I am testing my new (dual boot) Ubuntu install. When playing with basic terminal commands I noticed that i was logged in (or something to that effect) twice! Here are my commands and the terminal results.  ~$ who karsus   :0           2016-01-27 21:24 (:0) karsus   pts/9        2016-01-27 21:24 (:0) ~$ w 21:26:46 up 3 min,  2 users,  load average: 0.28, 0.34, 0.15 USER     TTY      FROM             LOGIN@   IDLE   JCPU   PCPU WHAT karsus   :0       :0               21:24   ?xdm?  55.54s  0.14s init --user karsus   pts/9    :0               21:24    1.00s  0.03s  0.00s w ~$    Did I do something wrong? When I first saw this I restarted my laptop and went to the terminal straight after log in. Then I got the results posted above.  Is that normal? - If so what does it mean?  Thank you for your help.
I was looking for some shell commands, and I took a look in "users" command.  I was hoping to get only 1 name, but I got 2:  nori@nori-hidamari:~$ users nori nori   And when I run the command "who"  nori@nori-hidamari:~$ who nori     :0           2015-04-09 09:31 (:0) nori     pts/0        2015-04-09 09:48 (:0)   Is this behaviour normal? Or it's bad?  Thank you guys for helping me.
Density function for RV The density function for a random variable X is given in terms of a constant $c$.  Find the value of $c$.  What is the corresponding distribution function?  Sketch both the density and the distribution functions. Finally, find the probabilities.  5.1 $f(x)=0$ for $x&lt;0$ and $f(x)=\frac{c}{(x+1)^4}$ for $0&gt;x$   $P(X&gt;4)$  $P(X&lt;2)$  $P(1\le\ X&lt;3)$   I get $c=3$ by taking the integral, and then I am a little confused as to why  $F(x)=1-\frac{1}{(x+1)^3}$  Is that because in solving for $c$, I ended up with $1=\frac{c}{3(x+1)^3}$, so substituting c in I get $1=\frac{1}{(x+1)^3}$?  And, then  $P(X&gt;4)=1-P(X\le\ 4)$ $=1-(1-{1}{(1+4)^3})$ $=1/125$  $P(X&lt;2)=1-{1}{(1+2)^3}$ $=26/27$  I guess I am a little confused about what $F(x)$ and $f(x)$ actually MEAN? And thus that leads to my confusion about what the differences between $&gt;$ and $&lt;$ and greater than or equal to are, etc etc in terms of the equations. The ones above I solved by comparing to the book but I still don't understand what they mean really.  So as a result, I don't really get how to solve $P(1\le\ X&lt;3)$.  5.2 $f(x)=ce^x$ for $x&lt;0$ and $f(x)=ce^{-x}$ for $0&gt;x$  5.3 $f(x)=0$ for $x&lt;-1$ or $x&gt;2$ and $f(x)=cx^2$ for $-1&lt;x&lt;2$ Can you use Magical Secrets to choose high level spells when multiclassing as a Bard? Say you have a Wizard 7/Bard 9. You gain your 17th level and choose to gain the level in Bard (which grants you Magical Secrets). According to the Multiclass Spellcaster: Spell Slots per Spell Level table, you now have a single 9th level spell slot. Can the spells you choose from Magical Secrets be 9th level spells even though you can only cast up to 5th level Bard spells? If a series converges, then the sequence of terms converges to $0$. What is the need for Autobiographer badge? What is the reason that Autobiographer badge is kept in Stack Exchange?  This does not show any participation and people can just fill garbage to achieve this badge.   Is there a reason behind it? We have previously determined that  or  can attune to magic items, but one of those is a sapient creature, and the other "always obeys your commands".  A paladin's steed (per the Find Steed spell) is also 'unusually intelligent' and falls within the score range for sapient creatures.  But what about a regular old animal? If my ranger has a wolf companion, can he make that wolf attune to, say, an Amulet of Health? According to the Beast Master archetype, a companion animal "obeys your commands as best it can".  Is spending an hour 'focused only on the item' (as required for attunement) something a beast can manage?  Or what if it's not an Animal Companion, but just a riding horse, a pet dog, a trained magpie?  I know, probably this is going to be down to the DM to determine, but is there any guidance we can use to help decide whether my cat can attune to an item, and whether rubbing it with catnip would help? How to install apps which require a newer version of iOS on a 1st gen. iPad? states that if $f:X \rightarrow Y$ is a morphism of ringed space, $G$ is a locally free $O_Y$-module, then $f^*G$ is a locally free $O_X$ module.     Suppose that $G$ is a locally free $O_Y$ module, hence it is a free $O_Y|_U=O_U$ module. We have an induced map  $$f^{-1}(U) \rightarrow U$$ given by restriction of morphism of ringed spaces.   Hence, as $\bigoplus O_U \simeq G|_U$, $f^*:Mod(O_U) \rightarrow Mod(O_{f^{-1}(U)})$ is functorial, $f^*(G|_U) = (f^*G)|_{f^{-1}(U)}$, we have isomoprhism,  $$ \bigoplus O_{f^{-1}(U)} \simeq (f^*G)|_{f^{-1}(U)} $$ Possible Beamer bug: Frame number has different color than date in infolines footer Expansion of $(1+\sqrt{2})^n$ I was asked to show that $\forall n\in \mathbb N$ there exist a $p\in \mathbb N^\ast$ such that $$(1+\sqrt{2})^n = \sqrt{p} + \sqrt{p-1}$$   I used induction but it wasn't fruitful, so I tried to use the binomial expansion of $(1+\sqrt{2})^n$ but it seems I lack some insight to go further.   Any hint is welcomed. Convergence of integrals in $L^p$ Stuck with this problem from Zgymund's book.   