terminal will not allow upgrade of 1604 lts
Unable to lock the administration directory (/var/lib/dpkg/) is another process using it?
Management of fruit bowls on the Enterprise D I have noticed that guest quarters on the Enterprise D have fruit bowls on their tables.  A prominent instance is the fruit bowl in Berlinghoff Rasmussen's quarters in "".  The first thing that Rasmussen does when Data takes him to his guest quarters is take a piece of fruit and shove it in his pocket.  Who replicates fruit for these fruit bowls before guests arrive?  More generally, who removes unused fruit and tidies quarters after guests leave?  Is there a ship hospitality staff, perhaps including Guinan's wait staff in Ten Forward? How to initialize private static members in C++? What is the best way to initialize a private, static data member in C++?  I tried this in my header file, but it gives me weird linker errors:  class foo {     private:         static int i; };  int foo::i = 0;   I'm guessing this is because I can't initialize a private member from outside the class.  So what's the best way to do this? Website is under maintenance - how to restrict access? Does Windows 7 allow auto-login with a stored password, like TweakUI did? Proving the two given vectors are orthogonal I am given the vectors $\mathbf{w}, \mathbf{v}, \mathbf{u}$ in $\mathbb{R}^n$ such that $\mathbf{u} \neq 0$ and $\mathbf{w} = \mathbf{v} - \frac{\mathbf{u}\,\bullet\,\mathbf{v}}{\|\mathbf{u}\|^2}\bullet\mathbf{u}$. I am asked to show that the vector $\mathbf{w}$ is orthogonal to $\mathbf{u}$.     So far, I have written out the definition of orthogonal: two vectors are orthogonal if and only if their dot product is zero.   So what we need to prove is $\mathbf{w}\bullet\mathbf{u} = 0$ where $\mathbf{w}\bullet\mathbf{u}$ is defined as $\mathbf{w}^T\bullet\mathbf{u}$.   However, I have been stuck on this problem for about an hour and haven't made any significant progress from here. How do we go about proving that the vectors are orthogonal? Residue fields of schemes of finite type (over $\mathbb{Z}$) Suppose $X$ is a scheme of finite type over $\mathbb Z$. I want to prove that:  (1) The residue fields of closed points of $X$ are finite;  (2) For a given $q=p^n$ with $p$ prime, there is only a finite number of closed points of $X$ whose residue field is $\mathbb F_q$.  For (1), I see that one has to use some form of Nullstellensatz. First, we suppose $X=\operatorname{Spec}(A)$ affine, and $A=\mathbb{Z}[X_1,...,X_n]/I$. We need to show that if $m$ a maximal ideal of $A$, then $A/m$ is finite. Note $p=\mathbb Z\cap m$. If $p$ is maximal, we get that $A/m$ is of finite type over $\mathbb F_p$ thus a finite extension by Nullstellensatz and we are done. But $p$ could be the $(0)$ ideal in which case I neither conclude nor get a contradiction.  For (2), we can again argue locally, so we need to show that $A$ contains only a finite number of maximal ideals $m$ with $A/m$ of fixed cardinality $q=p^n$. I get an impression that to count these ideals its the same as to count the number of automorphisms of $\mathbb{F}_{q}$ which fix $\mathbb F_p$, but the corrspondence is not bijective, so we only get an upper bound which is enough. Is this idea correct? Proving AM-GM with induction I am trying to prove AM-GM with the following steps:    Prove that AM-GM holds for two variables Prove that if AM-GM holds for $k$ variables then it holds for $2k$ variables Prove that if AM-GM holds for $k$ variables then it holds for $k-1$ variables   If I prove all of these, I will have proved AM-GM. I have proved (1) and (2), but I am still struggling with (3).   Proof for (1)  By the Trivial Inequality, we know that the first statement is true. Therefore \begin{align} (a-b)^2 \ge 0 \implies\\ a^2-2ab+b^2 \ge 0 \implies \\ a^2+2ab+b^2 \ge 4ab  \implies\\ a+b \ge 2\sqrt{ab}  \implies\\ \frac{a+b}{2} \ge \sqrt{ab}\hspace{3mm}\blacksquare\\ \end{align}  Proof for (2)  Let our numbers be $a_1, a_2, a_3, \ldots, a_{2k}$. Denote $$x = \frac{\displaystyle\sum_{i=1}^{k}a_i}{k}, y = \frac{\displaystyle\sum_{i=k+1}^{2k}a_i}{k}$$  We know that by AM-GM for 2 variables, that $$\frac{x+y}{2}\ge \sqrt{xy}$$ By our definition of $x, y$ this means that $$\frac{x+y}{2} = \frac{\frac{\displaystyle\sum_{i=1}^{2k}a_i}{k}}{2}=\frac{a_1+a_2+a_3+\ldots+a_{2k}}{2k}$$ Again by definition, $$\sqrt{xy} = \sqrt{\left(\frac{x_1+x_2+\ldots+x_k}{k}\right)\left(\frac{x_{k+1}+x_{k+2}+\ldots+x_{2k}}{k}\right)}$$ By AM-GM for $k$ variables, $$\sqrt{\left(\frac{x_1+x_2+\ldots+x_k}{k}\right)\left(\frac{x_{k+1}+x_{k+2}+\ldots+x_{2k}}{k}\right)} \ge \sqrt{\sqrt[k]{x_1x_2\ldots x_k}\sqrt[k]{x_{k+1}x_{k+2}\ldots x_{2k}}}$$ This is simply equal to $$\sqrt[2k]{x_1x_2x_3\ldots x_{2k}}\hspace{3mm}\blacksquare$$  However, I have no idea how to proceed on (3). I tried using the definition of AM and GM but did not come up with anything useful. Feel free to point out any errors or flaws on my proofs for (1) and (2). Ran out of inodes - 100% Full I am using Ubuntu 16.04 on AWS EC2 instance which has been working fine until this problem.  