How can even the value of g at the centre of the earth be zero and what does it has to do with the weight?
If you could travel to the center of the Earth (or any planet), would you be weightless there?
If $|f(z)|\leq |f(z^2)|$ on the unit disk, show that $f$ is a constant function. Suppose $f$ is holomorphic in the unit disk $D=\{z: |z|&lt;1\}$ and $|f(z)|\leq |f(z^2)|$ on $D$. Show that $f$ is a constant function.   My Try:  I wanted to use Strong Maximum Principle, but failed to prove that $f$ is bounded on $D$. I want to try this problem in my own. Can anybody please give me just a hint? For example I want to use \iint from ams package  and also mathabx package in one file together. Actually I want a command that neutralizes ams package effect and replace it with mathabx package effect from here on in my file. Thanks for your responsibility.  This is my example minimal file:  \documentclass[12pt,a4paper]{report} \usepackage{amsmath}  \usepackage{mathabx}  \begin{document} i want this one in ams style:        \[ \iiint\,\iiint\, \iiint\,\oint\, \] text text text text text text text text text text text text   and this one in mathabx style:   \[ \iiint\,\iiint\, \iiint\,\oint\, \]   but both of them are the same and i don't like it ..... \end{document} I don't have administrator account on my mac On my mac I have 2 accounts and the both are normal account. So in this moment I don't have a Administrator account, only one that was in the past a administrator, but now is not.  How I can have again a Administrator account? I want to write a survey on one emerging research topic in wireless communications (It can be applied to any field!). There are almost 500 papers on this topic as published or in early access. And the publishing rate in this topic is increasing day by day. So, I want to write a survey on this topic keeping in mind that it will get high citation and it will help new scholar who are in struggle with this topic. I found only one survey written by some reputed authors, however it lacks in many ways, like detailed information related to particular direction, it just assembles the papers in a good manner. I want to pick some directions and discuss  important approaches with good connection between them. However, I find it very difficult to proceed with large number of papers. Is there any good way to handle the survey process in a good efficient and quick way? PS. According to me, many people have already started to write this. i would like to know how to prove that if $a^2+b^2=c^2$ then   a) $3|a$ or $3|b$  b) $5|a$ or $5|b$ or $5|c$  c) $4|a$ or $4|b$   Also that $a^2+b^2+c^2+1$ can't be divisible by 8  Thank you very much! What is a word that means "someone who pretends to be your friend but is actually your enemy?" How do I disable a bottom panel with the list of open windows on GNOME 3? Find & Delete duplicated files on multiple harddisks at once I have 4 hard disks and want to find out which files on this four harddisks (including sub directories) are duplicates. It should be checked not only within a harddisk but against all the others as well.  The hard disks are large (3TB) therefor it has to be efficient (first filename than checksum checks or so) Propose Newbie-Overflow site or section Because the perl section is looking like that right now. I believe that Stack Overflow is going out of it's charter in becoming a newbie FAQ when as far as the original reasoning it was meant to be something along the lines of an expert site.   is a good example of what I mean in Perl. It probably could be closed because it's a duplicate, or some other reason.   I would also like to indicate that I don't hold back answering newbie questions. It's just when I think of an obscure "stack overflow" error that's beating you some 3 am close to deadline, that's not "Howcum Perl print ..." and follows with something that causes a vast majority of Perl programmers to say oops, because they know exactly what's going on.   So the proposal is   A new site. "Move to Newbieville" A new "section" A new status somewhat similar to Closed ("Newbied") but still can be updated all the same as an open question.   I'm not against giving some newbies an assist, but I feel a FAQ for rank newbieism is not something that SO started out to be, based on the original concept of a Expert Site.   Including comment to Gnoupi:   I said nothing about making newbies unwelcome. Like I said. I answer them--heck, I think I've even answer homework questions. I've answered on the vague impressions that I can glean from posts that have 4 close votes. It can even lead to avoiding downvoting or yelling at newbies by more established curmudgeons if there is a special action you can do to gently inform newbies that this is a real newbie question.  However, you have to know that to some people newbies are already unwelcome. There is a site ethic, but the individual is also going to decide how much they welcome newbies. And people do post RTFM answers already.   Anyway, I'm one vote away from a peer pressure badge it seems. (Nope, nailed it.)    EDIT  For somebody jumping to the conclusion that I'm hostile to newbies:  just earlier Are Mersenne prime exponents always odd? I have been researching  so I can write a program that finds them. A Mersenne prime looks like $2^n-1$. When calculating them, I have noticed that the $n$ value always appears to be odd. Is there confirmation or proof of this being true? Can I run my CPU at 100% usage for a long time? I have a Dell XPS 15 9570, 32 GB ram, 2.2 ghz and 6 cores. When i use an application (The parsim command on MATLAB) ()  then my fan starts running fast , during this my PC doesn't seem to be heating but it never got this noisy in the past so it got me worried. In my task manager , the CPU usage shows 100% when this application is running.   Is it a problem for the life of laptop, if I run the PC at CPU 100% for like 4 hours in a day? Do I need to be worried about the noisy fan during the application? Probably a basic issue, but still something that irks me and I can't find an answer online. I want to change the default folder for saving new shapes/processing outputs from &quot;last used folder&quot; to &quot;project folder&quot; or &quot;something in relation to project folder&quot; - is this possible? If so, how can I achieve this? Are all continuous one one functions differentiable? My professor has stated the following lemma:  Let $U$ and $V$ be two vector spaces and $B$ a basis for $U$. If $f:B\rightarrow V$ is a map, then there exists a unique linear map $A: U \rightarrow V$ such that $A(x)=f(x)\ \forall\ x\in B$  How can I prove this lemma? (This is not a homework problem.) What is a subnet mask, and the difference between a subnet mask of 255.255.255.0 and 255.0.0.0? My DSL/WiFi router provided by my ISP has an internal IP address of 10.0.0.138, the addresses provided by DHCP are in the format of 10.0.0.xxx.  Now, I want to start using static IP addresses on my local network, and I don't know what to provide for the subnet mask.  What is a subnet mask?  Should I be using 255.255.255.0 or 255.0.0.0 as my subnet mask? What is the difference? Convert .jar to .deb package Change Folder Permissions I started off with changing to the folder I want to change permissions for, and that is the opt folder.  $ cd /opt/ test@testVM:/opt$   So I tried changing the permissions for this folder now using:  sudo chmod 775   And that hasn't worked. It showed this message:  Try 'chmod --help' for more information.   There is something I am forgetting or leaving out.  Please can you show me what I am doing wrong?  Thanks in advance. How to get the ASCII value of a character How do I get the  value of a character as an int in ? Show (within ZF Set Theory without choice) that for any sets $A,B,C:$   If $|A|^{|B|} = |B|$, then $|A| = 1 = |B|.$   That is, if there is a bijection from $|A|^{|B|}$ to $|B|$, then  $|A| = 1 = |B|.$  Please help me.. L1 regression estimates median whereas L2 regression estimates mean?