In the story of Star Wars there have been instances where the specific Sith female was considered a "Sith Witch." However there have also been instances where the Sith female was just a Sith.  Now my question is... is "Sith Witch" an actual title bestowed upon certain Sith females that have completed some achievement, or is "Sith Witch" a general term for all Sith females?  Also any other terms and info about the title would be most helpful.
Would a female Jedi be referred to as Jedi Mistress instead of Jedi Master? Likewise would a Sith female be referred to as a Sith Lady instead of a Sith Lord?
It's stated that the gradient of:  $$\frac{1}{2}x^TAx - b^Tx +c$$  is   $$\frac{1}{2}A^Tx + \frac{1}{2}Ax - b$$  How do you grind out this equation? Or specifically, how do you get from $x^TAx$ to $A^Tx + Ax$? Representation of electromagnetic wave? In Representation of electromagnetic waves we show both electric and magnetic fields perpendicular to each other and having zero magnitude at one point and maximum at other point. This representation and understanding of EM waves violating law of conservation of energy... Identify GoogleTv from Android app Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer Let $a,b$ be positive integers.  When $$k = \frac{a^2 + b^2}{ab+1}$$ is an integer, it is a square.    Proof 1: (Ngô Bảo Châu): Rearrange to get $a^2-akb+b^2-k=0$, as a quadratic in $a$ this has two values: $a$ and $kb - a = (b^2-k)/a$. (The second root is determined in two different ways from the expansion $(x-r_1)(x-r_2) = x^2 - (r_1 + r_2)x + r_1 r_2$.)  Now suppose we have $a,b$ such that $k$ is an integer but not a square, by the investigation about roots we have that the second root is a nonzero integer since $k,b,a$ are integers and $k \not = b^2$, futhermore it is positive which is easily seen from its defining equation.  WLOG assume $a \ge b$ so that the second root is strictly smaller than $a$. This leads to a decent, replacing $a$ with the second root.    Proof 2 (Don Zagier): Apply reduction theory (specifically, Sätze 1 and 2 of Section 13 of my book on quadratic fields) to the quadratic form $x^2 + kxy + y^2$, which is the unique reduced quadratic form in its equivalence class.    Note that Proof 2 is pretty much the same as Proof 1 when written out in explicit detail, but I could not read Zagier's book because I cannot read German.  I would like to know more approaches to this and other alternative proofs of this result if possible! Thanks in advance.  I would also be interested in related problems (especially easier ones of a similar nature) and texts which cover the reduction theory in English. Digitizing Free Satellite Imagery in QGIS without getting Alignment issues with Openlayers Plugin How can I get all three Kalos starters? Currently the migration path options from SO are:   Meta.SO Serverfault SuperUser Webmasters Programmers   If we are going to be limited to 5 options, shouldn't we periodically re-evaluate which sites are most appropriate?   (10k only) indicate that the top sites for the last 90 days are:   Superuser - 564 - 5% rejected ServerFault - 278 - 10% rejected Tex - 157 - 13% rejected DBA - 144 - 2% rejected Sharepoint - 127 - 1% rejected Programmers - 126 - 26% rejected CodeReview - 100 - 3% rejected Meta.SO - 81 - 18% rejected Wordpress - 75 - 14% rejected Webmasters - 58 - 8% rejected   All these migrations for sites out of the list required a flag and a moderator to process it.  This is just extra work for the mod team!  If we had the top 5 destinations by volume as the 5 options, we would have had a net savings of 160 flags to be processed.  I suspect we will actually see these numbers change quite a bit if it's easier for users to put questions in the appropriate spot without moderator intervention.  Can we have a review of the migration path list based on migration volume?  Think of the flags! .NET - What's the best way to implement a "catch all exceptions handler" I'm wondering what the best way is to have a "if all else fails catch it".  I mean, you're handling as much exceptions as possible in your application, but still there are bound to be bugs, so I need to have something that catches all unhandled exceptions so I can collect information and store them in a database or submit them to a web service.  Does the AppDomain.CurrentDomain.UnhandledException event capture everything? Even if the application is multithreaded?  Side note: Windows Vista exposes native API functions that allow any application to recover itself after a crash... can't think of the name now... but I'd rather not use it, as many of our users are still using Windows XP. Can a regular salaried (w2) employee opt to pay quarterly taxes? As a consultant, I got used to paying quarterly taxes. Now that I'm a regular w2 salaried employee, I'm subject to normal withholding on each pay statement. I would like to keep making exact quarterly payments instead of having a (generally incorrect) amount held back each paycheck.   I haven't been able to find any information on the 1040-es that would make me think I'm ineligible to do so, but I suspect that it may be the case. I'd have to stop paycheck withholdings by updating my w4 to either have a high number of exemptions or mark myself as exempt from taxes, which I assume is where the rub lies.   