Show that $X$ has no mean
Mean of a Cauchy Distribution
jQuery - Is it okay to use $('#ElementId') everytime? $\mathbb{R}P^4$ and $\mathbb{R}P^6$ do not admit fields of tangent $2$-planes See the related question . This is the second part of question 4-C in Milnor and Stasheff's book on characteristic classes. In the solution to the first part, we rely on the fact that having a field of tangent $1$-planes allows us to split the tangent bundle into a direct sum. It doesn't seem like this should be true for a field of tangent $2$-planes (otherwise the question wouldn't just be asking about $P^4$ and $P^6$), so I'm not sure exactly where to start.  edit: actually, since $P^n$ can be given a Riemannian metric, any subbundle should be a Whitney summand; this doesn't answer the question as to why they only ask for $P^4$ and $P^6$ though, so I'm still confused. Calling a function from a string in C# Why there is "the" before some names but not others Is there a rule beyond the common "no the with proper nouns and names" for the following problem?     I saw the Empire State Building.      We went to the White House.      We saw the Golden Gate Bridge.   but     I went to Death Valley National Park.      I crossed Brooklyn Bridge. Is $$d_1\mid n,d_2\mid n\iff [d_1,d_2]\mid n$$ true ? And if yes, how can I prove it ? I recall that $[d_1,d_2]$ is the least common multiple.  My tries  For the implication : Let $d_1\mid n$ and $d_2\mid n$. Then, $d_1d_2\mid n^2$. By the way, since $d_1,d_2\mid n$, we have that $(d_1,d_2)\mid n$ where $(d_1,d_2)=:\gcd(d_1,d_2)$  and thus $$[d_1,d_2](d_1,d_2)\mid n^2.$$  Question: How can I get $[d_1,d_2]\mid n$ from this?  For the converse, since $d_1,d_2\mid [d_1,d_2]\mid n$, the claim follow. Map "Super+ArrowDown" to minimize a window while the window is focused & the window is not in fullscreen I would like to add a conditional key mapping to Ubuntu 19.10.   Normally when a window is in full screen mode and you press super+arrowDown it enters window mode (or whatever it is called).   When a window now is in "window mode" I would like to be able to minimise it (and only then) by using super+arrowDown on it.  Is it possible to create such a shortcut without affecting the mapping of super+arrowDown on full screen windows? With powershell get exactly the same application list as in Add/Remove programms PHP/MYSQL login error? Why aren't Christoffel symbols tensors? - asked from a fibre bundle perspective What happens to waves when they hit smaller apertures than their wavelenghts? I was wondering this for quite a long time now. Let's say you have a water wave (like ripples, not the ones you see during tsunamis) with wavelength 10 m. Imagine you put a boundary with an opening of 1 m. Will diffraction be observed? According to my research, no. But, then, what would be seen? In Ruby on Rails, how do I format a date with the "th" suffix, as in, "Sun Oct 5th"? I want to display dates in the format: short day of week, short month, day of month without leading zero but including "th", "st", "nd", or "rd" suffix.  For example, the day this question was asked would display "Thu Oct 2nd".  I'm using Ruby 1.8.7, and  just doesn't seem to do this.  I'd prefer a standard library if one exists. Why the Principle of Least Action? Is there a word that means "a span of six months"? That is, I want to connote a stretch of time that lasts half a year, not an event that happens every six months. Map of with object references as keys? Z-axis issue with the floating review info panel, permits various elements to flow over it I was having a look at an old question of mine when I browsed the  from the timeline. I scrolled downwards and realized the Review completed panel comes along for the ride. While that might be , tags flowing over top of it as pictured below probably isn't.  Here's a .gif of the Question and Duplicate tabs flowing over it as well. Note that the timeline button also flows over. If vote buttons are present, they will also flow over it.  Reproduced on Chrome and Microsoft Edge. Update Per  by Tiago Martins Peres, this issue also happens in other Review types, namely Late Answers, First Posts and Low Quality Posts. In addition to that, it is causing the action buttons on reviews to become unclickable if you scroll low enough.  As a temporary workaround, you can use 's , which  this issue. Clock time is off on dual boot I just did a clean install of 20.04 and I noticed that no key shortcuts for files manipulation work when my focus in on Desktop (not in Nautilus).   When I have copied a file to clipboard, I cannot Ctrl+V it to Desktop, when I click on a file on Desktop, I cannot Ctrl+C it, or I cannot Delete it with keys. Only ways to do it is either navigate to the Desktop folder in Nautilus, or right-click the file on the Desktop and copy/move to trash/paste...  