I am going through my weekly assignment of complex analysis but I am stuck at two points, since I don't understand a condition in the first case and what I'm being asked in the second one.  In the first part of the assignment I am given an entire function $f : \mathbb{C} \to \mathbb{C}$ such that  $$|f(z)| \leq \frac{1}{|\mathfrak{Im}(z)|}, \qquad \forall z \in \mathbb{C}$$   I have to prove that $f(z) = 0, \ \forall z \in \mathbb{C}$.  What is supposed to happen when $\mathfrak{Im}(z) = 0$? We are not working in $\overline{\mathbb{C}}$, so we don't assume that $f(z) = \infty$ for some $z \in \mathbb{C}$. How should I interpret this condition?  In another part of the assignment I am told to classify entire bi-periodic functions. I know what is meant by classification when one is  talking about e.g. manifolds or surfaces, but I am finding it hard to interpret in this case. At least this follows just from the definition:  Let $f$ be an entire bi-periodic function with periods $p_1, p_2 \in \mathbb{C}$, such that $p_1, p_2$ are $\mathbb{R}$-linear independent. Then we have  $$f(z + jp_1 + kp_2) = f(z) \qquad \forall z \in \mathbb{C}, \ \forall j, k \in \mathbb{Z_{\geq0}}$$    How should I categorize these functions?
Let $f(z)$ be an entire function such that $$|f(z)|&lt;\frac{1}{|\text{Im}(z)|},\qquad z\in\Bbb C-\Bbb R.$$ The question asked me to prove that $f(z)=0$. At least looking at it, it really seems to have an application of Liouville's theorem lurking around somewhere, but I haven't found it.   My thoughts first led me to think about doing this by contradiction and using Picard's little theorem. So, I've considered a strip containing the real axis (say of width $2$ for simplicity). This will imply the complement maps into the unit disk, which implies that this strip has to map almost everywhere else on the complex plane. Now, on the imaginary axis, I know that $f(z)$ will vanish as $z\to\infty$, and this seems like it might be useful. I'm sort of under the impression $f(z)$ might have an essential singularity at $\infty$, which would mean $f(1/z)$ has an essential singularity at $0$. Either way, it of course can't have a pole at $\infty$ because of $f(z)$ vanishing on the imaginary axis, and if it is a removable singularity, it must be $0$, which still gives the solution. Therefore, I think it must have something to do with $f(z)$ having an essential singularity at $\infty$.   I was hoping to combine this with the above inequality and deduce a contradiction, but I haven't thought of one yet.   Any hints or suggestions? I'm studying for a prelim. exam, so this isn't homework.  Update: So, in the spirit of searching methods using the essential singularity at $z=0$, we have $$\left|f\left(\frac{1}{z}\right)\right|\leq\frac{1}{\left|\text{Im}\left(\frac{1}{z}\right)\right|}=\frac{|z|^2}{|y|}.$$ Thus, for $|y|&gt;1$, we have $$\left|f\left(\frac{1}{z}\right)\right|&lt;|y|\left|f\left(\frac{1}{z}\right)\right|&lt;|z|^2.$$ Thus, if I can show that $|f(1/z)|$ is a polynomial, we'll know it can't have an essential singularity at the origin, concluding my proof.
How long does the new dwellers queue last? When clicking the radio room icon that attracts a new dweller to your vault, how long will they stay queued out in front of the vault for before giving up?  Or will they?  I'm at max population and would rather not kill existing dwellers to accommodate them in my vault. How do I get to Orgrimmar from Silvermoon City at level 11? I have a level 11 Blood Elf and want to spend some of my honor points. I've heard that I could spend them in Orgrimmar, but the only problem is getting there.  How do I get to Orgrimmar from Silvermoon City? I'm not in a level 25 guild, so nobody can teleport me there. :( If $x+{1\over x} = r $ then what is $x^3+{1\over x^3}$? If $$x+{1\over x} = r $$ then what is $$x^3+{1\over x^3}$$  Options: $(a) 3,$ $(b) 3r,$ $(c)r,$ $(d) 0$ First player rolls a 6-sided die 100 times and the second player 101 times. What are the odds of the second player getting more odd numbers than the first one?  I tried solving this via listing the options which led to a nasty sum that I wasn't able to solve neither by hand nor by using wolfram alpha. Clearly there has to be a more clever solution using the properties of a binomial distribution, but so far I haven't come across anything useful. How should we handle downvote retaliation? I have a situation where I'm trying to figure out what the right thing to do is on SO.    I see a question.  I answer the question.  I see there are a couple other answers.  One answers the question well, though with less explanation than my answer.  The other answer seems both wrong and irrelevant to the question (doesn't answer the question at all).  I comment to that effect.  The "wrong" part is edited out, but the author of the answer doesn't respond to how their answer actually answers the question.  In fact, they seem offended that I don't "get" it.  After giving them several chances to explain how their answer is relevant to the question and seeing their attitude, I decide to downvote their answer as I don't see how it addresses the question at all and the author won't explain.  