My friend went to a concert of Bob Dylan 3 weeks ago. Today I met him and spoke with him about the concert. I know I can say, "hope you enjoyed the show," because the show is over, but would it be possible to use present perfect in this case instead? (Suppose I had not seen my friend since he went to the concert.)  Could I use the sentence below?     I hope you have enjoyed the show.
I saw a dog.       I have seen a dog.   What are the differences between them? Did these events happen on the same day?
Question. Let $M = \left\{ \begin{bmatrix} a &amp; b \\ -b &amp; a \end{bmatrix} \,\middle\vert\,  a, b \in \mathbb R \right\}$.  Show that $(M,+)$ and $(\mathbb C,+)$ are isomorphic.  Show that $(M^{*},*)$ and $(\mathbb C^{*},*)$ are isomorphic.    (Here, $M^{*}$ is defined as excluding the zero-element) I understand that there exists an isomorphism $\phi:M \rightarrow\mathbb C$ defined by $\begin{bmatrix} \alpha &amp; \beta \\ -\beta &amp; \alpha \end{bmatrix}\mapsto \alpha+i\beta$, ie. I can show that $\phi(M_{1}+M_{2}) = \phi(M_{1})+\phi(M_{2})$ and $\phi(M_{1}*M_{2}) = \phi(M_{1})*\phi(M_{2})$. However, I'm unsure how to go about the two subquestions seperately. Where is the denoiser? Redundant prepositions? This is a tooltip in an application:     Identifies the site name to which the GL code belongs to.   Can I say that it is incorrect to use "to" twice here and we should remove 1 of them?  Other examples:       Identifies the vendor to which the port speed is associated with.   Provides the vendor to which the milestone is associated with.   (They are both tooltips, too)  The repetitions here are incorrect, aren't they? Please confirm. multiple Open Drain UART over long distance I have 9 microcontrollers  and I have connected the RX and TX lines of 8 of them in parallel. My configuration is in master-slave. The master microcontroller send data to one of the 8 RX lines but only one of them can respond at a time. The cable length is about 3 to 5 metres between each node.  I have two questions. My test was done with 2 slaves instead of 8. UART at 9600bps.  If I setup the TX lines of the slaves as Open Drain it works fine, but the signal doesn't have steep ramps. I thought this happens due to Pull-up resistors. And I also think that is going to be better with 8 slaves on the bus, right?  Why doesn't that topology work if the TX lines of the slaves are not Open Drain?  I managed to make it work by disabling the transmit of the UART in all of them except one, and it worked fine. I had two slaves, so I disabled the one and left the other. Also I noticed that the edges of the signal was sharper. Why are they sharper in that case?  Regarding resistors: The value of the resistors for both RX and TX lines are 2.7KΩ. However the Open Drain topology would parallel the internal pull-up resistors. According to the datasheet that resistor is about 20KΩ at minimum. So, using a 2.7KΩ in the output would give us a total resistance of 2.52KΩ (20+2.7)/9. And the Open Drain would make a voltage divider 2.52KΩ + 2.7KΩ (Schematic 2). Which means with 8 slaves and Open Drain topology the signal will not go lower than 1V which is the threshold of the low level. Is that correct?  Wouldn't it be better to disable all the internal pull up resistors and place two (let's say: 4.7KΩ) only at the master side?  Distance: What is the maximum baud rate for such distance? I'm a little worried about the signal integrity. The test was done with 9600bps but I didn't notice any significant difference in 4800bps. The distortion of the signal didn't have a difference.  Voltage values are 3.3V for the UART bus.  Schematic 1. (all resistors are 2.7KΩ)        &ndash; Schematic created using   Schematic 2. (U4, U5, U6, U7, and U8 are omitted for simplicity).          EDIT: Thank you all very much about your answers so far. I wanted to point out that this is a question about UART only. I am not looking for alternative solutions. I'm just trying to find some answers about the above implementation.  EDIT2: Thank you very much for your answers! I ended up modifying a little my schematic. I disabled the internal pullup resistors of the microcontrollers and I placed external ones at the master's board. Their value would be around 1 KOhm to 3 KOhm. I have to do some tests more to decide the final value. I also replaced all series resistors with 130 Ohm.   I tested 5 slaves over 20 metre cable (with pullup 3 KOhm and 130 Ohm series resistors) and it worked fine.   