My problem is that I've used 100% of available inodes, as I discovered with this command:  $ df -i Filesystem     Inodes  IUsed  IFree IUse% Mounted on udev           124464    360 124104    1% /dev tmpfs          126787    449 126338    1% /run /dev/xvda1     524288 522638   1650  100% / tmpfs          126787      1 126786    1% /dev/shm tmpfs          126787      5 126782    1% /run/lock tmpfs          126787     16 126771    1% /sys/fs/cgroup tmpfs          126793      4 126789    1% /run/user/1000   The main culprits I discovered:  $ find / -xdev -printf '%h\n' | sort | uniq -c | sort -k 1 -n    1155 /usr/src/linux-headers-4.4.0-62/include/linux    1155 /usr/src/linux-headers-4.4.0-65/include/linux    1155 /usr/src/linux-headers-4.4.0-66/include/linux    1155 /usr/src/linux-headers-4.4.0-70/include/linux    1155 /usr/src/linux-headers-4.4.0-71/include/linux    1155 /usr/src/linux-headers-4.4.0-72/include/linux    1155 /usr/src/linux-headers-4.4.0-75/include/linux    1155 /usr/src/linux-headers-4.4.0-78/include/linux    1155 /usr/src/linux-headers-4.4.0-79/include/linux    1155 /usr/src/linux-headers-4.4.0-81/include/linux    1155 /usr/src/linux-headers-4.4.0-83/include/linux    1155 /usr/src/linux-headers-4.4.0-87/include/linux    1155 /usr/src/linux-headers-4.4.0-89/include/linux    1155 /usr/src/linux-headers-4.4.0-91/include/linux    1155 /usr/src/linux-headers-4.4.0-92/include/linux    1514 /usr/src/linux-headers-4.4.0-62-generic/include/config    1516 /usr/src/linux-headers-4.4.0-65-generic/include/config    1516 /usr/src/linux-headers-4.4.0-66-generic/include/config    1516 /usr/src/linux-headers-4.4.0-70-generic/include/config    1516 /usr/src/linux-headers-4.4.0-71-generic/include/config    1516 /usr/src/linux-headers-4.4.0-72-generic/include/config    1516 /usr/src/linux-headers-4.4.0-75-generic/include/config    1517 /usr/src/linux-headers-4.4.0-78-generic/include/config    1517 /usr/src/linux-headers-4.4.0-79-generic/include/config    1517 /usr/src/linux-headers-4.4.0-81-generic/include/config    1517 /usr/src/linux-headers-4.4.0-83-generic/include/config    1517 /usr/src/linux-headers-4.4.0-87-generic/include/config    1517 /usr/src/linux-headers-4.4.0-89-generic/include/config    1517 /usr/src/linux-headers-4.4.0-91-generic/include/config    1517 /usr/src/linux-headers-4.4.0-92-generic/include/config    1517 /usr/src/linux-headers-4.4.0-93-generic/include/config   Is it safe to delete these files, and if yes could you please tell me the exact command or commands to use on my PuTTY client? $ KC $ spaces imply $ US $ spaces , but vise versa is false. In the $ US $ space , each convergent sequence has unique limit.      In the $ KC $ space , every compact subset is closed.      It easy to show that $ KC $ spaces imply $ US $ spaces.   The example below show that $ US $ spaces do not imply $ KC $ spaces.      Let $ X = [ 0, 1 ] $ with the the usual topology and attach  a new point z whose neighborhood are open dense subsets of $ [ 0,1 ]$. Observe $ [ 0,1 ]$ is a compact non-closed  of $X$ and then $X$ is not a $KC$ space. However no sequence in $ [ 0,1 ]$ converge to $z$ and in particular  all convergent in $X$ have unique limits.   can you give me more details?   Why $X$ is not closed? Why no sequence in $ [ 0,1 ]$ converges to $z$ and in particular all convergent sequences in $X$ have unique limits ? I am trying to take pictures of large rugs. The rug size is about 10mx5m, and I'm  planning to purchase , and Canon 7D Mark II with Canon EF 50MM F/1.2L USM lens, since we need high quality images.  We want to set up a studio to take giga-pixel quality images of the large rugs for museum conservation purposes  Could you please suggest the best way for mounting the camera to the ceiling, and any other recommendations for my camera/lens setup, and required lighting? It will be  an indoor shoot. Just we want to setup a studio to shoot the large rugs. How to add a user to sudoers file? I have an account named as Chankey (local user). I had to use some commands like viewing the shadow file etc. I tried it using sudo command     sudo vim /etc/shadow   It said:      Chankey is not in the sudoers file. This incident will be reported.   How can I add this user Chankey to the sudoers file? You can think this of the following as a 3d QFT where we try to calculate the self-energy of two fields. $I$ is a this external self-energy and let us assume it does not depend on the loop momenta which I denote a $\vec{x}=(x,y)$. Consider the following propagator  $$ P(\vec{r}) = \frac{x-ia}{2i^2[\,(x-ia)^2+(y-ib)^2+(z-ic)^2]\,} \,\, \gamma_i. $$ Then we want to calculate $$ I(x) = \int \frac{\,dx \,dy\, dz}{(2\pi)^3} \text{Tr} \left( \frac{x-ia}{2i^2[\,(x-ia)^2+(y-ib)^2+(z-ic)^2]\,}\gamma_x \gamma_x  \right), $$ where Tr$(\gamma_i \gamma_j)=2\delta_{ij}$. Therefore  I am trying to resolve the following integral where $x,y,z \in \mathbb{R}$ and $a,b,c$ are constants (internal self-energies if you wish) in $\mathbb{R}$.  Then, after simplifying the propagator $P(x,y)$ we end up with the following expression for the $x$ component:  $$ I = \frac{1}{2i^2} \int \frac{dxdy}{(2\pi)^2} (x-ia) \int \frac{dz}{2\pi} \frac{1}{[\,(x-ia)^2+(y-ib)^2+(z-ic)^2]\,} $$ but it can be shown that  $$ \int \frac{dq}{(q+iv)^2+w^2} = \frac{\pi}{|w|}\theta(|w|-|v|).  $$ (e.g. see here ) Thus we get that for $|(y-ib)^2+(x-ia)^2|&gt;|a|$, $\theta=1$ (for this is what we are interested about) and then we are left with $$ I = \frac{1}{4i^2} \int \frac{dxdy}{(2\pi)^2} \frac{(x-ia)}{|(x-ia)^2+(y-ib)^2|}.   $$ The question is wether I can make the transformation $$ (x-ia) = q \cos \theta  $$ $$ (y-ib) = q \sin \theta $$ in polar coordinates. Then $dx dy = qdqd\theta$ and the previous integral becomes, assuming $|q|&gt;0$, $$ I = \int_0^{\infty} dq \int_0^{2\pi} d\theta \frac{q \cos \theta}{|q|} =0. $$ Is this correct? I am confused since one can find complex poles in the $I$. If not, what would the correct way to resolve this be? I have a suspicion that this integral should indeed give zero but how can we find this? Was Tracy Mills a part of John Doe's plan from the beginning? In , John Doe is shown as being extremely meticulous and patient while carrying out his plan of murdering and/or torturing people in accordance with the seven deadly sins.  At the end of the film, it is revealed that John Doe had killed and decapitated Tracy Mills, the wife of Detective David Mills.  Was Tracy Mills his intended target from the beginning?  Did John Doe decide to kill Tracy only after Detective Mills and Somerset discovered his residence? Is it wasteful to use a heating element, instead of doing useful work? Consider a computer CPU consuming electrical energy to perform calculations and consequently emitting heat.  Assumption: That a CPU consuming x Watts of power, emits the same amount of heat as an incandescent heating element which consumes the same amount of power.  The rest of the question assumes that this is true: the energy has to go somewhere, and I can't see that the outcome of the calculations counts as "somewhere".  I've long repeated the claim that "wasteful" appliances such as incandescent lightbulbs, over-full kettles, computers left running, etc. are not wasting power if we make the assumptions:   the appliance is in a room which we aim to maintain at above a certain temperature, warmer than the external temperature (cf a home in winter) the room leaks heat to the outside faster than the "wasteful" appliances emit heat. the room contains an electric heater the electric heater is regulated by a thermostat   In these circumstances, I think (?), if a light bulb produces excess heat, its only effect is to cause the thermostat to switch off sooner, so what energy you've "wasted" in the light bulb, is "saved" at the heater.  I don't think that's controversial.  But my question is:   If a CPU does useful work, and emits all the input energy as heat as a side effect But a heating element emits the same heat, without doing useful work Is it therefore wasteful to use heating elements? Is it more efficient to (for example) run  on a CPU, to get "free" computation as a side-effect of heating?   One reason to heat a room with a heating element, rather than with CPUs, is that the heating element is much cheaper to produce. But ignoring the initial cost of the hardware, would a "heater" made out of 20 CPUs, each running at full capacity and consuming 50W each, output less thermal heat than a 1KW element that does nothing else useful?  