Can I build a transistor through two diodes?
Why can't two series-connected diodes act as a BJT?
Possible Duplicate:                If in a multiple linear regression (enter method) the general model isn't significant (F>.05) but one of the predictors is significant (β&lt;.05), should I consider it as a significant result? Evolutionarily speaking, why do humans have 46 chromosomes Electromagnetic Tensor in Cylindrical Coordinates I understand that the  is given by  $$F^{\mu\nu}\mapsto\begin{pmatrix}0 &amp; -E_{x} &amp; -E_{y} &amp; -E_{z}\\ E_{x} &amp; 0 &amp; -B_{z} &amp; B_{y}\\ E_{y} &amp; B_{z} &amp; 0 &amp; -B_{x}\\ E_{z} &amp; -B_{y} &amp; B_{x} &amp; 0 \end{pmatrix}$$  where $\mu$, $\nu$ can take the values {0,1,2,3} or {$t,x,y,z$}.  So, for example  $$F^{01}=F^{tx}=-E_x$$  My question is, what would the following expression be?  $$F^{t\rho}=?$$ or $$F^{z\rho}=?$$  where $\rho=\sqrt{x^{2}+y^{2}}$ is the radial coordinate in ?  And more generally, how can we construct the Electromagnetic Tensor in cylindrical coordinates? Where $\mu$, $\nu$ now take the values {$t,\rho,\varphi,z$}. divisibility question in abstract algebra over a field $d|n \Rightarrow x^{p^d} - x$ divides $x^{p^n} - x$ over $\mathbb{F}_{p}$ where $\mathbb{F}$ is a field.  Attempt:   $d|n \Rightarrow x^{p^d} - x$ divides $x^{p^n} - x \Rightarrow x^{p^d - 1} - 1$ divides $x^{p^n - 1} - 1 \Rightarrow p^d - 1$ divides $p^n - 1$ since $p^n - 1 = (p^d)^{\frac{n}{d}}-1$.  How does this look? Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere? I wanna prove that   "if $f: \mathbb{R}^n \to \mathbb{R}$ is continuous and satisfies $f=0$ almost everywhere (in the sense of Lebesgue measure), then, $f=0$ everywhere."  I am confident that the statement is true, but stuck with the proof. Also, is the statement true if the domain $\mathbb{R}^n$ is restricted to $\Omega \subseteq \mathbb{R}^n$ that contains a neighborhood of the origin "$0$"? How do I unlock all the other ships in the hangar? $f^{-1}([-\infty,r))$ measurable for all rational numbers $r$ If $X$ is measurable space, $f : X\to [-\infty,+\infty]$, function such that $f^{-1}([-\infty,r))$ measurable for all rational numbers $r$,prove than $f$ is measurable  I know that $f$ is measurable iff set $\{x\in X : f(x)&lt;a\}$ is measurable for all $a\in \mathbb{R}$ but for $a\in\mathbb{Q}$ I don't know how to proceed. Combine two columns into a list of all possible combinations of entries I have two columns such as:  a   1  b   2  c    and I need to combine them like:  a   1 a   2 b   1 b   2 c   1 c   2   Is it possible with a formula? As I understand this, firewalls (assuming default settings) deny all incoming traffic that has no prior corresponding outgoing traffic.  Based on  and , reverse SSH tunneling can be used to get around pesky firewall restrictions.  I would like to execute shell commands on a remote machine. The remote machine has its own firewall and is behind an additional firewall (router). It has an IP address like 192.168.1.126 (or something similar). I am not behind a firewall and I know the remote machine's IP address as seen from the Internet (not the 192.168.1.126 address). Additionally, I can ask someone to execute ssh (something) as root on the remote machine first.  Could anyone explain me, step by step, how reverse SSH tunneling works to get around the firewalls (local and remote machines' firewalls and the additional firewall between them)?  What is the role of the switches (-R, -f, -L, -N)? What happened to the Grid at the end of Tron Legacy? Closing as "off topic" has just gotten painful I know that useability and friendliness are given priority in the features implemented on StackExchange, but after using the new close-as-off-topic flow for the first time I would have to say I'm somewhat underwhelmed.  Why do we not have a simple It's off topic type reason? And why do I have to write half a book chapter as my custom close reason, especially when I can go back and edit the automatically posted comment so that it's way shorter?   