In the The Hobbit and The Lord of the Rings series, there are many descriptions of dwarves. But there isn't any mention of female dwarves. Are there any in-universe mentions of female dwarves? If there aren't, then how do they reproduce? Is there any explanation from Tolkien?
I may have missed it with the 3D, but I could have sworn I saw what I suspect was a lady Dwarf or two running from the Erebor in the beginning of the Hobbit, but they didn't seem bearded.    If dwarf women aren't bearded, then was Aragorn just kidding in the Two Towers (movie) when he intimated that they all had beards?    It's also stated by Tolkien in appendix A to The Lord of the Rings that female dwarves appear identical to males and we can assume they are also born with beards, just like their male counterparts.
I've been modeling an F-15, but when I rotate the flaps on Y-Axis the Flaps offset from the wing and they look like they are about to fall out, so I end up correcting it by rotating in the X and Z-axis to align them correctly.  However when I rotate them back from the Y-Axis they look distorted again because I did rotations on the X and Z axis. I tried riding it, no help. I saw something about custom orientation to fix it but that was not clearly explained and it was done on an ideal plane that was (0,0,0); mine is pre-rotated on all axis.   I'll take scripts if needed and I'm using Blender 2.8.  When I rotate it on the Y-Axis:    Fixing it using X and Z rotation:    Rotating it back on the Y distorted it again:    Here's the wing with ailerons and flaps: I'm being asked to find 2 subgroups of $S_3$, one of which is normal and one that isn't normal. I guess, to find the non normal subgroup is easier. I would do this by trial and error, but since the group is $S_3$ and easily visualizable, I guess that there should be a geometrical property that makes it easy to find a normal subgroup. Any of you guys know one? Or should I try this by brute force? Multiple outputs for beamer handouts I'm currently generating some presentations with beamer for students of my course. Some like to print the material, so I created a handout. Some students prefer to have 2,3,4,6 etc. pages per sheet of A4 paper. How can I go about to automatize the following code, so that it outputs 4 different files in 1x2,1x3,2x2,2x3 format?  I'd like to avoid having to compile it again everytime for the different formats.  \documentclass[a4paper]{article} \usepackage{pdfpages}  \begin{document} \includepdf[pages=1-last,nup=1x2,landscape=false,frame=true,             noautoscale=false,scale=1,delta=0mm 5mm]{Pres7Chap13-Handout.pdf} \end{document} Finding $\int_0^{\infty}xe^{-\lambda x} \, dx$ How to integrate:  $$\int_0^\infty x \, \lambda e^{-\lambda x} \, dx$$    I tried using integration by parts:  Let $u = x$ and $dv = \lambda e^{-\lambda x} \, dx$  Then $du = dx$  And $v = - \lambda e ^{-\lambda x}$  Correct so far?   Then   $$\begin{aligned} uv - \int v \, du &amp;= -\lambda x e^{-\lambda x} - \int (- \lambda e^{- \lambda x}) dx \\ &amp;= -\lambda x e^{-\lambda x} - \lambda e^{-\lambda x} \end{aligned}$$    The correct answer from lecture notes      UPDATE 2  Let $u=\lambda x$ and $dv = e^{-\lambda x} dx$  Then $du = \lambda \, dx$  $$dv = e^{-\lambda x} \, dx$$  Let $y = -\lambda x$  Then $dy = -\lambda \, dx$  So $dx = -\frac{1}{\lambda} dy$  $$\begin{aligned} v &amp;= \int e^u \cdot - \frac{1}{\lambda} du \\ &amp;= - \frac{1}{\lambda} e^{-\lambda x} \end{aligned}$$  But here I seem to have an extra $- \frac{1}{\lambda}$ in $v$?  If I continue using integration by parts, I get:   $$-x e^{-\lambda x} + \color{red}{\frac{1}{\lambda}} \int e^{-\lambda x} \, dx$$ What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic? Evidently, $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ has order $4$, but I think it's infinite.   The four cosets are listed as $(0,0) +  \langle (2,2) \rangle$, $(0,1) +  \langle (2,2) \rangle$, $(1,0)+  \langle (2,2) \rangle$ and $(1,1) +  \langle (2,2) \rangle$. However, $(2,0)$ doesn't appear to be in any of these cosets. Maybe the answer I'm being told is wrong. What is a meta for? A guest at my house over the weekend stood puzzled next to my driveway. &quot;What is that for?