Peskin & Schroeder equation 3.17
Lie bracket for Lie algebra of $SO(n,m)$
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$. Is the complement of a prime ideal closed under both addition and multiplication? How can I execute `date` inside of a cron tab job? I'm having a problem finding out a way to project from top view and the side view so I texture better. It just replaces the current projection with the top view    So is it possible to project from view twice on the same image? Can a lambda function call itself recursively in Python? A regular function can contain a call to itself in its definition, no problem.  I can't figure out how to do it with a lambda function though for the simple reason that the lambda function has no name to refer back to.  Is there a way to do it?  How? Primary ideals in Noetherian rings How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$? For my proof I distinguished the two possible cases which derive from $7 \mid a^2+b^2$:   Case one: $7\mid a^2$ and $7 \mid b^2$ Case two (which (I think) is not possible): $7$ does not divide $a^2$ and $7$ does not divide $b^2$, but their sum.  I've shown that case $1$ implies $7\mid a$ and $7\mid b$, so I just have show that case 2 isn't possible - I'll be happy for any input.  MfG, Karl Schengen visa validity start date My Chinese in-laws intend to visit us in one month from now. Their visa is valid from Nov 23rd. Would it be possible for them to take the airplane on November 22nd in China and arrive in Schengen area on November 23rd?  Or does the visa already have to be valid upon departure?  In our particular case, they still need to transfer in Beijing first. The actual flight to Schengen zone effectively only departs on the 23rd so I guess that should be completely fine then? Right now, I have everything in a partition (except EFI system partition). How can I split the partition into two, one for / and one for /home?   How would you use parted to do that step by step?  How would you use gparted to do that step by step?  How would you use LVM to do that step by step?   One thing I am not sure of is that I can't just shrink the partition and create a second partition on the space that is freed by shrinking, because that doesn't move /home to the new partition.  Thanks.    $ sudo parted -l [sudo] password for t:  Model: ATA TOSHIBA MQ01ABF0 (scsi) Disk /dev/sda: 500GB Sector size (logical/physical): 512B/512B Partition Table: gpt Disk Flags:   Number  Start   End    Size   File system  Name                  Flags  1      1049kB  538MB  537MB  fat32        EFI System Partition  boot, esp  2      538MB   500GB  500GB  ext4  $ sudo df -h [sudo] password for t:  Filesystem      Size  Used Avail Use% Mounted on udev            1.7G     0  1.7G   0% /dev tmpfs           340M  1.4M  338M   1% /run /dev/sda2       457G  6.7G  428G   2% / tmpfs           1.7G   27M  1.7G   2% /dev/shm tmpfs           5.0M  4.0K  5.0M   1% /run/lock tmpfs           1.7G     0  1.7G   0% /sys/fs/cgroup /dev/sda1       511M  6.1M  505M   2% /boot/efi tmpfs           340M   20K  340M   1% /run/user/1000 tmpfs           340M     0  340M   0% /run/user/106 What is the difference between "lay" and "lie"? Researching English/Christian families in India during first half of 19th century? How can we change root password? How exactly does a  work?  This is an extremely broad question. What code keeps things bouncing against each other, what code makes the player walk into a wall instead of walk through the wall? How does the code constantly refresh the players position and objects position to keep gravity and collision working as it should?  If you don't know what a collision engine is, basically it's generally used in  to make the player acutally hit walls and the like. There's the 2D type and the 3D type, but they all accomplish the same thing: collision.  So, what keeps a collision engine ticking? A thin-walled container of mass $m$ floats vertically at the separation surface of the two liquids of density $ρ_1$ and $ρ_2$  . The whole mass of the container is concentrated in the part of height $h$.  The question is to determine the immersion depth $h'$of the container in the lower liquid if the bottom of the container has a thickness $h$ and an area $S$ and if the container itself is filled with the liquid of density $ρ_1$.    