Do i need visa to travel to the united kingdom with USA refugee travel documents ?
I am planning to visit the UK on a USA travel document but there’s nowhere I am able to find information about visas: I’m a Zimbabwean but using a USA refugee travel document do I need to apply for a UK visa before I travel or I can they just give them on arrival.
Does "corresponding author" carry an implied meaning? After reading the question , I got the impression that (at least in the writers' field) the "corresponding author" flag could carry an implied meaning, such as "did more work than the other authors", or "is a more senior author". Is it the case?  I am in mathematics, a field where we typically sort the authors alphabetically, and I've never given any importance to that role (apart from "this author is willing to answer a couple of extra e-mails, if needed"). Coordinate-Free Definition of Trace. $\DeclareMathOperator{\tr}{trace}$ I am reading the  on the trace operator. The section titled Coordinate-Free Definition defines the trace as follows.  Let $V$ be a finite dimensional vector space over a field $F$ and define a bilinear map $f:V\times V^*\to F$ as $f(v, \omega)=\omega(v)$ for all $(v, \omega)\in V\times V^*$. This maps induces a unique linear map $\tr:V\otimes V^*\to F$. Since $\text{End}(V)$ has a canonical isomorphism with $V\otimes V^*$, we have now a notion of trace of a linear operator on $V$.  The Question: The second paragraph of the section in the article says that  This also clarifies why $\tr(AB)=\tr(BA)$.  I can't see how $\tr(AB)=\tr(BA)$ follows from this definition at all. Can somebody give me a hint? Assume you have a flat table that stores an ordered tree hierarchy:  Id   Name         ParentId   Order  1   'Node 1'            0      10  2   'Node 1.1'          1      10  3   'Node 2'            0      20  4   'Node 1.1.1'        2      10  5   'Node 2.1'          3      10  6   'Node 1.2'          1      20   Here's a diagram, where we have [id] Name.  Root node 0 is fictional.                          [0] ROOT                           /    \                [1] Node 1          [3] Node 2               /       \                   \     [2] Node 1.1     [6] Node 1.2      [5] Node 2.1           /            [4] Node 1.1.1   What minimalistic approach would you use to output that to HTML (or text, for that matter) as a correctly ordered, correctly indented tree?   Assume further you only have basic data structures (arrays and hashmaps), no fancy objects with parent/children references, no ORM, no framework, just your two hands. The table is represented as a result set, which can be accessed randomly.   Pseudo code or plain English is okay, this is purely a conceptional question.  Bonus question: Is there a fundamentally better way to store a tree structure like this in a RDBMS?    EDITS AND ADDITIONS  To answer one commenter's ('s) question: A root node is not necessary, because it is never going to be displayed anyway. ParentId = 0 is the convention to express "these are top level". The Order column defines how nodes with the same parent are going to be sorted.  The "result set" I spoke of can be pictured as an array of hashmaps (to stay in that terminology). For my example was meant to be already there. Some answers go the extra mile and construct it first, but thats okay.  The tree can be arbitrarily deep. Each node can have N children. I did not exactly have a "millions of entries" tree in mind, though.  Don't mistake my choice of node naming ('Node 1.1.1') for something to rely on. The nodes could equally well be called 'Frank' or 'Bob', no naming structure is implied, this was merely to make it readable.  I have posted my own solution so you guys can pull it to pieces. Consider the following code:  foo () {     echo $* }  bar () {     echo $@ }  foo 1 2 3 4 bar 1 2 3 4   It outputs:     1 2 3 4       1 2 3 4   I am using Ksh88, but I am interested in other common shells as well. If you happen to know any particularity for specific shells, please do mention them.  I found the follwing in the Ksh man page on Solaris:     The meaning of $* and  $@  is   identical  when  not  quoted  or  when  used  as a parameter   assignment value or as a file name. However, when used as  a   command argument, $* is equivalent to ``$1d$2d...'', where d   is the first character of the IFS variable,  whereas  $@  is   equivalent  to  $1 $2 ....   I tried modifying the IFS variable, but it doesn't modify the output. Maybe I'm doing something wrong? Let $g(x)\in \mathbb{Z}[x]$, a nonconstant polynomial. Show that the set of primes $p$ such that $p\mid g(n)$ for some $n\in \mathbb{Z}$ is infinite.  I don't know how to start. I have tried asuming that the set is finite but i haven't reached any contradiction. How to return to the GUI? I am very new to Linux and Ubuntu. I use Ubuntu 11.10.  I was trying to exit the X server (in order to install some Nvidia drivers) and I typed in the terminal:  sudo service lightdm stop   How can I return to the Ubuntu interface? My Windows folder takes up too much space - how can I reduce it? In typical PCs the Size of Windows Folder is 6 to 8 GB but in my Case its 25GB. How can I delete the unwanted files from the Windows Folder (which, in turn, will optimize my C Drive size).  My system is Windows 7 with 60 GB in C Drive with 59 GB occupied. Getting "'file' is different from the same file on the system" when I attempt to update through synaptic Energy-momentum tensor transformation VirtualBox Toolbar is hidden! How to show it? I accidentally hide the main Toolbar from my VirtualBox Manager UI? In my ubuntu 12.04 .   Can anyone let me know the detail steps to display the Toolbar again? I search the whole blogs but can't figure it out! There is no fruit jet pack. I can't get it. How do I get it? I looked at the jetpacks many times. There are none. How do I get started creating an Ubuntu Desktop App? Modiagram will not compile How to locate a font in Ubuntu? Ubuntu desktop with 12.04 is about to crash.  Installed 13.04 on a new machine, want to transfer Book Antiqua font from old machine to the new one.  How do I find it on the old machine?  My /usr directory is empty. My fonts.conf file has these lines: &lt;!-- Font directory list --&gt; &lt;dir&gt;/usr/share/fonts&lt;/dir&gt; &lt;dir&gt;/usr/x11R6/lib/X11/fonts&lt;/dir&gt;  &lt;dir&gt;/usr/local/share/fonts&lt;/dir&gt; &lt;dir&gt;~/.fonts&lt;/dir&gt;  Don't know what this means, but my /usr directory has nothing in it. Let $\alpha(t)$ be a regular curve. Suppose there is a point $a$ in $R^3$ such that $\alpha(t)-a$ is orthogonal to $T(t)$ for all t. Prove that $\alpha(t)$ lies on a sphere.  So, I let $\alpha(t)=(x(t), y(t),z(t))$ and $a=(a,b,c)$.  Since, $\alpha(t)-a$ is orthogonal to $T(t)$,  $&lt;\alpha(t)-a,T(t)&gt;=0$.  But I don't know how to solve this.. Proving the two given vectors are orthogonal Am I going to have trouble flying without my full name on the ticket? In my passport, my name is Firstname middlename1 middlename2 lastname, and in the ticket is LASTNAME/FIRSTNAME MR.  Will be a problem? I'll travel from Brazil to Bali, Indonesia and according to the agency I bought the ticket from, there's no problem and it's common.  The airline is Qatar Airlines and I have looked , which says that the passenger name can't be changed after the booking has finished.  But I don't know if it is a problem. Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$ Taylor series $\frac{z^2+z}{(z-1)^2}$ at $z=-1$ Update Migration Path List for Non-Moderators