Suppose that $f_{n} \rightarrow f$ almost everywhere and that $f_{n}, f \in L^{p}$ where $1&lt;p&lt;\infty$. Assume that $\|f_{n}\|_{p} \leq M &lt; \infty$. Prove that:  $\int f_{n}g \rightarrow \int fg$ as $n \rightarrow \infty$ for all $g \in L^{q}$ such that $\dfrac{1}{p} + \dfrac{1}{q} = 1$.  Right, so I estimate the difference of the integrals and using Hölder end up with:  $$\left|\int f_{n} g - \int fg\right| \leq \|g\|_{q} \|f_{n} - f\|_{p}$$  From here I'm stuck because we are not assuming convergence in the seminorm but just pointwise convergence almost everywhere. How to proceed? Is a "split plot" ANOVA with two factors the same as two-way ANOVA with repeated measures in one factor? Is a "split plot" ANOVA with two factors identical to two-way ANOVA with repeated measures in one factor? if not, what is the distinction? Font corruption: lines through characters I have a problem where a one-pixel high white line is displayed through certain letters of text. Almost always only a single character type is affected at once, and only in one font size (though that size can change over time). Most of the time things are fine, but this happens several times a day. It happens frequently in Firefox, but system dialogs, menus, etc. can also be affected. It's been happening ever since I upgraded to 10.10. Only restarting seems to fix it.  Two examples (in the first, only the larger "r" is corrupted):     Any help would be appreciated, thanks.  Edit: I've since noticed that I can (sometimes) make the fonts appear correctly by zooming in/out all the way and returning to the default in Firefox (one or two steps, then going back, does nothing) seems to make the problem go away temporarily.  Edit 2: I figure it's worth noting that the solution below doesn't fully work for me any longer (I'm now using Ubuntu 11.10). It does significantly reduce the frequency of this problem occurring.  Edit 3: Still around in 12.04. The fix provided by Vanni works perfectly now for me, but apparently doesn't for some.  Edit 4: This seems to be an xorg problem, with Vanni's answer fixing it for many Intel video cards. I've had this occasionally happen with AMD graphics cards in 13.10 and 14.04, but very rarely (only two or three times). Fractions with large elements What is best practice for typesetting fractions with large objects in the numerator and denominator?  For example, fractions with limits, integrals, summations, etc... cause the expressions to look contracted and somewhat odd.  I understand that it is probably best to leave this as is when writing mathematics inline, but as a stand-alone fraction I feel it would be much less distracting if the symbols were typeset at normal size and the fraction was given more height in which to place itself.  Are there standards (for pure mathematics) regarding this problem? And what are the options - if it's generally permitted - for expanding the fraction size to incorporate large objects?    Example  \frac{\sum_{i=0}^{n} i^2}{\iint_{D}\frac{\partial (x,y)}{\partial (u,v)}\,\mathrm{d}u\,\mathrm{d}v}   Both the summation and the integral look somewhat cramped. Subdivision Surface not making things smooth as they are in the tutorial I am following Seeking neighborhood boundaries globally? Besides Zillow's creative-commons licensed  shapefiles, what sources of neighborhood boundaries are there? Not just in the US, but all over the world.  Free/open source is ideal, but paid sources could be interesting too. Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$. Can “zealot” have a positive connotation? A zealot is a person who is fanatical and uncompromising in pursuit of their religious, political, or other ideals.  I have never seen this word used with positive connotation, but could it (without causing raised eyebrows)? For example, “Gandhi was a zealot and should be admired by all who believe in non-violence.”  Also, do “zealous” and “zeal” carry the same connotation as “zealot”? Wildcard certificates with short hostnames? I'm trying to generate a certificate with the following subjectAltName:  hostname *.hostname hostname.mydomain.local *.hostname.mydomain.local   I generate the CSR via OpenSSL and then get the certificate from Microsoft Active Directory Certificate Services. Certificate works OK for the following alternative names:  hostname hostname.mydomain.local *.hostname.mydomain.local   But, *.hostname just doesn't work. Testing with Curl, I get the following output:  % curl https://m.example/ curl: (51) SSL: certificate subject name '*.example' does not match target host name 'm.example'   If, on the other hand, I add 'm.example' as a subjectAltName, then it works. So, wildcard with shortened hostname just refuses to work. Good tool for finding photo duplicates based on image data What is a good (and preferably free) tool for finding photo duplicates based on the photos themselves?  So, not filename, filesize etc., but how the photos look like. It would be nice if it managed to match photos that were the same image, but not exactly the same size for example too. ... namely that if $n &gt; 1$ and $(n − 1)!\equiv−1\pmod{n}$, then $n$ is prime.  This is for a number theory class I'm in at Penn State. My idea is to follow accordingly, but I can't get it concretely..  Reason by contradiction, suppose that $n$ is not prime.   Then $n = ab$, where $1 &lt; a, b &lt; n$  In particular $(n-1)! = ai$ for some $i\in\Bbb{Z}$. $\\$ If $(n-1)! = nj - 1$ for some $j\in\Bbb{Z}$ then it follows that a probably doesn't divide $-1$?