This question:     I cannot remove tag because I get error "title must be at least 15 characters long." Then how was it posted in the first place?
Test to see if the title length requirement can be circumvented by appending lots of dots.
Should I have separate threads for rendering and logic, or even more?  I'm aware of the immense performance drop caused by data synchronization (let alone any mutex locks).  I've been thinking of taking this to the extreme and doing threads for conceivable every conceivable subsystem. But I'm worried that may slow things too. (For example, is it sane to separate the input thread from rendering or game logic threads?) Would the data synchronization required make it pointless or even slower? I'm trying to work with  in Java.   I want to implement arithmetic functions.  For this, I will first require a way to normalize the functions.  I know I can't add 1/6 and 1/2 until I have a common denominator. I will have to add 1/6 and 3/6.  A naive approach would have me add 2/12 and 6/12 and then reduce.  How can I achieve a common denominator with the least performance penalty?  What algorithm is best for this?    Version 8 (thanks to ):     Improvements include:         the equals() method is now consistent with the compareTo() method      final class Fraction extends Number {     private int numerator;     private int denominator;      public Fraction(int numerator, int denominator) {         if(denominator == 0) {             throw new IllegalArgumentException("denominator is zero");         }         if(denominator &lt; 0) {             numerator *= -1;             denominator *= -1;         }         this.numerator = numerator;         this.denominator = denominator;     }      public Fraction(int numerator) {         this.numerator = numerator;         this.denominator = 1;     }      public int getNumerator() {         return this.numerator;     }      public int getDenominator() {         return this.denominator;     }      public byte byteValue() {         return (byte) this.doubleValue();     }      public double doubleValue() {         return ((double) numerator)/((double) denominator);     }      public float floatValue() {         return (float) this.doubleValue();     }      public int intValue() {         return (int) this.doubleValue();     }      public long longValue() {         return (long) this.doubleValue();     }      public short shortValue() {         return (short) this.doubleValue();     }      public boolean equals(Fraction frac) {         return this.compareTo(frac) == 0;     }      public int compareTo(Fraction frac) {         long t = this.getNumerator() * frac.getDenominator();         long f = frac.getNumerator() * this.getDenominator();         int result = 0;         if(t&gt;f) {             result = 1;         }         else if(f&gt;t) {             result = -1;         }         return result;     } }     I have removed all previous versions.  My thanks to: How can I set the maximum amount of characters in a UITextField on the iPhone SDK when I load up a UIView? How can I deploy a connected app from my sandbox environment to my production environment? I built a changeset and I was able to include all my classes, but it was a surprise that salesforce has not provided any option to deploy a connected app.  So how do I go about deploying a connected app? Do I need to create it in every other environment? Making separate Python installation that can call ArcPy? A loss and gain problem This is a very simple but confusing puzzle.  A customer buys goods worth $200$ rupees from a shop. The shopkeeper selling these goods makes zero profit from this purchase.  The lady gives him a $1000$ rupee note.  The shopkeeper has no change, so he goes next door to another shopkeeper to get change for the $1000$ rupee note. He keeps $200$ for himself and returns $800$ to the customer.  Later, the second shopkeeper from next door comes back with the $1000$ rupee note with a stamp on it saying "counterfeit" and takes his money back.  How much loss does the first shopkeeper face? The PS3 version of Portal 2 comes with a code to link it to a Steam account. Apparently this allows you to play on both the PC and PS3 with one purchase.  Can this be used to play co-op between the two platforms? proving $\left(1+\frac 1n\right)^{n} = 1 + \sum_{k=1}^n \{\frac 1{k!}\prod_{r=0}^{k-1}(1-\frac rn)\}$ using the binomial theorem In a script I'm trying to find the Terminal.app window containing a specific tty device and raise that window to the top. Here's what I have in Applescript so far:  tell application "System Events"   set foundWin to false   if (name of processes) contains "Terminal" then     tell application "Terminal"       set theTabs to first tab of every window where tty is "$(tty)"       repeat with theTab in theTabs         if class of theTab is tab then           set theWin to (first window whose tabs contains theTab)           set selected tab of theWin to theTab           set foundWin to true         end if       end repeat     end tell   end if   if foundWin then     --RAISE THE WINDOW?!   end if end tell   Where I'm getting stuck is the "raising the window" part.  Here are some things that are not quite what I want:  set frontmost of theWin to true -- this brings the window to the front of the group of Terminal.app windows but doesn't raise it above any other windows.  tell application "Terminal" to activate -- this brings every Terminal window to the front in a big stack. I just want the one window.  tell application "System Events"     set theSysWin to first window of process "Terminal" whose name is (name of theWin)     perform action "AXRaise" of theSysWin end tell   This almost does it, but what it does is to raise the terminal window to the #2 position, still underneath the active window (if the active app is something other than Terminal.app.)  click theSysWin at {10,50} -- doesn't seem to do anything.  click first static text of theSysWin -- doesn't seem to do anything.  Is there a way to do this? It doesn't have to be in Applescript.  EDIT I did find this web page (  ) quoting an Obj-C/Cocoa call:  SetFrontProcessWithOptions(&amp;psn, kSetFrontProcessFrontWindowOnly);  I'm not familiar with either ObjC or Cocoa, and this is (ultimately) getting invoked from a shell script, so not sure where to go from there. I have seen some users show a picture of their network profile on the profile tab. How can I add this for my own account? When is the vector space of continuous functions on a compact Hausdorff space finite dimensional? I know that the vector space of all real valued continuous functions on a compact Hausdorff space can be infinite dimensional.  When will it be finite dimensional?  And how will I identify that vector space with $\mathbb{R}^n$ for some $n$? Is there a way to set my current location manually on Windows 8? Is there a way to set my current location manually on Windows 8? I don't have a GPS module, but the device is always located at the same place. The automatic detection via network sets a place 200 kilometers from here.  I searched for a setting that allows me to set the location by hand, but I didn't find one. When should N-Gons be used, and when shouldn't they? Can I uninstall and reinstall Ubuntu Software Center? Since migrating to a true install and upgrading to 12.04 I have had several problems that seem to relate to the Ubuntu Software Center. Hanging at applying changes and blank screen on screen lock only when it is running, for instance.  My question is: Can I safely uninstall and reinstall Ubuntu Software Center and could this possibly fix those problems or are they just bugs I have to wait for updates for? Conservation law of energy and Big Bang? Did the law of conservation of energy apply to the earliest moments of the Big Bang? If so, what theoretical physics supports this?   I hear that Einstein's theory of relativity disputes the law of conservation of energy- so does that mean the law is false, or only some aspect of it? What characters are valid in a Java class name? What other rules govern Java class names (for instance, Java class names cannot begin with a number)? C++ cout hex values? I want to do:  int a = 255;  cout &lt;&lt; a;   and have it show FF in the output, how would I do this? Does magic jack work on Ubuntu? Does magic jack work with Ubuntu? I originally had my magic jack on a computer with windows XP and I decided to switch to Ubuntu but I still want Magic jack. I'm trying to write a script which creates a Nurbs path curve, bevels it, and then stores the location of each vertex/point in that curve. I've been writing it based on the code displayed in the info panel, but it doesn't show what the vertices are supposed to be called - so I can't refer to them in the script.  Update: After following Ratt's links, I modified  for Nurbs Path and am now stuck again, though it's still progress. Below is one version I tried out, but the error message says that Curve has no attribute path_points. Of course it doesn't, because I made that up because I don't know what the Nurbs Path equivalent for bezier_points is.  import bpy import random  def pathPointLoc(cu, typ, points):      for (n) in enumerate(points):         nurb = cu.path_points[n]         print(nurb.location)      return  cu = bpy.data.curves.new("MyCurve", "CURVE") ob = bpy.data.objects.new("MyCurveObject", cu) scn = bpy.context.scene scn.objects.link(ob) scn.objects.active = ob  cu.bevel_object = bpy.data.objects["BezierCircle"] cu.taper_object = bpy.data.objects["BezierCircle"]  pathPointLoc(cu, "NURBS", [(0,0,0,1), (0,0,1,random.randint(1,4)), (0,1,1,1), (1,4,1,1)] ) Suppose that $(U,V)$ has the following joint pdf: $$f_{U,V}(u,v)=\exp(-\theta u-\theta^{-1}v)$$ , where $u\geq0$, $v\geq0$, $\theta&gt;0$. Define $X=UV$ and $Y=U/V$. Find the marginal pdf of $X$ and $Y$.  With transformation, I got $U=\sqrt{XY}$ and $V=\sqrt{X/Y}$ and the absolute value of Jacob is $1/2Y$. Then, the joint pdf of $(X,Y)$ is  $$f_{X,Y}(x,y)=\exp(-\theta \sqrt{XY}-\theta^{-1}\sqrt{X/Y})1/2Y, X,Y&gt;0.$$  But I am not sure how to get the marginal pdf?  Thank you!