Would it be better to add open drain/open collector line drivers on every TX lines? I see in my company's IT installations that there are numerous disks with one partition occupying all of the space on disk. There is typically something like a /dev/sdb with a partition /dev/sdb1, and the size of /dev/sdb1 is the size of the whole block device. The partition is then mounted with the required file-system format, mountpoint etc.  I do not understand why we would use a partition rather than the whole disk for such (1-partition) configurations. Is there any reason why a partition would be used in this case rather than a whole disk ? Are there any best practices that recommend this approach ?  For example, we could create a Filesystem on a whole raw block device and mount it without needing any partition:  mkfs.ext4 -E stride=16,stripe-width=64 /dev/xvde mount /dev/xvde /mnt/abc   That creates a mountpoint without a specified partition. As a verification:  # sfdisk -l /dev/xvde  Disk /dev/xvde: 6527 cylinders, 255 heads, 63 sectors/track  # fdisk -l /dev/xvde  Disk /dev/xvde: 53.7 GB, 53687091200 bytes, 104857600 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes   For something with a partition, we get the list of partitions under it:  # fdisk -l /dev/sdb  Disk /dev/sdb: 2000.4 GB, 2000398934016 bytes, 3907029168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk label type: dos Disk identifier: 0x00082e8c     Device Boot      Start         End      Blocks   Id  System /dev/sdb1            2048  3907026943  1953512448   83  Linux   My fundamental question is this: Is there some advantage in creating a partition and then creating a filesystem on that partition, as compared to creating a filesystem on the whole disk and then mounting the whole disk ? Is there anything beyond subtle hints that Jack becomes the Face of Boe? "No, I didn't see him" vs "Yes, I didn't see him" Bob didn't come to office today.  I was asked "Didn't you see Bob today?"  Should I say "Yes, I didn't see him today" or "No, I didn't see him today"? Here is what I tried doing:  #!/bin/sh res=`df | awk 'FNR == 2 { print $5 }'` res2=$((res+0))   Here is my error:     -bash: 53%: syntax error: operand expected (error token is "%")   I Googled 'string to int bash' which showed me $((res+0)) but it doesn't work due to the % in the string (53%). How do I convert it in such a way I can do an if statement such as the one below (but that works)?  if [ "$res2" -ge 50 ] then     echo "Your disk &gt;=50% full!" fi How do we play multiplayer minecraft on iPads? We have two iPads, and both of them have Minecraft PE. My son wants to connect the two and play with me. I have absolutely no idea what I am doing here, so I do not know how to do this.   One game says "Broadcast to LAN", and the other one says "Local Server Multiplayer". I have switched both to on.   What do I need to do to be able to play joined? We are both on the same WiFi. Why isn't Google Chrome available in the Software Centre? Where can I find a large palette / set of contrasting colors for coloring many datasets on a plot? I need large set (20 and more) of contrasted and easily visually-distinguishable colors for coloring different datasets on a scientific plot (the set of colors should not include white or black, and colors should be as bright as possible).   The plot is generated programmatically and intended to be included in a presentation which will be displayed using a projector.   Are there any ready-made sets of colors for such a task (I need colors as a set of RGB values)?   Or maybe there is some algorithm which generates such a set of colors programmatically (I use  for plot generation)?  P.S. The plot itself may look, for example, similar to this one: I am trying to achieve something like this:     This image is linked from .  also provides a solution and seems simpler. Both answers deal with the algorithmicx package however. I am interested in the solution for the algorithm2e package.   I read the documentation of the algorithm2e package but didn't find an answer.   How can I achieve the colored effect?  EDIT:  Here is sample code to create a minimum working example.  \documentclass{article}  \usepackage[ruled]{algorithm2e} % http://www.ctan.org/pkg/algorithm2e  \begin{document}  \begin{algorithm}[h]  \caption{Evolutionary algorithm}   initialize population \;  \For( \emph{Evolutionary loop}){$g := 1$ to $G_{max}$}  {     do things \;     evolve population \;  }  celebrate \; \end{algorithm}  \end{document} Flip x and y axes in Excel graph This should not be very difficult, but I cannot figure out how to do it.  I have a table similar to this     %low %high  0   0   12  1  13   26  ... 