"Failed to start session" for main and guest accounts
How do I reset a lost administrative password?
I've been asked by some schoolmates why we have $$ \sum_{n=0}^\infty \frac{1}{n!}=e.$$ I couldn't say much besides that the $\Gamma$ function, analytic continuation of the factorial, is defined with an integral involving $e$. Then I also know that actually $$ \sum_{n=0}^\infty \frac{x^n}{n!}=e^x.$$ Is there a reason for these facts?  P.S. I added the tag "intuition", please remove it if you think it is not pertinent. A couple years ago I ran upon a  video demonstrating how researchers used x-rays given off by tearing tape off its spindle in hopes to miniaturized and cheapen future x-ray devices. As of late I have been wondering what interactions are causing this. I understood from the video that the electrons are being ejected due to the added energy to the system (peeling). This instinctively pointed me towards QED where interactions between electrons produce a photon for short periods. 1)Are those same photons from electron interaction the resulting x-rays? 2)Are the frequencies of the photons being limited by the $\Delta$energy$\Delta$time uncertainty, and/or $\Delta$position$\Delta$momentum uncertainty (at the vertex of the ripping tape, where high densities of electrons may accumulate) ? Note: I've also considered that the van der Waals force may come into consideration, not certain though. Looking for a QED based descriptions/answers. Any elementary references to this work is appreciated. How could Luke hide from Vader during the duel on Death Star II? In Return of the Jedi, Vader throws his lightsaber at Luke causing the catwalk come crashing down. Luke uses this in his advantage and hides from him under the throne room platform. Unable to locate his son, Vader tried to lure Luke out of hiding.  But how could Luke conceal himself from Vader in the first place? Did he use a Force power of some kind to blur Vader's sensors? I mean, the underneath of the platform was pretty much an open space with very little possibilities for hiding. The only places I see in the movie are the openings on the both sides of the floor (pointed by the yellow arrows):    The background of a close-up to Luke doesn't give much of a clue (although there is a round shape which could be the bottom of a window frame):    But as Luke reveals himself, he appears to be beneath of the staircase to the dais, right in the middle of it:    There's no way he could have hidden there all the time, because just a couple of seconds before, Vader walked towards and stared at the very same spot:    My first ideas were that Luke used the Force to make himself invisible, or to teleport him to the position. But after taking a look at one of the cross sections of the Emperor's throne room, I assume Luke could have slid almost straight under the floor of the lower level (yellow arrow) and then later  back to the staircase (although we don't see it in the movie, and I'm not sure if Luke knew the ability):    Does someone know better? This inequality $a+b^2+c^3+d^4\ge \frac{1}{a}+\frac{1}{b^2}+\frac{1}{c^3}+\frac{1}{d^4}$ let $0&lt;a\le b\le c\le d$, and such $abcd=1$,show that   $$a+b^2+c^3+d^4\ge \dfrac{1}{a}+\dfrac{1}{b^2}+\dfrac{1}{c^3}+\dfrac{1}{d^4}$$   it seems harder than We currently have about 50 pages, each of which I want a user (eg, bob, rob, smith) to be able to edit only 1 page.  For example, bob &amp; smith each have their own page.  I do not want bob to be able to edit smith's page.  I want bob to ONLY be able to edit bob's page.  I don't care if he can see other pages. Looking through the user roles, I don't see a way to currently to do this- I only see how to allow restrict access on a global scale.  Are their any plugins to help restrict edit access per user, or roles restricted to editing specific pages and I can just add 1 user per role?  Or was there a way to do this with default settings I missed. Got a bunch of .mp4 videos (info shows H.264 Video + AAC Audio) that are chapters of a larger video.  I'd like to merge them, but not sure which is the best way.  I don't have Quicktime Pro, but I'll get it if that's the best way to do this.  