I wonder who lives outside of Middle-earth and what is their life like? What are the names of the continents? Is there a big good map of Arda?
There are a number of times in Lord of the Rings where the "east" is mentioned -- the pirate ships, the slave-driven farms. And of course all of the peoples subservient to Sauron who come to fight Gondor and the West. Are there any maps of the East of Middle-earth, and what is out there?
What level should I be to kill Alduin I am level 31 and I have the Elder Scroll. I am not sure if my level is high enough to go to Whiterun and trap one of Alduin's minions. What level should I be before I attempt it? How can I get to Iceland on a cargo ship? Planning a low budget and environment friendly trip to Iceland from Helsinki, Finland next summer for me and my friend. Haven't been able to find relevant information on possibility for cargo travel (from where - eg. Norway, Denmark? - timetables, prices etc). Expected departure from Helsinki around June 18th, return at latest on July 7th 2015. I'm very thankful for any related advice (and first time on stackexchange, so apologies if I didn't formulate my question in a best possible way) How to find max of amount of opportunity related to account? I have a below requirement : I need to find maximum amount on related opportunities and to display on account. Ex: suppose I have account A1 and A1 have 5 opportunities with amount o1=>100 o2=>500 o3=>300 o4=>1000 o5=>50 on my account i should have max_opportunity_amount =1000.  I have written below trigger ,but  I am not sure what to do further  trigger maxOppAmountonAcc on Opportunity(after insert){      map&lt;id,Opportunity&gt; oppMap = new map&lt;id,Opportunity&gt; ();     set&lt;Id&gt; oppId = new set&lt;Id&gt;();     for(Opportunity o : Trigger.new)     {         oppMap.put(o.accountId,o);         oppId.add(o.id);     }       List&lt;Account&gt; accList = new List&lt;Account&gt;();      for(Account a : [Select id ,MaxOppAmount__c,(select id,max(amount)  from opportunities) from Account where id in : oppMap.keyset()])     {      }  } How to cut a mesh by specifying the angle Let $f$ be an entire function such that $\mid f(z) \mid \leq A \mid z \mid$ for all $z$, where $A$ is a fixed number. Show that $f(z)=a_1z$, where $a_1$ is a complex constant. Image uploads not working on Chrome When I try to upload an image, I'm presented with the following dialog box,    The dialog box does not allow uploading either from my computer or by posting a link.  This happens only on Chrome browser (running on Windows). Clearing cache and cookies, and restarting computer do not resolve.  Is this just my computer? Or is this a site-wide bug?  Additional info:  Clicking on 'click' to upload does nothing. Dragging an image onto dialog redirects me to the file location on my computer. Clicking 'Add picture' redirects me to http://[SE-domain].com/upload/image?https=true.  UPDATE: A Norton extension for Chrome was the source of the problem. Maximum number of edges in a bipartite graph Prove that for a bipartite graph $G$ on $n$ vertices the number of edges in $G$ is at most $\frac{n^2}{4}$.     I used induction on $n$.    Induction hypothesis: Suppose for a bipartite graph with less than $n$ vertices the result holds true.    Now take a bipartite graph on $n$ vertices.Let $x,y$ be two vertices in $G$ where an edge exist between $x$ and $y$. Now remove these two vertices from $G$ and consider this graph $G'$. $G'$ has at most ${(n-2)^2}\over4$. Add these two vertices back.  Then the number of edges $G$ can have is at most    $$|E(G')|+d(x)+d(y)-1$$   My question is in my proof I took $d(x) + d(y) \le n$, where $d(x)$ denotes the degree of vertex $x$.  Can I consider $d(x)+d(y) \leq n$? I thought the maximum number of edges is obtained at the situation $K_{\frac n 2,\frac n 2}$ Stack Exchange doesn't allow me to answer protected questions because I gave away earned rep in bounties I noticed that I can't answer protected questions. I don't want to actually, but it says:        It was , but I also didn't have an ability to answer other protected questions.  