I'm relatively new to QGIS. I've got a layer that shows the boundaries of the wards in the UK. In addition to this, I've got a csv file, which has long/lat plus an answer (binary). The problem is, that these two files use different CRS (the one with the wards uses a &quot;user defined coordinate system (USER 100001), and the point layer WGS 84. If I try to change them, either the points disappear or the wards... I actually wanted to find out how many points there are in one Query, but this doesn't work.. I assume because of the different CRS.. :( Is there a way I can change this? I've attached a screenshot.
I have a series of layers of lines (shapefiles) in My Project. The CRS of some are different and to merge them they all must have same CRS.  When I use Processing/Toolbox/Qgis_algorithims/Reproject_layer the reprojection only works if it is allowed to save to temporary file somewhere (it will not change the CRS when I reproject if I try to save and replace it in My Project directory);   I must remove the original from the layer list and reproject the temp file (without changing the CRS) to get it into my project and name it appropriately.  Is there a better way to reproject a layer in Qgis?
Integrate $\int_{0}^{2\pi}\log|1-e^{i\theta}| d\theta$ Here is exercise 11, chapter 3 from Stein &amp; Shakarchi's Complex Analysis II:  Show that if $|a|&lt;1$, then:  $$\int_{0}^{2\pi}\log|1-ae^{i\theta}|\,d\theta = 0$$  Then, prove that the above result remains true if we assume only that $|a|\leq 1.$ ($a\in \mathbb{C}$)  I've already proved it for $|a|&lt;1$, but couldn't make it for $|a|=1$, which I thought would be the easy part. But the only thing I could come up with was that, WLOG, it is enough to prove that:  $$\int_{0}^{2\pi}\log|1-e^{i\theta}|\,d\theta = 0$$  Tried to look for some kind of symmetry, but could't find it. Any ideas? Thanks! $z$ is a complex number, by the way.  I've tried a lot of things and always end up with a huge algebraic mess and I've wondered if anyone of you has any idea on how to approach this problem.  One of the most "satisfactory" things I've done so far is to expand both the real and imaginary parts for the equation \vert z + 1/z \vert^2 = a^2. These parts yield the constraints:  $2xy(1+1/(x^2+y^2)^2)=0$ ;   $x^2-y^2+\frac{2(x^2-y^2)}{x^2+y^2}+\frac{(x^2-y^2)}{(x^2+y^2)^2}=a^2 $  I've graphed the equations and supposedly the intersection should be my set of points, but this method is far from analytical.  What can I do? Any hints on how to approach this? How to map stock ticker symbols to ISIN (International Securities Identification Number)? How can I can convert ticker symbols (which include information on the exchange) to an International Securities Identification Number (ISIN) (which contains no information on the exchange)? Also I am interested in the other way round — given an ISIN and a market identification code (MIC) how can I determine the ticker symbol? Any databases around? This question is a possibly harder version of: .  Question.  Let $f,g :\mathbb R\to\mathbb R$, such that \begin{align} f(x-y)=f(x)\, g(y)-f(y)\, g(x), \tag{1}\\ g(x-y)=g(x)\, g(y)+f(x)\, f(y), \tag{2} \end{align} for all $x,y \in \mathbb{R} $. If $g$ is continuous at $x=0$ and not identically zero, then there exists an $\alpha\in\mathbb R$, such  $$ f(x)=\sin \alpha x\quad\text{and}\quad g(x)=\cos \alpha x. $$ Is there a pair of discontinuous $f$ and $g$ satisfying $(1)$ and $(2)$?  Update. If $\ell :\mathbb R\to\mathbb R$ is a linear functional over $\mathbb Q$ (i.e., $\ell(qx+ry)=q\ell(x)+r\ell(y)$, for all $x,y\in\mathbb R$ and $q,r\in\mathbb Q$), then $$ \sin\big(\ell(x)\big), \quad \cos\big(\ell(x)\big), $$ satisfy $(1)$ and $(2)$. Discontinuous such functionals do exist, and they are obtainable using Zorn's Lemma (equivalently the Axiom of Choice.) This takes care of the second question. Are there any expressions that describe going from a bad to a worse situation? Are there idioms or expressions in English that describe going from one bad situation to one that's even worse?  I heard "between a rock and hard place" but this describes a dilemma not really a transition. I am looking for an expression that describes someone trying to get out of a bad situation but after much effort, the situation only got worse. How can I see the phone number dialed after I initiate a call? How should I deal with becoming discouraged as a graduate student? I am a third year (starting fourth year in the fall) PhD student in mathematics. I've passed all qualifying exams and am currently doing research. As far as I can tell, I am not doing poorly. I have the good fortune of having a great advisor, being in a very supportive department, and having friends and family who genuinely care about my success.   