He staggers, and the security guard helps him stay on his feet. What makes Loki stagger?
In the Avengers movie, why is Loki sweating and weak when he first arrives on Earth, in the SHIELD base?
Command for argmin or argmax? How can you get the argmin or argmax in Latex? Two solutions I found are:  \underset{x}{\operatorname{argmax}}   \DeclareMathOperator*{\argmin}{arg\,min}   Any other ideas?  [1]   [2] Are the LIGO observations proof of a black hole merger, and what happened to the black holes? How do I properly install a system app given its .apk? I removed a system app (com.android.mms) and I have the .apk needed to restore it, however it won't install through the standard channels (running the .apk gives me "application not installed"). What's the proper way to install a system app's .apk? How to get rights of admin after I disabled all admin accounts in my computer I have a pretty simple table that needs to span multiple pages. This seems like a job for either the / package or the  package.   The voting on the answers to this  suggest that longtable is the preferred package, yet xtab is much newer and has been revised since that question was asked.  What are the differences between xtab and longtable and when is one preferable to the other? Difference between Analytic and Holomorphic function A function $f : \mathbb{C} \rightarrow \mathbb{C}$ is said to be holomorphic in an open set $A \subset \mathbb{C}$ if it is differentiable at each point of the set $A$.  The function $f : \mathbb{C} \rightarrow \mathbb{C}$ is said to be analytic if it has power series representation.  We can prove that the two concepts are same for a single variable complex functions. So why these two different terms? Is there any difference between these two concepts in general, please give example.  Thank you for your help. What permissions should my website files/folders have on a Linux webserver? how to redirect output to multiple log files Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that  $$ m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}. $$  My attempt is use inclusion to show. Let $a \in m\mathbb{Z}+n\mathbb{Z}$. Then we have $a=ms+nt$. Since $d=\gcd(m,n)$, by Bézout's Lemma, we have $d=ms+nt$ for some integers $s$, $n$. Hence, we have $a=ms+nt=d \in d\mathbb{Z}$. Let $a \in d \mathbb{Z}$. Then we have $a=db=msb+ntb \in m\mathbb{Z}+n\mathbb{Z}$. Is my proof valid?  Remark: the following is the part 2 of the question. Prove that $m\mathbb{Z}\cap n\mathbb{Z}=\frac{mn}{d}\mathbb{Z}$. This one I have no idea how to start Remove Meta Privilege for MSE (only) Can I see a list of gyms I left a pokemon at? I am thinking of building a model predicting a ratio $a/b$, where $a \le b$ and $a &gt; 0$ and $b &gt; 0$. So, the ratio would be between $0$ and $1$.  I could use linear regression, although it doesn't naturally limit to 0..1.  I have no reason to believe the relationship is linear, but of course it is often used anyway, as a simple first model.  I could use a logistic regression, although it is normally used to predict the probability of a two-state outcome, not to predict a continuous value from the range 0..1.  Knowing nothing more, would you use linear regression, logistic regression, or hidden option c? Show that $\sum\limits_{n=0}^\infty \frac{z}{(1+z^2)^n}$ converges for all $z\in \mathbb{C}$ outside $|1+z^2|=1$ Show that $\sum\limits_{n=0}^\infty \frac{z}{(1+z^2)^n}$ converges for all $z\in \mathbb{C}$ outside $|1+z^2|=1$  Actually, I have the problem to understand the meaning of "outside $|1+z^2|=1$". If it means that the collection of $z\in\mathbb{C}$ such that $|1+z^2|&gt;1.$ This problem will be easy to verify since for each given $z$ with $|1+z^2|&gt;1$, then we have $|1+z^2|^{-1}&lt;1$. Then, it is the geometric series with common ratio less than $1$ which implies that the series converges.   Do I have correct interpretation with "outside $|1+z^2|=1$"? If not, what is the correct interpretation with this? Thanks. I've read that flash memories can "only" be reprogrammed 100000 to 1000000 times, until the memory storage "deteriorates"  Why exactly does this happen with flash and not other memory types, and what does "deteriorate" refer to, internally?  EDIT: Since it's not only flash that this happens, I'd like to generalize a bit and inquire about the memories that have this problem. Also, does the wearing out between these memory types occur due to the same phenomenon? TikZ is undergoing lots of development with new features being added, but the versions distributed with standard TeX releases are often a little old. How do I get the latest version? If I want to be sure that I get the latest stable version, how do I do that?    Note: I'm not asking this question for myself, but because a question like this seems to be useful for pointing to it when a new feature of TikZ is mentioned in an answer to some other question. Feel free to post answers for any operating system/TeX distribution combination. How to get my 4yo daughter's fixation on my belly button under control? I don't know where to begin with this question. It's awkward and to be honest, it makes me feel rather uncomfortable. Simply put, I'm led to believe that my four year old daughter is obsessed with my belly button. It all started one day during the summer when she was three. I decided to take my family to the pool, and I guess I didn't see my daughter follow me into the changing room. Mind you, she's still at the age where it's appropriate to see her parents naked, so I wasn't surprised when, after I finished changing into my bikini, I turned around to see her staring at me.  