Sorry if I'm missing something obvious, all the key shortcuts worked normally for me in 18.04. This question is a bit more subjective, but I'm hoping to get some new perspective.  I'm so used to designing for certain screen size (typically 1024x768) that I find that size to not be a problem.  Expanding the size to 1280x1024 doesn't buy you enough screen real estate to make an appreciable difference, but will give me a little more breathing room.  Basically, I just expand my "grid size" and the same basic design for the slightly smaller screen still works.  However, in the last couple of projects, my clients were all using 1080p (1920x1080) screens and they wanted solutions to use as much of that real estate as possible.  1920 pixels across provides just under twice the width I am used to, and the widescreen makes some of my old go to design approaches not to work as well.  The problem I'm running into is that when presented with so much space, I'm confronted with some major problems.   How many columns should I use?  The wide-format lends itself to a 3 column split with a 2:1:1 split (i.e. the content column bigger than the other two).  However, if I go with three columns what do I do with that extra column? How do I make efficient use of the screen real estate?  There's a temptation to put everything on the screen at once, but too much information actually makes the application harder to use.  White space is important to help make sense of complex information, but too much makes related concepts look too separate. I'm usually working with web applications that have complex data, and visualization and presentation is key to making sense of the raw data.  When your user also has a large screen (at least 24"), some information is out of eyesight and you need to move the pointer a long distance. How do you make sure everything that's needed stays within the visual hot points? Simple sites like blogs actually do better when the width is constrained, which results in a lot of wasted real estate.  I kind of wonder if having the text box and the text preview side by side would be a big benefit for the admin side of that type of screen? (1:1 two-column split).   For your answers, I know almost everything in the design is "it depends".  What I'm looking for is:   General principles you use How your approach to design has changed   I'm finding that I have to retrain myself how to work with this different format.  Every bump in the resolution I've worked through to date has been about 25%: 640 to 800 (25% increase), 800 to 1024 (28% increase), and 1024 to 1280 (25% increase).  However, the jump from 1280 to 1920 is a good 50% increase in space--the equivalent from jumping from 640 straight to 1024.  There was no commonly used middle size to help learn lessons more gradually.    To help focus the question a little bit, I had a project that was somewhat similar to Atlassian JIRA, an issue management system.  There were about six different types of records the client wanted to keep, all of them could potentially be related to each other.  Gathering data wasn't the core problem, although it did play a part.  The more important side of the problem was creating a system which would suggest potential relationships between the records and helped the analysts recognize patterns in the reported incidents.  There were different types of analysts that focused on the different problem domains, and due to the nature of their exploratory type of work, they didn't know what they wanted.  They just knew they had to make sense of a lot of data, draw correlations, and characterize classes of issues.    (Originally asked here: , but told that this might be more appropriate)    For the bounty: Stretch your minds a bit.  The pat answer "Make everything bigger" has a limit to how useful the answer is.  We are talking about users who have to make sense of a lot of data and find relationships between records.  If I simply bump up the size on everything they are going to be very limited in what they can see on the screen--particularly because the vertical is so constrained. At the end of a makefile I saw   rm -f *~ *.class   I understand the *.class, but what's *~? , I shouldn't need to vote down or flag the answer, because the question itself is a dog.      Users should be allowed to also enable the "I'm done" button by down voting, close voting or flagging the question rather than directly taking action on the answer.    Currently, I have to click on the question's title, close or down vote it in the new tab, then go back to the review page, and click "Not sure" to continue on my adventure.