Present perfect or present perfect continuous with a participle?
How can I reliably and accurately identify the passive voice in writing or speech?
I am not very well versed on set theory or syntax, but I thought I knew the basics.  However, in a book about databases I am reading now, the author uses $2^x$ to signify "a set of $x$."  For example, $2^{\text{dogs}}$ is a set of $\text {dogs}$, etc.    The author never really explained this or why he does it, I just picked up the meaning from context.    I am not sure why the exponent operator is used, nor am I sure what the number $2$ has to do with it.  The sets being represented are NOT powers of $2$ (in size)... they come in all sizes.  Is this a valid notation?  I have not seen it anywhere before... Is volunteer work allowed in the US while visiting under the VWP or a B1/B2 visa? I am going to Santa Monica for 4 weeks to polish my English in July and would like to volunteer at the Planetary Society located in Pasadena.  I am a Swiss citizen and have a biometric passport. However, I don't have any special visa, as there is no visa needed for the school I am attending and using the Visa Waiver Program, I am allowed to stay up to 90 days in the US.  Am I allowed to do volunteer work during my stay? Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n  Hi everyone, for the proof to the above question,  Can I assume that since $(a, b) = 1$, then in the prime-power factorization of a and b, they have no prime factor in common, when they are taken to the $nth$ power, they will still have no prime factors in common, and so $(a^n, b^n) = 1$ for all positive integers n.  I think I'm jumping to conclusions here again, if so, leave some tips on how to do the proof properly, thanks :)  And also, I do not know how to approach the reverse problem where if $(a^n, b^n) = 1 then (a, b) = 1$, any guidance will be much appreciated! How to boot from iso with Grub2/Burg boot loader I'm using Ubuntu as my primary OS and alternative is Windows 7 for gaming, and another stuffs. I want to have menu to boot some live CD ISO. Is there anyway to make menu entry in Grub2/Burg to boot ISO file like the CD way?  I see there are some ways to make it possible but almost method need specified boot arguments (kernel parameters). But I have mixed kind of Live OS wan to boot up using boot loader included: Linux, Unix, DOS (for recovery purpose)...   I'm looking for more generic way to make it easy to discover and add to the menu config file. $f_n(x) = x - x^n$ for $x\in [0,1]$. Does the sequence converge pointwise or uniformly on $[0,1]$? $f_n(x) = x - x^n$ for $x\in [0,1]$. Does the sequence converge pointwise or uniformly on $[0,1]$?   We also have to prove why it is or isn't pointwise or uniformly convergent.   I have worked out that on $x\in[0,1)$, the limit as $n$ approaches infinity is $x$. And when $x=1$ the limit is $0$.   So this means its pointwise convergent right? But how do I prove this?  Also how on earth do I prove it is not uniformly convergent? (I'm just assuming it's not). Prove that a graph with the same number of edges and vertices contains one cycle What is a word that means "someone who pretends to be your friend but is actually your enemy?" What do you call someone who pretends to be your friend but is actually your enemy?  A friend suggested spy for me, but that does not nearly describe the word I need for an English project. The character is very good at manipulating how people see him. He's a good liar. And pretends to be your friend but actually is your enemy. I see more and more servers that have no domain defined in the /etc/resolv.conf file.  Only a search entry. In what cases is this setup used ? Are there any cases where it must not be used ?  nameserver xxx.xxx.xxx.xxx nameserver yyy.yyy.yyy.yyy nameserver zzz.zzz.zzz.zzz  search domain1 domain2 domain3 ... Is every discrete absolute value non-archimedean? I've been reading Milne's notes on absolute values and local fields (Chapter 7 of the book on algebraic number theory), and a possibly minor point is confusing me.   On page 126, Milne writes, "$K$ is a field complete with respect to a discrete absolute value $|\cdot|$..." and then he talks about things that only make sense for non-archimedean absolute values, like the ring of integers and its maximal ideal.   Is every discrete absolute value on a field $K$ also non-archimedean? This would explain a lot, but I also suspect that it is not true, because I can't find any statement of this fact anywhere.  EDIT: An absolute value is discrete if the value group $|K^\times|$ is a discrete subgroup of the multiplicative group $\mathbb{R}_{&gt;0}$. An absolute value is non-archimedean if it satisfies the stronger triangle inequality $$ |x+y| \le \max (|x|,|y|) $$ or equivalently if the set $\{|1|,|1+1|,|1+1+1|,\ldots\}$ is a bounded subset of $\mathbb{R}$. How to recover files from dead windows using dos? Let $L,M$ two subspaces of the vector space, $V$ such that both $L,M \ne V$.   Prove: $L\cup M \ne V$.     I think this is a case of a proof by contradiction. Lets assume $L \cup M = V$.   