So, as a regular salaryman, is it possible for me to pay taxes exclusively through quarterly payments in lieu of traditional withholdings? Badges loading broken in election statistics We have an  and I noticed the badges are not loading in the election statistics like they should be. It just hangs forever loading badge information:    Unfortunately I blew off reporting this for a couple days figuring it would resolve itself, but it doesn't seem to be a temporary problem. Converting case of all values in all fields of table using ArcPy & Python? Why doesn't a bike/bicycle fall if going with a high speed? When I run this command :  apt install libkf5*   I get the following error :  Unable to locate package libkf5*    I'm sure that the packages whose names start with libkf5 exist (tab-completion says so) . So the problem is not about the absence of those packages.(Note the asterisk at the end of that error message , the wildcard's not working at all) I use apt v.1.9. Thanks in advance. I usually disconnect my cellphone from the charger some time after it's fully charged because I'm afraid the battery could lose capacity over time if I don't. However, I believe modern electronics should be able to handle this kind of scenario and automatically stop charging the battery once it's full. Does this apply to modern Android phones? Or do I need to continue disconnecting it all the time? How to determine whether a unique factorization domain is a principal ideal domain? Could someone please provide an example of a unique factorization domain that is not a principal ideal domain?  Furthermore, is there some way to determine whether a UFD is a PID? Answering beyond the question's scope Is answering beyond the scope of the question a valid thing? Or should we just stick to the question asked and ignore any potential bugs which might be present (of course OP is unaware of that, as of now).  To make myself more clear, please have a look at this .  There are 3 answers which talk about the issue asked and that's it. If you look at my answer, I've added an additional point about a potential bug which the OP has missed now (may find out later). So is it a good thing to point out such potential bugs or not? Should this practice be encouraged? Binary Bomb Phase 5 - lookup table translation -> string compare Using expect to pass a password to ssh How to remove duplicate values from a multi-dimensional array in PHP How can I remove duplicate values from a multi-dimensional array in PHP?  Example array:  Array (     [0] =&gt; Array     (         [0] =&gt; abc         [1] =&gt; def     )      [1] =&gt; Array     (         [0] =&gt; ghi         [1] =&gt; jkl     )      [2] =&gt; Array     (         [0] =&gt; mno         [1] =&gt; pql     )      [3] =&gt; Array     (         [0] =&gt; abc         [1] =&gt; def     )      [4] =&gt; Array     (         [0] =&gt; ghi         [1] =&gt; jkl     )      [5] =&gt; Array     (         [0] =&gt; mno         [1] =&gt; pql     )  ) Cardinality of the set of all (real) discontinuous functions This is a question from the book Introduction to Set Theory (Hrbacek and Jech), chapter 5, question 2.6.     (Show that) The cardinality of the set of all discontinuous functions is $2^{2^{\aleph_0}}$. [Hint: Using exercise 2.5, show that $|\mathbb{R}^\mathbb{R}-C|=2^{2^{\aleph_0}}$ whenever $|C|\leq 2^{\aleph_0}$.]   Exercise 2.5, as referred to in the hint, provides the following result:     For $n&gt;0$, $n \cdot 2^{2^{\aleph_0}} = \aleph_0 \cdot 2^{2^{\aleph_0}} = 2^{\aleph_0} \cdot 2^{2^{\aleph_0}} = 2^{2^{\aleph_0}} \cdot 2^{2^{\aleph_0}} = (2^{2^{\aleph_0}})^n = (2^{2^{\aleph_0}})^{\aleph_0} = (2^{2^{\aleph_0}})^{2^{\aleph_0}}=2^{2^{\aleph_0}}$.   The only way I could answer this question was by making use of two theorems stated later  in the same textbook. First, it is easy to prove that $|\mathbb{R}^\mathbb{R}-C|$ is an infinite set, since if it was finite we would have \begin{equation}2^{2^{\aleph_0}}=|\mathbb{R}^\mathbb{R}|=|\mathbb{R}^\mathbb{R}-C|+|C| \leq n+2^{\aleph_0}=2^{\aleph_0}&lt; 2^{2^{\aleph_0}},\end{equation}which is a contradiction. Now I make use of a theorem requiring the axiom of choice: For every infinite set $S$ there exists a unique aleph $\aleph_\alpha$ such that $|S|=\aleph_\alpha$. So I let $|\mathbb{R}^\mathbb{R}-C|=\aleph_\alpha$ for some ordinal $\alpha$. Now assume $\aleph_\alpha &lt; 2^{2^{\aleph_0}}$. Here I make use of another theorem, which i am not sure I am allowed to do: For every $\alpha$ and $\beta$ such that $\alpha \leq \beta$, we have $\aleph_\alpha+\aleph_\beta=\aleph_\beta$. So I basically then say either $|\mathbb{R}^\mathbb{R}-C|+|C|=\aleph_\alpha$ or $|\mathbb{R}^\mathbb{R}-C|+|C|=2^{\aleph_0}$, depending on whether $\aleph_\alpha \leq 2^{\aleph_0}$ or vice-versa. The assumption I am making is that $2^{\aleph_0}=\aleph_1$, which as I understand it is basically equivalent to the continuum hypothesis, as we are saying that the least uncountable number is $\aleph_1$ (but by the previous theorem requiring the axiom of choice this seems reasonable?). So anyway assuming I can do that, we again have a contradiction since then we are saying $|\mathbb{R}^\mathbb{R}|=2^{\aleph_0}&lt;2^{2^{\aleph_0}}$ or $|\mathbb{R}^\mathbb{R}|=\aleph_\alpha &lt; 2^{2^{\aleph_0}}$.  My main problem with my proof is that I am not making use of the result given in exercise 2.5 as suggested in the hint. Can anyone help with a proof making use of this result (stated in the second block quote above).