I applied the fundamental principle of the statics on the container  $Balance$ $Sheet$:  The weight of the container ($-mg$)  The buoyancy force applied by the fluid with density $ρ_2$ ($ρ_2gSh$)  The weight of the fluid with density  $ρ_1$  (-$ρ_2gSh'$)  I summed up the forces and set them to zero and find my $h'$  but then  realised that the fluid with density  $ρ_1$  applied also a buoyoncy force on the top of the container , and the fluid with density  $ρ_2$  applied a buoyoncy force on the other fluid.  Where's the problem ? Conditional clause (then) In this first instance the main clause only stands alone if you  omit (then).  But in the other example it clearly has a main clause. So would this be classed as an embedded main clause as it only works as a independent clause if it's adjusted and or if it's joined with a dependent clause.  If I have enough money, then I will buy a new car.  If it rains, the picnic will be cancelled.  The picnic will be cancelled if it rains. How to construct an example of a probability distribution for which $\mathbb{E}\left(\frac{1}{X}\right)=\frac{1}{\mathbb{E}(X)}$ holds, assuming $\mathbb{P}(X\ne0)=1$?    The inequality which follows from Jensen's inequality for a positive-valued RV $X$ is like $\mathbb{E}\left(\frac{1}{X}\right)\ge\frac{1}{\mathbb{E}(X)}$ (the reverse inequality if $X&lt;0$). This is because the mapping $x\mapsto\frac{1}{x}$ is convex for $x&gt;0$ and concave for $x&lt;0$. Following the equality condition in Jensen's inequality, I guess the distribution has to be degenerate for the required equality to hold. A trivial case where the equality holds is of course if $X=1$ a.e. Here is an example I found in a problem book: Consider a discrete random variable $X$ such that $\mathbb{P}(X=-1)=\frac{1}{9}, \mathbb{P}(X=\frac{1}{2})=\mathbb{P}(X=2)=\frac{4}{9}$. It is then easily verified that $\mathbb{E}\left(\frac{1}{X}\right)=\frac{1}{\mathbb{E}(X)}=1$.   This example shows that $X$ need not be positive (or negative) a.e. for the equality in the title to hold. The distribution here is not degenerate either.  How do I construct an example, possibly like the one I found in the book? Is there any motivation? I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it. I have already read the question about  but this is not what I want, I want to be able to click on the file in Dash or in Nautilus and be able to open it with the specified app.  For example I have this case right now:  When I click on an EXE file it does not get executed by Wine, instead I get the following:    If I try to look for Wine in the Open With context menu option it is there. I am fine executing it from there the first time, but then the following times Wine does not appears selected in the main Context menu:    I then went to Properties to the Open With Tab to look for Wine. It was not in the Default apps nor was it in the Recommended ones when I clicked and search on Show other applications    This is not limited to EXE extensions. It also has happened with MKV files, MP4 files, JPG, PNG, MP3 and even SVG and CSS. So instead of trying to find a way of solving it for one, I want a way that can be done to any type of extension that can:   Make the app the default of that extension Appear on the context menu in Nautilus when I right click on the file Appears on the "Open With" tab on the Property window of the file Correctly executes the specified app when I click on the file with Dash   This might sound like it should be common sense for an app to execute the file but it does not always work like that. So for the cases where it actually does not work, how to fix it. A reset of the extension?, An update of the files that can open said extension?, an addition of the app via a command line or GUI tool? Why don't brakes come with 'Safety Levers' any more? It used to be very common to see bikes with dual pull brake levers (if that's even the right name) as shown below. However now it seems almost impossible to find brakes like this.  Even finding a picture to post was hard.  It seems like it would be quite useful to be able to brake from various hand positions.  There was an answer I read a while back (can't find it now) that stated that there was a reason they got rid of those, but no explanation as to why. So any technical reason, or is it just for looks? Can a matrix have a null space that is equal to its column space? I had a question in a recent assignment that asked if a $3\times 3$ matrix could have a null space equal to its column space... clearly no, by the rank+nullity theorem... but I have a hard time wrapping my head around the concept of such a matrix, no matter what size, even existing. How could this be possible, and does anybody have an example of such a $m\times n$ matrix?