"in which" vs "where"
“situation where” vs. “situation in which”
leaflet geojson coordinate problem I just started to play with leflet/geojson a little. But my coordinates are not rendered properly and I have no clue what is going on.  My coordinates are: 52.23943, 4.97599. They work correct with the setView function.  var map = L.map('leaflet_map').setView([52.23943, 4.97599], 15);   But using a geojasonFeature they are, hmmm, 'projected', somewhere east of Somalia.  var geojsonFeature = {             "type": "Feature",             "properties": {             "name": "Coors Field",             "amenity": "Baseball Stadium",             "popupContent": "This is where the Rockies play!"             },             "geometry": {                 "type": "Point",                 "coordinates": [52.23943, 4.97599]             }         };         var myLayer = L.geoJson().addTo(map);         myLayer.addData(geojsonFeature).bindPopup("I am a gjson point.");   Anyone who knows what is happening here?  EDIT  Out of pure curiosity I changed the coordinates around [4.976143930893815,52.23925499011473] and the point appears at its correct location. A known bug!? How can I remap a keyboard key? What packages do people load by default in LaTeX? Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$ How do I get a list of obsolete packages? I'm trying to figure out a way to get a list of the packages that are no longer available in the repositories that I have enabled. This workstation has been through quite a few versions of Ubuntu and has had many 3rd party repositories added and removed. I'd like to get a list of software that I have from these removed repositories, so I can clean it up or add back the appropriate repositories. sed fails to remove newline character Computing convex hull of points using shapely Disk Utility won't Unmount HD for formatting Jumping in an elevator? Can I use one Apple ID for Apple Music and another for iTunes & App Store? Let us suppose I want to use a shared Apple ID for logging into iTunes &amp; App Store, in order to share music and app purchases with a friend.  But let us also suppose that, despite this, my friend and I have very different tastes in music, so I don't want to share Apple Music playlists and "like" assertions with my friend. In other words, I don't want Apple Music to think I like the music my friend likes, and vice versa.  Is there a way that my friend and I can share an Apple ID for logging into iTunes &amp; App Store, but use different Apple IDs for Apple Music?  I suspect the answer is no, but I just wanted to ask. Prove that $\lim_{n\to\infty}a_n\le \lim_{n\to\infty}b_n$ Theorem  Let $\{a_n\}$ and $\{b_n\}$ be convergent real sequences. Assume that there exists a $N\in\mathbb{N}$ so  $a_n\le b_n$ (eq. 1)  for all $n\ge N$. Then  $\lim_{n\to\infty}a_n\le \lim_{n\to\infty}b_n$.  My attempt at proving  Let $a=\lim_{n\to\infty}a_n$ and $b=\lim_{n\to\infty}b_n$. $a$ and $b$ are real numbers because the limit of a sequence of real numbers is a real number (which is a corollary in my textbook). For proof by contradiction, assume  $b&lt;a$.  Let $\epsilon=\frac{a-b}{2}$. Then we can find $N_a,N_b\in\mathbb{N}$ so  $|a-a_n|\le\frac{\epsilon}{2}$ when $n\ge N_a$, (eq. 2)  $|b-b_n|\le\frac{\epsilon}{2}$ when $n\ge N_b$. (eq. 3)  In a textbook I found that I should do the following:  Choose a $n$ so $n\ge\max(N,N_a,N_b$), then eqs. (1-3) are satisfied. Then  $a-\epsilon\le a_n+\frac{\epsilon}{2}-\epsilon$  How do I get that last thing? Is it necessary to do a proof by contradiction or can one do a direct proof? Help evaluating a gamma function Interfaces with static fields in java for sharing 'constants' I'm looking at some open source Java projects to get into Java and notice a lot of them have some sort of 'constants' interface.  For instance,  has an interface called , and most other core classes implement this interface. The interface is riddled with static members. Is there a reason for this approach, or is this considered bad practice? Why not use enums where it makes sense, or a static class?  I find it strange to use an interface to allow for some sort of pseudo 'global variables'.  public interface PConstants {    // LOTS OF static fields...    