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The paradox:    We have a circle and there is another circle with smaller radius. They are co-centeric.  If circle make full turn without sliding, both smaller and bigger circle make full turn too. If we assume that the passed road is equal to the circumference of circles. We have got smaller circle's radius is equal to bigger one's.  Unsatisfying Solutions I found:    "Do not assume that smaller circle's circumference is equal to passed road since the surface that contacts to the ground is bigger one. " // Okey but it does not explain the paradox, it explains just what is the wrong assumption (even does not explain why it is a wrong assumption.) It is undeniable that every point on both smaller and bigger circle will contact exactly one and only one point on their path. Therefore we can think that this is a bijective maps and smaller circle is isomorphic to bigger one. (Okey but ....)   Question: What is the true answer? What is wrong with the definition of circumference of a circle and relationship with its taken path. I have the problem, that PHP replaces all spaces with underscores in POST and GET variables. For example if I have the URL: http://localhost/proxy.php?user name=Max the browser will convert it to http://localhost/proxy.php?user%20name=Max. But if I give the $_GET parameters out, the key is not user name but user_name (note the underscore)! Is there any possibility to change this behaviour? I have read a lot about the SB-800/SB-900 but I am on a low budget (around ~120$). Is there an external flash that I can have to start learning to use it? I do not need TTL compatibility so it can be an older model. I have a Nikon D5000. Is there a difference between DataTable.Clear and DataTable.Rows.Clear? Transferring a Windows 8 license and proper un- and reinstallation Long story short  I have two computers: a laptop and a desktop computer. Both have Windows 7 on them.  I buy the Windows 8 Pro upgrade. To see if it screws up anything, I install it on my laptop as a guinea pig. I intend to use Windows 8 for my main computer, my desktop, but I want to test it on the laptop, so I know I don’t risk losing access to my desktop and the data on it. I never use my laptop, and only used it, because it already has a Windows 7 installation on it.  The problem  At some point, I must have entered the license key on my laptop, because when I go to the activation screen on my desktop, I get this:    Uh-oh. I can’t use the key on my desktop. Now how the hell do I transfer the key from my laptop to my desktop computer?  Answers and suggestions so far  Let’s just say that I tried everything possible to get some answers on this matter. The best response I got from Microsoft is this:     To install Windows 8 on your desktop, do the following:         Uninstall Windows 8 on your laptop   Afterwards, install Windows 8 on your desktop   If it won’t activate, call product activation at (...)      I am not a fan of that last point. The error message does allude to such a solution, however:     If you’ve reinstalled Windows or made changes to your hardware recently, you may be able to use your current key.   The question  My main question is this: has anyone been in a similar situation, and if so, what did you do to resolve this?  Failing that, what is the proper way to   uninstall the Windows 8 installation on my laptop, and reinstall the Windows 8 installation on my desktop?   Ad 1  I have already tried using the “reset” feature on my laptop, but that only resulted in a new Windows 8 installation that was already activated. But which is the right way to uninstall the installation in a way that allows me to use the license key on the desktop computer?  Ad 2  Which is the proper way to reinstall the Windows 8 installation on my desktop computer? Why do I even have to reinstall it in the first place?  I won’t get around to do this, until my USB key with 3.0 support arrives in the mail, but it is going to be a while, until I find a assuaging response to the best way to go about this anyway. The Canon L lenses are much more expensive and presumably much better quality than non-L lenses. What makes an "L" lens? How much better are they over a similar length/speed "ordinary" canon lenses? This question is related to a couple of other questions ( and ) relating to some material that I teach in sampling theory.  Consider the critical points of the  defined as follows.  The value $t_{n-1, \alpha/2}$ is a function of $n$ defined by the implicit equation: $$\frac{\alpha}{2} = \frac{1}{\sqrt{(n-1) \pi}} \cdot \frac{\Gamma(\tfrac{n}{2})}{\Gamma(\tfrac{n-1}{2})} \int \limits_{t_{n-1, \alpha/2}}^\infty \Big( 1+ \frac{r^2}{n-1} \Big)^{-n/2} dr.$$ Normally we treat the input $n&gt;1$ as an integer, but it is possible to extend the treatment to consider it a real value (since the T-distribution is well-defined for non-integer degrees-of-freedom).  I'm trying to come up with a (relatively simple) proof that this critical point value is decreasing in $n$, but I seem to be making quite a mess.  Differentiation using Leibniz rule gets part way, but it quickly becomes a bit of a mess.  