Check ArrayList contains("") method with equalsIgnoreCase
ArrayList contains case sensitivity
Image of the union is the union of the images $$ f\left(\bigcup\limits_{\lambda \in \wedge} A_{\lambda}\right) = \bigcup\limits_{\lambda \in \wedge} f(A_\lambda)$$  Let $b \in f(\bigcup\limits_{\lambda \in \wedge} A_{\lambda})$ $\rightarrow b=f(a)$ for some $a \in (\bigcup\limits_{\lambda \in \wedge} A_{\lambda})$.  Since $a \in (\bigcup\limits_{\lambda \in \wedge} A_{\lambda}) \rightarrow a \in A_{\lambda}$ for some $\lambda \in \wedge$.  Since $b=f(a)$, then $b \in f(A_{\lambda})$ for some $\lambda \in \wedge$.  $\rightarrow b \in \bigcup\limits_{\lambda \in \wedge} f(A_\lambda)$ $\rightarrow f(\bigcup\limits_{\lambda \in \wedge} A_{\lambda}) \subset \bigcup\limits_{\lambda \in \wedge} f(A_\lambda)$.  I used a similar argument to prove $\bigcup\limits_{\lambda \in \wedge} f(A_\lambda) \subset f(\bigcup\limits_{\lambda \in \wedge} A_{\lambda})$.  Which shows $ f(\bigcup\limits_{\lambda \in \wedge} A_{\lambda}) = \bigcup\limits_{\lambda \in \wedge} f(A_\lambda)$.  Please let me know if this is valid. Context: I want to store the TIFF data to use it for running a linear regression model later on. Ultimate goal: Create a carbon map using field data as a basis. Libraries: library(sp) library(raster) library(tidyverse) library(rgdal)  plotcoord &lt;- SpatialPointsDataFrame(AGCplot[,3:4], AGCplot[,1:2],proj4string=CRS('+proj=longlat'))  pspcoord&lt;-spTransform(plotcoord, CRS('+proj=utm +zone=21')) #Omzetten naar UTM21N (= S1) plot(pspcoord)  s1 &lt;- stack('Some.tif')  colnamen = c(&quot;plotid&quot;,&quot;AGC&quot;,&quot;B2&quot;,&quot;B3&quot;,&quot;B4&quot;,&quot;B5&quot;,&quot;B6&quot;,&quot;B7&quot;,&quot;B8&quot;,&quot;B8A&quot;,&quot;B11&quot;,&quot;B12&quot;,&quot;NDVI&quot;,&quot;NDWI&quot;,&quot;MMRI&quot;,&quot;IRECI&quot;,&quot;MASI&quot;,&quot;VV&quot;,&quot;VH&quot;)  s1_e &lt;- extract(s1,pspcoord,method='bilinear')  Upon extraction I get the following message: Warning message: In proj4string(x) : CRS object has comment, which is lost in output How to convert a one digit number to a two digit number I have a table that represents a timetable for bus, so each cell contains time of departure as hour followed by minute, both as two digits, but sometimes I don't have two digits,just one so I have to switch eg. from 12 4 -&gt; 12 04. How is it possible? How do I enable automatic updates? I think my question relates to a fundamental of 3D modeling that I haven't picked up on yet. It's very simple:  Let's say I have a flat quad. A plane on the XY plane inserted into am empty blender file is a great example. Now let's say I start moving each of the 4 vertices around on in any direction, especially the Z axis.   At this point, there would still be one face, but its extremely unlikely that the face would be planar (I just learned this word). So blender does its best to make sense of what this should look like.  The problem I'm having is that it seems like my quads are always like this, but they never look the way I want. There are edges and seams that look like they are dangling in space, and what tends to happen is that my mesh looks great when viewed from most angles, but if you look at it from just the right angle, you notice the dangling edges or sometimes even some kind of impossible geometry. And so I might try to nudge the problematic vertices around, but this often seems to either make it worse, or just hide the bad geometry until you see it from a different angle.  For me, this always seems to happen whenever I'm trying to move vertices to add roundness to something that is originally square.   There is another question on here about how to actually flatten the quads. That's great, and I might use some of the techniques mentioned there. My question is:   Why does this happen? (Can someone explain this better?) What are some tips and tricks to avoid this situation? What are some tips and tricks to mitigate this situation?   EDIT Here is an illustration:  The overall mesh as viewed from a distance looks decent (for my skill level)    But if you get closer and look from a certain angle...    Super close up:    The "edge" that is pointed to by the arrow is not actually an edge, but some kind of artifact created when blender tries to show the quad. The way the vertices are positioned, it shouldn't actually be possible to see the sliver of the face that I marked in red, since this face is supposed to be around the corner from the edges. The edges should form the silhouette on the right side of my figure.     Here is the side view. Maybe it is the angled topology that skews the face in a funny way?  