Log-in bug with Area 51
Cannot log into Area 51 with OpenID
One of the answers in a reading exercise in my class today was:   100,000,000,000,000,000,000   ... which was the value of the highest denomination note ever issued. It was a 100,000,000,000,000,000,000 Pengo note, issued by Hungary in 1946. The students in my class wanted to know how they could say that last sentence in words in English. So I told them that I didn't know. They pointed out to me that if they wanted to read this bit of writing to someone they'd want to be able to use the words. Fair point.  Can anyone help?  [In case you're interested, a 100,000,000,000,000,000,000 Pengo note was worth about $0.20!] How can you print a variable name in python? Say I have a variable named choice it is equal to 2. How would I access the name of the variable? Something equivalent to  In [53]: namestr(choice) Out[53]: 'choice'   for use in making a dictionary. There's a good way to do this and I'm just missing it.  EDIT:  The reason to do this is thus. I am running some data analysis stuff where I call the program with multiple parameters that I would like to tweak, or not tweak, at runtime. I read in the parameters I used in the last run from a .config file formated as  filename no_sig_resonance.dat  mass_peak 700  choice 1,2,3   When prompted for values, the previously used is displayed and an empty string input will use the previously used value.  My question comes about because when it comes to writing the dictionary that these values have been scanned into. If a parameter is needed I run get_param which accesses the file and finds the parameter.   I think I will avoid the problem all together by reading the .config file once and producing a dictionary from that. I avoided that originally for... reasons I no longer remember. Perfect situation to update my code! Should I mention my Canadian visa refusal in my UK visa application? How to find the joint PDF? Ley X,Y two random variables with density $f(x,y)=8xy \  \text{if} \   0&lt;x&lt;y&lt;1$  Find the joint distribution F(x,y).  I find that $F(x,y)=2x^2y^2-x^4\ \text{  if}  \ 0&lt;x&lt;y&lt;1$ but I dont know how to find the didtribution in other points. Why are place names in some old books a capital letter followed by dashes, and what is this phenomenon called? This is something very odd I have noticed in some older books, most recently in "Crime and Punishment" by Dostoyevsky.  Place names, when not specifically essential or well-known, are made up of one letter followed by a line of underscores (i.e. "X_____").  I think I recall reading something similar in another older work, possibly by Jane Austin?  Apologies if this is a duplicate; I've searched quite extensively and can't seem to figure it out.  I don't know a name for this, so can't search easily for it. This question has bugged me for a while. I want to write a nested function, f(g(x)). If I naively enter it:  \begin{align}     f(g(x))=y \end{align}     The problem is that each and every parenthesis is the same size as all of the others. Shouldn't the outer parentheses be larger? But if I do this:  \begin{align}     f\left(g(x)\right)=y \end{align}     Now it looks even less like the functions are nested. What's the proper way to do this? Recall the definition of the Weyl Chambers: A Weyl Chamber is a region of $V \setminus \bigcup_{\alpha \in \Phi} H_{\alpha}$, where $V$ is underlying Euclidean space, and $H_\alpha$ the hyperplane that is perpendicular to $\alpha$ the elements of  $\Phi$ in $V$.   I want to show that:   The Weyl chambers are open, convex and connected.   My attempts:   A single hyperplane $H_\alpha$ separates the space $V$ into two half-spaces: positive half-space $H_\alpha^+=\{x \in V \mid (\alpha,x)&gt;0\}$ and negative half-space $H_\alpha^-=\{x \in V \mid (\alpha,x)&lt;0\}$. It is clear that $V \setminus H_\alpha = H_\alpha^+\cup H^-_\alpha.$ As the result, the Weyl chambers can be regarded as components of  $$V \setminus \bigcup_{\alpha \in \Phi} H_{\alpha}= \bigcap_{\alpha \in \Phi} \left( V \setminus H_{\alpha} \right)= \bigcap_{\alpha \in \Phi} \left( H_\alpha^+\cup H_\alpha^- \right).$$ By the discussion above, a Weyl chamber is simply a $\textbf{intersection}$ of finite half-spaces. It is the case since one may write $$\left( H_\alpha^+\cup H_\alpha^- \right) \cap \left( H_\beta^+\cup H_\beta^- \right) =\left( H_\alpha^+\cap H_\beta^+ \right)  \cup\left( H_\alpha^+\cap H_\beta^- \right)  \cup \left( H_\alpha^-\cap H_\beta^+ \right)  \cup\left( H_\alpha^-\cap H_\beta^- \right).