EXERCISE:  Consider that $Φ:G\rightarrow G'$ homomorphism and $a\in G$ which has order d. Show that the element $φ(a)\in G'$ has also order d.  I am sorry i could't appose any attempt here but i don't even know how to start.I have just started to examine homomorphism and i have to clear my mind on them! It would be very helpful if someone can give me some hints or a thourough solution to my problem. I want to learn how i can work with these problems as i don't have many experience with these type of problems! Thanks in advance!
I was reading an example about describing homomorphisms and I'm having a bit of trouble with this one.  Show there is no group homomorphism $f : \mathbb{Z}_{10} \to \mathbb{Z}_{25}$ such that $f(1) = 3$. The first step of the proof is  $|1| = 10$ in $\mathbb{Z}_{10}$, so $|f(1)| \in\{ 1, 2, 5, 10\}$.  Does this mean that $|f(1)|$ can be $1$, $2$, $5$ or $10$? I see that $|1| = 10$ since $1$ is a generator of $\mathbb{Z}_{10}$, and that $|f(1)|$ seems to be a factor of $10$. If $f(1)$ is the image of $1$ under $f$, how would I find the order of $f(1)$?  Thanks for your help.
32-Bit UEFI Boot Support I recently purchased a Dell Venue 8 Pro.  I have read online about what it needs in order to boot into Ubuntu or any other Linux distro.  From what I have gathered, what really needs to happen is 32-bit UEFI support.  I got information from several sites, but where it was really summed up was in this previous post:    "Ubuntu has no 32-Bit Uefi installer, ask them to add support, they may listen."  That thread was specifically about getting the Dell Venue 8/11 Pro to boot Linux.  However, there are a slew of new tablets coming out running 32-bit UEFI, and I think this is a trend that is going to continue to grow:  mjg59.dreamwidth.org/26734.html  "UEFI on IA32 isn't going away. It will show up on more embedded systems as time goes on."  Others have tried this before with mixed success, but haven't gotten things to work quite right:    "It doesn’t really work. But it’s interestingly close."  I'm trying to start a thread dedicated thread on 32-Bit UEFI support, because that is the piece that is missing (from what I understand).  I don't really know how to work with this stuff, but I'm hoping that some people who do will read this and either contact canonical or somehow patch Ubuntu (or any other distro, really) to work this way.  Again, I don't really know how to do any of this...I'm just hoping someone can help!  Dell Venue 8, 11 Pro, Toshiba Encore, Acer w3, w4, Lenovo miix, and the asus transformer a100 are all tablets that will be affected by this...I think these are going to be incredibly popular tablets once their prices go down, and I think people are really going to get interested in putting linux on these.  Any help is appreciated, and thank you all so much!  EDIT 4/1/14:  Just booted into Ubuntu on my DV8Pro!  All you have to do is follow the instructions here:    To summarize, what you need to do is download the latest Ubuntu 14 daily build (AMD 64 is what worked for me) and put that on a USB drive via Rufus.  'For “Partition scheme and target system type”, choose “GPT partition scheme for UEFI computer.”' You can get the latest daily build here:   You will need to put the file found below into your EFI/Boot directory:   Disable Secureboot and such--follow the original instructions link if you don't know how.  Then set the USB to boot first in BIOS.  This should get you to GRUB.  The rest I'll quote the original author, it's real straightforward:  In the GRUB menu, highlight “Try Ubuntu”, and press “e” to edit it. In the editing screen, scroll down to the command line options, where it says “quiet splash”. Delete “splash” and replace it with: video=VGA-1:1368x768e reboot=pci,force [EDIT: For those of us using the Dell Venue 8 Pro, you need to use this line instead: video=VGA-1:800x1280e reboot=pci,force That accounts for the different resolution of screen.]  Then press F10 to boot. You should get all the way to the Desktop.  There you have it!  This got me to the Unity Desktop.  Problems:  Wifi is not working, but I used an Ethernet adapter and that seems to work.  I tried rotating the screen, but it throws your touch input off to one side, so I left it.    Make sure to read the tutorial mentioned earlier, it is more comprehensive, even though it is made for the ASUS T100.  If nothing else, the instructions I have provided should be enough just to get you to the Unity Desktop, which for me was amazing!  Hope you too can have the same success and keep building on it!  For what it's worth, someone else did this and posted a youtube video here: Do you need to disavow on [HTTPS SSL] after performing a disavow on [HTTP] I have a client which disavowed a few thousand dirty links from his site profile back in February 2015. Recently the site was switch from HTTP to HTTPS (SSL enforced).   Google recommends that you add all variations to the Google Console (Webmaster Tools).  The site has a total of 4 variations, eg:    http://www.example.com (Previously Preferred) http://example.com https://www.example.com (Now Preferred) https://example.com   Question:  Since technically this is a new property in Google Webmaster Tools, do you need to submit the same disavow file added previously back in 2015? "Contact us"... and then what? Calculate Euler equations of fluid dynamics without division? I'm working on the calculation of the  with the . Unfortunately I'm not allowed to do a division. So I'm wondering if there's a form which does not need a division.  