To be useful, of course, the CPUs would need to output the result of their computations, which would account for a tiny amount of energy. Let's assume that's negligible.  I'm sure there's a flaw in there somewhere; probably that the assumption above is false. What have I missed? I tried to evaluate $$\lim_{x\to0}\frac{(1+x)^{1/x}-e}x$$but all my efforts were in vain . L'Hospital rule becomes very complicated. Is there any way to specify a suggested filename when using data: URI? Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$. Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$. I define a map $$\phi:D_{2n} \rightarrow \mathbb{Z}_2 \times D_n$$ by $R \mapsto (0,r^{\frac{n+1}{2}})$ and $M \mapsto(1,m)$. Then I am stuck at showing the map is bijective. By the way, do we need to show that $(0,r^{\frac{n+1}{2}})(1,m)(0,r^{\frac{n+1}{2}})^{-1}=(1,m)$ ? If we can prove this, then what can we conclude? There are several things that I don't understand. I know that zero is a real number, but I'm confused on the how and why aspects. What defines a real number, compared to a number that's considered non-real? For what reason is zero real, and how is it that a value such as infinity isn't when zero is?  Also, what purpose does zero even have? It's obvious that it's used as a place holder, but what value does it have alone? What makes it any different from other numbers? I realize that it is typically interchanged with nothing, but that would technically mean that zero is nothing—and that's not true. People have told me already so many times that zero does not necessarily mean nothing, and I figured it out a long while ago anyway. So, what I want to know is the actual value that can be associated with zero.  However, my question brings up another topic that has been argued and disputed about and disagreed on for years. Zero divided by zero, or 0/0. There are a lot of varying answers about this, but what's been constant throughout everything is that people claim 0/0 is not a real number. So, if I may ask, why is it that zero is considered a real number, and not 0/0? And why is it considered non-real in the first place? True, there is no defined value, but the expression is anything but meaningless; if it was, then there wouldn't be so many people trying to understand it. I guess what I'm trying to figure out is the reason behind the expression's classification as non-real—especially when the sole number of zero is real, despite not having an evident value.  This covers a few different things, so I was uncertain about what to make the title of these questions. I apologize for that. If anyone can answer, though, I'd be extremely grateful! Anti-Matter Black Holes Assuming for a second that there were a pocket of anti matter somewhere sufficiently large to form all the type of object we can see forming from normal matter - then one of these objects would be a black hole.  Question is, would there be a difference between an anti matter black hole and a normal matter black hole - in terms of how would the matter/anti-matter make the black hole different, or would they be the same?  I would expect the answer to be that the black hole formed from anti matter would retain the anti-matter properties in such a way that if it was to merge with a black hole at same size formed from normal matter that they would annihilate  each other con convert into pure energy - Would that be a correct understanding? Fast, accurate 2d collision I'm working on a 2d topdown shooter, and now need to go beyond my basic rectangle bounding box collision system.  I have large levels with many different sprites, all of which are different shapes and sizes. The textures for the sprites are all square png files with transparent backgrounds, so I also need a way to only have a collision when the player walks into the coloured part of the texture, and not the transparent background.  I plan to handle collision as follows:   Check if any sprites are in range of the player Do a rect bounding box collision test Do an accurate collision (Where I need help)   I don't mind advanced techniques, as I want to get this right with all my requirements in mind, but I'm not sure how to approach this. What techniques or even libraries to try. I know that I will probably need to create and store some kind of shape that accurately represents each sprite minus the transparent background.  I've read that per pixel is slow, so given my large levels and number of objects I  don't think that would be suitable. I've also looked at Box2d, but haven't been able to find much documentation, or any examples of how to get it up and running with SFML.