Can very strong gravitational wave collapse into a black hole?
Can colliding gravitational waves create a black hole?
Can I move Xcode and Android Studio to SD card I'm planning to buy a 64GB SD card to supplement the storage on my MacBook Air 128GB (early 2015)  I wanted to know if I can move my Xcode and android studio to it as both have them take a significant part of the memory.  If this can happen, I wanted to know how can I move these two to the SD card. I'm fairly new to macOS and have no idea how to do this. How do I configure Apache 2 to run Perl CGI scripts? I would like to configure Apache 2 running on Kubuntu to execute Perl CGI scripts. I've tried some steps that I came across by googling, but nothing seems to work.  What is the right way of achieving this? Using conjugates to find a limit with a cubic root: $\lim_{h\to 0}\frac{\sqrt[3]{h+1}-1}{h}$ I currently have $$\lim_{h\to 0}\frac{\sqrt[3]{h+1}-1}{h}$$  Now, I know that when you have square root instead of a cubic root it's easy. You just multiply by the conjugate and simplify afterwards. If it were a sqrt I know that the limit is 1/2. I know that the result here is 1/3 but I can't seem to get there. I always end up with 1/4 due to getting something like: $$\frac{h+1-1}{h(\sqrt[3]{h+1}+1)(\sqrt[3]{h+1}+1)}$$  After simplifying and evaluating the limit you end up with $$\frac{1}{(\sqrt[3]{0+1}+1)(\sqrt[3]{0+1}+1)}$$  which turns out to be $1/4$.  What am I doing wrong? Labels and nesting gather and align "Was" or "were" for "half a dozen" In Microsoft Word, the following sentence is flagged.  It tells me to use "was" instead of "were"     There were half a dozen books strewn about the floor.   I would think that you would use "were" since it's a quantity more than one.  You wouldn't say, "There was twelve books strewn about the floor."  Does the use of the "half" modify it somehow? My laptop which had Windows 7 on it crashed today. Being unable to access any file kept within, I found about the LiveCD. So I created a LiveUSB with Ubuntu in it, and managed to access my Windows desktop. I'm now backing up files important to me, but I have a question:  Now I'm cutting and pasting the files I want to save, using Ubuntu. Are these files being moved in Windows as well, or do the alterations I make through Ubuntu not affect the Windows state?   So let's say,if I cut and paste all of the D drive, and then format C and reboot with Windows, would the files in D have been gone (since they were cut and not copied) or still be there?  Thanks. Show that $$\lim_{x \to \infty} \frac{\log(1 + e^x)}{x} = 1$$ How do I prove this? Or how do we get this result? Here $\log$ is the natural logarithm. Possible Duplicate:          I have been downvoted for few answers of mine and the person who downvoted me did not leave any comments or reasons to say why I was downvoted. In such cases, how can I find out who has downvoted me and the reason for downvoting? I want to validate a set of credentials against the domain controller. e.g.:  Username: STACKOVERFLOW\joel Password: splotchy   Method 1. Query Active Directory with Impersonation  A lot of people suggest querying the Active Directory for something. If an exception is thrown, then you know the credentials are not valid - as is suggested in .  There are some serious  however:   You are not only authenticating a domain account, but you are also doing an implicit authorization check. That is, you are reading properties from the AD using an impersonation token. What if the otherwise valid account has no rights to read from the AD? By default all users have read access, but domain policies can be set to disable access permissions for restricted accounts (and or groups). Binding against the AD has a serious overhead, the AD schema cache has to be loaded at the client (ADSI cache in the ADSI provider used by DirectoryServices). This is both network, and AD server, resource consuming - and is too expensive for a simple operation like authenticating a user account. You're relying on an exception failure for a non-exceptional case, and assuming that means invalid username and password. Other problems (e.g. network failure, AD connectivity failure, memory allocation error, etc) are then mis-intrepreted as authentication failure.   