But I'm not looking for help with this one particular issue, but rather a better understanding of why this happens, and ideas to prevent this in future models. Is it acceptable to publish a paper using an affiliation with a former employer? Recently I've changed jobs, and consequently the field of research has also changed. But I'm still getting proposals for publications in the previous field, and it is interesting for me to accept some of them. My concern is about which affiliation to use: on one hand I gain all the knowledge in that field while working on the previous employer, also I hope they can cover my expenses related to the publication. On the other hand, I do not work for them anymore, and my current company has very little interest in my old field of research, and probably will not support it financially, but I think it is wise to mention them as well. As a compromise I'm thinking to put the previous employer in the affiliation, and the name of my new employer in the footnote, something like "currently at XYZ". Surely I'll discuss this issue with both, although the opinion of the community is also very valuable. Redirect parent window from an iframe action How do I Uninstall Windows 10 or Windows 10 preview? Viewer-independent copyable spaces at the beginning of a line? I need to include a couple of Python code listings, where the indentation of the lines (using some number of spaces) is significant. I would like for the code listings to be copyable, so the spaces at the beginning of the line need to be be copied along with the text.  This question has been asked in various ways before (e.g. , or ). Those questions focus on making line numbers uncopyable, though.  Making the spaces at the beginning of a line copyable seems to be harder: "I am not sure it is possible to specify in the PDF (at least in a viewer-independent way) that the indentation should be copied too" (). At , Philippe Goutet suggests a solution (turning the spaces into visible spaces, and coloring them in the background color so that they appear invisible) that works using Acrobat Reader, but not all readers. He says "It works under Acrobat Reader and it's extremely pleasant to be able to quickly copy/paste code without problem (perhaps the problem can be circumvented by writing direct PDF code to tell that it's a space, I've never had the time to try)".  Is it possible to produce a PDF with a code listing with copyable real spaces at the beginning of a line?  Minimal example: The line return x should start with four spaces.  \documentclass{article}  \begin{document} \begin{verbatim} def myfunction(x):     return x \end{verbatim} \end{document}   I know that I could attach the code to the PDF as a file, but that's not what I want. What makes Stealing Signs wrong? In a question on "along" vs "alongside", I have seen this question and the correct answer on the web site makes me confused.      The question is: I enjoyed my walk _________________ the river.  a) along b) alongside  I selected "...along the river" as the correct answer, but on the web site it is shown as wrong and the correct answer is "alongside".  How can that be? I still do not agree, because I have studied the difference between the two. "along" is just the right preposition for thin and long places like road, path, street, beach etc".   So, why would the correct answer be "alongside" which simply means "next to"? Do you not think "along" seems to be better fitting?  Regards,  Note: I would be more than gratefull, if somebody show it to me in a video, like "a walk along the river" and "a walk alongside the river". Maybe I can understand the how "a walk along the river" and "a walk alongside the river" would take place. How to query MongoDB with "like"? How can I display additional boot and shutdown information on the Windows 7 welcome screen? There is a small tweak, I believe it is a registry key, that allows to display additional information on the Welcome and Shutting down screens of Windows 7 (and most likely Vista, too). I have activated this tweak on one of my systems; unfortunately I forgot how I did it, and I can't seem to find the website that originally gave me that information.  Usually, the Windows 7 welcome screen will just display "Welcome" when logging in. With the tweak activated, my Welcome screen gives status information such as "Loading user settings" or "Preparing desktop". When shutting down, the default screen simply says "Shutting down". With the tweak activated, it gives additional status information such as "Stopping Windows services". This appears the same way that Windows gives information when updates are installed or configured during the startup or shutdown procedure, and I find them quite helpful in getting a feel for what task takes how long during that process.  