I want to call my equation $NS_\alpha$ in such a manner that rather than      (1.1)   the equation shows up with      ($NS_\alpha$)
When I have equations, as in  \begin{equation} ... \end{equation}   Can I arbitrarily assign the numbers to the equations? Instead of the usual order (1), (2), (3), ..., I'd like something like (1), (2.1), (2.2), (2.3), (3.1), (3.2), (4), ...
Cannot change lock screen background on Ubuntu 18.04 Before you mark the question as a duplicate, I read all of the posts regarding this, but nothing helped me. I'd like to change the background picture of the lock screen.    I changed the ubuntu.css and gdm3.css accordingly to   #lockDialogGroup {   background: #000000 url(file:///usr/share/wallpapers/minimalistic-gray_00323985.jpg);   background-repeat: no-repeat;   background-size: cover;   background-position: center; }   Which results in a change of the Background of the log in screen, not the lock screen. When I press super + L the screen containing time has the correct background. When I swipe it up to tipe in my password, the purple Ubuntu screen still appears. If I click to change the user, the log in screen appears with the right background. I have the same background picture enabled in gnome tweaks for desktop background and lock screen.   I'm running Ubuntu 18.04 GNOME on a TuXedo Laptop. And I use Communitheme - maybe thats the problem?  Any ideas why it doesn't work? (I rebooted multiple times, so that's not the problem.)  EDIT: The output of sudo nano /usr/share/gnome-shell/modes/ubuntu.json is  {     "parentMode": "user",     "stylesheetName": "ubuntu.css",     "enabledExtensions": ["ubuntu-dock@ubuntu.com", "ubuntu-appindicators@ubuntu.com"] } When I view most glass from the side it's green which I've found out is due to impurities in the glass specifically from iron oxide. Why is it when I view the larger face from an oblique angle, it isn't nearly as green? I cannot personally notice any different on the piece I have next to me even when I hold it at an angle that would be almost looking at the edge of the glass. It is pretty small (about 2.5" x 5" x .0625" or about 61mm x 127mm x 2mm, l x w x h) but I feel like it's big enough that I'd be looking through enough glass to get the green. What Do the Gringotts Goblins Do With Muggle Money? ‘But you’re Muggles!’ said Mr Weasley delightedly. ‘We must have a drink! What’s that you’ve got there? Oh, you’re changing Muggle money. Molly, look!’ He pointed excitedly at the ten-pound notes in Mr Granger’s hand.   Chamber of Secrets - page 47 - UK Hardcover - chapter 4, Flourish and Blotts   So Gringotts exchanges Muggle money for Wizarding money. What do the Goblins do with the Muggle money after the exchange has been made? Is it possible they keep a stash of Muggle money on hand for reverse exchange purposes, or do they surreptitiously feed the money back into the Muggle economy?  What do Goblins do with Muggle money? What would be a good approach to develop the render system for an oldschool type racing game that uses a pseudo 3D scenery, like for example Outrun or Lotus Esprit Turbo Challenge? There's an endless scrolling road and scenery graphics are placed like billboard items, etc. I think you get the idea.    Are these developed in a similar way like  or is there a different technique behind it? Does the technique has a specific name I could search for on the web? I need to develop something like that in Flash. percent signs in luacode* environment (LuaLaTeX) Can someone explain what happens here:  \documentclass{article} \usepackage{luacode} \begin{document}  \begin{luacode*} tex.print("xx\%a","yy\\%b","zz\\\%c") \end{luacode*}  \end{document}   The result is xxyy%b zz%c. (The xx,yy,zz is clear.) The \%a is "ignored", the \\%b and the \\\%c results in the "same" %b (or c). What is the preferred way to get a % in the PDF output? Why is the \%a ignored? What does TeX see after returning from the lua call? Behaviour of free electron with constant velocity Can a free electron with a constant velocity V то move eternally at this rate in the inertial frame? The question arises from the fact that a moving charge creates near its trajectory varying electric and magnetic fields. Whether kinetic energy of electron is spent for it? Who killed Ra's Al Ghul first, Batman or Arrow? So assume $Y$ and $X$ are exponentially distributed with parameters $y_1$, and $x_1$ respecitively.  assume c is a constant.  I am having huge trouble to understand the integration of the following expression.  $P(Y&lt;c/u(X))$  $=\int_{t}^{\infty}f_X(x)\int_{0}^{c/u(x)}f_Y(y)dydx +\int_{0}^{t}f_X(x)\int_{c/u(x)}^{\infty}f_Y(y)dydx$  where t is the cross-point that $u(x)$ change sign    here $c/u(x)$ is given by the plot below, t is the point crossing the zero:   Confusion:   I don't understand the second integration of the second term "$\int_{c/u(x)}^{\infty}f_Y(y)dydx$", this isn't right because Y an X only defined for y>0, and x>0. So it's the first quadrant in this plot. How did Harry become a Horcrux? What are the system requirements for each flavour of Ubuntu Desktop? Address is invalid on local machine [on windows 8 only] Binary Search in Array How would I implement a binary search using just an array? Today I saw a sentence:  She surely can do it.  What does that mean? How does it differ from:  She certainly can do it. Surely she can do it.  This slight difference in meaning of those sentences I am not able to notice. Could you please help me? Thanks in advance! Postfix SMTP banner show multiple hostnames We have a Postfix SMTP server that's bound to two IP addresses and serves mail for two different domains. We can't change the domains to both use the same, single IP. Both IP addresses have reverse DNS   1.1.1.1 reverses to mail.domain1.com 2.2.2.2 reverses to mail.domain2.com   In our Postfix config I have  myhostname = mail.domain1.com myhostname = mail.domain2.com  inet_interfaces = 1.1.1.1, 2.2.2.2  smtpd_banner = $myhostname Mail Server   (And some other stuff, which I think is irrelevant)  Using , running the smtp test command on mail.domain2.com returns everything as OK, however running it on mail.domain1.com returns an error because Postfix is identifying itself as 'mail.domain2.com' in the SMTP banner, how do I get it to return the correct banner based on the external IP address used? Prove $(a+b)^\frac{1}{n} \le a^\frac{1}{n} + b^\frac{1}{n}$ Prove: $$ (a+b)^\frac{1}{n} \le a^\frac{1}{n} + b^\frac{1}{n}, \qquad \forall n \in \mathbb{N} $$ I have have tried using the triangle inequlity $ |a + b| \le |a| + |b| $,  without any success. Concurrent requests limit exceeded - how to find the problematic code I am a developer for a Salesforce org that serves as a community portal for thousands of users. We have been consulting with a large team of developers for years and everything we have is custom coded. Our pages are built using AngularJS to remotely call Apex code. We are on an Unlimited Edition org and we are nearing 90% of our total allowed code. We have a lot of callouts to external services and many times these callouts can run long.  We are now running into issues where users are seeing the "Unable to Process Request - Concurrent requests limit exceeded" error. The issue is there is so much code written by so many different developers it is hard to identify what/where the problematic code is. Sometimes users see this error when they are trying to perform a callout. Sometimes it's when they are inserting a record and triggers are firing. The long-running code issue can be anywhere in our org. Another issue is error handling has been done very poorly, so if any process does run long, we most likely are not looking for it or logging it.  Other than enhancing the logging on our callouts, I do not know where to even begin to find other problematic code. Every developer before me has written code with no regards to limits, so inefficient code can be anywhere. Is there any way or best practice to being able to analyze such a complex org and find where the problems may be? All I can think of is enhanced logging EVERYWHERE, but that may not be the best approach and would be very time consuming, especially considering how many developers we have constantly writing and pushing new code.  I have tried to replicate the issue in a sandbox however I cannot seem to get it working. I wrote Javascript to remotely call an Apex method that waits for 6 seconds. I called this remotely 11 times at once, causing 11 synchronous transactions running concurrently each longer than 5 seconds. However instead of getting the concurrent limit error, each Apex transaction just errors out with a timeout.  Any help would be greatly appreciated. I am not familiar with the majority of the code/functionality of our org, so I do not know how to really solve this issue considering I don't even know what could be problematic aside from long running callouts. Thanks! What is a good strategy to deal with lots of engineers turtling on the other team? Now that the Engineer update has come, there will be lots of Engineers building up everywhere.  How should this best be handled? How do I fix a "Problem with MergeList" or "status file could not be parsed" error when trying to do an update? I have a shapefile with 3800 polygons representing the smallest administrative areas in Ireland. Many of these, in rural areas, have tiny populations, under 100 people. In urban areas, all would have adequate populations.  For each area I have a population figure, and various other attributes, all of which can be intelligently summed to give valid results for areas produced by combining the smaller areas.  I need to merge the areas to get say, 500 or 600 areas of reasonable population. I need to leave the larger (in population) areas alone, where possible. I would greatly prefer to do this automatically. This is necessary for model fitting purposes, primarily.  I've looked at a number of the dissolve questions here:   'Batch Dissolve Polygons based on Attributes in QGIS or FWTools' I think would require me to know which areas to merge, when this is what I need to calculate. 'Practical way of managing polygons and unions of them' and 'How do dissolve polygons from shapefile using open source tools?' have the same issue.   Any suggestions? Will tcpdump see packets that are being dropped by iptables?