Hence, $$\dim(V) = \dim(L) + \dim(M) - \dim(L\cap M)$$  How to proceed? What software can join videos? What's the best &amp; easiest GUI software that can join a video that I have downloaded in several parts? Can anybody explain the necessity of the RC network shown in the figure. I found this in circuit for a logic power supply using Fly-Back converter? UV Maps not showing in render I can not add all the images because the account is new and I don't have enough reputation.  I have an object (a tube of a cream) with three diferent materials, the base "plastic" material and I have created two separated materials to add the front and black labels to the tube.  The front and back label materials is the same as the "base material" but I'm trying to overlay the PNG image on top of it.  For doing that I have unwraped the parts of the object where the labels should go and placed the islands on top of the image.  I have created separated UV Maps for that purpose.     On the viewport view everything seems ok: As you can see the texture is correctly placed.   Render / Rendered view unexpected output: When rendering or in the rendered mode of the viewport the material with the UV Map appears as black.   Material nodes: For further info in case it's needed here are the screencaps of the material of the front label:        How can I solve this? Thank you! How to view the output of a running process in another bash session? I have left a script running on a remote machine from when I was locally working at it. I can connect over SSH to the machine as the same user and see the script running in ps.   $ ps aux | grep ipcheck myuser  18386  0.0  0.0  18460  3476 pts/0    S+   Dec14   1:11 /bin/bash ./ipchecker.sh   It is simply outputting to stdout on a local session (I ran ./ipchecker.sh form a local terminal window, no redirection, no use of screen etc).  Is there anyway from an SSH session I can view the output of this running command (without stopping it)?  So far the best I have found is to use strace -p 18386 but I get hordes of text flying up the screen, its far too detailed. I can stop strace and then sift through the output and find the text bring printed to stdout but its very long and confusing, and obviously whilst it's stopped I might miss something. I would like to find a way to see the script output live as if I was working locally.  Can anyone improve on this? The obvious answer is to restart the script with redirection or in a screen session etc, this isn't a mission critical script so I could do that. Rather though, I see this as a fun learning exercise. Compact topological space with closed graph implies continuity Let $X,Y$ be topological spaces and $f:X \rightarrow Y$  If $Y$ is compact and $G(f)$ (graph of $f$) is closed, show that $f$ is continuous.   I consider an open set in $X$, and as $G(f)$ is closed, $(X \times Y)-G(f)$ is open. And I guess I need to do something here. Then I can get some open sets. Also, I notice that compact is something relate to "finite". I guess I can use the compactness to do finite intersection or union and get the result finally.  But what should I do in the middle or I am not even on a right track. Editing Photoshop (PSD) files on Ubuntu? I was wondering that is it possible to edit PSD files on Ubuntu (like with Gimp). Actually, I need to edit layers. I haven't managed to do it. It would be nice if there is a chance! :) This is actually a two part question:   Which methods are there to calculate average slope by unit (say km²) for a given area? Are there any special requirements on the data - like additional information besides height measurements? Which open source GIS implement methods usable to calculate average slope on a grid (e.g. TIF file)? Lost supplementary user groups for GUI login session Ubuntu 16.04.5  Very weird situation - after Xorg crash, now every time when I login into Unity, my user account doesn't have it's system groups like adm, sudo, plugdev, fuse etc. But when I login on virtual console (Alt+F1) or over SSH - all my additional groups are there, as reported by id command.  Neither of /etc/group* or /etc/gshadow* files have changed, my user is still listed there in many system groups.  It looks like some systemd session parameters for GUI logins or lightdm cache files got screwed. But I have no idea where to start looking..  A lightdm log:  $ journalctl -au lightdm  -- Reboot -- systemd[1]: Starting Light Display Manager... systemd[1]: Started Light Display Manager. lightdm[3223]: pam_kwallet5(lightdm-greeter:setcred): (null): pam_sm_setcred lightdm[3223]: pam_unix(lightdm-greeter:session): session opened for user lightdm by (uid=0) lightdm[3345]: pam_succeed_if(lightdm:auth): requirement "user ingroup nopasswdlogin" not met by user "chm" lightdm[4867]: pam_ecryptfs: Passphrase file wrapped lightdm[3345]: pam_kwallet5(lightdm:auth): (null): pam_sm_authenticate lightdm[3345]: pam_kwallet5(lightdm:setcred): pam_kwallet5: pam_sm_setcred lightdm[3345]: pam_unix(lightdm:session): session opened for user chm by (uid=0) lightdm[3046]: Error writing to daemon: Bad file descriptor lightdm[3046]: Error writing to daemon: Bad file descriptor lightdm[3046]: Error writing to daemon: Bad file descriptor lightdm[3046]: Failed to write utmpx: Permission denied 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.