I have a periodic function $g(x)$. I want to know what else $g(x)$ has to satisfy so its undefined integral will be a periodic function.  Thanks!  PS: I noticed that if $g(x)=f(x)+a$ where $a$ is a constant the integral will not be periodic.
If $f$ is a periodic function with $T = \pi$, does that mean that $F$ (a primitive of $f$) has the same period ? What about the inverse implication (periodic primitive implies periodic function) ?
Hydrogen radial wave function infinity at $r=0$ How can I use Netflix on Ubuntu? Is there a way to stream Netflix content to my Ubuntu machine? Why do some tag info pages show who created them and others don't? Some  show who created the tag:    while  don't. I'm pretty sure I created that one as well, if you hover over the timestamp you can see when it was created:    which more or less matches with  where I created the tag:    I understand that some tags like  were probably created by the Community user while the site itself was created (so it ), but some newer tags like   even though  still has an account here.  What's going on here? Would this also mean I wouldn't get a  for  if I ? How do I set 'nomodeset' after I've already installed Ubuntu? I'm quite confused about attacking with two weapons in both hands and wondering what is required to be able to do to (in Pathfinder).  1. Base Attack Bonus Looking at the base attack bonus tables for different classes (e.g. the ) it seems like up to +5 you get only one attack per full action but starting from base-attack-bonus of +6 you get a second attack with +1.  2. Feats There is a feat . The existence of the feat sounds like you could not do two-weapon-fighting without it. However, in the description of "normal" it says:     If you wield a second weapon in your off hand, you can get one extra attack per round with that weapon. When fighting in this way you suffer a –6 penalty with your regular attack or attacks with your primary hand and a –10 penalty to the attack with your off hand. If your off-hand weapon is light, the penalties are reduced by 2 each.   3. Core Rulebook Chapter about combat If I understand the  it says that you need a full-round action do attack with both weapons in two hands.  So how do these things interact? Can I only attack with my off-hand weapon if my base-attack-bonus is high enough that I get second one with +1?  If not, how does the "multiple attacks from high base-attack-bonus" interact with dual-wielding? Assuming I reached a state of base-attack-bonus with +11/+6/+1 and have a full-round action to attack. Does that mean I can either attack with my primary weapon three times or use the primary weapon and off-hand weapon to attack only twice? Why would I then ever choose dual-wielding? Or can I attack three times with both weapons (leading to a total of 6 attacks with heavy malus) Or would I get 3 attacks with the primary weapon + 1 attack with the off-hand weapon? If so, what attack bonus do I have to use for each of the attacks? Show that the function $g(x) = x^2 \sin(\frac{1}{x}) ,(g(0) = 0)$ is everywhere differentiable and that $g′(0) = 0$ What is the difference between Parse() and TryParse()?  int number = int.Parse(textBoxNumber.Text);  // The Try-Parse Method int.TryParse(textBoxNumber.Text, out number);   Is there some form of error-checking like a Try-Catch Block? Command and Conquer 3 exeption in exception handler I have command and conquer 3 from Origin, but when I try to start it, I get the 'exception in exception handler' error and the game exits.   I've tried the Origin launcher fix as well as -runver to make the game run a different version (although this just says that it can't find any version). I run Windows 10 (I know, experimental) but this game worked at one point, and then stopped working suddenly - there wasn't even an update in between.   I suspect that it's got to do with Origin, but any help would be appreciated. How does damage dealt increase as you level up I've recently taken over as GM in my group.  We are all new to RPGs except for our original GM, so they decided to run an adventure path so it would be easier to change GMs if they had to stop playing.  Along this path, we had one CR 4 encounter that took us an hour, almost killed our bloodrager and knocked our brawler unconscious. When we leveled up, our GM told us to increase the damage we did by "one level," so my 1d6 became 2d6 and my friend's 2d6 became 4d6.  I saw no problem with this as a player, but I was looking over the adventure path and later encounters that also have a CR of 4 could be ended in one turn by our bloodrager. This would make encounters really boring, and my goal is to avoid boredom.  My question is: As you level up, how does the damage you do increase? Does it go up like my GM said so that at level 3 my rapier does 3d6 and the bloodrager's earth breaker does 6d6, or does it go up by some other method?  I have read the PHB and I don't think that what the GM was saying is correct, but being a first-time player I wasn't sure if had just missed something, so I figured I should ask elsewhere. Time reversal symmetry and T^2 = -1 Consider this reverse biased diode :     I read that no or very small current flows in reverse biased diode as depletion layers get widened and huge resistance is offered so no electrons can cross it. But, why the electrons or holes need to cross the depletion layer? In the diagram above, the positive charges (holes) are moving towards left and the current due to electrons is also in left, so won't the circuit be completed? Regression: Transforming Variables When is "self" required? I have been using classes for only a short while and when I write a method, I make all variables reference self, e.g. self.foo.  