I am building a small set of utility bash functions and aliases that will live on a special /root partition. I've noticed that whenever I touch aFile or vim aFile, the result is aFile with the permissions -rw-r--r--.  This is highly undesirable if your goal is to run some shell scripts, and that's kind of what I thought the whole point of /root was.  My /root directory permissions are dr-xr-x--- and my umask is 0022. As I understand, I should expect new files to be 0755... but they aren't.   Why? Is this the default? How can I make new files executable?
How can one set the executable bit on files using umask? According to documentation, a umask of 000 should work, but in practice this only works on directories.  Also open to other methods of automatically setting +rwx on a particular user's created files if you have any.
If $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$,then prove that $\sin y=\frac{\sin x(3+\sin^2 x)}{(1+3\sin^2 x)}$ If $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$,then prove that $\sin y=\frac{\sin x(3+\sin^2 x)}{(1+3\sin^2 x)}$    $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$ $\frac{1+\tan\frac{y}{2}}{1-\tan\frac{y}{2}}=(\frac{1+\tan\frac{x}{2}}{1-\tan\frac{x}{2}})^3$ Applying componendo and dividendo rule on both sides, $\tan\frac{y}{2}=\frac{\tan\frac{x}{2}(3+\tan^2\frac{x}{2})}{(1+3\tan^2\frac{x}{2})}$ I am stuck here. How to do vlookup and fill down (like in Excel) in R? With no good reason I had a look at my computer's storage going on the apple and About this Mac. Here is the display:    The pink bar doesn't make much sense. It obviously does not represent the 80.67GB of free storage. Two sections correspond to pink; "Photos" and "Backups". I obviously don't have 140.76TB of backups. And probably not on this computer that has only 320GB of storage.  What is going on here? Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field. I have been having a lot of trouble teaching myself rings, so much so that even "simple" proofs are really difficult for me. I think I am finally starting to get it, but just to be sure could some one please check this proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field. Thank you.  Proof: Notice that $$\langle 1 - i \rangle\\  \Rightarrow 1 = i\\  \Rightarrow 2 = 0.$$ Thus all elements of the form $a+ bi + \langle 1 - i \rangle$ can be rewritten as $a+ b + \langle 1 - i \rangle$. But since $2=0$ this implies that the elements that are left can be written as $1 + \langle 1 - i \rangle$ or $0 + \langle 1 - i \rangle$. Thus  $$ \mathbb Z[i]/ \langle 1 - i \rangle = \{ 0+ \langle 1 - i \rangle , 1 + \langle 1 - i \rangle\}. $$  This is obviously a commutative ring with unity and no zero-divisors, thus it is a finite integral domain, and hence is a field. $\square$ Excessive water when cooking scallops This is partly a continuation of  question, since that one was already closed, but my question is about a specific problem encountered the last time I cooked scallops.  I got the pan up to a reasonable temperature and put the scallops in, and as they were cooking, TONS of water came out of the scallops and filled the pan.  I poured it out, continued cooking, and more water came out.  Several iterations later, I thought they were done, but they were still very raw inside, so we ended up tossing the batch (it definitely wasn't sushi grade).  Where did all the liquid come from, and is there any way to avoid that the next time? Will Windows 10's reset delete my Linux partitions? What is the difference between "thee" and "thou"? How to set systemwide "XP style DPI scaling" in Windows 8.1? I run my ThinkPad with a system DPI setting of 140%. In Windows 7 and 8, I enabled the "Use Windows XP style DPI scaling" checkbox in the Custom DPI Setting dialog. When this setting is off, non-DPI-aware applications get DPI virtualization via bitmap stretching, which results in large but fuzzy text. Turning on the checkbox disables this bitmap stretching, so non-DPI-aware apps get smaller text but without the fuzzy stretching. I find most apps to be more readable with the smaller crisper text, so I enable XP style scaling (i.e. disable DPI virtualization).  Windows 8.1 RTM has removed this option completely. After upgrading, all of my non-DPI-aware apps are running with ugly bitmap stretching. I'm able to fix this by going into the Properties for each app and setting the "Disable diplay scaling on high DPI settings" box in the Compatibility tab, but that is a bit of a pain.  