Method 2. LogonUser Win32 API   have suggested using the  API function. This sounds nice, but unfortunately the calling user sometimes needs a permission usually only given to the operating system itself:     The process calling LogonUser requires   the SE_TCB_NAME privilege. If the   calling process does not have this   privilege, LogonUser fails and   GetLastError returns   ERROR_PRIVILEGE_NOT_HELD.       In some   cases, the process that calls   LogonUser must also have the   SE_CHANGE_NOTIFY_NAME privilege   enabled; otherwise, LogonUser fails   and GetLastError returns   ERROR_ACCESS_DENIED. This privilege is   not required for the local system   account or accounts that are members   of the administrators group. By   default, SE_CHANGE_NOTIFY_NAME is   enabled for all users, but some   administrators may disable it for   everyone.   Handing out the "Act as a part of the operating system" privilege is not something you want to do willy-nilly - as Microsoft points out in a :     ...the process that is calling   LogonUser must have the SE_TCB_NAME   privilege (in User Manager, this is   the "Act as part of the Operating   System" right). The SE_TCB_NAME   privilege is very powerful and   should not be granted to any arbitrary user just so that they can   run an application that needs to   validate credentials.   Additionally, a call to LogonUser() will fail if a blank password is specified.    What is the proper way to authenticate a set of domain credentials?    I happen to be calling from managed code, but this is a a general Windows question. It can be assumed that the customers have the .NET Framework 2.0 installed. Captured variable in a loop in C# I met an interesting issue about C#. I have code like below.  List&lt;Func&lt;int&gt;&gt; actions = new List&lt;Func&lt;int&gt;&gt;();  int variable = 0; while (variable &lt; 5) {     actions.Add(() =&gt; variable * 2);     ++ variable; }  foreach (var act in actions) {     Console.WriteLine(act.Invoke()); }   I expect it to output 0, 2, 4, 6, 8. However, it actually outputs five 10s.  It seems that it is due to all actions referring to one captured variable. As a result, when they get invoked, they all have same output.  Is there a way to work round this limit to have each action instance have its own captured variable? How do you transpose tensors? We transpose a matrix $A$ by replacing $A_{ij}$ with $A_{ji}$, for all $i$ and $j$.  However, in case $A$ has more than two dimensions (that is, it is a tensor), I don't know how to apply the transpose operation.   If A has dimensions $3\times 3 \times 8$, then what will replace $A_{ijk}$?  If $A$ has shape $3\times 3\times 8\times 8$, then what will replace $A_{ijkl}$? Alternatively, why does the force created by blowing out air feel so much stronger than the force created by sucking in air?  Ok, so forget the human factor involved in blowing out candles. Consider a vacuum cleaner with a suction end and a blower end. Anyone who has tried it out notices the blower end creates a much stronger force than the suction end, despite the discharge being (more or less) equal at both ends.  Why does this happen? Internet through wireless hotspot, intranet through wired network - can I use both at the same time? I have been tring this for a while now, without success. I have read online this can be done, either by changing the default gateway (DG) or messing with the DG's metric  The short story is: I need to connect to my company's ERP system (port 80 for some web services and port 22 for sftp and bash) with using my notebook computer's LAN card - but I can't connect to the Internet on this network. So I have my mobile phone's 3g hotspot when I need to go online. But I want to use both at the same time without so much as opening another web browser process.  At the moment, I am using the ERP system regularly - and whenever I need to go online to check a mail or research something related to work, I need to unplug the network cable so the wifi can kick in... which is starting to become annoying especially if I am connected to the ERP system using FTP (Filezilla) or Shell (putty)  Can someone help me with the configurations?  