$$ Therefore openness and convexity of the Weyl chambers are straightforward since half-spaces are open and convex, so are their intersections. Moreover, we would replace $V$ by $\Bbb R^{\dim V}$ since they are isomorphic. Now we can prove that the Weyl chamber is connected by showing that every convex set in $\Bbb R^{\dim V}$ is connected. And I'm sure that proof of this statement existed. So am I done? How to make putty to not break my session after some time? How to draw open-close interval in LaTeX I am using the following commands to have half-open interval in a real line:   \begin{tikzpicture}[scale=7] \draw[-&gt;, thick] (-0.1,0) -- (1.7,0); \foreach \x/\xtext in {0/8,0.2/$S_1$,0.4/$T_4$,0.6/$S_3$,0.8/$T_2$,1/$S_3$,1.2/14,1.4/$S_3$,1.6/16}     \draw[thick] (\x,0.5pt) -- (\x,-0.5pt) node[below] {\xtext}; \draw (0.2,0.5pt) node[above] {$c$}; \draw[[-), ultra thick, blue] (0.2,.01) -- (.4,0.01); \draw[(-, ultra thick, green] (0.6,.02) -- (1,0.02); \end{tikzpicture}   Now, I need to have an open-close interval, but I am not able to have that close interval at the end, using the following command:  \begin{tikzpicture}[scale=7] \draw[-&gt;, thick] (-0.1,0) -- (1.7,0); \foreach \x/\xtext in {0/8,0.2/$S_1$,0.4/$T_4$,0.6/$S_3$,0.8/$T_2$,1/$S_3$,1.2/14,1.4/$S_3$,1.6/16}     \draw[thick] (\x,0.5pt) -- (\x,-0.5pt) node[below] {\xtext}; \draw (0.2,0.5pt) node[above] {$c$}; \draw[(-], ultra thick, green] (0.6,.02) -- (1,0.02); \end{tikzpicture}   May I ask for anybody help? Generated Frattini Lemma Let $A$ be a normal subgroup of a group $G$. Let $B$ be a subgroup of   $A$ with the property that whenever $B_1 \leq A$ is conjugate to $B$   in $G$ then it is conjugate to $B$ in $A$. Prove that $G=AN_G(B)$   Help me some hints. Let  $f(xy) =f(x)f(y)$ for all $x,y\geq 0$. Show that $f(x) = x^p$ for some $p$.    I am not very experienced with proof. If we let $g(x)=\log (f(x))$ then this is the same as  $g(xy) = g(x) + g(y)$   I looked up the hint and it says let $g(x) = \log f(a^x) $   The wikipedia page for functional equations only states the form of the solutions without proof.  Attempt  Using the hint (which was like pulling a rabbit out of the hat)  Restricting the codomain $f:(0,+\infty)\rightarrow (0,+\infty)$ so that we can define the real function $g(x) =  \log f(a^x)$ and we have $$g(x+y) = g(x)+ g(y)$$   i.e $g(x) = xg(1)$ as $g(x)$ is continuous (assuming $f$ is).  Letting $\log_a f(a) = p$ we get $f(a^x) =a^p $. I do not have a rigorous argument but I think I can conclude that $f(x) = x^p$ (please fill any holes or unspecified assumptions) Different solutions are invited How to replace plain URLs with links? How do I install and manage GNOME Shell extensions? I'm trying to change the cpu frequency on my laptop (running Linux), and not having any success. Here are some details:    # uname -a Linux yoga 3.12.21-gentoo-r1 #4 SMP Thu Jul 10 17:32:31 HKT 2014 x86_64 Intel(R) Core(TM) i5-3317U CPU @ 1.70GHz GenuineIntel GNU/Linux  # cpufreq-info cpufrequtils 008: cpufreq-info (C) Dominik Brodowski 2004-2009 Report errors and bugs to cpufreq@vger.kernel.org, please. analyzing CPU 0:   driver: intel_pstate   CPUs which run at the same hardware frequency: 0   CPUs which need to have their frequency coordinated by software: 0   maximum transition latency: 0.97 ms.   hardware limits: 800 MHz - 2.60 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 800 MHz and 2.60 GHz.                   The governor "powersave" may decide which speed to use                   within this range.   current CPU frequency is 2.42 GHz (asserted by call to hardware). (similar information for cpus 1, 2 and 3)  # cat /sys/devices/system/cpu/cpu0/cpufreq/scaling_available_governors performance powersave   I initially had the userspace governor built into the kernel, but then I also tried building it as a module (with the same results); it was loaded while running the above commands (and I couldn't find any system messages when loading it):  # lsmod Module                  Size  Used by cpufreq_userspace       1525  0 (some other modules)   And here are the commands I tried for changing the frequency:  # cpufreq-set -f 800MHz Error setting new values. Common errors: - Do you have proper administration rights? (super-user?) - Is the governor you requested available and modprobed? - Trying to set an invalid policy? - Trying to set a specific frequency, but userspace governor is not available,    for example because of hardware which cannot be set to a specific frequency    or because the userspace governor isn't loaded?  # cpufreq-set -g userspace   Error setting new values. Common errors: - Do you have proper administration rights? (super-user?) - Is the governor you requested available and modprobed? - Trying to set an invalid policy? - Trying to set a specific frequency, but userspace governor is not available,    for example because of hardware which cannot be set to a specific frequency    or because the userspace governor isn't loaded?   Any ideas? Word for person who looks for flattery I have:  \documentclass[a4paper,11pt]{report}   with no special customisation.  In one page, at the end of a section, I have a big figure with two paragraphs of text below it, and these two paragraphs are not enough to fill up the rest of the page.  When I use the \documentclass as above I get some extra white space at the end of the page, which is fine: the vertical spacing from the figure caption and between the two paragraphs is standard and correct.  