As I learnt freq. observed by a observer from a moving source is given by $$f=f_0(1+v_s/v)^{-1}$$ If $$v_s=-v$$ f is infinity.Whats going on? Will Doppler effect will be observed if the source say is a fighter plane moving at mach 1 towards observer? My intuition is that Doppler effect is not observed am I correct?
Say an airplane flies at Mach 1. The doppler effect causes the front of the sound emitted by the plane to reach infinite frequency:    $f = \left ( \frac {343+0}{343-343} \right ) f_0 = ∞$  If the plane suddenly stopped, and there was an observer in front of the sound waves to receive the sound, what would the bunched up waves sound like to the observer? Would they cancel each other out and cause no sound?
My disk already has 4 primary partitions, how can I install Ubuntu? I would like to install Ubuntu alongside Windows 7 on a HP G62 Notebook. Although I have installed  Ubuntu in a dual-boot many times before, I found out that this model has already four partitions.    Partitions:   SYSTEM (NTFS, 199MB, used 66.59MB) Partition without any tag: NTFS (579GM, used 129GB)  RECOVERY (NTFS 16.74 GB, used 2.42GB)  HP_TOOLS (FAT32, 103.34 MB, used 13.23MB)   Since I am not an expert with partitions I would like to get advice on how to do this.  My first idea is this one:   Free some space from /dev/sda2 (I don't know if could also free some other space) delete the HP_Tools partition (I have already created a backup) create an extended partition with the free space in #1 containing three parititions: swap (1gb); / (EXT4, 30GB);  /home (EXT4, 120GB)   Another option is to use wubi instead.  What do you think? Is there any other way to achieve this?  PS: I really think this HP policy of using 4 partitions is not a coincidence  PS: I tried using gparted from the live CD and I got a warning message saying that if I freed some space from /dev/sda2 I could create serious issues in the system Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$ I tried to use xrandr to set 1680x1050 as a new mode to VGA output, but it says:  sudo xrandr --addmode VGA-0 1680 X Error of failed request:  BadMatch (invalid parameter attributes) Major opcode of failed request:  140 (RANDR) Minor opcode of failed request:  18 (RRAddOutputMode) Serial number of failed request:  35 Current serial number in output stream:  36 Prove that $(\mathbb{Z}_n , +)$, the integers $\pmod{n}$ under addition, is a group. Prove that $(\mathbb{Z}_n , +)$, the integers  $\pmod{n}$ under addition, is a group.  To show that this is a group, I know I need to show three things (in our text, we do not need to show that addition is closed-- rather, we show these three items):  $(a)$ Associative Law  $(b)$ Existence of Identity  $(c)$ Existence of Inverse  This is what I have been working with so far:     $(a)$ Associative Law:   First, assume that $n$ is a composite number and that $a,b \in \mathbb{Z}$ s.t. $a=nx$ and $b=ny$ for some integers, $x$ and $y$. Then $a+nx+nx=n(x+y)$.     So, this is where I am stuck for the Associative Law. I'm not sure if I am headed down the correct path to show that $\mathbb{Z}_n$ is associative.      $(b)$ Existence of Identity:   Generally, when showing the existence of an identity we can use this information for addition :  $a + 0 = 0 + a =a$.    I am unsure how to insert the modular portion of the definition into the existence of this identity. I realize that for addition, we generally look at $0$ (rather than $1$ for multiplication).     $(c)$ Existence of Inverse: I need to show that for each element $a \in \mathbb{Z}_n$ that $a^{-1}=-a$. Again, I do not know how to insert the modular portion of definition into this aspect of the proof.   My question is how to incorporate this modular information into the proof that this is a group. We have not covered the integers modulo $n$, binary operations, nor groups in my intro to proofs course. I am trying to read my text to figure out how to prove this, but have a difficult time reading and interpreting math speak. getting error when I compile the Java code using package in commandline? When I used  pip install ipython   or  pip install "ipython[notebook]"   I get the following error:  Downloading/unpacking ipython   Downloading ipython-2.3.1-py27-none-any.whl (2.8MB): 2.8MB downloaded Installing collected packages: ipython Cleaning up... Exception: Traceback (most recent call last):   File "/usr/lib/python2.7/dist-packages/pip/basecommand.py", line 122, in main     status = self.run(options, args)   File "/usr/lib/python2.7/dist-packages/pip/commands/install.py", line 283, in run     requirement_set.install(install_options, global_options, root=options.root_path)   File "/usr/lib/python2.7/dist-packages/pip/req.py", line 1435, in install     requirement.install(install_options, global_options, *args, **kwargs)   File "/usr/lib/python2.7/dist-packages/pip/req.py", line 671, in install     self.move_wheel_files(self.source_dir, root=root)   File "/usr/lib/python2.7/dist-packages/pip/req.py", line 901, in move_wheel_files     pycompile=self.pycompile,   File "/usr/lib/python2.7/dist-packages/pip/wheel.py", line 206, in move_wheel_files     clobber(source, lib_dir, True)   File "/usr/lib/python2.7/dist-packages/pip/wheel.py", line 193, in clobber     os.makedirs(destsubdir)   File "/usr/lib/python2.7/os.py", line 157, in makedirs     mkdir(name, mode) OSError: [Errno 13] Permission denied: '/usr/local/lib/python2.7/dist-packages/IPython'  Storing debug log for failure in /home/username/.pip/pip.log   What does this error mean? How do I fix it? How to run sudo command with no password? How does the ubuntu user on the AWS images for Ubuntu Server 12.04 have passwordless sudo for all commands when there is no configuration for it in /etc/sudoers?  