&quot; she asked, pointing to a framework of 2x4s and hardware cloth perched on an old tire amid piles of sand. &quot;Sifter.&quot; I said. &quot;For what?&quot; &quot;For sifting gravel.&quot; &quot;Why?&quot; &quot;To line walking paths, such as the one you're standing on...&quot; Spend enough time working with something, and it's easy to forget how strange and unnatural your makeshift tooling can appear to those unfamiliar with it.  Such is the nature of these meta sites. For 5 years, we've been directing folks to them for discussion and feedback, to commune with their community, hash out misunderstandings, propose changes and document the current state of things. And... We haven't always been good about helping them get past the initial shock and confusion of dealing with this system. This has manifested in several unfortunate behaviors:  Downvoting of legitimate support questions - those that are not duplicates and reflect an actual bug or honest misunderstanding of how the system operates. Folks who are acting in good faith should be treated as such - , not shutting them down.  Closing questions that seek input and discussion from the community - in hindsight, adding &quot;primarily opinion based&quot; as a close reason on meta sites was... a terrible idea. The old &quot;not constructive&quot; close reason made some sense for rants and so on, but for a discussion site closing down questions that solicit opinions is just silly. Here on MSE, we prefer the following off-topic reason instead:  This question does not appear to seek input and discussion from the community. If you have encountered a problem on one of our sites, please describe it in detail. See also:    The perception that Stack Exchange is disrupting the normal operation of the site by talking about future plans - even when those plans involve the community. I talked about this a bit more on , but seeing this kind of backlash toward folks at the company who were trying to be open and receptive to discussion about what they were doing was kinda disheartening - we need to be doing more of that, not less.  A reluctance to ask questions about asking questions - which is about as meta as you can get, and yet we probably get more of these via email than we see on meta, while being the least-qualified to answer them well.   After an increasing number of complaints from both core users and moderators on a number of sites, we're taking a hard look at how we can improve this situation... Starting with a change to :  Meta is for...  ...$SiteName users to communicate with each other about $SiteName (asking questions about how the websites work, or about policies and community decisions) ...$SiteName  users to communicate with Stack Exchange the company (posting bugs, suggesting improvements, or proposing new features), and ...Stack Exchange to communicate with the community (soliciting feedback on new ideas or features, or discussing policies that affect the whole network)  Lots of topics are fair game, as long as they are about the Stack Exchange family of Q&amp;A sites in some way. Any issue that concerns the core Stack Exchange engine that runs all Stack Exchange websites is welcome here.  This replaces the previous bullet list of specific topics, and aims to outline broad purposes with examples for clarification rather than constraining the scope to those examples. So... that's a start. But a documentation change isn't going to change misconceptions that've already built up among newer users. So I'm asking y'all for help: What do you think meta should be used for, and how can we better communicate this intent to new users? Showing $\sum\limits_{p \in P} \frac{1}{p}$ where $P$ is the set of all primes is divergent Assigning Float Pointers in C Is the Ohm's law violated here? And also why is electricity generated at 11,000 V in India? I'm trying to prove that  $$ \left| \frac{1}{x}-\frac{1}{y} \right| $$  is a metric on $X = \mathbb R^+$.  