At the moment the Euler equations look like this:  $$ \frac{\partial}{\partial t} \begin{pmatrix} \rho \\ \rho v_1 \\ \rho v_2 \\ \rho v_3 \\ \rho E \end{pmatrix} = -\mathrm{div} \begin{pmatrix} \rho v_1 &amp; \rho v_2 &amp; \rho v_3 \\  \rho v_1^2 + p &amp; \rho v_1 v_2 &amp; \rho v_1 v_3 \\  \rho v_2 v_1 &amp; \rho v_2^2 + p &amp; \rho v_2 v_3 \\  \rho v_3 v_1 &amp; \rho v_3 v_2 &amp; \rho v_3^2 + p \\  (\rho E + p) v_1 &amp; (\rho E + p) v_2 &amp; (\rho E + p) v_3 \end{pmatrix} $$  As you can see, I first need to calculate $\frac{\rho v_1}{\rho}$ to get $v_1$ so I can calculate e.g. $\rho v_1^2$ Can't connect to wireless networks on a Dell Latitude D430 As stated above, I can't connect to my home wi-fi with natty but can with Windows 7. The strange thing is I that I have gotten it to connect to other password protected networks with natty, it's just mine that it dosn't like.   I am using a WPA2 pass-code with AES Encryption and all other devises work fine on my network. Laptop used is a Dell Latitude D430. Why is chi square used when creating a confidence interval for the variance? This is a very basic question. Why do we use a chi square distribution? What is the meaning of this distribution? Why is this the distribution used for creating a confidence interval for the variance?   Every place I google for an explanation just presents this a fact, explaining when to use chi, but not explaining why to use chi, and why it look the way it does.  Many thanks to anyone that can point me towards the right direction and that is - really understanding why I am using chi when I am creating a confidence interval for the variance. Difference between projection and datum? Is space expanding equally in every direction? Does space expand equally in every direction, so that it draws a perfect sphere or is expansion asymmetric, so it creates "bubbles" (when seen from the outside)? Detect browser language in Rails If $Var(X)=0$ then is $X$ a constant? We know that the variance of a constant is $0$. Is the converse also true? Can we say that if the variance of some random variable is $0$ it is a constant? Passing directly an array initializer to a method parameter doesn't work Indian Trains Wait List - will I get a seat? After the  of registering an account to book train tickets online using my British VISA card, I finally got into a position of being able to book a ticket, but what it appears to be telling me is that I'm only being added to a wait list, which I assume means my tickets aren't confirmed.  Can someone explain how the wait list works, and what my chances are of getting on the train successfully?    It currently says the wait list is 7 The train is the Mandor Express, from Delhi to Jodhpur on the 18th of Nov   Update: So I got the train! Although it didn't get confirmed until a few hours before it was due to leave. Encode multi-class response variable In a classification problem when the response variable has multi-class, e.g., "sunny","rainy","cloudy", how should we encode it? I know that for predictors like this, usually we do , and if a predictors have too many classes, then we might just use the .   When this multi-class issue occurs in the response variable, I guess we can just use LabelEncode() rather use using One Hot encoding right? Because if we use One Hot encoding, then we will have 2 variables as the response variable, and the machine learning algorithm in sklearn usually expects the response variable not to be a vector right? (I mean it expects a long 1D vector with length equal to the number of observations but not a 2D matrix). But on the other hand, if we just map "sunny", "rainy","cloudy" to {1,2,3} or {0,1,2}, or whatever 3 numbers, that will create a less than or greater than relationship among "sunny", "rainy","cloudy", which is not inherited in the original problem. Binomial Distribution Problem - Airline Overbooking Variance of the future value of a cash flow I want to compute the variance of $FV =A\sum_{k=1}^n(1+r)^k=:g(r)$, assuming interest rate $r\sim\mathrm{N}(\mu,\sigma^2)$ and constant equal payments $A$. As discussed in the comments, the Delta Method gives an approximation $\mathrm{Var}[FV]≈\sigma^2\times(g′(\mu))^2$. Is there a way to get an exact answer? I'm wondering if it's possible to hide a folder without renaming it with a dot on the Desktop.  Ubuntu 12.04  Thanks Short story identification: society partitioned off by high wall override Home key in android ICS I just installed Solaris 11.3 on the laptop. This laptop have Broadcom BCM4312 WiFi card.  It looks like the install does not have a driver for this card just like 11.1 version.  I have a Linux installed on this same machine (Gentoo) and this OS does have a driver.  Is it possible to get the driver for this card somewhere? Maybe broadcom.com? Failing that is it possible to use Linux driver inside Solaris?  On the kind of related side - I tried to connect a wire and run Driver Manager, but it does not want to finish. All controls are  still disabled. Any idea?  Thank you for any pointers you can provide. Sort a set of multidimensional arrays by array elements