Below are some of the details I can provide:  Wired network - office LAN - for connection to the ERP system: DHCP -    Yes IPv4      10.64.200.245 Subnet    255.255.240.0 DG        10.64.193.254 DHCP Serv 10.64.17.191 DNS       10.68.72.200           10.68.20.200 WINS      10.68.77.200           10.64.20.200   Below are the details for my WiFi internet connection - over my mobile hotspot  DHCP      Yes IPv4      192.168.43.39 &lt;- I'm guessing this changes every time I restart the wifi subnet    255.255.255.0 DG        192.168.43.1 DHCP      192.168.43.1 DNS       192.168.43.1   Finally, here is the tracert results (btw, I'm on Windows 7, 64bit and the remote system should be on Linux) - the target ERP ip address is 10.76.142.39  Tracing route to 10.76.142.39 over a maximum of ...    1    &lt;1 ms    &lt;1 ms    &lt;1 ms  10.64.193.253   2    &lt;1 ms    &lt;1 ms    &lt;1 ms  10.64.4.13   3    &lt;1 ms    &lt;1 ms    &lt;1 ms  10.76.23.124   4     1 ms    &lt;1 ms    &lt;1 ms  10.76.23.93   5     1 ms    &lt;1 ms    &lt;1 ms  2xx-xx-xx-9.adsl...   6     1 ms     1 ms     1 ms  2xx-xx-xx-9.adsl...   7     1 ms     1 ms     1 ms  2xx-xx-xx-10.adsl..   8     2 ms     1 ms     2 ms  10.76.135.125   9     1 ms     1 ms     1 ms  10.76.142.39   sorry, I had to mask out some details above... wasn't sure if they would have any confidentiality issues.  Any help is much appreciated. Closure of identity element in a topological group is the intersection of its neighborhood system Consider a topological group $G$. I want to prove that      if $\cal{U}$ is the set of all neighborhoods of $e$ (the identity element), then $\overline{\{e\}}=\cap_{U\in \cal{U}}U$.   What I thought was:  i) If $x\in \overline{\{e\}}$, then every neighborhood $V$ of $x$ intersects $\{e\}$, hence every $V$ is a neighborhood of $e$ as well, i.e. $V\in \cal{U}$.  ii) On the other hand, if $x\in \cap_{U\in \cal{U}}U$, then $x\in U$ for all $U \in \cal{U}$, meaning every $U$ is a neighborhood of $x$ intersecting $\{e\}$.  Now, I think that the missing part is an argument justifying that there is no neighborhood of $e$ that is not a neighborhood of $x$ (part i)), and that there is no neighborhood of $x$ that is not a neighborhood of $e$ (part ii)). My idea for this is to argue that there is a homeomorphism taking $e$ to $x$, therefore the neighborhood system of one cannot have more elements that the neighborhood system of the other.  Is this correct? If not, is there a way I can fix it? What is the meaning of the term "thread-safe"? Does it mean that two threads can't change the underlying data simultaneously? Or does it mean that the given code segment will run with predictable results when multiple threads are executing that code segment? When I boot Ubuntu 10.04.3 from a live CD, it asks me to enter a username and password. I have not booted before, and I haven't created an account. The cardinality of the set of all finite subsets of an infinite set How are Wolverine's claws still in his body? Everyone knows that Wolverine's adamantium claws are super-sharp — sharper than even a razor — and virtually indestructible. What puzzled me the first time I saw Wolverine is: how do the claws stay in his body?  As it is shown, Wolverine's flesh and skin are human in strength, but the healing factor makes it superhumanly durable and strong. Still, when Wolverine slashes something, or someone, extremely hard, dense, or thick (as he has to use great amount of force), the claws don't tear through his hand and leave his hand through the opposite side of the palm (because of the action having equal and opposite reaction). I need help with this:  If a is an element of $\mathbb Z_n$ and $\gcd(a,n) &gt; 1$ , then a is not invertible.   First you show that if $a$ is an element of $\mathbb Z_n$ and $\gcd(a,n)&gt;1$, then there  is an element $b$ of $\mathbb Z_n$ and ($b$ is not equal to the zero element) from which $ab = 0$.   The second part I cant get. i.e. show if $b$ is not the zero element  and $ab=0$ then $a$ is not invertible. "Do you know where's Linda?" vs "Do you know where Linda is?"