Let $f$ be entire in $\Bbb C$. If $Re(z)&gt;0$ $\forall z \in \Bbb C$. Then prove that $f(z)$ is constant.  Please read below before marking duplicate.  If $Re(f(z))&gt;M$ then taking $|\frac 1f|&lt;\frac 1M$. Applying Liouville's theorem we are done. But if $Re(f)&gt;0$ then can we conclude $|\frac 1f|&lt;\infty$ &amp; $\frac 1f$ is bounded so $f$ is constant. If it is so then comment otherwise give me some solution.
Let $u:\mathbb{C}\rightarrow\mathbb{R}$ be a harmonic function such that $0\leq u(z)$ for all $ z \in \mathbb{C}$. Prove that $u$ is constant.  I think i should use Liouville's theorem, but how can i do that? Help!
Should we use wheatstone bridges nowadays? For measuring strain gauges, the Wheatstone bridge is the historical choice.  In a quarter Wheatstone brigde (\$350 \Omega \$ typically (?)), with a high input impedance amplifier, and some bridge power voltage \$V\$, the ratio between the bridge output voltage w.r.t. any resistor is 1/4, which is the same ratio in a voltage divider between the output voltage w.r.t. any resistor, compared with a stable voltage reference of \$V/2\$.    A voltage divider with a voltage reference would have a voltage noise of about 35.16 nV/rtHz (from a voltage reference of 35 nV/rtHz plus two resistors), and the Wheatstone bridge a voltage noise of 4.86 nV/rtHz (from four resistors), which should be enough (?) for most ADC systems (i.e. for 24 bit, 0-5V range: 300nV resolution).  And a voltage reference (\$0.02\%\$ initial error, \$2 \ ppm/C^\circ\$, ), would be more stable and precise (?) about \$4\ ppm/C^\circ\$, than a precision resistor (\$0.005\%\$ error, \$2 \ ppm/C^\circ \$, ), about \$8 \ ppm/C^\circ\$.  Hence, why bother using Wheatstone bridges? Need help identifying the fantasy book about a portal to a fantasy land in the basement of a house I can't remember any names of characters or locations where the story took place but I do remember the basic plot of this early 90's novel; a human man inherits his father's house. In the basement there is a doorway to a fantastic land where adventure ensues. He fights elves and wins their deadly elf swords which he buries under concrete at the end of the novel (because if you don't get rid of them they will come back and get you).  At the end of the novel he must remake the world in his own imagination, turning the tough Elf King into a cobbler and making Jesse Jackson President. I have been looking high and low and have drawn a blank.  Any help would be appreciated. Thanks! Limit values of struct member Atomic clocks were used in Hafele and Keatings experiment which supposedly helped to prove time dilation.    How can we be sure other forces didn't act upon the clocks as a result of their being at different speeds and elevations? Perhaps the elapsed time may have been the same for all and only appeared different as a result of the clock's atoms behaving differently in different environments.  How might the presence of dark matter (presumably all over the place) impacted the clocks if say the dark matter is stationary relative to the earth's rotation?  What experiments have been done to test the constancy of clocks at different speeds and elevations? Why do adult insects have 6 legs? Apparently, there is an advantage to having 6 legs in the insect world. What is that advantage, if anything? Why would such an advantage exist for insects, but not for other, larger land animals?  What do those middle legs do that the front and hind legs cannot, if anything? Are they really essential, or do they just generate more muscle power? Enable Careers and Jobs in app So, I'm running linux Mint (but I guess the same applies to Ubuntu) and as is common knowledge, their TeX distribution tends to be slightly outdated. Now I can't have none of that and decide to install it with the install-tl from the TeXlive homepage. Somehow, I cannot install it as a normal user (this I find normal as it is installing in the root directory), so I proceed to install TeXlive   sudo perl ./install-tl   and add the paths to .bashrc. All is well and my TeXlive installation works. Except for the texhash option. Running it as a normal user is no problem, except that I installed TeXlive as root, and so running texhash as normal user doesn't do anything (directory not writable. Skipping...). No problem I think, I'll just do it as root. But somehow texhash isn't installed for root.  