However, I'm looking through the wxPython in Action book and notice that "self" isn't used all the time. For example:   import wx  class TextFrame(wx.Frame):     def __init__(self):         wx.Frame.__init__(self, None, -1, 'Text Entry Example',             size=(300, 100))         panel = wx.Panel(self, -1)         basicLabel = wx.StaticText(panel, -1, "Basic Control:")         basicText = wx.TextCtrl(panel, -1, "I've entered some text!",             size=(175, -1))         basicText.SetInsertionPoint(0)         pwdLabel = wx.StaticText(panel, -1, "Password:")         pwdText = wx.TextCtrl(panel, -1, "password", size=(175, -1),             style=wx.TE_PASSWORD)         sizer = wx.FlexGridSizer(cols=2, hgap=6, vgap=6)         sizer.AddMany([basicLabel, basicText, pwdLabel, pwdText])         panel.SetSizer(sizer)   The one below does use "self".  import wx class ButtonFrame(wx.Frame):     def __init__(self):         wx.Frame.__init__(self, None, -1, 'Button Example',             size=(300, 100))         panel = wx.Panel(self, -1)         self.button = wx.Button(panel, -1, "Hello", pos=(50, 20))         self.Bind(wx.EVT_BUTTON, self.OnClick, self.button)         self.button.SetDefault()     def OnClick(self, event):         self.button.SetLabel("Clicked")   If I remember correctly, "self" is reference to a particular instance of the class, so when is it not necessary? Is there a general rule of thumb? Node.js on multi-core machines Is it possible to set the "urgent" flag in Gmail for outgoing mail? I'd like to be able to flag time-sensitive emails as such. With spells like Moonbeam or Flaming Sphere, how should we treat the movement of their areas-of-effect when it comes to passing them behind a thick pillar or around a blind corner?  Should we treat any movement of them as if they are being 're-cast' (and so requiring a clear unobstructed view)? Or could a mage presumably will them somewhere out-of-sight? Change default shell for Terminator I want to change the default shell of Terminator to zsh. In /etc/passwd/ I've changed the default shell to /bin/zsh. This settings changes the default shell in LXTerminal (the default terminal on Lubuntu), but not in Terminator. So I tried chsh -s /bin/zsh, but that doesn't work either. The Terminator  says:  How do I change my default shell? Terminator will always start the shell specified by the SHELL environment variable. (It will fall back to /bin/sh if the SHELL environment variable isn't set.) You could simply influence Terminator's environment, but the best solution is to tell your operating system which shell you'd like, and it will ensure that SHELL is set correctly for all applications, not just Terminator. See the documentation for your operating system for details on how to change your default shell.  So I expected my attempts to work, but they don't. How can I change the default shell in Terminator. I've been working through a bit of Ireland and Rosen's Number Theory for fun. Problem 4.11 of Ireland and Rosen asks     Prove that $1^k+2^k+\cdots+(p-1)^k\equiv 0\pmod{p}$ if $p-1\nmid k$, and $-1\pmod{p}$ if $p-1\mid k$.    My work is leading where I didn't expect to go. Here I assume $p$ id odd. First, if $p-1\mid k$, then we can wrike $k=(p-1)j$ for some $j$. But then $$ 1^k+\cdots+(p-1)^k\equiv 1^{(p-1)j}+\cdots+(p-1)^{(p-1)j}\equiv \underbrace{1+\cdots+1}_{p-1\text{ times}}=\frac{(p-1)p}{2}\equiv 0\pmod{p} $$ since $p-1$ is even.   Secondly, I suppose $p-1\nmid k$. WLOG, I can assume $0&lt;k&lt;p-1$, Since if $k=(p-1)j+r$ with $0&lt;r&lt;p-1$, then  $$ a^k\equiv a^{(p-1)j+r}\equiv a^r\pmod{p}. $$  Then if $g$ is a primitive root, $$ 1^k+\cdots+(p-1)^k=\sum_{i=1}^{p-1}(g^k)^i=\frac{g^k(1-g^{k(p-1)})}{1-g^k}. $$ Since $g$ is primitive, $p\nmid 1-g^k$, but $p\mid 1-g^{k(p-1)}$, so the above sum is again congruent to $0\pmod{p}$.  So in all cases, I get the sum is congruent to $0$ regardless. Have I messed up, or is there a typo? Thanks. For an odd prime $p$, prove that any primitive root $r$ of $p^n$ is also a primitive root of  $p$   So I have assumed $r$ have order $k$ modulo $p$ , So $k|p-1$.Then if I am able to show that $p-1|k$ then I am done .But I haven't been able to show that.Can anybody help me this method?Any other type of prove is also welcomed. Compare Debian (left) and Ubuntu (right):  $ ifconfig                                 $ ifconfig bash: ifconfig: command not found          eth0     Link encap ... $ which ifconfig                           $ which ifconfig $                                          /sbin/ifconfig   Then as superuser:  # ifconfig                                 # ifconfig eth0      Link encap ...                   eth0     Link encap ... # which ifconfig                           # which ifconfig /sbin/ifconfig                             /sbin/ifconfig   Furthermore:  # ls -l /sbin/ifconfig                     # ls -l /sbin/ifconfig -rwxr-xr-x 1 root root 68360 ...           -rwxr-xr-x 1 root root 68040 ...   It seems to me the only reason I cannot run ifconfig without superpowers on Debian is that it's not in my path. When I use /sbin/ifconfig it does work.   Is there any reason I should not add /usr/local/sbin:/usr/sbin:/sbin to my path on Debian? This is a personal computer, I am the only human user.    Versions used (uname -a): Ubuntu:   Linux ubuntu 3.13.0-51-generic #84-Ubuntu SMP Wed Apr 15 12:08:34 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux   Debian:  Linux debian 3.16.0-4-amd64 #1 SMP Debian 3.16.7-ckt11-1+deb8u3 (2015-08-04) x86_64 GNU/Linux