They retaliate and downvote my answer and admit in their comments that their downvote of my answer has nothing to do with the content of my answer and only because they don't like me disputing their answer.  Did I do the right thing by downvoting their answer?  Do I just have to live with their downvote retaliation?  Anything I should have done differently?  I also have no way of knowing this for sure, but the next question I answered was upvoted, then downvoted so perhaps this same person is stalking my answers and downvoting other answers of mine too with no comment.  As long as this doesn't continue, I'm not losing sleep over a couple downvotes, but I do wonder if I should have done anything differently.  Followup Later After I Posted This Question: After thinking about it for a little while, the person who disagreed with me decided to delete their post.  So, eventually the message did get through to them.  I don't know if they rescinded their downvote or not (or if they even could). Seasonal Loan Amortization Hi I can compute a Basic Loan Amortization Schedule, But now I'm trying to Calculate a Seasonal Loan Amortization Schedule . So for example A loan starts at January And Will go on for 3 years, with Monthly Payments. Interest is at 3% Annually and is compounded Annually. During the months of September, October, November, December It'll only accumulate Interest But no payments and principal. Principal is 100000. How Do I calculate Payments and interest. I'm trying to write a shell script that, when run, will set some environment variables that will stay set in the caller's shell.  setenv FOO foo   in csh/tcsh, or  export FOO=foo   in sh/bash only set it during the script's execution.  I already know that   source myscript   will run the commands of the script rather than launching a new shell, and that can result in setting the "caller's" environment.  But here's the rub:  I want this script to be callable from either bash or csh.  In other words, I want users of either shell to be able to run my script and have their shell's environment changed.  So 'source' won't work for me, since a user running csh can't source a bash script, and a user running bash can't source a csh script.  Is there any reasonable solution that doesn't involve having to write and maintain TWO versions on the script? Lost my APFS partition after using EaseUS partition manager on Bootcamp I used macOS mojave(APFS partition) and Windows10(Bootcamp). And I tried to expand Bootcamp partition with moving Windows OEM partition by EaseUS partition master in windows. After this, I can’t find APFS partition installed macOS.  I use MacBook Pro 2016.  I think “disk0s2” was APFS partition, but now it is “Windows Recovery” partition.  Do you have any ideas to solve this? (I am Japanese, so I'm sorry for my poor English)  I tried “gpt show” and “diskutil list” on macOS Recovery   Additional information  I tried dd if=/dev/disk0s2 count=1 bs=512 command in a Terminal app of macOS Utility from network boot, and the terminal says,  -bash-3.2# dd if=/dev/disk0s2 count=1 bs=512 | vis -c 1+0 records in 1+0 records out 512 bytes transferred in 0.005472 secs (93568 bytes/sec) )us??-ҵ?\^A\0\0\0\0\0\0\0?\M^F\^Z\0\0\0\0\0\^A\0\0\M^@\0\0\0\0NXSB\0\^P\0\0?\M^B?\^B\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\^B\0\0\0\0\0\0\0"\^R???\M^_@}\M^Bvy57 ?(h?8\0\0\0\0\0?\M^F\^Z\0\0\0\0\0\^X\^A\0\0 l\0\0?\M^J\0\0\0\0\0\0\^R\r\0\0\0\0\0\0\a\0\0\0004*\0\0\^E\0\0\0\^B\0\0\0\^S*\0\0!\0\0\0\M^Qr8\0\0\0\0\0\M^U?\b\0\0\0\0\0\^A\^D\0\0\0\0\0\0\0\0\0\0d\0\0\0\^C\^D\0\0\0\0\0\0\M^T\M^N\^A\0\0\0\0\0\M^V\M^N\^A\0\0\0\0\0?0\^B\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0-bash-3.2#   . What's up with Vic? In the TV series Glitch, we see several people returning from the dead.  We see Vic, a police officer,      getting in a car accident and seemingly .   Afterwards, he behaves very strange. He searches for the doctor and the risen, whom he seems to know a lot about, sometimes even more than they know themselves.      He rekills Maria by breaking her neck.   And he threatens the other risen.  Most of the risen, especially those that have been dead longer, have some difficulty remembering their past lives. Vic on the other hand, seems to remember fine but to have a complete change of character instead.   Why is he after the other risen? How does he know so much about them? Why did he have such a change of character?     Yes, these are several questions, but they are closely related, so I opted to ask them in one question. I always see pictures of the solar system where our sun is in the middle and the planets surround the sun. All these planets move on orbits on the same layer. Why? First off, sorry for my english. I am currently developing a new website that may be deployed in early 2017. This site may contain user login but that may be shipped later in that year.   