The only setting I was able to find is the Boot log checkbox on the Boot tab of the msconfig application. However, this results in Windows displaying console logs of drivers it is loading, etc., instead of the animated Windows title. This is NOT the setting I am looking for. The "additional boot information" setting that I have activated on this system still displays the regular animated Windows logo, and only replaces the strings displayed on the blue Welcome and Shutdown screens.  Could someone direct me to the registry key (or whatever setting) that is used to get this behaviour?  Edit: Here are a few pictures of the enhanced Welcome and Shutdown screens taken with my mobile phone—they're in German though.   Login screen "Waiting for User Profile Service"   Login screen "Preparing desktop"   Logout screen "Stopping Windows services": Parsing domain from a URL calculate slope for a road network I am working on a road network for routing operations using postgis and QGIS.    I am new to both of these tools and need to calculate the slope for each edge (by retrieving the Z value for the start and end node for the edge from a raster). Any ideas of the best approach to this?   I know postgis can dump points and get the value from a raster, but can I get the slope attribute to the edge without breaking the network topology (with edges that have corresponding start/end nodes) using this method?   thanks different font while using url I'm having troubles while using the url command in my bibliography.  I mean:  1) \bibitem{[8]} {\url{http://projects.webappsec.org/w/page/13246989/Web20Application20Security20Statistics\#Tableofcontent}}  2) \bibitem{[5]} Justin~Clarke ``SQL Injection Attacks and Defense'', Syngress Publishing, Inc.2009   Unfortunately font 1) is different from 2).  What should I do in oder to get the same font for both items?   I'd like the font used in 1)  to be identical to the one displayed in 2) Difference between myself and by myself Make bibliography appear in toc as a chapter, not section Unexpected gaps in IDENTITY column I'm trying to generate unique purchase order numbers that start at 1 and increment by 1. I have a PONumber table created using this script:  CREATE TABLE [dbo].[PONumbers] (   [PONumberPK] [int] IDENTITY(1,1) NOT NULL,   [NewPONo] [bit] NOT NULL,   [DateInserted] [datetime] NOT NULL DEFAULT GETDATE(),   CONSTRAINT [PONumbersPK] PRIMARY KEY CLUSTERED ([PONumberPK] ASC)     );   And a stored procedure created using this script:  CREATE PROCEDURE [dbo].[GetPONumber]  AS BEGIN     SET NOCOUNT ON;      INSERT INTO [dbo].[PONumbers]([NewPONo]) VALUES(1);     SELECT SCOPE_IDENTITY() AS PONumber; END   At the time of creation, this works fine. When the stored procedure runs, it starts at the desired number and increments by 1.  The strange thing is that, if I shut down or hibernate my computer, then the next time the procedure runs, the sequence has advanced by almost 1000.   See results below:    You can see that the number jumped from 8 to 1002!   Why is this happening?  How do I ensure that numbers aren't skipped like that?  All I need is for SQL to generate numbers that are:   a) Guaranteed unique.  b) increment by the desired amount.    I admit I'm not a SQL expert. Do I misunderstand what SCOPE_IDENTITY() does?  Should I be using a different approach? I looked into sequences in SQL 2012+, but Microsoft says that they are not guaranteed to be unique by default. We all know that the amount of current flowing b/w the plates is independent of the frequency. If I were to ask why doesn't it depend then you'd probably say that it depends on the number of electrons rather than the frequency or you might show me a current vs frequency graph.  But here is my theoretical argument. Electric current is defined as the amount of charge flowing through a point/space/wire per unit time. Let I be current due to photo electrons ejected by photons of some frequency. Now if I would increase the frequency, the kinetic energy of the ejected electron would increases, therefore it will move faster and therefore contribute more current (charge will through the same point many times per unit time) . Thereby, giving a net current greater than I.  What is wrong with my argument?  After thinking a lot, I came up with a possible reason. However fast the electrons may move, but when they hit the metal plate, they would lose their velocity and start moving in drift velocity. Now there is a problem with this argument. If this were to be true then I should expect to see a big chunk of extra electrons getting stuck at the anode.  If my reasoning was correct, then why can't I see a big charge buildup at the anode.