How to correctly change a page URL without losing SEO rankings? I've searched this site and plenty other sites, but nobody seems to be able to answer my question entirely (not even Google), so here goes...  What would be the proper procedure to change the url of one of my pages (not my website, just a single page) from an "somesite.com/unnecessarily-long-and-SEO-unfriendly-url-that-drags-on-longer-than-mondays" to a "somesite.com/short-and-sweet-url"?  Ok, so I switch the url for my page to a short URL and create a 301 redirect from the long url - but what do I do next?  If I change the old url in the sitemap and upload it to GWT - that could just send a signal to Google that one of my old articles is gone and that a new one emerged.  I could also submit the old url for deletion from index and submit my new article for indexing, but that could still cause my "old" article to disappear from search results (at least until the "new" article emerges).  So my question is, what is the correct procedure for an url change that will let google know that I'm changing an URL for an EXISTING article - that doesn't lead to a rankings drop or even a temporary disappearance from the SERPs?
To change URL to user friendly URL I'm refactoring my ASP.net application from ASP.net 3.5 to 4.0. Also I'm changing the URLs to user friendly URLs /product.aspx?id=100 to /product-name/100.  All my pages are indexed by search engines and the site has already been online for 6 years. I'm planning to do 301 redirect from the old pages to the new one.  I want to make sure I won't lose the rankings and traffic.  Any suggestion how to do it properly?
Why do harmonics occur when you pluck a string? When you energise a taut string, the following resonant modes of vibration occur:    Plotting on the frequency domain, you can see their corresponding frequencies:    But what is the underlying physical principle? Why does this happen?  Is there any way of explaining it that could be understood by a smart 15 year old?  EDIT: I'm going to give my best attempt so far. Here goes:   We can start with sympathetic resonance. Sounding a particular frequency, a pure sinewave.  And noticing the string resonates sympathetically at the frequency of each harmonic. Say this is explained and understood. Now imagine that plucking a string is equivalent to a burst of white noise, which contains frequencies all the way through the spectrum. This could be approached backwards, by starting with random frequencies and noticing that resultant wave produced looks like white noise.   If the above is scientifically correct, then it restricts the domain of the question.  I would really like to be able to understand it scientifically and also be able to explain it intuitively.  PS Images from How to show hidden files in Nautilus 3.20.3 Ubuntu 16.10? How to show hidden files in Nautilus 3.20.3 Ubuntu 16.10? Can I make an ender portal on creative? I've updated Minecraft PE, and in the update notes it states that they've added the End. But when I made a new creative world and built a portal, it didn't work.  I've been looking online at tutorials, but cannot get the portal to open. So how do you create an Ender Portal? Construction of "it's too hard a task" How does a Windows antivirus hook into the file access process? Find $\lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right]$ (a question asked at trivia) My friend's trivia league had this math question:  $$\lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right]$$  After computing a few values, one could guess the answer is $e$ = 2.718...But how can we prove that is the limit?  Someone offered up a hand-wavy proof like this:  \begin{align} \lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right] &amp; = \lim_{n \to \infty} \left[\frac{(n+1)(n+1)^{n}}{n^n} - \frac{n \cdot n^{n-1}}{(n-1)^{n-1}} \right] \\ &amp;= \lim_{n \to \infty} \left[(n+1)\frac{(n+1)^{n}}{n^n} - n\frac{n^{n-1}}{(n-1)^{n-1}} \right] \\ &amp;= \lim_{n \to \infty} \left[(n+1)\left(1 + \frac{1}{n} \right)^n - n\left(\frac{n - 1 + 1}{n-1} \right)^{{n-1}} \right] \\ &amp;= \lim_{n \to \infty} \left[(n+1)\left(1 + \frac{1}{n} \right)^n - n\left(1 + \frac{1}{n-1} \right)^{n-1} \right] \\ &amp;= \lim_{n \to \infty} \left[(n+1)e - n \cdot e \right] \\ &amp;= \lim_{n \to \infty} e \\ &amp;= e \end{align}  The part about substituting $e$ is hand-wavy since technically this is an indeterminate form of $\infty - \infty$. And using $e$ as as upper bound did not lead me to an easy proof either.  Is there a way to rigorously prove the limit? I tried a few approaches: (a) sandwiching the limit--I could prove $e$ was a lower bound, but I could not find a suitable upper bound converging to $e$, (b) using L'Hopital's rule with no luck, (c) using the mean value theorem--but that also got complicated.  So this is a pretty tough problem to ask at trivia! Is there a way to prove this limit formally?  Sources  Trivia question:   Thread on trivia:   Hand-wavy proof:   Idea for mean value theorem: Is there an easier or more 'correct' way to open gedit as root? I have ubuntu 12.04 running in a virtual machine on virtual box.  Its existence is mainly as a 'toy' to play about with Ubuntu, so for this reason I wanted the GUI (is that what 'Dash' is in ubuntu 12.04?  Anyway...)  One thing I am currently using this machine for is a LAMP server.     I use 'gedit' to edit my files, but because I haven't correctly set permissions yet I just open it with sudo in terminal.  Just now, to try to simplify this process I created a shell script on the desktop with a very simple job - sudo gedit  I can't help thinking there must be an even more obvious way to open gedit as root from the GUI than this.  So is there?  Edit:  I just 'improved' my script by replacing sudo with gksudo.  Now I don't have to have a terminal window open while gedit is open.   So I guess this is quite convenient for now :)   It would be good, for the sake of knowledge, to know if this is anything close to how the more seasoned ubuntu users would do this type of thing. Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $D_6$ (the group with $x^3=1$, $y^2=1$ and $xy=yx^2$).  