let $\sum_{k=0}^{n}|f_{k}|^{2}=g$ then if g is constant then $\forall k\in[n].f_{k}$ is constant
Show that holomorphic $f_1, . . . , f_n $ are constant if $\sum_{k=1}^n \left| f_k(z) \right|$ is constant.
Many sysv init scripts used a corresponding file in /etc/default to allow the administrator to configure it. Upstart jobs can be modified using .override files. How do I override or configure systemd units, now that systemd is the default in Ubuntu? Punctuations with relative pronouns Sogou is a Chinese search engine, which can search text, images, music and maps.  Is a comma required before "which" in the above sentence? How do I split a string so I can access item x? Using SQL Server, how do I split a string so I can access item x?  Take a string "Hello John Smith". How can I split the string by space and access the item at index 1 which should return "John"? Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$ Where can I ask about Software Licenses/Licensing? What is the word that is used to describe the oversimplification or non-academic discussion of a complex issue?   Typically, I'm looking for a word like pedantic, or puerile, except that the word covers the fact that the discussion is particularly non-academic. I know that such a word exists since I have used it before, but it has skipped my mind. How do you get a bad transcript past Ph.D. admissions? How can I use commercial at sign in Objective-C macro? Additional needed documents for UK trip if someone will shoulder all expenses Someone (a relative) from the UK (already a naturalized British Citizen) will be financing my trip, as well as taking care of my accommodation. What are the documents I need to submit aside from bank statements? Does the sponsor need to fill-out the Sponsorship Undertaking Form? ()  something to consider from my question: -my relative is a naturalized citizen in the UK. Is proof of naturalization needed? $$\tan(\theta_1+\theta_2+\cdots+\theta_n)=\frac{S_1-S_3+S_5+\cdots}{1-S_2+S_4+\cdots}$$  where  $S_i$ denotes the sum of product of tangent of angles taken $i$ at a time.     For example,$$\tan(\theta_1+\theta_2)=\frac{S_1}{1-S_2}=\frac{\tan\theta_1+\tan\theta_2} {1-\tan\theta_1\tan\theta_2}$$   (This formula is given  in my textbook with no derivation or background)  How to derive this? In the magical world (in Harry Potter) can ghosts use magic?  Can magic be used on ghosts?  Or, once they become ghosts, can they interact with magic at all? I've removed the poll style answers in favour of open discussion.  I realise now this isn't the best way to have a proper discussion about this issue - sorry to anyone who commented/voted.    This is mostly a followup on this question:    As I've answered, the reason this is happening is that the root database (in the production Stack Exchange database server) is still called StackExchange.Programmers - a database name that propagates to SEDE and through it to the data dump.  The question here is what to do about it - the current situation is somewhat broken for users of the data dump.  These are the options we have:   Do nothing Update the root database name (requires downtime - so very undesirable) Update the update scripts so the SEDE database name is the new name, change will flow to the data dump export (breaks any queries using the old name) Update the export to the data dump so only it gets the new name Something else we haven't thought about   I have added all of these options as answers below - please vote on the one you most prefer, we will try to accommodate the top voted answer. How can I make a logo in Adobe Illustrator like the AntiParticle logo below, from ?   It is a large number circles of different, varying sizes, which form the shape of a text character. What is $dx$ in integration? Where should looking-for-resources questions go? How to make generated classes contain Javadoc from XML Schema documentation I have this question :  Proof if $f$ continuous in $x_0$ then there is a neighbourhood of $x_0$ so $f$ bounded.  I want to know if my proof is valid :  If continuous in $x_0$ then :  $$\lim_{x \to x_0} f(x)= f(x_0)$$  Therefore :  All $\epsilon&gt;0$ exists $\delta&gt;0$ so any $x$ that implies $|x-x_0|&lt;\delta$ implies $|f(x)-f(x_0)|&lt;\epsilon$.  Therefore for $\epsilon=1$ there is $\delta&gt;0$ so any $x$ that implies $|x-x_0|&lt;\delta$ implies $|f(x)-f(x_0)|&lt;1$.  $|x-x_0|&lt;\delta \rightarrow x_0-\delta&lt;x&lt;x_0+\delta$.  Lets choose $x_1,x_2$ that implies $x_0-\delta&lt;x_1&lt;x_2&lt;x_0+\delta$  Therefore in $[x_1,x_2]$ from Weierstrass from theorem bounded there. When I add LIMIT 1 to a MySQL query, does it stop the search after it finds 1 result (thus making it faster) or does it still fetch all of the results and truncate at the end? Limit $\frac{x^2y}{x^4+y^2}$ is found using polar coordinates but it is not supposed to exist. Set same icon for all my Forms Is there any way to set the same icon to all my forms without having to change one by one? Something like when you setup GlobalAssemblyInfo for all your projects inside your solution.