Simplify geometry of multiple features without losing shape
Simplifying adjacent polygons using QGIS Simplify Geometries tool
Deriving the speed of the propagation of a change in the Electromagnetic Field from Maxwell's Equations I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can be empirically found, and, when plugged into the expression, yield the empirically found speed of light)  I'm really not sure how I would go about finding $v = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ simply from Maxwell's equations in the following form, in SI units --  $$\nabla \cdot \mathbf{E} = \frac {\rho} {\epsilon_0}$$  $$\nabla \cdot \mathbf{B} = 0$$  $$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$$  $$\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}} {\partial t} \right)$$  Is what I believe true? (that the speed of propagation is derivable from Maxwell's Equations)  If not, what else is needed?  If so, can you provide a clear and cogent derivation? Which is correct: "what if there was" or "what if there were"? Possible Duplicate:          Is this correct grammar?     What if there was a Stack Overflow on…    Shouldn't it be "what if there were a Stack Overflow on…"? $\operatorname{Hom}(X \times Z, Y) \cong \operatorname{Hom}(X, \operatorname{Map}(Z, Y))$ is not true in $\textbf{Top}$ I read that in the category of topological space it is not true that $\operatorname{Hom}(X \times Z, Y) \cong \operatorname{Hom}(X, \operatorname{Map}(Z, Y))$ for every $X, Y, Z$ topological spaces. In particular, I read that this does not work when $Z = \mathbb{R} \setminus \{ 1/n \mid n \in \mathbb{N}\}$. This was not explained, i.e. there was no example.   I am looking for an example or – maybe better – just a hint.  EDIT   $\operatorname{Map}(Z, Y)$ is endowed with the compact-open topology $\cong$ means just bijection; i.e. there is already an obvious bijection as sets, but the claim is that (I think) sometimes the "output function" is not continuous I'm working with some code that widely uses the idiom of returning a pointer to a static local variable.  eg:  char* const GetString() {   static char sTest[5];   strcpy(sTest, "Test");   return sTest; }   Am I right in thinking that this is safe?  PS, I know that this would be a better way of doing the same thing:  char* const GetString() {   return "Test"; }   Edit: Apologies, the function signature should of course be:  const char* GetString(); Combinatorics Question Asking How Many Integer Solutions Given Different Restrictions How many integer solutions of $x_1 + x_2 + x_3 + x_4 = 28$ are there with:  (a) $0 ≤ x_i ≤ 12$?  (b) $−10 ≤ x_i ≤ 20$?  (c) $0 ≤ x_i, x_1 ≤ 6, x_2 ≤ 10, x_3 ≤ 15, x_4 ≤ 21$?  \ \  My attempts (I was really only able to solve part (a) but I would appreciate if you could check my work for this one as well):  (a) First I took the total number of integer solutions with no restrictions: There would be ${28+3\choose 3}$ = ${31\choose 3}$ total solutions with no restrictions.   Then I used the inclusion exclusion principle and knew I would have to subtract [P(A) + P(B) + P(C) + P(D)] where A --> $x_1$ is greater than or equal to 13, ..., D--> $x_4$ is greater than or equal to 13. The probabilities of all these cases would equal ${15+3\choose 3}$ = ${18\choose 3}$ because once we assign 13 to one of the $x_i$ there would be $28 - 13 = 15$ remaining to distribute among the $x_i$ values. We would also need to choose which of the $x_i$ to give the 13 to so we would multiply the ${18\choose 3}$ by ${4\choose 1}$ = ${4\choose 1}{18\choose 3}$  We would then have to add back, since we "oversubtracted", the case in which there is an intersection between two of the $x_i$ or in other words two of the $x_i$ receive 13 or more. P$(A\bigcap B)$ = $28-2(13) = 2$ remaining to distribute among the $x_i$ values. So we would also have to choose which of the $x_i$ to give the 13 to so we would have ${4\choose 2}$ ways to choose them. So there would be ${4\choose 2}{2+3\choose 3}$ = ${4\choose 2}{5\choose 3}$ solutions in this case.   Thus the number of solutions would be: ${31\choose 3} - {4\choose 1}{18\choose 3} + {4\choose 2}{5\choose 3}$.  I'm not sure if this is correct and I'm really stuck on b and c so I would appreciate any help or feedback. Thank you! Modifying list while iterating unzip error "End-of-central-directory signature not found" I try to unzip a zip file, but got an error:  $ unzip COCR2_100.zip  Archive:  COCR2_100.zip   End-of-central-directory signature not found.  Either this file is not   a zipfile, or it constitutes one disk of a multi-part archive.  In the   latter case the central directory and zipfile comment will be found on   the last disk(s) of this archive. note:  COCR2_100.zip may be a plain executable, not an archive unzip:  cannot find zipfile directory in one of COCR2_100.zip or         COCR2_100.zip.zip, and cannot find COCR2_100.zip.ZIP, period.   I googled but didn't find a solution. I was wondering why it is and how I should fix it? Thanks!  The zip file can be downloaded from . It is an application, and here is its website .  My OS is 10.10. I am not sure what caused this error, but here is what the whole error says, and also this is sitting as a notification, and preventing me from updating any software using Update Manager - Please provide some assistance or tell me how to figure out what to do to fix it.  