I'm not really sure how to express the elements of $\operatorname{Aut}(C_2 \times C_2)$. Would it be sufficient to show the elements of $\operatorname{Aut}(C_2 \times C_2)$, find their order and show they bijectively map to every element of $D_6$ and satisfy $xy=yx^2$? Reason behind this self invoking anonymous function variant Should not we apply pseudo-forces all the time as the Earth is a non-inertial frame of reference? How do you match only valid roman numerals with a regular expression? Thinking about , i decided I can't even create a regular expression that will match roman numerals (let alone a context-free grammar that will generate them)  The problem is matching only valid roman numerals.  Eg, 990 is NOT "XM", it's "CMXC"  My problem in making the regex for this is that in order to allow or not allow certain characters, I need to look back. Let's take thousands and hundreds, for example.  I can allow M{0,2}C?M (to allow for 900, 1000, 1900, 2000, 2900 and 3000). However, If the match is on CM, I can't allow following characters to be C or D (because I'm already at 900).  How can I express this in a regex? If it's simply not expressible in a regex, is it expressible in a context-free grammar? Loading custom configuration files I know I can open config files that are related to an assembly with the static ConfigurationManager.OpenExe(exePath) method but I just want to open a config that is not related to an assembly. Just a standard .NET config file. Getting all files that have been modified on a specific date Is it possible to find all php files within a certain directory that have been modified on a certain date  I'm using   find /var/www/html/dir/ -mtime -28 | grep '\.php'    to get files modified within the last 28 days, but I only need files that have been modified on the following date: 2011-02-08 Why there isn't any integer solutions in non-zero integers for $z^3 = 3(x^3 +y^3+2xyz)$? Consider the following Diophantine equation  $$z^3 = 3(x^3 +y^3+2xyz)$$  Is there any elementary proof for the non-solubility in non-zero integers for this  Diophantine equation, where the absolute value of $x, y$ and $z$ are pairwise coprime integers?  I have proved the impossibility of solution of this Diophantine equation in non-zero integers, but that took quite a few pages and I consider this too long. I hope for a much more elementary and shorter proof for this puzzle.  Hint: It should be noted that is also true for the non-availability of the similar form (replacing coefficient 3 by 1) as the following:   $$z^3=x^3+y^3+2xyz,$$ but this case is very simple to prove, where $x, y\;\&amp;\; z$ are nonzero integers. remote action function encountering CPU time out limit exception CPU time out limit was being hit while processing child records on the inline opportunity visualforce page, to handle this i wrote a remoteActionFunction on the page that invokes controller method that's taking long to process and when i get CPU LIMIT exception in the result, i am invoking javascript call back function that invokes a action function which handles the same code asynchronously(@future).  Question: by setting the timeout (Visualforce.remoting.timeout = 120000;) can't we overcome CPU TIME out limit of 10,000 ms. Induction and electromagnetic fields I've got a few questions on induction and electromagnetic fields. My current understanding of induction and electromagnetic fields is that, when electricity/current flows through a wire, it creates an electromagnetic field. If you twist that wire into a coil then you can concentrate that field. You can then induce current into a different coil by placing it inside of the electromagnetic field created by the first coil.  So here are my questions:  Q1. Does the electromagnetic field contain any energy?  EDITED QUESTION  Q2. Electromagnetic fields are the same as waves, so does that mean that when current is induced, they get the energy from electromagnetic waves being exchanged, or do they induce current directly from the electromagnetic field?   Q3. If electromagnetic fields and waves are the same, then doesn't that mean that you can induce current from waves? Therefore transferring electricity over long distances?  Q4. What spectrum of light are the electromagnetic waves that are in a field created by electricity?  Q5. Finally, why is it not possible to induce current from the Earth's magnetic field? I thought Maxwell said that electric fields and magnetic fields were the same thing.   Thank you to anyone who answers.  Edited Q2: So my original question (although asked poorly) still stands. Where does the current that gets induced in the secondary coil come from? How does the electricity transfer from the primary coil to the secondary? For example, is it taken from the stored energy in the e.m field? Does the field just act as a bridge between the 2 coils? Or do the 2 coils exchange e.m waves which carry the electricity that is being transferred from coil 1 to coil 2? Or is it none of these things and something completely different? How to get next/previous record in MySQL? I'm unable to access the following website from my Internet Explorer 8 under Windows XP with Internet Explorer unable to display web page error. By the other hand the FireFox browser at the same Windows XP can access this website.  How to solve the issue with IE8 ? The  makes use of the term "the author."  When Bob makes a post, it's obvious Bob "owns" the content, but what happens when he checks the Community Wiki button? Does it become the property of the Stack Overflow community? Even if Bob is the only one to have edited it?  Say I were to use a Community Wiki answer for something or other &#8212; say, in a book &#8212; who would I attribute the content to? "Learn More" link on tags broken in latest Chrome stable Note: This is identical to , but that bug was declined because Chrome 30 was in dev. Chrome 30 has now been released, and still has this issue.   The "Learn More" link for tags is broken in the latest release of Google Chrome.    If I right-click and open in new tab, I get the tag's page, but just clicking doesn't work.  I'm using Chrome 30.0.15599.69, the latest stable release: