subdivision creates unwanted creases
Weird line in my mirrored mesh
Novel about a man who has his car stolen and is cryogenically frozen with his cat? So this is a bit of a memory game of my behalf, but I'm trying to remember the name of a (presumably) Sci-Fi novel with only a recollection of the following:   A man owns a (yellow?) car parked outside his house along with a cat The car goes missing or is stolen The man decides to be cryogenically frozen for 75 (fairly sure, could be 50?) years along with his cat (I might be muddling up novels but I'm sure there was a cat...?) He takes a walk along the street X years in the future when he wakes up and the currency he has in his pocket is now worthless   I don't think I got that far into the book and all the above happened relatively early.  I read it about 10 years ago and at a guess, it's an 80's novel - all of the above details might be inaccurate, but I'm certain about the cryogenic freezing and the currency aspects.  I'd be surprised if this one gets anywhere! How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$ $A$ is a $n\times n$ matrix such that $ A^m = 0 $ for some positive integer $m$.   Show that $A^n = 0$.   My attempt: For $n &gt; m$, it's obvious since matrix multiplication is associative.  For $n &lt; m$, $A^n\times A^{m-n} = 0$; not sure what to do next. Also I know that $\det A = 0$. There are two vectors called $\vec{a}$ and $\vec{b}$. Vector $\vec{c}$ is the bisector and it can be given as  $$\vec{c} = |b|\vec{a} + |a|\vec{b}$$  How to prove that? I have used the dot product method. But there I can't find the angle between them. Then I tried to do this by using unit vectors. Then I got an answer like in the given picture. . Can you help me to get the correct answer Please do not close this as a duplicate unless you can remove the “status-completed” tag from the  (because it’s obviously not been completed).  Steps to reproduce:   Have someone post an answer. Downvote the answer. Have the someone edit the answer within the initial 5 minutes of the answer’s existence. Try to undo the downvote more than 10 minutes later.   You cannot undo the downvote. I'm trying to find  $$\lim_{n\to\infty}\frac{n}{\sqrt[n]{n!}} .$$   I tried couple of methods: Stolz, Squeeze, D'Alambert  Thanks!  Edit: I can't use Stirling. I need an approach to allow delegated admins (i.e., non-Administators) to add members to Public Groups and Collaboration Groups (the GroupMember and CollaborationGroupMember objects).  I added a custom object (UserGroupRequest__c) to capture which Users should be added/removed to which Groups.    I've also built a batchable class to process the requests.  However, GroupMember is a Setup object, and CollaborationGroupMember is not.  So this doesn't work if I combine the operations in a single batchable class.  Should I instead be using 2 batch classes, calling one from the finish method of the other?    Any recommendations on how best to proceed?  Am I way off base?    Would a trigger on the Request object perhaps be better? I'm guessing that there may be a permission problem if this is attempted via a trigger as the delegated admins won't be able to add users to public Groups.  Also, I'm guessing the trigger approach would run into the same mixed DML issue - on Insert of the Custom object, I would need to Insert/Delete from GroupMember and from CollaborationGroupMember, and then perform a 2nd update on the Custom object to indicate that processing was completed... How to update Ubuntu terminal? How to update Ubuntu terminal? Is there a "theirs" version of "git merge -s ours"? When merging topic branch "B" into "A" using git merge, I get some conflicts. I know all the conflicts can be solved using the version in "B".  I am aware of git merge -s ours. But what I want is something like git merge -s theirs.   Why doesn't it exist? How can I achieve the same result after the conflicting merge with existing git commands? (git checkout every unmerged file from B)  UPDATE: The "solution" of just discarding anything from branch A (the merge commit point to B version of the tree) is not what I am looking for. What word indicates spatial data within the geographical and geological domains? In particular, what word is precise enough for a science journal article (i.e., formal prose)? Candidates might include &quot;spatial data,&quot; &quot;geodata,&quot; &quot;geospatial data,&quot; and &quot;geographic data.&quot; &quot;Spatial data&quot; seems too generic (not necessarily within the geographical and geological domains). What is the consensus, if any exists? How to get permission number by string : -rw-r--r-- I need to set the same chmod, how to get number for -rw-r--r-- ? Do photons have acceleration? Photons travel at the fastest speed in our universe, the speed of light.  Do photons have acceleration? Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$ I'm having problems with an exercise from Apostol's Introduction to Analytic Number Theory.     Given $x$ and $y$, let $m=ax+by$, $n=cx+dy$, where $ad-bc= \pm 1$. Prove that $(m,n)=(x,y)$.   I've tried to give a proof, but I suspect it's wrong (or at least not very good). I would be very thankful for any hints/help/advice!  My proof:     We observe that since $ad-bc= \pm 1$, $ad=bc \pm 1$, and $(ad,bc)=1$.   Now, $(a,b) \mid m$ and $(c,d) \mid n$ but      $$(a,b) = ((d,1)a,(c,1)b)=(ad,a,bc,b)=(ad,bc,a,b)=((ad,bc),a,b)=(1,a,b)=1.$$      Similarly, we determine $(c,d)=1$. So, $1=(a,b) \mid m$ and $1=(c,d) &gt; \mid n$. But $(x,y)$ also divide $m$ and $n$. Since $(x,y) \geq (a,b)=(c,d)=1$, this implies that $(x,y)=m,n$. Hence   $(m,n)=((x,y),(x,y))=(x,y)$. states that the isomorphism type of a finite simple group is determined by its order, except that:   $L_4(2)$ and $L_3(4)$ both have order $20160$ $O_{2n+1}(q)$ and $S_{2n}(q)$ have the same order for $q$ odd, $n &gt; 2$   I think this means that for each integer $g$, there are $0$, $1$ or $2$ simple groups of order $g$.  Do we need the full strength of the  to prove this, or is there a simpler way of proving it? Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$ I need hint proving this $$\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$$ Do IE standalone-browser still exist (and run on Win 7?) Everybody has to obey their own parents I am new here and I don't really know how to post, so please forgive my mistakes. My question is this: Is a sentence like "everybody has to obey their own parents" nowadays completely acceptable under a grammatical point of view or it is still preferable, in written form, to use "everybody has to obey his/her own parents"? Thank you very much and sorry if this has been asked before. How can I install Windows after I've installed Ubuntu? I have Ubuntu on my laptop. Now I want install Windows 7 in a dual-boot. How can I do this? I can't lose my Ubuntu files, and I'm afraid that I might break . Go  for UEFI only! Effect on Google rankings if my site is down? Suppose that $n \ge 2$. How to prove that the set $\mathcal D \subset M_n(\mathbb R)$ of the diagonalizable real matrices is not dense in $M_n(\mathbb R)$? How does commands like ls know what its stdout is?  It seems ls is operating different depending on what the target stdout is. For example if I do:  ls /home/matt/tmp    the result is:  a.txt b.txt c.txt   However if I do  ls /home/matt/tmp | cat   the result is (i.e. new line per result):  a.txt b.txt c.txt   The process is passed a file descriptor 1 for stdout right? How does it determine how to format the result? Does the file descriptor reveal information?