Edit: Just to clariify this is Mac OSX 10.6 I'm on. Basic Electronics Book Modifying agsm.bst package bibliography output I would like to change the URL output from:  URL: the html link  into:  [Online]URL: [Accessed on]  I am using:  \usepackage[comma]{natbib} \bibliographystyle{agsm} How to download/read only the first 80KB of a file? Making tags visible when using a Tumblr theme that doesn't show them Cross tabulation of two categorical variables: recommended techniques Coordinate-Free Definition of Trace. $\DeclareMathOperator{\tr}{trace}$ I am reading the  on the trace operator. The section titled Coordinate-Free Definition defines the trace as follows.  Let $V$ be a finite dimensional vector space over a field $F$ and define a bilinear map $f:V\times V^*\to F$ as $f(v, \omega)=\omega(v)$ for all $(v, \omega)\in V\times V^*$. This maps induces a unique linear map $\tr:V\otimes V^*\to F$. Since $\text{End}(V)$ has a canonical isomorphism with $V\otimes V^*$, we have now a notion of trace of a linear operator on $V$.  The Question: The second paragraph of the section in the article says that  This also clarifies why $\tr(AB)=\tr(BA)$.  I can't see how $\tr(AB)=\tr(BA)$ follows from this definition at all. Can somebody give me a hint? Does Stack Exchange have an Economics section? My mortgage came up for renewal right at the time in 2009 when UK interest rates hit rock bottom. This was unprecidented, and most financial advice was to take out a fixed-rate mortgage. So I perhaps went overboard and got one for ten years.  Five years on, interest rates haven't moved and I'm losing money on it to the tune of £100 a month. Obviously, this is ongoing: so that decision has cost me about £5000 in real terms so far. It'll come to a lot more by the end of the mortgage, unless interest rates rise.  Being fixed rate, it's been designed so you can't get out early. If I decide to end the mortage, it'll cost me £1,000 per year of the mortgage remaining - which is roughly what I'm losing anyway, so that seems a bad idea.   I can overpay by up to £500 per month. However, doing this doesn't help pay down the mortgage at all: the total is just added up and will cause the mortgage to end early, by a period dependent on the overpayment total.   This seems to me to be a very bad idea because hoping interest rates rise over the next five years is the only hope I have of making good on some of the losses that I've made.   Is this sensible thinking? If so, is there anything at all I can do to try and ameliorate the financial pain this product is causing me? Where can I find Ghost/Poison/Psychic type Pokémon? I frequently login to a server, then cd into a specific directory. Is it possible to simplify these two commands into one?   ssh bob@foo   cd /home/guest   I'd like to avoid changing anything on 'foo' if possible, as I'll have to clear it with the server administrator. I use bash, but I am open to answers in other shells. What is the easiest way to resolve apt-get BADSIG GPG errors? I frequently cross this issue, and always have to google for an answer. Does anyone have a permanent fix for BADSIG errors from apt-get?     W: GPG error:    lucid   Release: The following signatures were   invalid: BADSIG 54422A4B98AB5139   Oracle Corporation (VirtualBox archive   signing key) Show an Ideal is the principal ideal for some polynomial. Let $F$ be a ﬁeld and $R = F[X]$. Suppose $I$ is an ideal of $R$. Show that $I = (p(X))$ for some $p(X)$ in $F[X]$. (Hint: consider a polynomial $p(X)$ of least degree in $I$.)  I'm trying to do this question but can't seem to start. if anyone could give me a hint that would be appreciated.  My instinct was to take a monic polynomial (which exists since we are in a field) of degree $1$ and divide given the first two parts of the question were about polynomial division.  Thanks. I have just fitted a new screen to my iPhone 5s, and i need to restore it to factory settings.  One problem though, it's disabled for over 23,000,000 minutes and the home button doesn't work.  Does anyone know how I can restore it? sudo apt update &amp;&amp; sudp apt upgrade -y now shows the error message E:The package linux-modules-5.4.0-56-generic needs to be reinstalled. But I can't find an archive for it.  and nothing proceeds. How can I fix this problem? Thanks.