I'm using Ubuntu server 12.04 on Amazon. I want to add a new user that has the same behavior as the default Ubuntu user. Specifically I want passwordless sudo for this new user.   So I've added a new user and went to edit /etc/sudoers (using visudo of course). From reading that file it seemed like the default ubuntu user was getting it's passwordless sudo from being a member of the admin group. So I added my new user to that. Which didn't work. Then I tried adding the NOPASSWD directive to sudoers. Which also didn't work.   Anyway, now I'm just curious. How does the ubuntu user get passwordless privileges if they aren't defined in /etc/sudoers. What is the mechanism that allows this? Prove that a set of connectives is inadequate I'm new to blender and have this issue: I'm using the "Industry Compatible" keymap. In "Edit Mode" the keys 1, 2 and 3 swap between vertex, edge and face select - Great!  Now i want to customize it, so i'm adding a new preset "My keymap". As far as i understand this now is based on the "Industry Compatible" keympap and everything works accordingly. But if i close and start blender again, the 1, 2 and 3-key aren't working anymore. I need to go back to the preferences, set the "Industry Compatible" keymap and then set back to "My keymap". Then the 1, 2 and 3-key work again as expected.  This is reproduceable on the last Blender 2.8 version on several different machines. Am i doing something wrong? Is this a bug? Invalid group name: Group names must begin with a word character I received the following exception when I was using the Regex class with the regular expression: (?'named a'asdf)  System.ArgumentException: parsing \"(?'named a'asdf)\" - Invalid group name: Group names must begin with a word character.   What is the problem with my regular expression? How to translate and rotate the heading of landscaped pages? Objective  How to change the heading of landscaped pages from    to    ?  Minimal Code  \documentclass{book} \usepackage[a5paper,hmargin=3cm,vmargin=5cm]{geometry} \usepackage{lscape,lipsum}  \begin{document} \chapter{One} \lipsum[1]  \section{One One} \lipsum[2]  \newgeometry{hmargin=5cm,vmargin=3cm}  \begin{landscape} \lipsum[3-5] \end{landscape}  \restoregeometry \lipsum[6]  \end{document}   Edit 1 (my real scenario layout)  In my real scenario, the left-right margins should not be occupied by headings. Is Highschool of the Dead on hiatus again? Accidentally created directory named "~" (tilde) I managed to make a directory literally named ~.  (Apparently, Python's os.mkdir('~/something') does this.)  How do I remove it without nuking my home?  Also, if it helps, I have my real /home on a separate partition. And the duplicate ~ is located in (the real ) ~. Standard error of regression coefficient without raw data How does the propagation of gravity work for photons? Scenario: My friend John has a personality disorder, intensely paranoid for example.  Can I say:     There were three events last year that told me John had a problem.   or can I say:     There were threee events last year that told me John has a problem. Problem with patching babel package I am trying to use babel and biblatex package together but I am getting following error:    ! Package biblatex Error: Patching 'babel' package failed.    This is my code example:  \documentclass[12pt,a4paper,twoside,openright]{book} \usepackage{cmap} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage[slovak]{babel} \usepackage{xpatch} \usepackage{csquotes} \usepackage{biblatex} \begin{document} \enquote{quote} \end{document}   I would need the result look like this:    Well, it seems like I could get rid of the error when using xpatch package, but it works only when I delete 'slovak' option for babel package. That way the result look like this:    Please, is there any workaround for this problem? I am really stuck in this. Enumerate non-isomorphic graphs on n vertices In the following the graphs are assumed to be undirected and simple.  1.Enumerate the number of non-isomorphic graphs on $n$ vetrices where $n$ is fixed.  Here are some ideas I had:  The number of labeled graphs is $ 2^{\frac{n(n-1)}{2}} $.  So it is enough to find the number unlabeled graphs on $n$ vertices.I have no idea for this.  2.Enumerate the number of non-isomorphic graphs on $n$ vertices and $m$ edges where $n,m$ are fixed.   Can we find a closed formula for each of this?  Any help?   Thank you! What are the differences between a HashMap and a Hashtable in Java? What are the differences between a  and a  in Java?  Which is more efficient for non-threaded applications? Cleaning Circuits with Compressed Air I've been arguing with a colleague whether it is a sensible solution to clean dusty PCBs with compressed air. While I think this is the best solution (nothing touches the PCB), he claimed that spraying off the dust can cause ESD, because the charges that may have accumulated in the dust win't bleed off in the process (and it's better to leave everything as it is). I'm not really convinced by this argument and my (limited) knowledge of ESD production doesn't help getting peace of mind in this matter. What is your input?