Now, texhash is somehow connected to updating the directory tree, but I don't really know what it does. I use it on my ~/texmf/ folder to add my packages to a global path (I think), but when looking at info for this question I see in a comment for  question that this is apparently not needed, though I don't understand what I'm to do now.  So if I'm not adding new packages from CTAN or updating, I really don't need texhash and all is good?   To summarize: I'd like to know:    Why should I need texhash? Can I avoid installing as root on linux Mint/ubuntu ( they say you don't have to be root, that it's even discouraged)? Should I somehow install texhash for root?   I realize this might be a vague question at best, but I didn't find an answer I readily understood, so I'd appreciate any thought on this. Practical uses for the "internal" keyword in C# Could you please explain what the practical usage is for the internal keyword in C#?  I know that the internal modifier limits access to the current assembly, but when and in which circumstance should I use it? How to Create Bootable Windows 10 image in Debian? Pseudocode but originally developed for Windows 7 iso file but applied for Windows 8 in the thread  but it does not work with Windows 10 iso  # https://rwmj.wordpress.com/2010/11/04/customizing-a-windows-7-install-iso/ # https://unix.stackexchange.com/a/312477/16920 $ dd if=../en_windows_10_x64_dvd.iso \     of=boot.img bs=2048 count=8 skip=734  $ mkisofs -o ../new-win.iso -b boot.img -no-emul-boot -c BOOT.CAT \     -iso-level 2 -udf \     -J -l -D -N -joliet-long -relaxed-filenames .   Unsuccessful output when run on Windows 10 image  dd if=/home/masi/Downloads/en_windows_10_multiple_editions_version_1511_x64_dvd.iso of=/home/masi/Downloads/boot.img bs=2048 count=8 skip=734 8+0 records in 8+0 records out 16384 bytes (16 kB) copied, 0.000392973 s, 41.7 MB/s    Some of the following fields have changed for the iso file used in dd   bs=2048 count=8  skip=734   How can you study which field values you can use for Windows 10 iso?  OS: Debian 8.5 64 bit Hardware: Asus Zenbook UX303UA Linux kernel: 4.6 of backports Related threads: ,  Motivation: I need Windows 10 to use Canon P-150 duplex scanner, but when I started my Windows, I got Error 0xC0000428 because Windows update has again broken things there and I use Windows otherwise so rarely; and I have no spare Windows left to make bootable media Want to cancel a 'Pending Erase' on iphone... Any suggestions? I lost my phone on vacation and activated 'Lost Mode' for a couple of days. The night before heading home I decided to do the Remote Erase ´cause I thought there's no way I'd get it back, I also called my carrier and canceled the data service on my number. The phone has been offline ever since but the hotel just called to say they found my phone at the spa and they are mailing it back to me. So I want to cancel the 'Pending Erase', all I care about is recovering all the pictures from that trip that I hadn't backed up on iCloud yet... Will removing the device from my iCloud account work?  And if I don't have service on the phone, will the 'Erase iPhone' command still go through when I turn it on?  Please help! I have two days to figure this out Database synchronization between dev/staging and production I have a problem with WordPress database synchronization between development and production and I am wondering how other people solving it. I am aware about  but it doesn't really cover the nastier and more realistic use case.  Say I have a live WordPress website. I took a dump of everything, replicating it on our dev environment. I started making changes. 1 week later I am ready to deploy my updates. In the meantime, database on production site has changed(new posts, new comments, etc.). How do I synchronize changes between production and development during the rollout and is it possible to automate(somewhat at least) this process? How can I figure out why my washing machine is tripping the GFCI receptacle? I have a Kenmore 80 Series (Model No. 110.24872300) washing machine which up to this point has been working fine. Since it is near a sink, the outlet it is plugged into is a GFCI outlet. On the last load I came back after letting it run for some time to find that it had tripped the GFCI in the middle of the wash cycle - the washer was still full of soapy water. I reset the outlet and let it run again, only to come down the next morning and find it full of water still (it had tripped during the rinse cycle this time). I reset the outlet again and this time it finished the rest of the cycle.  