But if I switch to:  \documentclass[a4paper,11pt,twoside]{report}   I get extra blank space between the figure caption and the 1st paragraph and also between the 1st and 2nd paragraph.  I want to use twoside to set the headings with fancyhdr. How can I get rid of these ugly white spaces? 'I have decided to purchase a jet for getting to NYC and back more quickly.' Are the following sentences grammatical or not? If not, does substituting a to-infinite make them grammatical? (Optional: designate if the sentence expresses purpose, reason, aim, or function)  1 I have decided to purchase a jet for getting to NYC and back more quickly. 2 I have decided to buy a jet for having a quicker way to get to NYC and back.  This is my only reason and aim; this will be the jet's only purpose and function.  3 I hate hairdryers, so I am buying a space heater for drying my hair more naturally, and that is my only aim &amp; purpose &amp; reason and that will be its only function 4 For having a lasting shine in your hair, buy ShineOn Shampoo. 5 My neighbor and I have decided to cooperate more for having a better life together.   Research done: ELL  (Note the  here is a restatement of Cambridge Dictionary's ) ELL  ELL  BBC English  (Currently the best site I've found.) ELU  All of which have answers that I find  (i) incomplete (ii) contradictory (iii) terribly confusing, if not (iv) wrong. To sort through the haze, I am focusing on one issue. Background Some sources say that you need to use a to-infinitive for expressing purpose, aim, function, reason, etc. I find these to be rather hazy distinctions, given that the ODO defines  as The reason for which something is done or created or for which something exists and the same work lists as : aim, reason, function, etc. It is my assertion that at least some of the following sentences demonstrate that one can use the -ing form (be it a gerund, verbal noun, participle) to express individual purpose (aim, reason, function, intention, whatever you want to call it). Do you agree, or not? Why (not)?  In shorter terms, are the sentences grammatical? or do we have to substitute a to-infinitive (including in order to + infinitive) to make them grammatical? (Optional: designate if the sentence expresses purpose, reason, aim, function, etc.) Not able to execute a .sh file: /bin/bash^M: bad interpreter I wanted to execute a shell script:  -rwxr-x--x 1 root root   17234 Jun  6 18:31 create_mgw_3shelf_6xIPNI1P.sh   I tried to do a standard procedure, but I got this error:  ./create_mgw_3shelf_6xIPNI1P.sh  localhost 389 -l /opt/fews/sessions/AMGWM19/log/2013-06-06-143637_CLA-0  DEBUG   cd/etc/opt/ldapfiles/ldif_in ; ./create_mgw_3shelf_6xIPNI1P.sh  localhost 389 -l /opt/fews/sessions/AMGWM19/log/2013-06-06-143637_CLA-0 **ERROR  sh: ./create_mgw_3shelf_6xIPNI1P.sh: /bin/bash^M: bad interpreter: No such file or directory**   What does it mean? I was doing this as the root user under the root group.  Does it mean that the file does not have the correct permission for the root user? Customized prompt does not hold when a child bash is ran I have been learning bash, and while doing so I played around with the .bash_profile file to be able to put greeting messages etc. Later I just removed these changes. But after doing that my default configuration of prompt got lost: originally, the prompt was all in bold, and \w part was blue so that when I was in a deeply nested directory the prompt would not seem so entangled. I think that was the default for Ubuntu (correct me if i'm wrong), however like  I said it got lost and my prompt was non-bold and monochromatic resulting in a mess when I'm in long named directories.  So, last night I tried customizing my prompt in the fashion I mentioned above. It worked well after I added the code to .bash_profile  Code was like this:  export PS1="\[$(tput bold)\]\u@\h:\[$(tput sgr 0)\]\e[1;34m\w$ \e[m"   However if I try to run another bash shell in the current one, the prompt becomes unformatted:    Is that normal? Isn't the whole point of exporting a variable to make it accessible from all the child processes forked from that shell? Why it doesn't that apply to this situation? How can we recover the Newtonian gravitational potential from the metric of general relativity? The Newtonian description of gravity can be formulated in terms of a potential function $\phi$ whose partial derivatives give the acceleration:  $$\frac{d^2\vec{x}}{dt^2}=\vec{g}=-\vec{\nabla}\phi(x)=\left(\frac{\partial\phi}{\partial x}\hat{x}+\frac{\partial\phi}{\partial y}\hat{y}+\frac{\partial\phi}{\partial z}\hat{z}\right)$$  However, in general relativity, we describe gravity by means of the metric. This description is radically different from the Newtonian one, and I don't see how we can recover the latter from the former. Could someone explain how we can obtain the Newtonian potential from general relativity, starting from the metric $g_{\mu\nu}$?