I earned 270 reputation points + 100 reputation point bonus. Then I  350 reputation points as a bounty. Then I earned 59 reputation points. Today I started another bounty (50 reputation points), etc – I offered 4 bounties with total 500 rep.  Despite the fact I started from the association bonus, I must have an ability to answer protected questions, as I earned reputation points here. But offered them as bounties.    I now have enough reputation points, but I would like it to be fixed, because I like offering bounties very much.  I would like system to check for my bounties when it checks if I can answer protected question. Gravitational field intensity inside a hollow sphere Homemade coconut milk separates into different layers after a day in the fridge Is there any difference between "offense" and "offence"? How can I achieve more clarity in my photos of the moon? I took this photo of the blood moon this morning and I am finding many of my photos, especially landscape photos, have a significant lack of clarity. I'm not looking for a photo critique because I know this particular photo is crap. I'm looking to identify my source of failure to nail a significantly clear photo.     Setup  Canon EOS 70D with a 100-300 telephoto lens (I'm sorry I don't know the exact model. It's from Canon but not one of their professional quality lenses.)   Aperture: f/5.6 Shutter: 1 sec. ISO: 1000 Focal Length: 300mm Metering mode: Spot White Balance: I manually set the WB to 5500 kelvin, it looked fine in live view. Focus Mode: Manual Drive: 2 sec timer delay   Mounted on a decently stable tripod  Process  I turn on live view, and square up the target in the display. I then set my focal length, focus in using live view, adjust the focus as sharp as possible and take the pic. I've noticed that in this case, the picture was incredibly grainy, which doesn't translate to the final photo, but wonder if it has anything to do with it.  This particular shoot I found it difficult to balance out the variables with a dark sky and a moving moon that starts blurring after 1-2 seconds of exposure, which is why I had the aperture wide open and the ISO cranked up.  I can't tell where I'm failing:  Equipment:  The 70d takes great photos but the telephoto is not great when it's totally zoomed in. My wallet doesn't hold enough cash for a motorized mount to track objects in the sky.  Circumstance: I've seen great photos of the moon with the use of a camera and a tripod, so I know this is possible. Although, I keep seeing pictures of this big gorgeous moon over the landscape, and when I use my wide-angle, the moon shows up as a dot. What the hell are people doing to get the moon so big?  Beginner skill level: I know this is the biggest culprit, but being the beginner, I'm unable to know where to adjust. I am using Google Chrome 48.0 32-bit. Today when I launched Google Chrome, I got this message:    This computer will soon stop receiving Google Chrome updates because this Linux system will no longer be supported   I thought Ubuntu 14.04 is supported for five years, what's exactly happening here?  And on 64-bit Ubuntu, I get an error from Update Manager and apt-get update:  Failed to fetch http://dl.google.com/linux/chrome/deb/dists/stable/Release  Unable to find expected entry 'main/binary-i386/Packages' in Release file (Wrong sources.list entry or malformed file)   Some index files failed to download.   They have been ignored, or old ones used instead. I want to be able to close an alert box automatically using Javascript after a certain amount of time or on a specific event (i.e. onkeypress).  From my research, it doesn't look like that's possible with the built-in alert() function.  Is there a way to override it and have control over the dialog box that it opens?  Also, I don't want an override that shows a hidden div as the alert.  