19  90   94 20  95  100   When I graph it, excel defaults to having the first column on the x axis and plotting the second and third column as y values. I want the first column to be on the y axis instead. I assume there is an easy way to do this, but I cannot figure it out. Most of the things I have found from searching have suggested the "Switch Row/Column" button, but that does something else.  Thanks for the help. Why are high white balance temperatures redder when warmer objects are bluer? I know it's dumb to ask this type of questions. But, I still don't get this. I've read the "Black body" story and know that when it's heated, it gives off colors; 'warm' colors (red→orange→yellow..) that have low color temperatures, at low temperatures, (I mean, when it is cooler than afterwards) right? And, the black body gives off 'cold' colors (white→blue..) that have high color temperatures at high temperatures (when it is hotter than before), right? Correct? So there're two, yes, very dumb, questions and the latter one is dumber..     Why are that 'warm' colors said to have low temperatures? And 'cold' colors vice versa? So the redder colors have lower c/t and bluer colors have higher c/t, then   why does the camera's color temperature - adjusting slider has the bluer colors on the left, and the redders on the right?       Please, forgive me for my ignorance... I found this animal, which I suspect it's an insect, on the floor of a kitchen in Spain some days ago. It's about 8-10 mm long. I don't think I've ever seen it before. What is it? Group of order $p^2$ is abelian. Yes, I know that there are tons of solutions of this up here, but I, essentially, wanted to try it a different way and ah, well.  Let $|G| = p^2$ for some prime $p$.  Consider $x \in G$. So, $|x| = p, $ or $ p^2$. If it is the latter, then, we are done.  So, if $|x|= p$, then, let, $H = [h|  h=x^i, i \in Z] \Rightarrow |H|= p$.  As $p$ is the smallest prime dividing $|G|$, $H$ is a normal subgroup.  Now, consider some $y \in G$, but not in $H \Rightarrow y^p= e$. Then, its easy to show that $G = \langle x,y \rangle$.  Now, consider a homomorphism $f:G \rightarrow \operatorname{Aut}(H), g \to c_g $, wherein $c_g$ represents conjugacy by $g$. So, for example, $c_g(x) = gx g^{-1}$.  Then, it is clear that, $H \subset \operatorname{Ker}(f) $, as it is cyclic and therefore abelian. So, we need only look at $G/H$.  Basically, I am asking for a hint as to why $c_y(x) = yxy^{-1} = x = c_e(x)$, where $x$ and $y$ are the generators of $H$ and $G/H$, respectively?  Because, if I establish it for the generators, then it follows that it applies for for all elements, i.e, that $\operatorname{Im}(f)$ is trivial and therefore that $G$ is abelian.  Thank You! Will the below code cause memory leak in c++ class someclass {};  class base {     int a;     int *pint;     someclass objsomeclass;     someclass* psomeclass; public:     base()     {         objsomeclass = someclass();         psomeclass = new someclass();         pint = new int();          throw "constructor failed";         a = 43;     } }  int main() {     base temp(); }   In the above code, the constructor throws. Which objects will be leaked, and how can the memory leaks be avoided?  int main() {     base *temp = new base(); }   How about in the above code? How can the memory leaks be avoided after the constructor throws? How can light be called electromagnetic if it doesn't appear to be electric nor magnetic?  If I go out to the sunlight, magnets aren't affected (or don't seem to be).  And there is no transfer of electric charge/electrons (as there is in AC/DC current in space).   In particular, the  (which light is supposed to be composed of) have no electric charge (nor do they have ).   I'm looking for an explanation that can be appreciated by the average non-physicist Joe. What are tag synonyms? How can tag synonyms be distinguished from "real" tags? How are new tag synonyms created? Who can create tag synonyms? How can I delete/reverse/undo bad tag synonyms? What are merged tags? Run as a different user on a shortcut How do I run as a different user on a shortcut in Windows 7?   On Windows XP, I had the ability to mark a shortcut as being run by a different user, so that every time I ran it it would prompt me for a username/password. This let me have two shortcuts for things like , one for my normal account and one for my domain administrator account which has access to production servers.  I can get to the 'Run as different user' option with Shift + right-click, but I can't see an option anywhere that would let me mark the shortcut as doing this every time.