Could not calculate the upgrade  An unresolvable problem occurred while calculating the upgrade.  Please report this bug against the 'update-manager' package and include the following error message: 'E:Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages.' Facebook message notification showing blank message Since I updated the system to 10.11.5, the Facebook message notification is not showing message text.   Is this a bug in this software upgrade of OSX? Why do we let hostile users dictate the perception of Stack Overflow? Java Constructors I am trying to learn how to specify class constructors in Java. I am starting to understand that they specify the types of instance variables of objects made from that class. They also can be used to set the instance variable initial values. The follow example is from the Java tutorial on Sun's website:  public Bicycle(int startCadence, int startSpeed, int startGear) {     gear = startGear;     cadence = startCadence;     speed = startSpeed; }   Where in your classes source code should you put the constructor(s)?  Are these arguments the names of the variables?: (int startCadence, int startSpeed, int startGear) or are gear, cadence and speed the names of the variables?  What is the difference between (int startCadence, int startSpeed, int startGear) and gear, cadence and speed?  In the unlikely event that my instructor or any administrator from Salt Lake Community College ever comes across this question, let me make my intentions clear. This question is posted in the greatest spirit of academic honesty. I ask this question to seek general advice and help in understanding the proper way to use the Java programming language. I in no way use the work of others and represent it as my own work. I use the answers provided here as a general aid in my understanding. I do all my own work and do not copy work provided by people answering my question. I have a scenario where I have multiple threads adding to a queue and multiple threads reading from the same queue. If the queue reaches a specific size all threads that are filling the queue will be blocked on add until an item is removed from the queue.  The solution below is what I am using right now and my question is: How can this be improved?  Is there an object that already enables this behavior in the BCL that I should be using?  internal class BlockingCollection&lt;T&gt; : CollectionBase, IEnumerable {     //todo: might be worth changing this into a proper QUEUE      private AutoResetEvent _FullEvent = new AutoResetEvent(false);      internal T this[int i]     {         get { return (T) List[i]; }     }      private int _MaxSize;     internal int MaxSize     {         get { return _MaxSize; }         set         {             _MaxSize = value;             checkSize();         }     }      internal BlockingCollection(int maxSize)     {         MaxSize = maxSize;     }      internal void Add(T item)     {         Trace.WriteLine(string.Format("BlockingCollection add waiting: {0}", Thread.CurrentThread.ManagedThreadId));          _FullEvent.WaitOne();          List.Add(item);          Trace.WriteLine(string.Format("BlockingCollection item added: {0}", Thread.CurrentThread.ManagedThreadId));          checkSize();     }      internal void Remove(T item)     {         lock (List)         {             List.Remove(item);         }          Trace.WriteLine(string.Format("BlockingCollection item removed: {0}", Thread.CurrentThread.ManagedThreadId));     }      protected override void OnRemoveComplete(int index, object value)     {         checkSize();         base.OnRemoveComplete(index, value);     }      internal new IEnumerator GetEnumerator()     {         return List.GetEnumerator();     }      private void checkSize()     {         if (Count &lt; MaxSize)         {             Trace.WriteLine(string.Format("BlockingCollection FullEvent set: {0}", Thread.CurrentThread.ManagedThreadId));             _FullEvent.Set();         }         else         {             Trace.WriteLine(string.Format("BlockingCollection FullEvent reset: {0}", Thread.CurrentThread.ManagedThreadId));             _FullEvent.Reset();         }     } } Should we put the references in slides/poster when we already have them in paper? After reading this question about  and asking myself two questions about  and , I realize that these activities are for showing what you found, make the audience be attracted. If they need further explanation, they should read your paper, which has successfully defensed and proved that your work is validated. One important thing when you attempt to attract people is concentrate on the important, which means unnecessary things need to be trimmed. I think the reference is one of those. So, should we put the references in slides/poster when we already have them in paper? How can I repair a buried 120v cable splice to make it meet code? I have an electrical question. I have a cable feeding an outdoor yard light. It was cut, I spliced it, soldered it and wrapped it with tape. Is there a way to splice and bury it safely to code? If not, I'll need to dig a 30 foot trench to replace the whole length.  Was about 8 inches below ground, surfaced over the years and probably hit with the weed trimmer.   It is outdoor cable inside copper tubing. Years ago when I bought the wire I knew outdoor was gray. The box said outdoor but it is white like indoor wire.   