Homeomorphism between 2 metric spaces
Homeomorphism that maps given points to given points
'\r' added end of the script command This is my script:  #!/bin/bash hd='pwd' cd $hd   When I try to run it, it fails with:  line 3: cd: $'pwd\r\r': No such file or directory   What is going on? Async Await Handler Deadlock How to integrate this nasty integral How do you go about integrating this? For context purposes, $s$ is a constant and $n$ is just the variable we need to integrate for. If needed, a number can be substituted for $s$, but I would like it without preferably.   $$\int\frac{s\sqrt{3}\sqrt{s^2-2ns\sqrt{7}+4n^2}}{2s^2-4ns\sqrt{7}+8n^2}dn$$ Let $A$ be a ring with $0 \neq 1 $, which has $2^n-1$ invertible elements and less non-invertible elements. Prove that $A$ is a field. Which is the best visualization for contingency tables? Which is best plot, from statistical standpoint, to show a , which is typically being analyzed by chi-square test? Is it a dodged barplot, stacked barplot, heatmap, contour plot, jitterred scatterplot, multiple lines plot or something else? Should one show absolute values or percentages?  Edit: Or as @forecaster suggests in the comments, the table of numbers is itself a simple plot and should be sufficient. Counting the number of surjections. I'm creating a function where I need to pass an object so that it can be modified by the function. What is the difference between:  public void myFunction(ref MyClass someClass)   and  public void myFunction(out MyClass someClass)   Which should I use and why? What are the most accepted ways to visualize the results of an independent two sample t-test? Is a numeric table more often used or some sort of plot? The goal is for a casual observer to look at the figure and immediately see that they are probably from two different populations. The formal solution of the time-dependent Schrödinger equation Consider the time-dependent  (or some equation in Schrödinger form) written down as $$ \tag 1 i \partial_{0} \Psi ~=~ \hat{ H}~ \Psi . $$ Usually, one likes to write that it has a formal solution of the form $$ \tag 2 \Psi (t) ~=~ \exp\left[-i \int \limits_{0}^{t} \hat{ H}(t^{\prime}) ~\mathrm dt^{\prime}\right]\Psi (0). $$ However, this form for the solution of $(1)$ is actually built by the method of successive approximations which actually returns a solution of the form $$ \tag 3 \Psi (t) ~=~ \hat{\mathrm T} \exp\left[-i \int \limits_{0}^{t} \hat{H}(t^{\prime})~\mathrm  dt^{\prime}\right]\Psi (0), \qquad t&gt;0, $$ where $\hat{\mathrm T}$ is the time-ordering operator.  It seems that $(3)$ doesn't coincide with $(2)$, but formally $(2)$ seems to be perfectly fine: it satisfies $(1)$ and the initial conditions. So where is the mistake? Goofy looking alien robots lose a "Kleptonite Ball" towed behind their spacecraft My professor proved that the kernel is a normal subgroup under a homomorphism f by saying. Let $h\in H$  by applying f to it  $f(ghg^{-1})=f(g)f(h)f(g)^{-1}=e $  My question is how is this a proof that the kernel is normal. What is the reason we apply f to it ? By applying f dont we just prove that $f(ghg^{-1})$ is normal ? How can I dual boot Windows and Ubuntu? I currently have Windows 7 on my computer and I want to install Ubuntu alongside Windows safely.  Could someone please provide clear instructions? Integrating Knowledge into an existing website So basically, I'd like to use iwconfig to connect to my wifi network when I'm not inside X. But I just don't see a way to do it in the man page. Any idea? indentation of a whole paragraph If two variables have 0 correlation, why are they not necessarily independent? Are zero correlated variables independent under special circumstances ?  If possible, I am looking for an intuitive explanation, not a highly technical one. I'm trying to parse json response.. but keep getting this error      Invalid conversion from runtime type List ANY> to Map String,ANY>   Map&lt;String, Object&gt; MapLv3 = new Map&lt;String, Object&gt;();      Integer x2 = 0; for (Object oh : CallsList){     MapLv3.put(String.valueof(x2), oh);     x2++; } index = x2; System.debug('Map Lv 3 ==&gt;'+MapLv3);  Map&lt;String, Map &lt;String, Object&gt;&gt; Map3 = new Map&lt;String, Map &lt;String, Object&gt;&gt;(); for (Integer a2 = 0; a2 &lt; index; a2++){     Map3.put(String.valueof(a2),(Map&lt;String,Object&gt;) MapLv3.get(String.valueof(a2))); } System.debug('Segment ==&gt;'+Map3.get('0').get('segments')); Cast ray to select block in voxel game A tank of 425 liters capacity has been filled with water through two pipes, the first pipe having been opened 5 hours longer than the second. If the first pipe were open as long as the second pipe, the first pipe deliver half the amount of water delivered by second pipe; if the two pipes were open simultaneously, the tank would be filled up in 17 hours. How long was the second pipe open?    a. 10 b. 12 c. 15 d. 18 Moderncv has a line of empty space between address and phone/email, like this:   MWE:  \documentclass[12pt]{moderncv} \moderncvstyle{banking} \name{Sherlock}{Holmes} \address{221B Baker Street}{London}{U.K.} % Your current address \phone[mobile] {+44~(0)71234 00000}    % Your mobile phone number \email{superdetective@mail.com}  \begin{document} \makecvtitle \end{document}   How do I remove/decrease that space by shifting the phone and email line up?