I need an actual dialog box. Extracting extension from filename in Python Is there a function to extract the extension from a filename? How much electronics and other valuables can I bring duty-free when going to India? I'm on Ubuntu 16.04.1 at the moment, and system windows like the Files window, Terminal or System Software open behind the Unity launcher, which means they are partially hidden behind it. I can move them with Alt+F7, but I'd like a more permanent solution to this problem. Primary decomposition of a monomial ideal Can anyone give me an idea about the primary decomposition of the ideal $I=(x^3y,xy^4)$ of the ring $R=k[x,y]$?    I am trying to connect the primary decomposition with the set Ass(R/I) which i have find before.. How to fix Permission Denied (Public key) error? While trying to communicate between my desktop Ubuntu 12.10 and Fedora 19 desktop, I am facing the error of Permission Denied (Public key). I am able to login through ssh from fedora to Ubuntu, but not vice-versa. I even performed telnet on both machines via port 22 and both machines are listening, but not through ssh. What to do? Any idea?  My sshd_config file is as follows:  # Package generated configuration file # See the sshd_config(5) manpage for details  # What ports, IPs and protocols we listen for Port 22 # Use these options to restrict which interfaces/protocols sshd will bind to #ListenAddress :: #ListenAddress 0.0.0.0 Protocol 2 # HostKeys for protocol version 2 HostKey /etc/ssh/ssh_host_rsa_key HostKey /etc/ssh/ssh_host_dsa_key HostKey /etc/ssh/ssh_host_ecdsa_key #Privilege Separation is turned on for security UsePrivilegeSeparation yes  # Lifetime and size of ephemeral version 1 server key KeyRegenerationInterval 3600 ServerKeyBits 768  # Logging SyslogFacility AUTH LogLevel INFO  # Authentication: LoginGraceTime 120 PermitRootLogin yes StrictModes yes  RSAAuthentication yes PubkeyAuthentication yes #AuthorizedKeysFile    %h/.ssh/authorized_keys  # Don't read the user's ~/.rhosts and ~/.shosts files IgnoreRhosts yes # For this to work you will also need host keys in /etc/ssh_known_hosts RhostsRSAAuthentication no # similar for protocol version 2 HostbasedAuthentication no # Uncomment if you don't trust ~/.ssh/known_hosts for RhostsRSAAuthentication #IgnoreUserKnownHosts yes  # To enable empty passwords, change to yes (NOT RECOMMENDED) PermitEmptyPasswords no  # Change to yes to enable challenge-response passwords (beware issues with # some PAM modules and threads) ChallengeResponseAuthentication no  # Change to no to disable tunnelled clear text passwords PasswordAuthentication yes  # Kerberos options #KerberosAuthentication no #KerberosGetAFSToken no #KerberosOrLocalPasswd yes #KerberosTicketCleanup yes  # GSSAPI options GSSAPIAuthentication no GSSAPICleanupCredentials yes  X11Forwarding yes X11DisplayOffset 10 PrintMotd no PrintLastLog yes TCPKeepAlive yes #UseLogin no  #MaxStartups 10:30:60 #Banner /etc/issue.net  # Allow client to pass locale environment variables AcceptEnv LANG LC_*  Subsystem sftp /usr/lib/openssh/sftp-server  # Set this to 'yes' to enable PAM authentication, account processing, # and session processing. If this is enabled, PAM authentication will # be allowed through the ChallengeResponseAuthentication and # PasswordAuthentication.  Depending on your PAM configuration, # PAM authentication via ChallengeResponseAuthentication may bypass # the setting of "PermitRootLogin without-password". # If you just want the PAM account and session checks to run without # PAM authentication, then enable this but set PasswordAuthentication # and ChallengeResponseAuthentication to 'no'. UsePAM yes   This is sshd_config of ubuntu system. Let $f : U \to V$ and $g : V \to W$ be linear transformations on the vector spaces $U$, $V$, and $W$. Supposedly,  $$ \dim(\ker(g \circ f)) = \dim(\ker(f)) + \dim(\ker(g) \cap \operatorname{im}(f)). $$  How might I go about proving that?    (Attempt:) The $\dim(\ker(g)\cap\operatorname{im}(f))$ term suggests to me that I should define a vector space $V' = \ker(g) + \operatorname{im}(f)$ to invoke the theorem that  $$ \dim(V') = \dim(\ker(g)) + \dim(\operatorname{im}(f)) - \dim(\ker(g) \cap \operatorname{im}(f)), $$  but I don't really see where to go from there.