Including imported libraries in jar
How can I create an executable JAR with dependencies using Maven?
\dots versus \ldots - is there a difference? Is there a difference between \dots and \ldots, the ellipsis?  If yes: Which? When to use \dots and when to use \ldots?  If no: Why are there both at all? If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t Let  $f(xy) =f(x)f(y)$ for all $x,y\geq 0$. Show that $f(x) = x^p$ for some $p$.    I am not very experienced with proof. If we let $g(x)=\log (f(x))$ then this is the same as  $g(xy) = g(x) + g(y)$   I looked up the hint and it says let $g(x) = \log f(a^x) $   The wikipedia page for functional equations only states the form of the solutions without proof.  Attempt  Using the hint (which was like pulling a rabbit out of the hat)  Restricting the codomain $f:(0,+\infty)\rightarrow (0,+\infty)$ so that we can define the real function $g(x) =  \log f(a^x)$ and we have $$g(x+y) = g(x)+ g(y)$$   i.e $g(x) = xg(1)$ as $g(x)$ is continuous (assuming $f$ is).  Letting $\log_a f(a) = p$ we get $f(a^x) =a^p $. I do not have a rigorous argument but I think I can conclude that $f(x) = x^p$ (please fill any holes or unspecified assumptions) Different solutions are invited How to reinstall PulseAudio (Ubuntu 12.04) A word for "every two days" What can I do with .chk files in FOUND.000 folders? Just discovered I have gotten a FOUND.000 folder on my usb drive. I guess from running chkdsk once. It has three files in it:   FILE0000.CHK FILE0001.CHK FILE0002.CHK   What exactly can I do with these files? What are my options? Are they lost files? Are they garbage? Can I use them for anything at all? Or will I just have to delete them? extracting energy from cosmological expansion This question is a more concrete reincarnation of an .  Are there mechanisms to extract energy from the cosmic rate of expansion? putting some extremely long ropes across the universe and extract work from their increase of separation?  assuming this is possible ( i don't see why it would not ), what form would take the back-reaction force? in all physics, every time you extract work from some system by some force, this system will exert a force back. Can we slow down cosmic expansion by variations of these mechanisms? Are there any other methods to apply to solving simultaneous equations? We are asked to solve for $x$ and $y$ in the following pair of simultaneous equations:  $$\begin{align}3x+2y&amp;=36 \tag1\\ 5x+4y&amp;=64\tag2\end{align}$$  I can multiply $(1)$ by $2$, yielding $6x + 4y = 72$, and subtracting $(2)$ from this new equation eliminates $4y$ to solve strictly for $x$; i.e. $6x - 5x = 72 - 64 \Rightarrow x = 8$. Substituting $x=8$ into $(2)$ reveals that $y=6$. I could also subtract $(1)$ from $(2)$ and divide by $2$, yielding $x+y=14$. Let $$\begin{align}3x+3y - y &amp;= 36 \tag{1a}\\ 5x + 5y - y &amp;= 64\tag{1b}\end{align}$$ then expand brackets, and it follows that $42 - y = 36$ and $70 - y = 64$, thus revealing $y=6$ and so $x = 14 - 6 = 8$. I can even use matrices! $(1)$ and $(2)$ could be written in matrix form: $$\begin{align}\begin{bmatrix} 3 &amp;2 \\ 5 &amp;4\end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix}&amp;=\begin{bmatrix}36 \\ 64\end{bmatrix}\tag3 \\ \begin{bmatrix} x \\ y\end{bmatrix} &amp;= {\begin{bmatrix} 3 &amp;2 \\ 5 &amp;4\end{bmatrix}}^{-1}\begin{bmatrix}36 \\ 64\end{bmatrix} \\ &amp;= \frac{1}{2}\begin{bmatrix}4 &amp;-2 \\ -5 &amp;3\end{bmatrix}\begin{bmatrix}36 \\ 64\end{bmatrix} \\ &amp;=\frac12\begin{bmatrix} 16 \\ 12\end{bmatrix} \\ &amp;= \begin{bmatrix} 8 \\ 6\end{bmatrix} \\ \\ \therefore x&amp;=8 \\ \therefore y&amp;= 6\end{align}$$  Question Are there any other methods to solve for both $x$ and $y$? What do I need to consider to choose between dSLR, mirrorless, or a compact as my first "serious" camera? In $Sets$, the initial object is $0 = \emptyset$. We have $C \times \emptyset = \emptyset$ for any set $C$. As there are no maps to the empty set, we don't get much of the universal property of the product.  I am now wondering what is special about arbitrary categories $\mathscr{C}$ with $C \times 0 \cong 0$ for all objects $C$ of $\mathscr{C}$, where $0$ is the initial object of $\mathscr{C}$.   From Sheaves in Geometry and Logic by MacLane (p.194), in any topos $\mathscr{C}$, any arrow $k:C \to 0$ is an isomorphism. The universal property of the product would then also not yield very much.   