Is there any way to restore the systemwide XP-style DPI scaling in Windows 8.1? Use the new helpcenter for the question/answer ban message Negative energy levels in the diagram for a hydrogen atom The higher the number of the shell (n), the higher is the energy level of the electron. However, why was it necessary to have negative values. So for example, when $n=1$, the energy could be $5 eV$ and for $n=2$, $6 eV$... having positive values could also have supported the idea that as $n$ increases, energy of electron increases. What is the point of having negative numbers, does it somehow aid calculations? System settings won't open on Ubuntu 20.04 LTS after adding System76/pop PPA I'm trying to open System Settings but it won't open in any way. Using GUI, Settings are trying to load for a moment and then they are gone. Using Terminal (gnome-control-center), I get: (gnome-control-center:8823): GLib-ERROR **: 14:44:15.433: ../../../glib/gmem.c:138: failed to allocate 13477064712 bytes Trap Trace/breakpoint (core dumped)  I tried: sudo apt-get remove gnome-control-center sudo apt autoremove sudo apt-get install gnome-control-center  With multiple reboots, but I had no result. UPDATE!: Same errors persist BUT, when I type: sudo gnome-control-center  (instead of just &quot;gnome-control-center&quot;) suddenly System Settings appear! Is it a user permissions issue? Any suggestions? UPDATE#2: After some system updates, sudo gnome-control-center now spawns &quot;Segmentation fault&quot;. Easiest way to setup Ubuntu as a VPN server Can we define flat connection on any given smooth manifold? For example, a sphere $S^2$ in $\mathbf{R}^3$ is apparently not flat with respect to the Euclidean connection, but can we define a flat connection and thus with affine charts on $S^2$? How can I make iconv replace the input file with the converted output? I have a bash script which enumerates through every *.php file in a directory and applies iconv to it. This gets output in STDOUT.   Since adding the -o parameter ( in my experience ) actually writes a blank file probably before the conversion takes place, how can I adjust my script so it does the conversion, then overwrites the input file?  for file in *.php do     iconv -f cp1251 -t utf8 "$file" done How soon can I re-apply for a UK visa after getting a refusal? Get client IP address via third party web service Equivalence Relation problem Let $S$ be the relation on $\mathbb{N} \times \mathbb{N}$ defined by $(a,b)S(c,d)$ if and only if $ad=bc$. Prove this is an equivalence relation on $\mathbb{N} \times \mathbb{N}$.  I think I've found this to be reflexive and symmetric, but I'm stuck on transitivity. Can someone check my work so far and assist with testing transitivity?  Reflexive: Let $(x,y)S(x,y)$. Then $xy = yx$. So $S$ is reflexive. Symmetric: Suppose $(a,b)S(c,d)$. Then, $ad = bc$. Therefore, $da = cb$ and $cb = da$. Therefore, $(c,d)S(a,b)$. Thus, $S$ is symmetric.  Transitive: Suppose $(a,b)S(b,c)$. Then $ac = bb$.   This is where I'm stuck. Any ideas? Enable External Sharing Programmatically We have a scenario on which we are creating site collections from a provider-hosted app. Some of these site collections will be used by external users. Is there a way from CSOM (server-side) to enable external sharing on the site collection? I haven't found any resources stating whether this is or not doable.  I'm trying to replicate the settings you can specify at the site collections page on the tenant admin site:    Thanks! There is a kind of situation that seems to occur somewhat commonly, that goes something like:   Figure out some way to handle a particular situation do it regularly, and make a habit of it, as it seems to work OK … … and only much later actually realize that it very much isn’t OK, that it’s been doing harm all the time, and that it’s too late to fix anything.   Does there exist any good words or phrases for this kind of situation? Error propagation with asymmetric uncertainties I red the Wikipedia  on error propagation. I get into some trouble when I want to calculate the error propagation in a specific case. I have real numbers $A$ and $B$ with related upper ($\Delta A_u$, $\Delta B_u$) and lower ($\Delta A_l$, $\Delta B_l$) uncertainties. I have two functions calculated as follows: $$F = \sqrt{A^2+B^2}$$ and  $$G = \tan^{-1}\frac{B}{A}$$ What are the related upper and lower errors of $F$ and $G$?  I found general formulae for Gaussian error distributions ($\Delta A_u = \Delta A_l$ and $\Delta B_u = \Delta B_l$), for instance the first formula of the first answer on . Is there a way to generalize that formula for arbitrary distributions with asymmetric errors as in my example?