I followed her gaze and saw her looking directly at my belly button. I asked her what she was looking at and she screamed "mommy, I can see your belly button!" which made me giggle. I picked her up and kissed her forehead, telling her that everyone has a belly button.  I think I might have accidentally given her a green light, because over the next year she constantly asks me if she can stick her finger in my belly button, and if I don't let her, she begins to scream.  For her fourth birthday, she requested that I wear nothing but a sports bra and underwear (in toddler speak. It sounded like "mommy, show your belly button for my birthday!" I could have simply worn a crop top but i didn't want to risk her throwing a temper tantrum)  My husband obviously doesn't mind, because he gets to look at my belly button all the time but it really upsets me that my daughter's finger is constantly in my belly button.  Tomorrow is her fifth birthday and I want to discuss with her that it's not appropriate to always be poking my belly button. Any ideas on how i can talk to her without her throwing a screaming fit? Conjectures that have been disproved with extremely large counterexamples? I just came back from my Number Theory course, and during the lecture there was mention of the Collatz Conjecture.  I'm sure that everyone here is familiar with it; it describes an operation on a natural number – $n/2$ if it is even, $3n+1$ if it is odd.  The conjecture states that if this operation is repeated, all numbers will eventually wind up at $1$ (or rather, in an infinite loop of $1-4-2-1-4-2-1$).  I fired up Python and ran a quick test on this for all numbers up to $5.76 \times 10^{18}$ (using the powers of cloud computing and dynamic programming magic).  Which is millions of millions of millions. And all of them eventually ended up at $1$.  Surely I am close to testing every natural number? How many natural numbers could there be?  Surely not much more than millions of millions of millions. (I kid.)  I explained this to my friend, who told me, "Why would numbers suddenly get different at a certain point?  Wouldn't they all be expected to behave the same?"  To which I said, "No, you are wrong!  In fact, I am sure there are many conjectures which have been disproved by counterexamples that are extremely large!"  And he said, "It is my conjecture that there are none! (and if any, they are rare)".  Please help me, smart math people.  Can you provide a counterexample to his conjecture?  Perhaps, more convincingly, several?  I've only managed to find one! (Polya's conjecture). One, out of the many thousands (I presume) of conjectures. It's also one that is hard to explain the finer points to the layman. Are there any more famous or accessible examples? Formulae for Catalan's constant. Some years ago, someone had shown me the formula (1). I have searched for its origin and for a proof. I wasn't able to get true origin of this formula but I was able to find out an elementary proof for it.  Since then, I'm interested in different approaches to find more formulae as (1).  What other formulas similar to ($1$) are known?  Two days ago, reading the book of Lewin "Polylogarithms and Associated Functions" I was able to find out formula (2).  $\displaystyle \dfrac{1}{3}C=\int_0^1 \dfrac{1}{x}\arctan\left(\dfrac{x(1-x)}{2-x}\right)dx\tag1$   $\displaystyle \dfrac{2}{5}C=\int_0^1 \dfrac{1}{x}\arctan\left(\dfrac{\sqrt{5}x(1-x)}{1+\sqrt{5}-\sqrt{5}x}\right)dx-\int_0^1 \dfrac{1}{x}\arctan\left(\dfrac{x(1-x)}{3+\sqrt{5}-x}\right)dx\tag2$   $C$ being the Catalan's constant.  I have a proof for both of these formulae.  My approach relies on the following identity:  For all real $x&gt;1$,  $\displaystyle \int_0^1 \dfrac{1}{t} \arctan \left (\dfrac{t(1-t)}{\frac{x+1}{2}-t}\right) dt=\int_1^{\frac{\sqrt{x}+1}{\sqrt{x}-1}}\dfrac{\log(t)}{1+t^2}dt$ Choice of ECC curve on USB token I would like to get a USB token to secure my keys. My use case is protection of 3 GnuPG keys that I will be using 10 times per day at least. I plan to create a new key ring from scratch. Because ECC seems more future-oriented than RSA, this is what I chose to use. I'm wondering which USB token to choose as well as which curve.  On  it is said that many people think curves recommended by the NIST or defined by Brainpool have a doubtful origin; therefore, they recommend the non-standardized Bernstein’s Curve 25519. On  one poster says that    He is not aware of any profound criticism of Brainpool curves, and Bernstein’s Curve 25519 is hard to protect against side-channel attacks when implemented in embedded devices.   As a result, I'm a bit lost as to which key/curve to choose. Is there a way to fix a small chip in a wall's paint? I'm not sure exactly with what I've bumped my wall and caused this this:    Is there anything that can be done to fix this without repainting the entire room?  I've been reading around a bit, and not sure exactly what to call this, hence the weird question title.  The paint is a beige-ish colour, not exactly white. The hole is about 2 x 1.5 cm in size.   I've read a bit about spackling paste, though I understand that's for small cracks and holes.  Here are some picture with a better resolution:  and   Unfortunately, I don't have much experience with this sort of thing. Help please.  Also, this is in the UK, so you can tell what stores I might have access to for materials.