The properties of non-negativity and symmetry are obvious (do I actually even need to prove them?), but the tricky one is, as usual the inequality property, i.e.  $$ d(x,z) \le d(x,y) + d(y,z) \text{ for any } z \in X. $$  So, ok, I have that  $$ d(x,z) \le d(x,y) + d(y,z) \\ \iff \left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right| \\ \iff \left| \frac{1}{x} \right|- \left| \frac{1}{z} \right| \le \left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right| $$  ...and that's about as far as I've gotten–which is to say, not very far. I also tried multiplying both sides by $ \left| \frac{1}{x}-\frac{1}{z} \right| $, but that wasn't very fruitful. If someone could point me in the right direction, it'd be greatly appreciated. Thanks. I need to make my (BibTeX) references section appear in the table of contents of my LaTeX document (documentclass: article), with section numbering too.  My approach until now has been making a new section and including the bibliography (references.bib) at that point:  \section{References} \bibliography{references}   However, the final document shows both the section title that I have written and the section title that BibTeX writes, which is quite redundant and I definitely dislike.  How can I either remove BibTeX's section title, or make the BibTeX bibliography appear in the table of contents without making a new section?  If I were to make the BibTeX bibliography appear in the table of contents without making a new section, how could I assure that the section title that BibTeX writes looks exactly like sections typeset with \section? If someone could claim me as a dependent, but they will not, am I required to check the "Someone can claim me..." box on my 1040? Let's say that an adult is living with his parents.  He meets all of the  of his parents.  Now let's say that he wants to file a tax return and claim the , as he did not receive any of the stimulus payments in 2020.  His parents decide not to claim him as a dependent on their taxes.  Can he leave the &quot;Someone can claim me as a dependent&quot; box on his  unchecked and claim the Recovery Rebate Credit?  This does not apply to me, but it could apply to many people this year, with the new Recovery Rebate Credit putting people in the situation where it could be advantageous to not be claimed as a dependent. Surprisingly, the  do not provide any guidance on checking this box in any way, that I can find.  I have seen it asserted many times in answers and comments here on Money.SE that because the form says, &quot;Someone CAN claim...,&quot; the box must be checked whether or not anyone actually will claim them.  But I have not yet found this explicitly stated in any official IRS website or publication.  The ideal answer here will cite an official source. I know enough amount of set theory and logic to study grad-level math. However, I don't know more advanced set theory and logic, such as the ones on Kunen's or Shoenfield's texts. Although it's good to learn such advanced topics, I may not have enough time to do so, since I will probably put my emphasis on algebra, analysis or geometry as well as mathematical physics.   Although how much set theory and logic I should learn is totally up to what sort of analysis, algebra or geometry I will study, I want to know how much of them typical competitive algebraists/analysts/geometers know. If you are one of them, how much do you know? How to fit a tight ellipse around nodes I have a set of two nodes and I would like to draw tight ellipses around them in my tikz picture. Note that this is part of a beamer presentation.    I have attached an image that illustrates the wanted effect.    