Why does the frequency of a wave does not change on reflection and on transmission?
Why doesn't the frequency of light change during refraction?
Facebook changed how their API serves profile pictures that are requested with a non-application scope UID. Now because before Graph API 2 all applications shared the original UID, if users like me has joined Stack Exchange websites before  2, rolling out their profile pictures are not shown properly. Facebook suggests to use an access token to query those profile pictures, either an application access token or a user access token. A user access token is not a reliable option at all, because it would only work for users who joined website with Facebook and are currently logged in. Application access tokens, by the way, can be used by creating sort of a proxy that would retrieve a profile picture from Facebook and display it. Yet still it's not perfect. I think the best solution is to communicate with Facebook and ask them to offer an opportunity to convert old Graph API 1 UID's to application scope user IDs. Stripped out bottom bracket The bottom bracket of my bike was completely stripped to the point that when you push the left side crank arm, the right crank moves and you can see the bottom bracket lock move out the frame. The bike shop tried putting Teflon tape but it's temporary. It's a 26' xc hard tail. For all I know both sides of the bottom bracket(square tapered) are stripped clean hence the Teflon tape put by the previous owner. Can I fix the problem by changing into a hallow tech cranks because it works like a thread less bb, or should I just buy a thread less square tapered bb? Any suggestion on what to do? Could the Olympians use modern celestial weapons? Instead of using short range celestial bronze (CB) weapons like swords and arrows why not make advanced weapons like machine guns or grenades with CB shrapnel in it? The default in lyx is to have   I. First part (roman number)   Section 1   1.1 Subsection 1  and I'd like to have   First part (arabic number)   1.1 Section 1  1.1.1 Subsection 1  etc.   Any suggestion? Thanks a lot in advance! What is the Euler Totient of Zero? Wolfram MathWorld defines the Euler Totient function as follows:  The totient function phi(n), also called Euler's totient function, is defined     as the number of positive integers &lt;=n that are relatively prime to (i.e., do  not contain any factor in common with) n, where 1 is counted as being  relatively prime to all numbers   By this definition would $\phi(0)=0$? I don't understand an answer. Should I add a comment, or post a new question? I recently (today) asked a question that received what seems to be a clear, concise answer, but one that's beyond my ability to understand (I'm at the cut-and-paste stage with JavaScript, and the answer seems to assume more knowledge than I actually have).  Is it considered better to ask follow-up questions as comments to the answer given, or should I post "fresh" questions to Stack to help me understand the answer that's been given? How long does the ubuntu installation take and what to do after it? Reverse String order How does LSTM prevent the vanishing gradient problem? LSTM was invented specifically to avoid the vanishing gradient problem. It is supposed to do that with the Constant Error Carousel (CEC), which on the diagram below (from ) correspond to the loop around cell.  (source: ) And I understand that that part can be seen as a sort of identity function, so the derivative is one and the gradient stays constant. What I don't understand is how it does not vanish due to the other activation functions ? The input, output and forget gates use a sigmoid, which derivative is at most 0.25, and g and h were traditionally tanh. How does backpropagating through those not make the gradient vanish ? "Reflexive only" verbs English can use a lot of verbs in a reflexive context. Even ones that usually are used intransitively.     I laugh myself silly.   However, it seems like there are very few – perhaps no – verbs that ONLY work in a reflexive context.  Are there any? Script at Startup The repository 'http://dl.google.com/linux/chrome/deb stable Release' does not have a Release file After executing this command  sudo apt-get update &amp;&amp; sudo apt-get -y upgrade   I get this error  W: The repository 'http://dl.google.com/linux/chrome/deb stable Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details.   I've seen past inquiries on same issue but the answers given are specific to other repositories.  Any help will be appreciated. How many $6$-integer subsets of $\{1, 2, 3, \ldots, 20\}$ have no consecutive integers? I have to determine how many six-integer subsets of $\{1, 2, 3, \ldots, 20\}$ are possible if no two consecutive integers are in a set. Help me identify this fantasy book about two near-omnipotent wizard run empires Linearization of PDE: $0$ is an eigenvalue since all translates of travelling waves are also travelling waves Sci-Fi short story that involved time travel and a couple who keep losing each other I read a collection of Sci-Fi short stories back in the 1970's or early 80's that had one about a couple in love who kept losing each other. The book was my dad's so the story itself could be much older than that. I am very fuzzy on the details as I was young when I read it and it was so long ago. I believe the woman/girlfriend was "taken" (by some bad guy aliens??) while she was sleeping. I think it involved time travel and the man had to search through time to find her. After he found her, when he was asleep one time, he somehow was then "taken" and I think transported through time and had to fight his way back to her again. He may have been some sort of police officer. I just remember in the end, at night when they went to bed, the couple always wore handcuffs so they were never separated when they went to sleep ever again. Does this ring a bell with anyone?  (There is a possibility it is in a short story collection that also contained " The Twonky " by Lewis Padgett (1942), as I remember reading that story around the same time) Algorithm for offsetting a latitude/longitude by some amount of meters $X$ is homeomorphic to $X\times X$ (TIFR GS $2014$) Question is :  Suppose $X$ is a topological space of infinite cardinality which is homeomorphic to $X\times X$. Then which of the following is true:   $X$ is not connected. $X$ is not compact $X$ is not homeomorphic to a subset of $\mathbb{R}$ None of the above.   I guess first two options are false.  We do have possibility that product of two connected spaces is connected.  So, $X\times X$ is connected if $X$ is connected. So I guess there is no problem.  We do have possibility that product of two compact spaces is compact.  So, $X\times X$ is compact if $X$ is compact. So I guess there is no problem.  I understand that this is not the proof to exclude first two options but I guess the chance is more for them to be false.  So, only thing I have problem with is third option.  I could do nothing for that third option..  I would be thankful if some one can help me out to clear this.  Thank you :) Construction of uncountably many non-isomorphic linear (total) orderings of natural numbers I would like to find a way to construct uncountably many non-isomorphic linear (total) orderings of natural numbers (as stated in the title).  I've already constructed two non-isomorphic total orderings. They are $$ 1 &lt; 2 &lt; 3 &lt;\ldots\\ 1 &gt; 2 &gt; 3 &gt;\ldots $$ where "$&lt;$" and "$&gt;$" are  strict total ordering relations.  Thanks in advance for your help. How to add spaces at every X digit in a binary or hexadecimal number? I would like to format binary or hexadecimal numbers with a space separator at each 2 or 4 digit (or any other value like 8 digit or more).  A small picture is better than a long explanation, here is what I would like to do:    As you can see in this mwe, I use the fmtcount package with padzeroes:      \documentclass{article}     \usepackage[utf8]{inputenc}         \usepackage[T1]{fontenc}               \usepackage{fmtcount}     \begin{document}             Binary value : {\padzeroes[16]\binarynum{129}}$_{(2)}$ %             should display 0000 0000 1000 0001$_{(2)}$              Hexadecimal value: {\padzeroes[8]\Hexadecimalnum{65000}}$_{(16)}$ %             should display  00 00 FD E8$_{(2)}$     \end{document}   What I want to do is displaying numbers with various radix (2, 3, 7, 8, 10, 16) given a decimal number and format these numbers correctly with spaces and leading 0 (without having to perform the conversion by myself).  I already found some posts with similar questions, but none of them achieve this (they display number with thousand separators, like the numprint package, every 3 digits; or they do not make it automatic). Here are these posts :         EDIT two other linked questions:       I also prefer to use pdflatex.