It was spliced about 20 years ago but am fixing up house and like to hide the ugly splice. How does one get the MinionPro \qoppa? Since I have switched to the 2014 texlive, one issue is not working: the character \qoppa. The command is defined in polutonikogreek in babel. It is an archaic greek letter, but was used also in classic times for the number 90.  The glyph is available in the cmr font and in MinionPro and in the beautiful MinionMath font of Johannes Küster. I want the latter. In MinionPro/MinionMath, it is unicode character 03d9 (formerly u+03DE, it recently changed, as it turns out), see   How do I get the glyph into latex? I tried  \def\testqoppa{\begingroup\fontfamily{MinionPro}\fontencoding{LGR}\selectfont\char19\endgroup}   and   \def\testqoppab{\begingroup\fontfamily{minionmath}\fontencoding{LGR}\selectfont\char19\endgroup}   But all this gives the cmr glyph, because latex complains  LaTeX Font Warning: Font shape `LGR/MinionPro/m/n' undefined LaTeX Font Warning: Font shape `LGR/minionmath/m/n' undefined (Font)              using `LGR/cmr/m/n' instead on input line 571.   This seems like a beginner error from my side. Can somebody help me to get it right? I need \qoppa only in two places, so a nasty trick is also sufficient. The MinionMath font is installed and is working for all other purposes. Here is an extract of the .cls file:  \usepackage[fullfamily,textlf, opticals, swash, onlytext]{MinionPro} \usepackage[extraops,textcomp,withamsmath,amssymb]{minionmath} \usepackage{amsmath}             \usepackage{minionamsmath} \usepackage[polutonikogreek,greek,latin,french,italian,german,british]{babel} I bought a Mac (13", early 2011) almost 5 years ago. When I first got it, it was running under OS X 10.7 and it was pretty fast. I've being upgrading it ever since and it's now running under Mac OS X 10.11.  I guess it didn't totally survive the upgrades because, today, there's a lot of bugs, freezes, lags, "spinning beach ball" appearing,... for example, when I write something on a normal program/editor, the cursor freezes for a few seconds, then catches up to what I'm writting.  As you can guess, that's really annoying! I've been thinkning about upgrading the hardware but I don't know what to do: should I change the RAM to 8 GB - 1 333 MHz (currently my computer has 4 GB - 1 333 MHz)? Or should I upgrade to an SSD (which is pretty expensive and difficult to install)?  Thank you very much. How do I boot Windows 8 into Safe Mode? I have Windows 8 Enterprise x64. It's installed a virtual machine. After trying to update VMWare's guest extension it black screened. After resetting it, now the virtual machine won't boot. It just says "automatic repair couldn't repair your PC"   Everything I do ends with an error or it coming back to this screen. If I go to Troubleshoot > Advanced Options > Start up settings and then go to Safe Mode, all it will do is say "preparing automatic repair" and then "diagnosing your PC" and then will come straight back to the "automatic repair couldn't repair your PC" screen. It's as if it doesn't even attempt to go into safe made.   Is there anything else I can do before I reformat? The phrase for when: working in a group to divide responsibility and reduce malicious intent How can friction do no work in case of pure rolling? I have read various answers , on PSE and elsewhere , and most of them explain that the point of contact of the rolling object undergoes 0 instantaneous displacement in the direction of friction, I agree , but then there is a feeling that the friction does provide a torque , so how can it do 0 work . ( The pure rolling here is under a constant external force on the object so friction does act ). Neopronouns or trolling? It’s the  question: Am I looking at someone’s legitimate pronouns or trolling?   (It’s unfortunate I have to ask, but this is just where we are right now.)  I’ve seen “my pronouns are [insert ridiculous fake stuff here]” trolling recently (in posts) when before I never did. Also stuff that looks to be trolling, but could also maybe not be. Trolls deserve red flags while everyone else specifying pronouns does not, right?  (To clarify, the problem is not just about not wanting to use a troll's words. The purpose of some of this trolling is to try and convince people that transgender people—or their neopronouns—are stupid or unreasonable. Ignoring the trolls allows us to avoid the first problem, but not the second since it allows them to still reach people with their message, which is not something that I want to see promoted.)  Some neopronouns are clearly legitimate. Some trolling is clearly trolling. But unfortunately there’s a big grey area where it’s not clear to me what is what.   Does anyone have a good method for dealing with this? There just doesn’t even seem to be a good way to ask about someone’s specified pronouns in such a way that doesn’t sound insulting if the user isn’t trolling.     Note: A while ago, I did some research on neo-/third person pronouns which can be found . There are several important things I found:   There are more neopronouns than I could ever hope to keep track of The most popular neopronouns are very uncommon. On the other end of the spectrum, it looks like some neopronouns are neologisms used by a single person  Some neopronouns come from unlikely places, such as SciFi