Are there any categories of higher interest? Do I need Transit Visa to visit London for 4-5 hours during layover? Let $a$ and $b$ be positive reals. Show that $$\lim\limits_{n\to\infty} \left(\frac{a^{\frac{1}{n}}+b^{\frac{1}{n}}}{2}\right)^n =\sqrt{ab}$$ My Panda USB wi-fi adapter works just fine on 16.10, but when I try to connect to my wi-fi router in 17.04, GNOME network manager reports "Connection failed." I did some tinkering, and noticed that my MAC address for my wifi adapter, according to GNOME, is DIFFERENT every time I make it forget my wifi settings and try to reconnect. Any leads on a possible fix or work-around?   I'm running Ubuntu GNOME 17.04, kernel 4.10.0-19-generic, GNOME 3.24.0. Old title - "change resolution to 1280x1024 using xrandr gives: X Error of failed request: BadValue (integer parameter out of range for operation)"  I have installed a fresh Ubuntu 17.10 and have a monitor with 5:4 resolution. settings has no resolution higher than 1024x768. But I need the resolution 1280x1024 (5:4).  I use the default motherboard graphics card:  # lspci|grep VGA 00:02.0 VGA compatible controller: Intel Corporation 4 Series Chipset Integrated Graphics Controller (rev 03)   Also xrandr gives the following:  $ xrandr Screen 0: minimum 320 x 200, current 1024 x 768, maximum 8192 x 8192 XWAYLAND0 connected 1024x768+0+0 (normal left inverted right x axis y axis) 0mm x 0mm    1024x768      59.92*+   I tried to add the 1280x1024 resolution using xrandr. so first created the resolution information using gtf:  $ gtf 1280 1024 60    # 1280x1024 @ 60.00 Hz (GTF) hsync: 63.60 kHz; pclk: 108.88 MHz   Modeline "1280x1024_60.00"  108.88  1280 1360 1496 1712  1024 1025 1028 1060  -HSync +Vsync   Then added to resolutions:  xrandr --newmode "1280x1024_60.00"  108.88  1280 1360 1496 1712  1024 1025 1028 1060  -HSync +Vsync   then again did the command: xrandr --addmode XWAYLAND0 1280x1024_60.00  Then nothing changed. When I tried to change it using xrandr --output XWAYLAND0 --mode 1280x1024_60.00 --rate 60 But an error occurred:  $ xrandr --output XWAYLAND0 --mode 1280x1024  --rate 60 X Error of failed request:  BadValue (integer parameter out of range for operation)   Major opcode of failed request:  140 (RANDR)   Minor opcode of failed request:  7 (RRSetScreenSize)   Value in failed request:  0x0   Serial number of failed request:  21   Current serial number in output stream:  22   I don't know what did I do wrong. Or how to change resolution to the correct one: 1280x1024 When do merchants start paying the actual value of items without bonus effects and perks? If $R$ is an integral domain and a subring $S$ has identity $1_S$, how would you show that $1_S=1_R$ (here $1_R$ is the identity of the ring $R$)? I am unsure about what an integral domain really is and how the subring comes into play here. How to effectively deal with Imposter Syndrome and feelings of inadequacy: "I've somehow convinced everyone that I'm actually good at this" Uncountable subset with uncountable complement, without the Axiom of Choice Let $X$ be a set and consider the collection $\mathcal{A}(X)$ of countable or cocountable subsets of $X$, that is, $E \in \mathcal{A}(X)$ if $E$ is countable or $X-E$ is countable. If $X$ is countable, then $\mathcal{A}(X)$ coincides with the power set $\mathcal{P}(X)$ of $X$. Now suppose that $X$ is uncountable. Assuming the axiom of choice, we can conclude that $\mathcal{A}(X) \ne \mathcal{P}(X)$, since $|X| = |X| + |X|$. So the question is:     Can we prove in ZF that $\mathcal{A}(X) \ne \mathcal{P}(X)$ for every uncountable set $X$?   I'm assuming that a set $X$ is uncountable if there is no injective function $f : X \rightarrow \mathbb{N}$. An equivalence relation is defined by three properties: reflexivity, symmetry and transitivity.  Doesn't symmetry and transitivity implies reflexivity? Consider the following argument.  For any $a$ and $b$, $a R b$ implies $b R a$ by symmetry. Using transitivity, we have $a R a$.  Source: Exercise 8.46, P195 of Mathematical Proofs, 2nd (not 3rd) ed. by Chartrand et al Show that $U_n:=\left(1+\dfrac{1}{n}\right)^n$, $n\in\Bbb N$, defines a monotonically increasing sequence.   I must show that $U_{n+1}-U_n\geq0$, i.e. $$\left(1+\dfrac{1}{n+1}\right)^{n+1}-\left(1+\dfrac{1}{n}\right)^n\geq0.$$  I am trying to go ahead of this step. Cheese from UHT Milk I live in a town where fresh or whole milk is not readily available. I was wondering if I could make cheese from UHT Milk. If so, what kind of cheese and what method I should use? Or rather, Should I?