Time dilation (special and general relativity)
Cancelling special & general relativistic effects
I've recently started playing Minecraft, and I only have a little experience with enemies (I've been playing with the peaceful setting so I can figure out what the heck I'm doing).  When I did play some survival mode, I happened to be at the top of a pretty large cliff when night hit, and this seemed to protect me - the baddies just piled up at the bottom of the cliff.  However, it seems like this probably only worked due to pathing flukes.  The terrain behind me was pretty easy going, so I suspect if enemies spawned in the right areas, they could still come up and visit.  That said, how can I set up a quick protective shelter for the first night or two?  The days don't seem to last very long, so I don't expect I would be able to generate a lot of high-end materials, tools, etc. to work with.  Also, the zombies caught fire nicely when the sun came up, but there were still some spiders and some other things (creepers? - they were explosive) that didn't go away at daybreak.  Do I need multiple exits for my shelter or some other way to avoid running into all the enemies outside the front door that have accumulated overnight? Prove the map has a fixed point Assume $K$ is a compact metric space with metric $\rho$ and $A$ is a map from $K$ to $K$ such that $\rho (Ax,Ay) &lt; \rho(x,y)$ for $x\neq y$. Prove A have a unique fixed point in $K$.  The uniqueness is easy. My problem is to show that there a exist fixed point. $K$ is compact, so every sequence has convergent subsequence. Construct a sequence ${x_n}$ by $x_{n+1}=Ax_{n}$,$\{x_n\}$ has a convergent subsequence $\{ x_{n_k}\}$, but how to show there is a fixed point using $\rho (Ax,Ay) &lt; \rho(x,y)$? I honestly have no idea how to approach this question. I have done easier questions eg. show $gcd(a,b)lcm(a,b)=ab$ by letting $a=Alcm(a,b)$ and $b=Blcm(a,b)$ and then using the fact that $A$ and $B$ are coprime. However this approach only works in two variables. Any help with the question in the title would be greatly appreciated, as well as the thought process behind the answer so that I can approach similar problems. Batch jobs error emails report:      The transaction log for database 'WebDB' is full.   No, it isn't. Its 90% free. The transaction log backups run normally. My hardware guy tells me the hardware is running perfectly, with plenty of space. SQL Server 2008 SP3, but not R2.  I'm a developer, we no longer have a DBA. So it falls to me to try and fix this. PHP: Return all dates between two dates in an array List has no rows for assignment to SObject The novel centers around a man living a comfortable existence in the pretty distant future.  To support himself, he is occasionally asked to enter a box which will copy his entire body, and send it out faster than the speed of light to some developing world, to work.  His copy on this world wakes up and realizes what a big mistake he's made.  The copy does grueling work, feels lonely, and eventually just dies of radiation sickness.  Back on earth, the man never realizes how bad it is out there, and keeps sending out more copies.  I think the story is probably 80s or earlier - not sure if it's a short story, or the beginning of a novel which I lost &amp; never finished. Do I need to tame my twitchy F5 finger? I just got this error message for the first time (I was getting this as the response to any request on the SE network for about the last five minutes, until now):     We're sorry...      There are an unusual number of requests coming from this IP address.   To protect our users, we can't process any more requests from this IP   address right now. We'll restore access as quickly as possible, so try   again soon. If you believe you have reached this page in error,   contact us.   As far as I know, I was not spamming SE or participating in DOS attack, and I find it unlikely that any of my office coworkers who share my IP address were doing so either.  Granted, I was pressing F5 a lot. But I've always pressed F5 a lot on SE, and have never gotten this message before. So my question is: Is it possible to get this error message simply by refreshing too much or too often? Or is that message reserved for a truly massive number of requests that are unlikely to be caused by one person refreshing a lot? (In the former case, I can't explain why I've never gotten it before; in the latter case, I can't explain why I just got it now). Solve congruence system $\ x\equiv m_i-1 \pmod{m_i}\,$ for $\,i = 1,\ldots, k$ How can I install a package on MikTeX? I need to install a LaTeX package on my MikTeX system.  Specifically, I am trying to make biblatex work, but I always get the error message:    ! LaTeX Error: File `biblatex.sty' not found.   I have changed the options to have the "Quick Build" command that includes biblatex too.   Code/commands are correct because it's working under Overleaf. How can I show or hide boot messages when Ubuntu starts? Is there a way to easily turn on/off showing the boot messages (loading the services) when Ubuntu starts? Is it something in Grub2?  I am running 10.04. Polygonizing a raster yields lots of little squares? I have a pdf with the area of a county that I want to separate into multiple shapefiles (polygons) based on color.   As shown in the first picture there are 4 colors so I would need to separate based on color between those four. But first, I need to convert it into a vector (unless there is an easier way).   Doing so, I get the second image as an output by using the polygonize tool which when zoomed in very close, has a lot of tiny squares where color should be different. I was wondering if there is a way to break a raster up by color even though the image isn't smart. Why are the dineutron and diproton unbound? When conducting multiple regression, when should you center your predictor variables & when should you standardize them? Display Top X results for each unique value I am trying to figure out how I can output any machine that has had the latest 3 backups be larger than 10GB. My SQL Table looks similar to the below table:  ComputerID | BackupImageName | WindowsVolumeGUID | FileSize | TimeCreated 1234       | PCBackup.spi    | kjsdfai-dadad-ddd | 10400    | 05-22-20 1234       | PCBackup1.spi   | kjsdfai-dadad-ddd | 10500    | 05-23-20 1234       | PCBackup2.spi   | kjsdfai-dadad-ddd | 10300    | 05-24-20 1234       | PCBackup3.spi   | kjsdfai-dadad-ddd | 10900    | 05-25-20 1225       | PCBackup4.spi   | kjsdfa5-dadad-ddd | 10600    | 05-22-20 1225       | PCBackup5.spi   | kjsdfa5-dadad-ddd | 5000     | 05-23-20 1225       | PCBackup6.spi   | kjsdfa5-dadad-ddd | 10000    | 05-24-20 1225       | PCBackup7.spi   | kjsdfa5-dadad-ddd | 4588     | 05-25-20   I need to output all machines (computerID's) or Volumes (WindowsVolumeGUID) that have their latest 3 files in the list greater than 10000 file size. So from the above table it would output the computerID of 1234 because its latest 3 are greater than 10000 file size and even though the computerID 1225 has 2 files greater than 10000 it would not output the result because there is a break in-between the two large files. The search will need to take into account the WindowsVolumeGUID since some machines have more than one volume and I need to take into account the individual volume backups and count the latest entries based on that.  Alternatively, I can also accomplish the same thing if there is a way to output the top 3 results for each unique WindowsVolumeGUID and not just across the board.   Any help would be greatly appreciated! Nested regression model Cyclic vector implies commuting linear operator is a polynomial Let $T$ be a linear operator on the finite dimensional vector space $V$. Suppose $T$ has a cyclic vector. Prove that if $U$ is any linear operator which commutes with $T$, then $U$ is a polynomial in $T$. Nothing shows up in the terminal when I type my password A very quick question:   Is it correct to say "In case I won't be able to watch that"?  If it's acceptable to say that, what type of sentence is it?  UPDATE:  As a clarification, I want to say "Can you give me that in case I won't be able to have it later". Probably, it's more a supposition than a conditional. How to extract the n-th elements from a list of tuples?