The fact is research is hard. It appears to consist primarily of staring at a problem for days and days and days without getting anywhere. Sometimes, rarely, I do figure something out and that feels wonderful, but the overwhelming majority of my time appears to be spent banging my head against a mostly figurative wall. I am not complaining about the material being hard, and I am not averse to putting in hard work, but I get frequently discouraged when I realize the vast volumes of mathematics that I yet know nothing about (and probably never will). It's very hard to quantify progress - in particular, there are too few tangible returns after too many hours worked. I find myself thinking along the lines of "Oh, if only someone actually smart were thinking about this problem they would have solved it in moments" and so on.   I've talked about this to some number of people; here is some advice I have received:   Take a day off. Putting in hours upon hours of trying things doesn't magically lead to a solution, particularly if the brain is tired and just wants to sleep. Have a hobby. Since math research doesn't exactly provide instant gratification, a hobby might provide some instead.  Talk to other graduate students. Realize that many graduate students go through this.   I'm interested to know how other folks have dealt with being discouraged as a graduate student. Does it get better with time and experience? Is this a sign that research is not for me and that I should seriously consider a life outside academia? Currently, when someone suggests an edit, they are unable to keep track of it without watching reputation levels or constantly refreshing the page. What I would like is a notification, that shows up like the notification where someone has edited your question, that shows whether a suggested edit has been approved or rejected after the last vote is cast. This way, the community can be notified when their edit has been rejected/approved, while focusing their efforts on another question/answer. Galois extension is (not) transitive Let $ K/ L /F $ be fields. If $K / L$ is Galois and $ L / F $ is Galois, then $ K / F$ is Galois. We mentioned this very quickly in today's class without justifying. But I have trouble seeing this. Any help is appreciated.  Our definition for $ K / F$ being Galois is the $F$-automorphism group $G = G( K / F) : = \{ \sigma \in aut (G) : \sigma_F = id_F \}$ fixes only $F$, i.e. $ \{ x \in K : \sigma (x) = x \text { for all } \sigma \in G  \} = F$.  But we also showed that $ K /F$ is Galois if and only if $ K/F$ is normal and separable. Why is there no article in "We are Family"? What is the standard team composition for a conquest game? I'm very new to Smite, and I'm wondering if there is some kind of standard team composition in high level play, comparable to the top, jungle, mid, dual lane meta in LoL.  What are the roles, and where should they go to start the game? I know that a gas is made of atoms or molecules moving freely in space.  When these particles hit the walls of where they're kept in they cause something called pressure.  But these particles never pile up on each other and push a surface down by their weight so that we can measure it as weight, not pressure.  So why do gases have weight? Inexact measurement and wavefunction collapse Can bounties be awarded multiple times by the same person on the same question? Is there any restriction to prevent multiple bounties ( not simultaneously) being awarded to different answers on the same question ?  i.e., on a question  -  I want to set multiple bounties since I've received 2 awesome answers. Can I set award a bounty on answer A first, and then set the bounty and award it to answer B ? Maclaurin Expansion for $e^{e^{z}}$ at $z=0$ I want to do research but I'm too old for a PHD I really love research. I started a research project in graduate school for my M.A. in English. My research topic is a very viable and interesting topic for a dissertation. I'll be 60 on my next birthday and I know that many Ph.D programs are traditionally geared toward younger students.I was wondering are there any programs that I can continue this research in without facing the issues of ageism in academia? Is $2^\sqrt{2}$ irrational? Is it transcendental? What is a word for "cannot-be-wrong" attitude? When speaking with someone recently I was continuously taken aback by how he could not concede even the slightest detail in my argument (which was not unreasonable), and it happened another time previously. Both times had to do with me pointing out 'error' in his action.  He very much exhibits that 'I cannot be wrong' attitude.  I first thought to call this arrogance or pride but he is not overbearing like arrogance demands and he does not show excessive self esteem that pride demands.  What is a word that can accurately describe this attitude? How can momentum but not energy be conserved in an inelastic collision? In inelastic collisions, kinetic energy changes, so the velocities of the objects also change.  So how is momentum conserved in inelastic collisions? Is there a program that can make live USBs for any distro, iso, you get the point. I can only find ones that make live USBs for other linux distributions and none for anything else.