Proof that $a^b>b^a$ if $a<b$ are integers larger or equal to two and $(a,b)\neq (2,3),(2,4)$
Given $a>b>2$ both positive integers, which of $a^b$ and $b^a$ is larger?
Can I choose to use only Shapiro-Wilk? Hi currently Nagios sends notifications from nagios@server.domain.com, How do I go about configuring this? Thanks I am in trouble with polarization and entanglement. Let's consider three cases : Case 1) : Statistical mixture of $|H\rangle$ and $|V\rangle$ polarized photons Case 2) : Photons in a superposition state $1/\sqrt{2}(|H\rangle+|V\rangle)$ Case 3) : Photons which are entangled with twin ones in $1/\sqrt{2}(|H,H\rangle+|V,V\rangle)$ state Which experiments can be conducted to differentiate the case  statistical mixture from the case  superposition state ?   Which experiments can be conducted to differentiate the case  statistical mixture from the case  entangled photons in superposition state ?   Using a $45^\circ$ polarizer I think you can differentiate case 1/case 2 but not case 1/case 3 I don't know how to differentiate case 1/case 3 except maybe using quantic tomography and Wigner function. Is it true ? Is there any other simpler way ? Thanks a lot for your answer and sorry for this maybe dummy question... How to get permanent token? I really need to get permanent token or dynamic generator. We set job in the server and this service will come to salesforce and get the data. To provide this, I created connected app, got the token from postman by myself and gave it. After a while (approximately 1 day), we faced with session id problem.   What can I do? Character reading from file in Python How to read the following Itinerary What do the abbreviations mean in the following itinerary:     2  EK 641 L 29NOV 2 KBLDXB HK1       I  1630 1905   *1A/E*                      3  EK 344 L 29NOV 2 DXBKUL HK1       3  2140 0835+1 *1A/E*                      4  MH 704 V 30NOV 3 KULMNL HK1       M  1245 1630   *1A/E*                      5  UA 184 Y 01DEC 4 MNLGUM HK1       1  2255 0440+1 *1A/E*                      6  UA 155 Y 02DEC 5 GUMTKK HK1          0820 1008   especially, the numbers (2,2,3,4,5) before KBLDXB, KULMNL.... The letters and numbers before time (I, 3, M, 1) *1A/E*? How do I create a D&D character correctly as a total newbie? ON an American street, but IN a British one. Do the twain ever meet? In the United States, we say that someone lives on a street, whereas I've noticed that British people say in. For instance:     Bubba lives on Washington Street.   Colin lives in Cavendish Avenue.   I believe we both would use at when a number is given. For instance:     Bubba lives at 16 Washington Street.   Colin lives at 7 Cavendish Avenue.   I don't think it matters if it's a road, avenue, street, circle, or lane — as far as I know, in America, we always live on a street. Does it vary in British English, or is it always in? If it varies, what are the rules? I have iterate over numbers in various order. I am able to display them in increasing order, even with steps like:  $ seq --separator="," 1 10 1,2,3,4,5,6,7,8,9,10 $ seq --separator="," 1 2 10 1,3,5,7,9   I am also able to display them in reverse order, neither continuous nor step wise.  $ seq --separator="," 10 1    $ seq --separator="," 10 2 1   No output for above commands.   My shell details:  $ bash --version GNU bash, version 3.2.25(1)-release (x86_64-redhat-linux-gnu) Copyright (C) 2005 Free Software Foundation, Inc.   Let me know how I would be able to display the numbers in descending order? How to determine if Javascript object is an event? When watching US television news or reading US news articles there is this affectation where instead of saying:     "Spotify music-streaming service to launch in U.S. on Thursday" ()   or      "Leading credit rating agency Moody's said on Wednesday that the U.S. government's impeccable credit..." ()   The on preposition is missed out.  Is this just a peculiar US journalistic "news speak" shortcut or do American non-journalist writers write this way too? How to prove that $\lim\limits_{h \to 0} \frac{a^h - 1}{h} = \ln a$ In order to find the derivative of a exponential function, on its general form $a^x$ by the definition, I used limits.  $\begin{align*} \frac{d}{dx} a^x &amp; = \lim_{h \to 0} \left [ \frac{a^{x+h}-a^x}{h} \right ]\\  \\ &amp; =\lim_{h \to 0} \left [ \frac{a^x \cdot a^h-a^x}{h} \right ] \\  \\  &amp;=\lim_{h \to 0} \left [ \frac{a^x \cdot (a^h-1)}{h} \right ] \\  \\ &amp;=a^x \cdot \lim_{h \to 0} \left [\frac {a^h-1}{h} \right ] \end{align*}$  I know that this last limit is equal to $\ln(a)$ but how can I prove it by using basic Algebra and Exponential and Logarithms properties? Thanks Are tile bonuses counted twice if 2 new words are formed? An example:    O  O?   There is a triple letter tile to the right of the bottom O, indicated with a ?.  If I place an X on it, making the words OX (vertical) and OX (horizontal), do I score 50 points (scoring the tile twice) or 34 (scoring it once)? When or why would you use a right outer join instead of left? states:  "In practice, explicit right outer joins are rarely used, since they can always be replaced with left outer joins and provide no additional functionality."  Can anyone provide a situation where they have preferred to use the RIGHT notation, and why? I can't think of a reason to ever use it. To me, it wouldn't ever make things more clear.  Edit: I'm an Oracle veteran making the New Year's Resolution to wean myself from the (+) syntax. I want to do it right How to get Beamer Math to look like Article Math In a LaTeX article, the math characters are more "curvy" than the text characters:  \documentclass[12pt]{article} \begin{document}  $x^2 + y^2 = z^2$ \end{document}     In a beamer presentation, the math characters do not have the same curves:  \documentclass{beamer} \begin{document} \begin{frame}  $x^2 + y^2 = z^2$ \end{frame} \end{document}     Question  How can I get the beamer math to look just like the article math?  I would prefer if the solution was a single line (that I could place at the top of my LaTeX file) as opposed to something that needs to appear next to every piece of math. I'm using pdflatex, and use \includegraphics to include content of figures from PDF. PDF are exported from InkScape.  \begin{figure} [!h]     \centering     \includegraphics[height=3cm]{fig/SUSAN.pdf} \end{figure}   Included PDF or source SVG has same colors. Green has always RGB value (0, 255, 0). Problem occurs when I include this files from LaTeX. In output PDF on some pages colorspace is darker. Even same image on other page has different colourity.  My PDF  . As you can see on page 7 (11 in PDF) USAN areas are bright green, but then on page 5 (9 in PDF) are green points on corners more darker. Show that is $\int_A f$ exists, then so does $\int_A |f|$ Let $f$ be a real-valued function on $A$ in $E^n$. Show that is $\int_A f$ exists, then so does $\int_A |f|$ and $\left | \int_A f\right | \le \int_A |f|$.   I am trying to finish Rosenlicht's Introduction to Analysis and the last chapter is awful. But I do want to finish it because I have come this far. Could someone show me how to do this, so I can at least have some example problems to understand the material. This chapter (Multiple Integrals) really just left more confused than before I started reading the chapter.  Thank you in advance. I have some Python code that makes Raster Attribute Tables for GeoTiffs using GDAL.    In ArcGIS I can see these attribute tables fine and they behave how I like (as classifications) but in QGIS the whole concept of an attribute table seems to be missing.    Is there any way to access a RAT in QGIS? Why does switching to the tty give me a blank screen? After booting to the GUI in 12.04, I attempt to move to the virtual terminal (or shell, or tty) via Ctrl-Alt-F1 (F1 through F6), and the screen remains blank. I have tried all 6 tty instances and the results are the same. Ctrl-alt-F7 brings me back to the GUI without a problem. Any thoughts? This is an unproven proposition I've come across in multiple places.   Suppose $A$ is a commutative Noetherian ring, and $S$ a multiplicative subset of $A$. Then $S^{-1}A$ is Noetherian.  Why is this? I thought about taking some chain of submodules $$ S^{-1}M_1\subset S^{-1}M_2\subset\cdots $$ and pulling back to a chain  $$ M_1\subset M_2\subset\cdots $$ of submodules of $A$ which must eventually stablize. Is there more to it than this? I kind of wary of assuming all submodules of $S^{-1}A$ have form $S^{-1}M$ for $M\leq A$.