Here is what I have so far:  \documentclass[10pt,aspectratio=1610]{beamer} \usepackage{tikz} \usetikzlibrary{shapes,arrows,backgrounds,fit,positioning}  \begin{document}  \tikzset{res/.style={ellipse,draw,minimum height=0.5cm,minimum width=0.8cm}} \tikzset{literal/.style={rectangle,draw,minimum height=0.5cm,minimum width=0.8cm,text width = 1.2 cm, align = center}}  \begin{frame}[fragile]{Example}{} \begin{tikzpicture}[node distance = 2 cm,auto, ] \node[res,] (obs1) {\footnotesize :obs1} ; \node[res, left = 1cm of obs1] (shop1) {\footnotesize :shop1} ; \node[literal, left = 1cm of shop1] (shopName1) {\footnotesize ``Barnes \&amp; Noble''} ; \node[res, above of = shop1] (book1) {\footnotesize :book1} ; \node[literal, left = 1cm of book1] (bookName1) {\footnotesize ``Dune''} ; \node[res, below of = obs1] (obs2) {\footnotesize :obs2} ; \node[res, left = 1cm of obs2] (shop2) {\footnotesize :shop2} ; \node[literal, left = 1cm of shop2] (shopName2) {\footnotesize ``Amazon''} ; \node[res, below of = shop2] (book2) {\footnotesize :book2} ; \node[literal, left = 1cm of book2] (bookName2) {\footnotesize ``Dracula''} ; \node[literal, below of = obs2] (measure2) {\footnotesize 12} ; \node[literal, above of = obs1] (measure1) {\footnotesize 7} ; \node[literal, right = 1cm of obs1] (monthName) {\footnotesize ``January''} ; \node[literal, right = 1cm of measure1] (yearNum) {\footnotesize ``2016''} ; \node[res, right = 1cm of monthName] (month) {\footnotesize :january2016} ; \node[res, above of = month] (year) {\footnotesize :2016} ; \node[res, below of = month] (day) {\footnotesize :date31012016} ;  \path[-&gt;,draw]     (obs1) edge node[midway,above=-6pt,fill=white,inner sep=0pt] {\footnotesize :shop} (shop1)     (obs2) edge node[midway,above=-6pt,fill=white,inner sep=0pt] {\footnotesize :shop} (shop2)      (obs1) edge node[midway,above=-6pt,fill=white] {\footnotesize :book} (book1)     (obs2) edge node[midway,above=-6pt,fill=white] {\footnotesize :book} (book2)      (book1) edge node[midway,above=-6pt,fill=white,inner sep=0pt] {\footnotesize :name} (bookName1)     (book2) edge node[midway,above=-6pt,fill=white,inner sep=0pt] {\footnotesize :name} (bookName2)      (shop1) edge node[midway,above=-6pt,fill=white] (title1) {\footnotesize :title} (shopName1)     (shop2) edge node[midway,above=-6pt,fill=white] (title2) {\footnotesize :title} (shopName2)      (obs1) edge node[midway,above=-6pt,fill=white] {\footnotesize :price} (measure1)     (obs2) edge node[midway,above=-6pt,fill=white] {\footnotesize :price} (measure2)      (obs1) edge node[midway,above=-6pt,fill=white]  {\footnotesize :date} (day)     (obs2) edge node[midway,above=-6pt,fill=white] {\footnotesize :date} (day)      (day) edge node[midway,above=-6pt,fill=white] {\footnotesize skos:broader} (month)     (month) edge node[midway,above=-6pt,fill=white] {\footnotesize skos:broader} (year)      (month) edge node[midway,above=-6pt,fill=white,inner sep=0pt] {\footnotesize :month} (monthName)     (year) edge node[midway,above=-6pt,fill=white] {\footnotesize :year} (yearNum)     ;  \begin{pgfonlayer}{background}   \node[fit=(shopName1)(shop1), fill=violet!30,ellipse] {};   \node[fit=(shopName2)(shop2), fill=violet!30,ellipse] {};   \node[fit=(bookName2)(book2), fill=violet!30,ellipse] {};   \node[fit=(bookName1)(book1), fill=violet!30,ellipse] {};   \node[fit=(measure1)(obs1), fill=blue!30,ellipse] {};   \node[fit=(measure2)(obs2), fill=blue!30,ellipse] {};   \node[fit=(year)(yearNum), fill=green!30,ellipse] {};   \node[fit=(month)(monthName), fill=green!30,ellipse] {}; \end{pgfonlayer} \end{tikzpicture} \end{frame} \end{document}   Here is the result that it produce    Note how the ellipses do not fit the nodes but cover much more. How can I create a tight ellipse around a pair of nodes? Will my Chinese visa still be valid if I renew my passport? Will my Chinese visa still be valid if I renew my passport? If so how does that work?  I have heard that you can travel with your new passport and just show the old passport with the valid visa when entering China. Has anyone done that? Recently?   I have also been told that you have to get a new visa, which seems somewhat logical but frustrating, especially when my Chinese visa is only a few months old.  My Chinese visa was issued in late Nov 2014 and I heard the rules changed between the US and China. My visa says it's good for 10 years and my US passport expires in 5. TikZ: Named nodes in nested `pic`s I am using the new TikZ/PGF 3.0 pic feature.  I use them heavily, including using a pic inside another pic.  The problem is that Tikz sometimes cannot find the node names of nested pics.  