Now, I googled about https and I hear mixed opinions, google wants the web in https and may punish those who don't use https in the future. Mozilla will also favor https over http for its Firefox. Let's Encrypt make it for free. So far so good.  What is worrying me is I read that many sites that switched to https suffered much lower revenues of adsense (I read also some terrible things about seo and ranking suffering after switching) and many returned again to http.  How much truth is in the suffering of revenues due to switching to https? My website is still in development so I have actually no links needed to be reindexed. My site isn't a blog type. It mainly provides profiles on local artists in my country.  The problem is I need every penny to cover the server and cdn hosting costs. I can't be sure how much using https will hurt the revenues. Making leaflet control open by default I'm using leaflet to display a map.  I have a control section that I'd like to be open by default, but I can't find a way to do it through the . Is there a way to do this? If $A\subseteq\mathbb N$ and $\sum\limits_{a\in A}\frac1a$ converges then $A$ has natural density $0$ In this  to a question about a series, a theorem was stated:     If $A= \{a_i \}$ is a set such that $\sum_{i = 1}^{\infty} \frac{1}{a_i}$ converges, then $d(A) = 0$, where $d(A)$ is the  of the set.   My background in number theory is basically zero and all my attempts to prove this have been utterly unseccessful; would anyone please help me, or at least provide me with a hint to prove it? As of today, a  has been found affecting versions 1.0.1 through 1.0.1f (inclusive) and 1.0.2-beta.  Since Ubuntu 12.04, we are all vulnerable to this bug. In order to patch this vulnerability, affected users should update to OpenSSL 1.0.1g.  How can every affected user apply this update now? How to load image to android and resize How do I identify which CPU a MacBook uses? I'd like to identify which CPU this notebook is using, in terms of code names such as "Ivy Bridge" and "Haswell". The little Apple logo in the upper left shows some information, but not this. Electric shock - was I stupid, unlucky, or a combination of both? One of the double sockets in our garage needed replacing (damaged after a washing pole hit it) - a pretty trivial job that I'd done before. So I flipped the MCB for the ring main, used a non-contact voltage tester to check nothing was there, and set to work. I disconnected the old socket fine, and was lining the cables up to fit into the new socket when... ow.  My finger bridged the live and earth pins, and suffice to say the live wire was very much alive. Bar a few finger spasms I was fine fortunately, and believe me I realise I was very lucky in that respect (I'm in the UK, so that was 240V.) Before finishing the job I then shut off the entire property's electrics - I was taking no more chances.  Further inspection confirmed two things I immediately suspected at this point - the MCB in the garage (installed before we moved into the house) was shutting off power via the neutral, not the live, and the voltage tester was dodgy (I had tested it on the same socket earlier and it seemed fine, further testing showed it presumably had a loose connection internally and only worked sporadically.) Needless to say it's now in the bin, and an electrician has been called to sort the MCB and check the rest of the house for similar issues.  Unsurprisingly this has shaken me up a bit - I would say I'm a rather safety conscious person, and in this case thought I'd done all the checks properly (including taping over the relevant trip switch to ensure no-one flipped it back on while I was working.) In some ways I can't help feeling I was unlucky that the MCB was wired by a cowboy, in combination with the voltage tester failing in the way that it did, at the time that it did. However, I'm not one to solely blame tools - clearly some, if not most of the blame here lies with myself also.  So in short, what should I have done differently - and was I primarily being stupid, or really quite unlucky? A 'for' loop to iterate over an enum in Java Where does gravity get its energy from? I would like to know where gravity gets its energy to attract physical bodies?  I know that the law of conservation states that total energy of an isolated system cannot change. So gravity has to be getting its energy from somewhere, or else things like hydropower plants wouldn't be able to turn the power of the falling water into a spinning rotor.  Just to be clear, Lets create an example:  Lets say we have two objects with equal mass close to each other. So gravity does its job and it pulls each other closer, this gets turned into kinetic energy. This is where I'm lost. According to the law of conservation energy can't be created or destroyed and the kinetic energy comes from the gravitational pull so where does the gravitational pull gets its energy.  If that energy isn't being recycled from some where else then that means you have just created energy, therefore breaking the law of conservation. Regarding running Watir scripts for UI Automation from Jenkins CI - How to hook up Jenkins and watir-automations