Consequently, I would like to solicit proofs of this result --- this simpler the better. Question: How do you prove that this critical point is strictly decreasing in $n$? Why am I getting black photos when I use the Manual feature on my DSLR? When and why is the [featured] tag removed by the Community user? Is it feasible to transform each variable differently while doing multiple regression Ubuntu installation is slow, why? Both are in the present perfect, but one uses the verb 'to go' and the other 'to be'. Is there a rule for this?  Is there any chance that the differences between "I have been" vs. "I have gone", are differences in English dialect (I don't know if this is the right word).  Edit Could I say that North American English speakers use "I have gone", and maybe U.K speakers say "I've been"? Or vice versa. Uninstall apps locked by phone vendor I'm using a Samsung I9000 and I have some annoying apps that came pre installed by the phone vendor, like a music store, a custom web browser and other memory leaking apps.  Those crappy apps can't be uninstalled neither by Manage applications tool, nor by editing the apps tiles in the front menu.  I guess I have to be a root user or something to get rid of those apps, but I don't know how. Since I upgraded to the latest version of Ubuntu, I cannot install the Java OpenJDK package needed to compile Android custom ROMs. When I run sudo apt-get install openjdk-7-jdk, the following error appears:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  openjdk-7-jdk :  Depends: openjdk-7-jre (= 7u51-2.4.6-1ubuntu4) E: Unable to correct  problems, you have held broken packages.   How do I fix this problem? How can I change Win 10 protected registry entries? What is the closed formula for finding      $$ \sum_{i=0}^{k} \binom{n}{2i}=?\quad ,k\leq \lfloor{n/2}\rfloor $$   I need summation only up to some intermediate  $k$ where $k\leq \lfloor{n/2}\rfloor$ .  SAY I need a closed formula to calculate $\binom{8}{0}+ \binom{8}{2}+\binom{8}{4} +\binom{8}{6}$  HERE $n=8$ and $k=6$ .NET create scheduled task on server fails with E_ACCESSDENIED I have an ASP.NET website (in C#) that takes in user data and then attempts to create a windows scheduled task.  Of course, this works great on the DEV machine, but fails to run on the server.  I'm trying to figure out what permission(s) are required on the ASPNET user (or anonymous web user) to create tasks.  The error is:  Access is denied. (Exception from HRESULT: 0x80070005 (E_ACCESSDENIED))  Stacktrace:      at MyScheduler.NewWorkItem(String TaskName, Guid&amp; rclsid, Guid&amp; riid, Object&amp; obj)      at MyScheduler.CreateTask(String name)   I've done some searching, and the suggested resolution is to use the web.config 'impersonate' flag to force the application to run as a user with sufficient permissions, as opposed to the ASPNET account which may not have those permissions.  Example:  &lt;system.web&gt;     &lt;identity impersonate="true" /&gt; &lt;/system.web&gt;    Unfortunately, this does not seem to resolve the issue.  From the documentation I read, this should run as the anonymous web user, but it seems that user does not have enough permissions.  I altered the setting to specify a specific domain user that happens to be an administrator on the machine.  Example:  &lt;system.web&gt;     &lt;identity impersonate="true" userName="WindowsDomain\YourUserName" password="YourPassword" /&gt; &lt;/system.web&gt;    Doing this allowed the application to successfully create the Windows Scheduled Task.  So, obviously, with the correct set of Windows 2003 permissions I can get the app to perform as it does in the development environment.  However, I'm not about to place the network or machine administrator account's user credentials in plain text on a Web.config file.  Does anybody happen to know what permissions exactly need to be set in order to get the ASPNET account to behave as desired?  EDIT:  The Win32 API is being used to create scheduled tasks. The  page says that Box-Jenkins is a method of fitting an ARIMA model to a time series. Now, if I want to fit an ARIMA model to a time series, I will open up SAS, call proc ARIMA, supply the parameters $p,d,q$ and SAS will give me AR and MA coefficients. Now, I can try different combinations of $p,d,q$ and SAS will give me a set of coefficients in each case. I select the set with the lowest Akaike information criterion.  My question is: where in the above procedure did I use Box-Jenkins? Am I supposed to use Box-Jenkins to come up with initial estimates of $p,d,q$? Or did SAS use it internally somehow? How should we treat questions that are, or have seeds of, evil or malicious purposes and actions, such as writing spambots and malware?    Should they be answered like regular "everybody keeps their pants on" questions? Or should there be some other type of response to this bad behaviour lot? is it problematic to cluster across two datacenters w/aag? In general is it problematic to cluster across two datacenters that are up to 15-miles apart?  For this one particular project the approach is the following?   2-Node Failover Cluster across two datacenters, one node per datacenter local SAN disks, no shared disks 'Node and FileShare Majority' at third location on-campus employ AAG, failover will be manual; asynchronous mode   Is anyone implementing something like this with success??!?  Thanks so much for the help!!