I expect the following to work:  \documentclass{standalone} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture} \tikzset{complex/.pic={   \node(re) {re};   \node[right=0mm of re](im) {im}; }} \tikzset{su3v/.pic={   \path pic(c0) {complex};   \path pic[right=1mm of c0im](c1) {complex};   \path pic[right=1mm of c1im](c2) {complex}; }} \tikzset{spinor/.pic={   \path pic(v0) {su3v};   \path pic[below=2mm of v0c2re](v1) {su3v};   \path pic[below=2mm of v1c2re](v2) {su3v};   \path pic[below=2mm of v2c2re](v3) {su3v}; }}  \path pic {su3v};       % Works \path pic(name) {su3v}; % ! Package pgf Error: No shape named namec0im is known. \path pic {spinor};     % ! Package pgf Error: No shape named v0c1im is known. \end{tikzpicture} \end{document}   What is wrong here? JQ (GET ID based on NAME) I get a long list of such arrays  {     "id": "byu6g6c4cjys5mdkg5znh8ju8c",     "create_at": 1511875272294,     "update_at": 1511875272294,     "delete_at": 0,     "display_name": "BMA",     "name": "BMA",     "description": "",     "email": "aleksandar.ivanov@random.com",     "type": "O",     "company_name": "",     "allowed_domains": "",     "invite_id": "gdgz1tbxuinntx1fbr1ax7kehy",     "allow_open_invite": false,     "scheme_id": null   }   I want to get by JQ only the ID where the name is BMA. At the moment I parse " jq -r '.[]["name"]" and I can filter the output from curl by name and I will get "BMA" and also 100 other names, but I need to filter only the ID where name is =BMA. Any ideas? Explain Root Mean Square Error to non-technical audience Trying to remember the name of a grade-school book about an alien in a cereal box When I was a kid (Grade school, Elementary, can't remember the exact grade, but it was between 1992 and 1999) I read a book about a kid who found an alien in his cereal.  This alien informed him that he was there to defeat an evil threat to Earth, that took the form of the school's most popular student.  The alien came with a gun that did nothing, and the alien in the popular kid disguise had the power to make the kid's fingernails bleed by damaging his nerve endings.  In the end, it was revealed that the evil alien had a huge craving for, and vulnerability towards, pizza flakes, and was defeated by gorging himself on them and then exploding. Benefits & Practicality of Virtual Machines I have been living under a rock for the past 5 - 8 years, and am just now getting up to speed with virtualization, virtual machines and platforms like VMware or VirtualBox.  I think I am starting to get them, but there are two concepts about VMs that I'm just choking on for some reason; one has to do with their intrinsic benefit to the enterprise, and the other has to do with their practicality when being used.  So I understand that you can have multiple VMs running on the same physical machine, all doing their own "thing" as if they were separate machines. So let's say I want to make a nice little virtual network of servers in my home office so I can have a big sandbox to play inside of for all my projects. I set up 2 physical machines as servers, and on each of them I have, say, 4 virtual machines running (1 might be an app server, another might be a RDBMS, another might be a message broker, etc.).   Besides saving me money (as I only have to provide 2 physical machines instead of buying 8 servers), what instrinsic benefit/purpose do these VMs serve here? I don't care how clever virtual machines are, if my computer only has 8GB of RAM, and I have 4 VMs running on it, those VMs only get 8GB of RAM to share between them. Putting 4 VMs on my server doesn't endow it with 4 times that amount of RAM! So, as far as I see it, VMs save you money on hardware, but just end up bogging down that hardware as you have multiple machines competing over the same pool of resources. What am I missing here? Can VMs communicate with each other over your network using high-level protocols like TCP/IP, HTTP, FTP, etc.? Otherwise, it just doesn't make sense to implement all these VMs if you have to feed them separate and independent chunks of data/requests to process.