This question complaint is prompted by  here on Meta. It's off topic, plain and simple. We now have a bunch of people wanting to close it, all potentially writing their own custom close reasons, it's just messy suboptimal. Regardless of how nice and friendly you want to be to the user, this particular question shouldn't need an explanation.    Does the off topic flow have to stay this way? Can we allow higher rep users to close as off topic without having to specify a (really long) custom reason, maybe have some canned reasons like we used to?  Edit: just to be clear, there are still three canned close reasons, but none of them were applicable to this example. The second one is closest, but does not appear to seek input... is quite different to It's a question, but doesn't belong here in any way, shape, or form. How to turn off Facebook notifications on Mac OS X? Complement of maximal multiplicative set is a prime ideal Let $R$ be a commutative ring with identity. I've been trying to prove the following:     If $S \subset R$ is a maximal multiplicative set, then $R \setminus S$ is a prime ideal of $R$.   I have spent some time in it, but nothing is coming to my mind. Any idea/solution will be appreciated. "like I" or "like me"? In high school we learned to say "than I" and "as I" because you could potentially add an "am" to the end of the sentence.  Examples:  "She is smarter than I."  (Think: "...than I am.") "He is as tall as I."  (Think "...as I am.")  So analogously, shouldn't it be "like I" as well:  "He is sincere, just like I."  (Think: "... like I am.")  But universally, it seems that we use "like me".  Where does this reasoning break down?  Is there history here? Review of a proof for De Moivre's theorem using mathematical induction The following is a rigorous proof of De Moivre's theorem by means of mathematical induction. The theorem put simply is that:  Any complex number, $z = a+bi$, on a cartesian plane can be expressed in polar form, where $a=r\cos\theta$ and $b=r\sin\theta$ and $r$ is the absolute distance from the origin to the point $z$. In light of this, the expression for the complex number $z$ in polar form is $z=r(\cos\theta+i\sin\theta)$ In order to find the $n^{th}$ power of $z$, the following rule applies: $$\displaystyle z^n=(r(\cos\theta+i\sin\theta))^n=r^n(\cos n\theta+i\sin n\theta)$$ where $n\in\mathbb N$ (I have confined $n$ to the natural numbers given that I intend on using mathematical induction to prove the theorem.  Base step: We must prove that what is stated is true for $n=1$, hence $$z^1=r^1(\cos 1\cdot\theta+i\sin1\cdot \theta)$$ $$=r(\cos\theta+i\sin\theta)$$ which is true. Next we assume it is true for $n=k$, and therefore proceed to the inductive step. Inductive step: When calculating $z^{n+1}$, it's the same as calculating $z^nz$, hence $$z^{n+1}=(r^n(\cos n\theta + i\sin n\theta))(r(\cos \theta+i\sin \theta))$$ $$=r^nr(\cos n\theta+i\sin n\theta)(\cos\theta +i\sin \theta)$$ $$=r^{n+1}(\cos n\theta\cdot\cos\theta+\cos n\theta \cdot i\sin\theta+i\sin n\theta\cdot\cos\theta+i^2\sin n\theta\cdot\sin\theta)$$ from here, $i^2=-1$, and therefore $+i^2\sin n\theta\cdot\sin\theta$ becomes $-\sin n\theta\cdot\sin\theta$. In addition to this, the following trigonometric identities will be used: $$\sin(n\theta + \theta) = \sin n\theta\cdot\cos\theta+\cos n\theta\cdot\sin\theta$$ $$or$$ $$k\sin(n \theta+\theta)=k\sin n \theta\cdot\cos \theta + \cos n\theta\cdot k\sin\theta$$ $$and$$ $$\cos(n \theta + \theta)=\cos n\theta\cdot\cos\theta-\sin n\theta\cdot\sin\theta$$ by using these, the original equation has now become $$=r^{n+1}(\cos(n \theta + \theta) + i\sin(n \theta + \theta))$$ then, after factoring out $\theta$, the theorem becomes $$=r^{n+1}(\cos((n+1)\theta)+i\sin((n+1)\theta))$$ which completes the proof. Question: is this proof correct all the way through? Or have I missed any conditions? If all is well in the case of this proof, could somebody aid me in proving it for $\{n|n\in\mathbb R,n\geq1\}$ Google Spreadsheets: IF not working I have problems with my IF command in Google Sheets. If gives #ERROR! all the time. See this simple test:    Not even if I put in the number directly and avoid references:    Am I using the IF wrong? Or what could such a problem be? This example is from a new document. {5,15,25,35} is a group under multiplication mod 40 Show that the set $\{5,15,25,35\}$ is a group under multiplication modulo $40$. What is the identity element of this group. Can you see any relationship between this group and $\mathbb U(8)$?   