'm trying to access a glyph, but it's only mentioned in the "Basic Latin and Latin 1" set for a font. The glyph has no name or unicode ID, but it does have a glyph ID or GID. fontspec doesn't mention possibilities for using this glyph. Neither does Adobe in the adobe feature file syntax:   I'd still like to be able to access a glyph through its ID, since it's the only way I can access it (I think).  My specific case requires to access the glyph ID 554 from Stevens Titling Pro Sable Brush. I will only post this font if it's strictly necessary, since I don't like to distribute these fonts to the wide world.  I posted an MWE containing another (free) font. This is not the font I intend to use, but perhaps a starting point to try and access glyphs manually.   \documentclass{article}  \usepackage{fontspec} \setmainfont{EB Garamond}  \parindent=0pt \begin{document}  Some text int EB Garamond. How can I access glyph 123 now?  \end{document} Using the same secret key for encryption and authentication in a Encrypt-then-MAC scheme Is it a weakness to use a single shared secret for protecting messages using a Encrypt-then-MAC scheme?    Assuming a system is using AES-256-CBC and a SHA1-HMAC and the same secret key for both operations.  Upon intercepting one of these messages and attacker could brute force this secret key by trying to solve the HMAC or by successfully decrypting the first block of the ciphertext.  Performing  a decryption on a single block of AES-256 should be a lighter operation than performing a SHA1-HMAC on a potentially large message.  Therefore AES-256 is ideal for a massively parallel brute-force attack and the use of the SHA1-HMAC doesn't hurt the system.  Is this approach sound, or is there an attack that has not been taken into consideration? For a vector space $V$ and a linear operator $f : V \to V$, under what conditions does $V = \ker(f) \oplus \operatorname{im}(f)$?  Is it always true, or only in special cases?  Edit: $V$ is finite dimensional. Getting error using JMeter behind a proxy I am new to JMeter and trying to run a test from behind a corporate proxy. I read on the same from apache site and followed the same process so as to run the test. However, i am still  unable to record a test from behind the proxy.      This message always appears after pressing on 'Start' recording:     After that, I have changed apache port to 8000 as in below and made it different      This time after pressing on start was this message Numbering in algorithmicx I have simple code:  \documentclass{article}  \usepackage{algorithm}  \usepackage{algpseudocode}  \begin{document}  \begin{algorithm}   \caption{Examples}\label{alg:Examples}   \begin{algorithmic}[1]   \State $X=45$   \State $X=45$   \State $X=45$   \State $X=45$   \State $X=45$    \end{algorithmic} \end{algorithm}          \end{document}     How to put a point after the number of the algorithm? I use chapters in report:  \documentclass[a4paper,12pt]{report}  \usepackage{algorithm}  \usepackage{algpseudocode}  \begin{document}  \chapter{Chapter 1}  \begin{equation} X_2=4 \end{equation}  \begin{algorithm}   \caption{Examples}\label{alg:Examples}   \begin{algorithmic}[1]   \State $X=45$   \State $X=45$   \State $X=45$   \State $X=45$   \State $X=45$    \end{algorithmic} \end{algorithm}  \end{document}     How to change the numbering to take into account the chapters? How do electrons jump orbitals? My question isn't how they receive the energy to jump, but why.  When someone views an element's emission spectrum, we see a line spectrum which proves that they don't exist outside of their orbitals (else we would see a continuous spectrum).  Electrons can be released in the form of beta decay, thus proving that they are capable of traveling outside of orbitals contrary to the statement my teacher said that they stay within orbitals. Then, to add to the confusion, the older model of rings floating around a nucleus has, from what I can tell, been outdated, which would support this model. My teacher's explanation was that the electrons made a quantum jump of some kind. How do electrons move between orbitals or do we know how they jump, excluding the reason that energy causes them to jump, and why are positrons formed sometimes instead of electrons in Beta decay?  When I'm asking "how do electrons jump" I would like to know how an electron can jump between each orbital such as how it moves and how it knows where to jump since it appears to be a jump where the electron doesn't slow into a orbital position. Specifically how they jump what is this Atomic electron transition, I understand that they jump and that they do this through absorbing and releasing energy but what is this Atomic electron transition other than what is already on the wikipedia article . I need something explained or corrected:  In my number theory class we proved that there are an infinite number of primes using Euler's Phi Totient. It went something like this:  Let $M = p_1 p_2 \dots p_n$ be the product of all primes. Consider $1 &lt; A \le M$:  Some prime must divide $A$, call it $q$. Since $q$ must be one of the primes, $q$ must divide $M.$  So the $gcd(A,M) &gt; 1.$ Thus $\phi(M) = 1$ ...?   Which is not even and contradicts the theorem that $\phi(N)$ is even for $N&gt;2.$ Therefore there exists an infinite number of primes.  I get confused by the statement "Thus $\phi(M) = 1$"....  Did i possibly copy this proof down wrong? or am I missing something? Thank you in advance.   Edit: by consider a such that...i meant consider an integer '$a$' I replaced it with $A$ to hopefully make it more clear.   Edit2: I'm sorry I am not familiar with using the equation editor. This is not a homework assignment, just studying for my exam. I just want to be able to understand this or clearify it. How much willpower do gravely wounded soldiers lose? The text says they suffer a permanent reduction? Degree of Field Extensions and $F(\alpha)$ Suppose that $[F(\alpha):F]$ is odd. Show that $F(\alpha)=F(\alpha^{2})$. Generalize this statement if possible.    Clearly, we always have that $F(\alpha^{2}) \subset F(\alpha)$ by definition of the field generated by $F$ and $\alpha$ (assuming that we have a field extension $K/F$ where $\alpha \in K$). However, how can we show the other inclusion? If the degree is odd, then it follows that $\alpha$ will solve a polynomial of odd degree in $K[x]$ (for the coefficients in $F$). What would be a way to proceed from here? (and as well to generalize the statement?)  I was thinking of using the formula: $[F(\alpha):F]=[F(\alpha):F(\alpha^{2})][F(\alpha^{2}):F]$ and maybe proceed from there.   Thanks for the help. How are local variables referenced in closures?