We have that $\lambda, \overline{\lambda} \in \rho(T)$ and $\lambda \in \mathbb{C}$. Now, I want to show that a symmetric operator and closed operator $T: \operatorname{dom(T)} \rightarrow H$ must be self-adjoint. Notice, that $T$ is not necessarily densily defined. Does anybody here have any ideas? Actually, I concluded the closedness of this operator from the fact that the resolvent is not empty by myself, so this may be somehow a tautology in this exercise.
For symmetric operators one has: $$A\text{ symmetric}:\quad\mathcal{R}(A\pm\imath)=\mathcal{H}\implies A^*=A$$ How to prove this in an unveiling way?
I have an Ubuntu 14.04 server that has no external monitor connected.  I use NoMachine to remote control the machine.  When I do so, the Unity/Gnome interface doesn't see any monitors connected, so I can only use 800x600 when connecting with NoMachine.  If I plug in a monitor, I can set the resolution to whatever size the NoMachine window is on the remote computer.  Is there a way to create a "fake" monitor device on Ubuntu so I can set a desktop resolution in Unity/Gnome? In mathematics, we like talking about idempotent matrices. In a masters program that I am currently enrolled in, I have heard one professor pronounce it one way, and another professor pronounce it another way. The  explains it better than I could:  Is there a correct pronunciation for idempotent? Is it like omnipotent (om-nip-o-tent), so id-EMP-o-tent, or is it more like the two seperate words idem + potent I'd say EYE-dm-POT-nt, but then I speak Brit. Charles Matthews 07:57, 30 Jun 2004 (UTC) Ditto, but then I speak Australian ;) Dysprosia 08:01, 30 Jun 2004 (UTC) Actually the British is more like EYE-dm-PO-tnt, I guess. Charles Matthews I'd just like to pedantically point out that it would be pronounced i-DEM-po-tent because because syllable onsets are maximized. daesotho 20:33, 21 Oct 2004 (UTC) The American pronunciation puts primary stress on the second syllable ('dem') and secondary stress on the fourth syllable ('tence'). Could somebody more familiar with IPA than I am please add this to the article as an accepted pronunciation? My American dictionary says |ˈīdemˌpōtənt| for the adjective. I speak American (non-natively) and I wouldn't stress the second syllable for itempotence. My only question is, right now it says /ˌaɪdɪmˈpoʊtəns/ -- but can't it be stressed on the first syllable too? Should we add /'aɪdɪmˌpoʊtəns/ as an alternative? -- 87.160.141.177 (talk) 14:50, 3 June 2011 (UTC) And by the way I think it's silly giving a pronounciation guide as this is just imposing a particular accent. (For what it's worth I pronounce idempotent with a short 'i', as in the word 'id'). Alex Selby I agree with Alex Selby - the pronunciation guide should be extended to show the variation, or removed. Strictly, there's no reason for the first i to be long (neuter idem has a short first syllable in Latin), and I can't find any authoritative source which advocates the pronunciation given. Ms7821 (talk) 22:59, 15 July 2015 (UTC)  Is there a &quot;correct&quot; pronunciation for this word? Is it safe to replace a 4400mAh laptop battery with a 8800mAh battery? I have an Acer Aspire 5536G. My battery is having problems so I am thinking of replacing it. I have searched online through many sites and I found some good deals. However, currently my laptop has a 4400mAh lithium ion battery so I was thinking of replacing it with 8800mAh 12-cell battery that lasts more hours than 4400mAh without power plug. Multiples of an irrational number forming a dense subset How can I make Firefox download different file types to different locations? 98% of what I download is music, so I set the download location to my music folder. However, the other 2% has no place there, so every time I download .doc files or PDF files I have to remove them. Is there a way to make Firefox change the download folder based on file extension? I'll settle for all non-MP3 files getting saved to the desktop.  I know I can right click, choose Save Link As and pick the download location myself, but it seems like there should be a better way. When conducting multiple regression, when should you center your predictor variables & when should you standardize them? How does gravity work underground? Would the effect of gravity on me change if I were to dig a very deep hole and stand in it? If so, how would it change? Am I more likely to be pulled downwards, or pulled towards the edges of the hole? If there would be no change, why not? I am looking to sell and buy a house. But with the current market being as crazy as it is (houses are selling fast for sometimes 150,000 over asking), I'm afraid if we sell first, we could be stuck without a new house. Or stuck settling on or over-paying for something and wishing we never sold at all. I'm wondering if it's possible to buy first. What is the best way to secure my next house before selling my current house without getting locked into a B-lender mortgage or risking too much?  I know there would be some risk putting an offer on a new house without knowing how much the current house will sell for, or the risk we don't sell the current house before the new house closes. I'm also afraid conditional offers will not be considered. Are there any other options?  (We do have a mortgage on the current house, but because the market has gone up so much there is also a good chunk of equity.) Festival stores voicepack data in the following example directory structure:  /usr/share/festival/voices/&lt;language&gt;/&lt;voicepack name&gt;  What is the simplest one-liner (preferably using ls) to print out just the &lt;voicepack name&gt;'s, in all the potentially numerous &lt;language&gt; subdirectories? Why is "glide symmetry" its own type? Artin's Algebra pages 155 &amp; 156 list the types of symmetry of a plane figure as:   Reflective Rotational Translational Glide   He then goes on to say "Figures such as wallpaper patterns may have two talk about other figures having combinations of independent" symmetries. EDIT: He says "... having combinations of independent translational symmetries". See Joriki's answer.  Why doesn't glide symmetry count as having two independent (reflection + translation) symmetries? If we're going to count combinations, why not have rotation + translation etc. as their own types too? My Realtek NIC in my Windows Home Server (essentially w2k3) box refuses to run at 1000Mb/s even if I change the driver settings from Auto Negotion to 1000Mb/s full duplex. I've installed the latest driver and tried changing the speed setting but I'm having no luck. Not sure what to try next. Any ideas?  I have a Netgear GS605 v2 Switch supports 10/100/1000 D Link DIR 655 router.  All my machines bar one/2 have 1000Mb/s NICs (Old laptop/Xbox being the exceptions)  The reason I noticed the problem was because I was copying files between two machines and maxing one NIC out and only seeing 10% on the other machine. I do have a fairly lengthy cable between the switch and the router (maybe 20m) could that be the issue? Should we improve time to first byte or Page Speed Insights score for SEO? Google posted last summer that "page speed" will impact the search result rankings also on mobile devices. But I think there is a little confusion about the term "page speed".  The test tool which Google offers is called "Page Speed Insights". Many people we are talking with, are thinking that the overall score of this tool for a particular site for example Desktop: 46/100 and Mobile: 45/100 is used for the ranking algorithm.  BUT I found a very interesting article in German language which states that only the TTFB (time to first byte) value is used and this should be optimized not all suggestions which "Page Speed Insights", further called PSI offers. Here is the link to the German article:   In short terms it says that a very large site in this case "The New York Times" has a low overall score of Mobile:41 and Desktop:45. As they are used to sell reader memberships they should  offer a great user experience. So, they should optimize their site. But when I call this site it is amazing fast. The overall PSI score does not reflect this behaviour. But when I believe this article the TTFB for this site is perfect. Also when I call it here from Austria it states 0.881sec.  I really like to know on which value we should focus our work for optimization not to fall in the ranking. Because as many of you already said it is not useful to implement all suggestions from the PSI site for one domain.  So, it would be real  if you could clarify things here or post links to official posts from Google. What I found about this, Google always is talking about "page speed" but what exactly is this? Does a car use friction to move? Could an argument with false Premises and a true Conclusion be logically valid? The game  has a very unique intro that I would like to show my friend again for the first time. I'm not sure how to reset all my progress on this game to achieve this though. Any thoughts? Free GIS workshops, tutorials, and applied learning material This Q&amp;A lists free as in $0 workshops in GIS and related fields that have their material available to view or download online. The list is not limited to FOSS GIS, as GISers usually use a combination of open and closed source tools to accomplish their tasks. Some of these tools are easier than others and some are better documented. This list will be a great benefit to the community especially for new comers to the field. General GIS   from   from   from   from   Open-source GIS   from   from   from   from   from   ESRI Products   from   from   Transportation These links include either theoretical or applied transportation knowledge in transportation planning          Disaster Management    Databases   from   Geo Statistics    from Automatic field should take the required entry Why are my objects in all layers? As I show below, typical alien depictions include an elongated, pale face, two dark elliptical eyes, and a small mouth.  Who first used this design for an alien?  Where does this design come from? I'm trying to approximate the computer's write speed using dd:  dd if=/dev/urandom of=/dev/null bs=1K count=10000   which gives the following output  10000+0 records in 10000+0 records out 10240000 bytes (10 MB) copied, 0.746313 s, 13.7 MB/s   How can I get the '13.7 MB/s' into a bash variable? I've tried piping the output from dd to progs like awk, sed and grep to no avail.  Ultimately, I'm calling this via os.system(...) from within a python script. If anyone knows of a more direct way to get a similar result inside python I'd be interested in that also. I'm trying to predict how long a file copy will take, based on the file size.  Any help would be greatly appreciated.