static public final int SHINE = 31;    // emissive (by default kept black)   static public final int ER = 32;   static public final int EG = 33;   static public final int EB = 34;    // has this vertex been lit yet   static public final int BEEN_LIT = 35;    static public final int VERTEX_FIELD_COUNT = 36;     // renderers known to processing.core    static final String P2D    = "processing.core.PGraphics2D";   static final String P3D    = "processing.core.PGraphics3D";   static final String JAVA2D = "processing.core.PGraphicsJava2D";   static final String OPENGL = "processing.opengl.PGraphicsOpenGL";   static final String PDF    = "processing.pdf.PGraphicsPDF";   static final String DXF    = "processing.dxf.RawDXF";     // platform IDs for PApplet.platform    static final int OTHER   = 0;   static final int WINDOWS = 1;   static final int MACOSX  = 2;   static final int LINUX   = 3;    static final String[] platformNames = {     "other", "windows", "macosx", "linux"   };    // and on and on  } In my experimentation, I've used only BJTs as switches (for turning on and off things like LEDs and such) for my MCU outputs. I've been repeatedly told, however, that N-channel enhancement-mode MOSFETs are a better choice for switches (see  and , for examples), but I'm not sure I understand why. I do know that a MOSFET wastes no current on the gate, where a BJT's base does, but this is not an issue for me, as I'm not running on batteries. A MOSFET also requires no resistor in series with the gate, but generally DOES require a pull-down resistor so the gate doesn't float when the MCU is rebooted (right?). No reduction in parts count, then. There doesn't seem to be a great surplus of logic-level MOSFETs that can switch the current that cheap BJTs can (~600-800mA for a 2N2222, for example), and the ones that do exist (TN0702, for example) are hard to find and significantly more expensive. When is a MOSFET more appropriate than a BJT? Why am I continually being told that I should be using MOSFETs? $D_8$ as a derived subgroup Every undergraduate student knows that there are (exactly) two non-abelian groups of order 8: Dihedral ($D_8$) and Quaternion ($Q_8$). The group $Q_8$ has many interesting properties; simple of them are: it has unique element of order $2$, all subgroups are normal, etc. A property, which is strange and not obvious, the group $Q_8$ has, is that there is no group $G$ such that $G/Z(G)$ is isomorphic to $Q_8$. On the other hand, $D_8$ has no such property; there are (infinitely many) groups $G$ such that $G/Z(G)$ is isomorphic to $D_8$; example - $D_{16}$.   The question, I would like to ask, is related to a property of $D_8$, which is not shared by $Q_8$. There are (infinitely many) groups whose derived subgroup is $Q_8$; example- $SL_2(3)$. For groups $G$ of order &lt;100, one can check on GAP that $D_8$ is not a derived subgroup of any group. The natural question is then:  Question 1: Does there exist a finite/infinite group whose derived subgroup is equal to $D_8$?  Question 2: Does there exist a finite/infinite group whose derived subgroup is equal to (general) dihedral group $D_{2n}$ of order $2n$ ($n&gt;2$)? Is there any Stack Exchange site where I can ask others to recommend me good web sites for solving specific problems?  For example I would like to know if there is any URL shortening website that can allow me to define the url.  For example instead of http://bit.ly/1gX2dD0 I would like it to be http://bit.ly/superflow - if "superflow" is not available then I will invent another word.  I can imagine that such services are paid but I don't need the link to last more than one day, and maybe there is such a website. How does new shield system work? After the upgrade I can't figure out how the new shield system works. I have the option to discard the shield, and I notice I have a new potion in the inventory.  More importantly, I got attacked (and lost) twice in a short amount of time and don't have a shield. When do you now get shield? Is there a way to override class variables in Java? How to trim whitespace from a Bash variable? Compute the integral $\int_{A} x^m y^n z^p (1-x-y-z)^q dx dy dz$ Let $A =$ {$(x,y,z) \in \mathbb{R}^3 |$  $x,y,z \geq 0$ and $x+y+z \leq 1$}.   Compute the integral $$\int_{A} x^m y^n z^p (1-x-y-z)^q dx dy dz$$  using new variables $u = x+y+z$, $v=\frac{y+z}{x+y+z}$, $w=\frac{z}{y+z}$.  Also, although it was not stated in the problem, I'm assuming that $m,n,p,q \in \mathbb{Z}$.   Since $f(x,y,z)=(x+y+z, \frac{y+z}{x+y+z}, \frac{z}{y+z}) = (u,v,w)$, $f^{-1}(u,v,w) = (u(1-v), uv(1-w), uvw)$  Thus J $= \begin{vmatrix} 1-v &amp; -u &amp; 0\\  v(1-w) &amp; u(1-w) &amp; -uv\\  vw &amp; uw &amp; uv\\ \end{vmatrix} = u^2v$  Skipping the part where I find the new limits of integration, and skipping some algebraic simplification we have:  $$\int_{A} x^m y^n z^p (1-x-y-z)^q dx dy dz$$   $$= \int_{0}^1 \int_{0}^1 \int_{0}^1 u^{m+n+p+2}(1-u)^q v^{n+p+1}(1-v)^mw^p(1-w)^n du dv dw$$  However, I have no  idea where to go from here. Any help would be much appreciated.