A graph that all its vertices are vertices cut
Proof that any simple connected graph has at least 2 non-cut vertices.
How do I remove repeated elements from ArrayList? Force floats to be typeset after their occurrence in the source text? I looked "$\divideontimes$" up on Google and now I know that it's Unicode U+22c7 but when would it be used?  I am guessing that $5 \divideontimes 5 = 25$ and $1$...? Does the pilot of a rocket ship experience an asymptotic approach to the speed of light? A question has recently come up that goes beyond my knowledge of special relativity.  Suppose a pilot has his foot on the gas pedal of a rocket ship and keeps it applied to achieve a constant acceleration, and he has a magical engine that can maintain the thrust needed to accomplish such acceleration even as the vehicle acquires mass.  He measures his acceleration at periodic intervals and sums it up as he goes.  Observers perceive the rocket to increase in speed and gradually approach the speed of light (but never reach it). Two possibilities are being debated for what the pilot observes, and my preference is for the first:   Time dilation gives him the impression that the summation of his readings are approaching light speed at a constant rate, but there is an asymptote involved here even in the inertial frame such that he never actually perceives himself to reach, let alone exceed, $c$, because time slows down to a crawl (as seen from the reference frame) before this can happen. Although to observers he is only approaching $c$, it is possible for the summation of the measurements on his accelerometer to indicate that he has surpassed $c$ and is now traveling faster than light.  From the reference frame he is approaching $c$ and his instruments in the inertial frame tell him that he has surpassed it.   I assume (1) is true beyond a doubt?  If so, is there a straightforward explanation for this? What is the "wheel" user in OS X? Convert a JSON string to object in Java ME? Have a look at the following code:  \documentclass[letterpaper]{article} \usepackage{amsmath,amssymb} \begin{document}  $2-\frac{2}{1-\left(\frac{2}{2-\frac{2}{x^2}}\right)}$\quad  $2-\dfrac{2}{1-\left(\dfrac{2}{2-\dfrac{2}{x^2}}\right)}$\quad  $2-\cfrac{2}{1-\left(\cfrac{2}{2-\cfrac{2}{x^2}}\right)}$\quad  $2-\dfrac{2}{1-\left(\cfrac{2}{2-\dfrac{2}{x^2}}\right)}$ \end{document}   This gives:    Evidently, the first display is not the proper way. The second and last are the same I guess. The third has a better display but there is too much space above the 2 in \left(\cfrac{2}{2-\cfrac{2}{x^2}}\right). Essentially, non of the above displays satisfies, for me, a good Mathematical typsetting. Although, it may be argued that it is the default in LaTeX. I just can't get it right? Any insights? In a book I got this example from it looks like this without the excessive bold (this is a scanned image): I've downloaded a driver for a video card (*.run) and tried to install within a terminal. When I started the installation process I got this error: ERROR: nvidia-installer must be run as root. I'm logged in with my own profile. Non-empty intersection. Let $A_1,A_2,...,A_{2019}$ be sets s.t. $|A_i|$=45 for each $i=\overline{1,2019}$ and $|A_i\cap A_j|=1$ for every $i\neq j$. Is it true that $$\Big|\bigcap _{i=1}^{2019} A_i\Big|=1?$$ What I thought of doing is proving by induction by i, the base is obvious. However I'm stuck on the next step. I would like to work out the Fourier transform of the Gaussian function   $$f(x) = \exp \left(-n^2(x-m)^2 \right)$$  It seems likely that I will need to use differentiation and the shift rule at some point, but I can't seem to get the calculation to work. Does anyone have any advice?  By the way, I am using   $$\mbox{FT}(f)(k)=\int_{-\infty}^\infty f(x)e^{-ikx}\,\mathrm d x$$  as my definition of a Fourier transform. Many thanks. My laptop has a function key which turns F keys into keys which change volume or brightness. I would like to swap a number of them so that they perform that function under normal operation and are an Fx key while the function key is being held.  I assumed that the function keys were just normal keys codes with the set of keys being large enough to include all the possible speical keys. I tried to so as this tutorial suggests () and use xev to obtain the key codes and then would use xmodmap to swap their value.  This does not seem to work though. The F12 key gives the xev output:  KeyPress event, serial 41, synthetic NO, window 0x4a00001,     root 0xb1, subw 0x0, time 468005, (23,-15), root:(89,37),     state 0x10, keycode 96 (keysym 0xffc9, F12), same_screen YES,     XLookupString gives 0 bytes:      XmbLookupString gives 0 bytes:      XFilterEvent returns: False   Which I think is to be expected. However, the Increase Volume button give this response:  KeymapNotify event, serial 41, synthetic NO, window 0x0,     keys:  65  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0               0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0    And so does the Decrease Volume key. How can I perform the swapping of the keys that I would like?  Thank you What is a single word for a person who, as a habit, exaggerates a lot when relating information?   So for example, they relate something that happened but exaggerate so much that they are including clear falsehood and they are well known for doing that. I have no idea how to prove that the set $\{(x, |x|): x\in\mathbb{R}\}$ is not the image of an immersion of $\mathbb{R}$ into $\mathbb{R}^2$  For example   If $f(t)=(t^3, |t|^3)$ then $f'(0)=(0, 0)$. Is it possible to get total render time via Python code when render’s done? At some point, the filesystem on my digital audio player has become read-only. I cannot copy files into it or remove files on it.  Are there some possible reasons for the player's file system to change permissions in this way?  I tried using chmod:  $ sudo chmod a+rw SGTL\ MSCN/  chmod: changing permissions of `SGTL MSCN/': Read-only file system   SGTL MSCN is the mount point of the digital audio player.  What else can I try to make it writeable? How to use an existing database with an Android application Is there an easy way to calculate the residue at one of the poles of a rational expression of the form $\frac{1}{1+z^n}$?  I end up having to add a bunch of polar-form complex numbers in the denominator which I have no idea how to do except to convert them to rectangular coordinates, which becomes really messy.  I feel like there ought to be simple pattern/rule for such a canonical expression. How to test multiple variables against a single value? Also schemas can communicate over database links to schemas in other remote databases.    Could one replace the preposition over with through? Will it change the meaning, and if so, when should we use over instead of through? Is there any way of making a Minecraft server lower than the current version? So me and my friends manged to make a server in Minecraft for us to play on and we would like to add mods. But the mods we want to add are a few versions lower than the updated version. Is there any way of making a server with a lower version of Minecraft that people can still play on?