My guess is that water is somehow getting onto the internal components of the washer and causing it to short - is there any way I can test this theory or fix the problem myself? My iPad mini retina is out of warranty,  I forgot to plug in my iPad after the critical battery warning and it went some minutes following the warning. I was not worried because same thing had happened a few times before and iPad was perfectly okay after charging it. However, this time I remember seeing a flash of blue screen immediately after it went black. Then, I plugged it in an waited for a while and tried starting it. Ever since, it fails to start hanging on the apple logo with white background screen.   I tried to connect to my Mac but nothing showed up in iTunes. I am worried now. Can I troubleshoot this or is it broken and needing repair? What does 'foo' really mean? I hope this qualifies as a programming question, as in any programming tutorial, you eventually come across 'foo' in the code examples. (yeah, right?)  what does 'foo' really mean?  If it is meant to mean nothing, when did it begin to be used so? Spoilers for A Storm of Swords / Season 4 episode 2 "The Lion and the Rose".  At the Purple Wedding,      Littlefinger and Lady Olenna Tyrell   perform their plan of      poisoning King Joffrey.   A short summary of their plan:  Littlefinger orders Ser Dontos Hollard to give Sansa Stark a beautiful silver hairnet adorned with amethysts. At least some of the amethysts are actually strangler crystals in disguise. Ser Dontos also, still under orders of Littlefinger, urges Sansa to wear the hairnet at the wedding, which she then does. At the wedding, when Lady Olenna greets Sansa, she fusses her hairnet a bit, while secretly taking one of the strangler crystals. Later, during the wedding, Lady Olenna puts the crystal in Joffrey's royal cup, poisoning him.  But why was their plan so complicated? Why couldn't Lady Olenna just bring a strangler crystal with her to the wedding (as suggested in )?  Then they wouldn't depend on Ser Dontos and Sansa who could unknowingly have done something to prevent the success of the plan.  The only reason that I could think of, is Littlefinger and Lady Olenna plan for Sansa (and Tyrion as her husband with her) to take the blame for Joffrey's death.  They put the crystals on her person, so that upon examination it would clearly show that Sansa had the murder weapon on her. But Littlefinger had a plan he did not tell Lady Olenna, namely rescuing Sansa during the chaos ensuing the murder (and thereby leaving Tyrion behind as the only accused).  Is there anything confirming or debunking this theory? If my theory doesn't hold up, is there another explanation for why the plan was so needlessly complicated? I use a Canon EOS Rebel T3i (600D) with the kit lens. I have experimented a lot with different settings and modes, but I feel like I have wasted many good shots that could have looked amazing, if only they were a little bit sharper.  I use auto-focus on most of my pictures and make sure to choose the right focus point, but all of my photos are still a little bit out of focus. When I zoom in, I can see that the pixels are not very crisp or well-aligned.  I am not sure if this issue is caused by my equipment or skills. Show that $xy=0$ is a variety but not a manifold Badges with long names overflow on the profile page Recursivly Deleted Root Directory I recursively deleted the contents of my root directory with sudo privileges. My display reset, and windowing stopped working. I could no longer run non-buitin commands. Most of my directories (including the home directory disappeared).  What I meant to run:  sudo rm ./* -rf   What I believe I ran:  sudo rm /* -rf   I understand how this command works (see ).  I'm trying to get a better sense of how much (and what parts) of the original files and directory-structure physically remains on the hard-drive.  How much of these "remains" are recoverable? E.g is it possible to use data recovery software like TestDisk/PhotoRec to recover the full home dir itself? What about config files? Should I always use a comma after "e.g." or "i.e."?