Geometric interpretation of the tensor product of two projectif spaces $\mathbb{R} P^n \otimes \mathbb{R} P^n$
Geometric intuition for the tensor product of vector spaces
What's the difference between postfix/smtp and postfix/smtpd A bit confused when reading through the logs of my smtp/mail server, I'm turning this questions to you guys.   In the maillog files I'm seeing entries for postfix/smtp as well as postfix/smtpd. I can also see that there are possible settings for smtp as well as smtpd in the file main.cf  Trying to find some reasonable explanation through google search seemed to be impossible, so here is my question to you guys.  My server was kind of compromised and the spam mails where going through postfix/smtp and not smtpd. Please help me to understand. Thanks in advance! In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? Am I looking for a better behaved distribution for the independent variable in question, or to reduce the effect of outliers, or something else? After most recent kernel update (4.15.0-44-generic) my tablet freezes whenever plugged into docking station I performed the most recent kernel update on my Dell 5290 2-in-1 earlier today.  But moments after I plug it into its docking station, the screen flickers, blanks and freezes.  The only item left on the screen is the mouse pointer, and it is stuck.   If I leave the tablet not plugged in, it runs just fine.  It seems to be the docking station that triggers the freeze.  That said, I can log into the tablet via ssh even with the screen frozen.  So the system is still running.  But if I try to reboot the tablet via the reboot command, nothing appears to happen. sudo reboot -f will reboot the system, while sudo reboot will not.  Any ideas where I should start looking to identify this problem? This is a question that has been addressed several times, not only here, but also in other sites of the stack exchange network (e.g. ). However, I cannot make any of the solutions work for me.  I'm running a command through ssh. Whenever I exit ssh, I want the command to die as well. This command is a daemon called ktserver that runs indefinitely until you press Ctrl-C.  I run it as follows: ssh -t compute-0-1 ktserver and, indeed, when I press Ctrl-C, the process ends gracefully and the ssh session ends.  However, if instead of pressing Ctrl-C, I kill the ssh process using the kill command (for example, sending SIGINT or SIGHUP), the ktserver process stays alive.  How can I make the ktserver always die independent on how ssh is killed?  EDIT: If, instead of ktserver I run something completely different, such as gedit, everything works like a charm (i.e. gedit dies when the connection dies). Therefore, there might be something wrong with the process itself. For example, I thought that it might be ignoring SIGHUP or SIGINT. However, when I run kill -1 ktserver or kill -2 ktserver, the process dies as expected.  EDIT2: As Mark Plotnick points out, the issue is related to the fact that there is no communication circulating on the ssh channel. I've confirmed by running ssh -t &lt;host&gt; read and killing the ssh process afterwards. readwas still alive and kicking. Number of connected components of the complement of a compact Let $X$ be a connected, locally compact space and let $K$ be a compact subset of $X$. Is the number of connected components of the complement $X\setminus K$ finite? If it is not, are there some hypotheses over $X$ for finiteness of connected components? Hexadecapole potential using point particles? We can get monopole $1/r$, dipole $1/r^2$, quadrupole $1/r^3$ and octupole $1/r^4$ potential falloff by placing opposite point charges at the corners of a point, line, square and cube, respectively. My book cryptically says "and so on", how does one get a $1/r^5$ and higher potential falloff with a finite number of point-charges in 3 dimensions? Change the Ubuntu program that runs when a command can't be found How to reduce the number of hyphenation? Sometimes, assume our document contain many long words, TeX may generate some hyphenation at the end of line. But it really hinder our smooth reading. Although I know we can add the hyphenation rule at the preamble. It can't reduce hyphenation number but effect the hyphenation position. It is said that microtype package can give us more compact output. But it require expert level to tuning the parameter. What's the difference between term_id and term_taxonomy_id If $\sum_na_n=\infty$ and $a_n\downarrow 0$ then $\sum\limits_n\min(a_{n},\frac{1}{n})=\infty$ If $\sum_na_n=\infty$ and $a_n\downarrow 0$ then $\sum\limits_n\min(a_{n},\frac{1}{n})=\infty$     My  idea:  $$b_{n}=\min(a_{n},\tfrac{1}{n})\Longrightarrow b_{n}\le a_{n},b_{n}\le\tfrac{1}{n}$$ then I don't know how to go on. Moving all files to a new computer, my concern is links I'm moving all files to a new computer, via an external hard drive. I am certain that broken links will be a concern. What can I do to fix this? Is there a 'Best Practices' kind of way to prevent this problem beforehand? I have many hundreds of .blend files, and of course, I fear losing them. When are infinities okay? I'm a little confused about how to handle infinities in physics. On the one hand, I always here things like infinities are not physically tenable answers. GR can't answer anything about the origin of the universe because of singularities. Throw away the radial solution that gives an infinite potential when solving the Laplace equation in spherical coordinates. But then there are other times that the infinities are okay. For instance, it is usually okay to set the reference point for your potential at infinity. There are certain times in David Tong's quantum field theory lecture notes where he seems to almost to hand wave away infinities. So, philosophically, physically, and mathematically when are infinities okay, and when are they not okay? Earth moves how much under my feet when I jump? If I'm standing at the equator, jump, and land 1 second later, the  Earth does NOT move 1000mph (or .28 miles per second) relative to me,  since my velocity while jumping is also 1000mph.   However, the Earth is moving in a circle (albeit a very large one),  while I, while jumping, am moving in a straight line.   How much do I move relative to my starting point because of this? I  realize it will be a miniscule amount, and not noticeable in practise,  but I'd be interested in the theoretical answer. Which of these sentences is correct, and why?   "What if the Moon was a Disco ball?" or  "What if the Moon were a Disco ball?" Proving replacement theorem? I want to see if I am understanding the proof of the replacement theorem correctly.   Let $V$ be a vector space that is spanned by a set $G$ containing $n$ vectors.  Let $L \subseteq V$ be a linearly independent subset containing $m$ vectors.  Then $m\leq n$ and there exists a subset H of G containing exactly $n-m$ vectors s.t. $L \cup H$ generates $V$.   The proof in the book says to start with $m=0$. In that case $L=\varnothing$, the empty set.        Let's assume this theorem is true for some integer $m \geq 0$.   Let $L = \{v_j\}_{j=1}^{m+1}$ and define it as a linearly independent subset of $V$ consisting of $m+1$ vectors.  Since any subset of a linearly independent set is linearly independent as well ($S_1 \subseteq S_2 \subseteq V$), then $\{v_j\}_{j=1}^m$ is linearly independent also.   It then says to use the induction hypothesis to say that $m \geq n$. Well, ok, but that seems sort of pulled out of nowhere to me. The next step is to say that there is therefore another subset, $\{u_k\}_{k=1}^{n-m}$ of G such that $\{v_j\}_{j=1}^m \cup \{u_k\}_{k=1}^{n-m}$ spans $V$.   That being the case there are scalars $(a_j)_{j=1}^m$ and $(b_k)_{k=1}^{n-m}$ which you can multiply by the vectors $v_j$ and $u_k$. You can then add the two sets of vectors, yielding $$\sum_{j=1}^m a_j v_j + \sum_{k=1}^{n-m} b_k u_k = v_{m+1}$$  At this point I am not sure I understand things. Because we are assuming $n-m&gt;0$ -- otherwise $v_{m+1}$ is linearly dependent. But then it says not only is $n&gt;m $ but $n&gt;m+1$, and that is where I am losing the plot to get to the next step. I have tried as following:  1. Turn off: export DISPLAY=:0.0 &amp;&amp; xset dpms force off  2. Turn on: export DISPLAY=:0.0 &amp;&amp; xset -dpms   Which works but that is a temporary solution, which does not fix my problem yet. When i reboot system it start again and again the same auto turn off mode.   How can i now remotely using SSH turn it off forever?  IMPORTANT:  - KIOSK (ATM machine will use this option) - 24/7 advertising display/slides will use this   Optional Note: this guide i followed   , but permanent solution did not worked. Want to set a guest session password for login. How do you do this after skipping it at OS install? Custom post type - posts list - white screen of death Increase iPhone call history Can you get to blocked-in areas?