I am very stuck on this question and I think my knowledge of abstract algebra is my liability at the moment. Right now I'm most confused by the fact that I learned: An element of a group of this nature must be relatively prime with the working mod.  Obviously here this is not the case, so I don't really know where to begin.  Do I need a Cayley Table?  Thanks. I followed Mike's solution from my first question:    My next question is how to add entries (for the abstract and acknowledgements pages) into the table of contents. How to treat differentials and infinitesimals? In my Calculus class, my math teacher said that differentials such as $dx$ are not numbers, and should not be treated as such.  In my physics class, it seems like we treat differentials exactly like numbers, and my physics teacher even said that they are in essence very small numbers.   Can someone give me an explanation which satisfies both classes, or do I just have to accept that the differentials are treated differently in different courses?  P.S. I took Calculus 2 so please try to keep the answers around that level.  P.S.S. Feel free to edit the tags if you think it is appropriate. I tried installing VLC Player yesterday, and I got the Requires installation of untrusted packages error.  I searched for hours for a solution to this problem, and finally came upon a suggestion that said to change servers for downloading updates from.  I did this, and it gave me a 404 error when I clicked on "Check" in the Update Manager.  I tried switching my server back to the main one (and after that, several other ones), but I am now still getting a 404 error:   And the other error I get when downloading or updating:   Edit: Output of cat /etc/apt/sources.list:  deb-src http://us.archive.ubuntu.com/ubuntu/ precise main restricted #Added by software-properties  # See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to # newer versions of the distribution. deb http://us.archive.ubuntu.com/ubuntu/ precise main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise multiverse universe #Added by software-properties  ## Major bug fix updates produced after the final release of the ## distribution. deb http://us.archive.ubuntu.com/ubuntu/ precise-updates main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-updates restricted main multiverse universe #Added by software-properties  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu ## team. Also, please note that software in universe WILL NOT receive any ## review or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ precise universe deb http://us.archive.ubuntu.com/ubuntu/ precise-updates universe  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu  ## team, and may not be under a free licence. Please satisfy yourself as to  ## your rights to use the software. Also, please note that software in  ## multiverse WILL NOT receive any review or updates from the Ubuntu ## security team.  ## N.B. software from this repository may not have been tested as ## extensively as that contained in the main release, although it includes ## newer versions of some applications which may provide useful features. ## Also, please note that software in backports WILL NOT receive any review ## or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse #Added by software-properties  deb http://us.archive.ubuntu.com/ubuntu/ precise-security main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-security restricted main multiverse universe #Added by software-properties deb http://us.archive.ubuntu.com/ubuntu/ precise-security universe  ## Uncomment the following two lines to add software from Canonical's ## 'partner' repository. ## This software is not part of Ubuntu, but is offered by Canonical and the ## respective vendors as a service to Ubuntu users. deb http://archive.canonical.com/ubuntu precise partner deb-src http://archive.canonical.com/ubuntu precise partner  ## This software is not part of Ubuntu, but is offered by third-party ## developers who want to ship their latest software.