In Back to the Future, we see Doc and Marty repeatedly returning to 1955. But they weren't the only ones. Biff meets his younger self, and a DeLorean waits hidden in a cave.  So am I correct in counting four DeLoreans at most?   The one from 1985, driven by Marty. Thid is the one we see in the first film. It goes back to 1985. The one from 2015, driven by Biff. It goes back to 2015. The one from the alternate 1985, driven by Doc and Marty. It disappears to 1885 with Doc. The one from 1885, mothballed by Doc, is waiting hidden in a cave. Marty drives it back to 1885, then back to 1985.
How many copies of the DeLorean time machine co-existed in the Back to the Future series?
Sneak Attack has the same type , this is easy, unless there are multiple damage types.  A Flame Tongue does slashing (or piercing) damage, and fire. Can I chose the Sneak Attack damage in this case to be fire too? Is every discrete absolute value non-archimedean? I've been reading Milne's notes on absolute values and local fields (Chapter 7 of the book on algebraic number theory), and a possibly minor point is confusing me.   On page 126, Milne writes, "$K$ is a field complete with respect to a discrete absolute value $|\cdot|$..." and then he talks about things that only make sense for non-archimedean absolute values, like the ring of integers and its maximal ideal.   Is every discrete absolute value on a field $K$ also non-archimedean? This would explain a lot, but I also suspect that it is not true, because I can't find any statement of this fact anywhere.  EDIT: An absolute value is discrete if the value group $|K^\times|$ is a discrete subgroup of the multiplicative group $\mathbb{R}_{&gt;0}$. An absolute value is non-archimedean if it satisfies the stronger triangle inequality $$ |x+y| \le \max (|x|,|y|) $$ or equivalently if the set $\{|1|,|1+1|,|1+1+1|,\ldots\}$ is a bounded subset of $\mathbb{R}$. Validate/verify PDF files integrity Is there any tool which I can run on the PDFs archives (all directories) and finally it lists/identifies the corrupt/invalid PDFs? I have hundreds of PDF files (related to documentation etc.) on my computer (Windows machine), and very often I receive/have to send dozens of PDFs via email. It is now a normal routine that the PDF I receive or send is corrupted. This creates serious trouble sometimes, when the source file (e.g. Word file or the Tex file) is missing/not available instantly. Checking these thousands of PDFs is not possible in finite time, so I have searched for a tool which I can run once and it would scan all PDFs (in directories and sub-directories), and finally I would get a list of files which I should re-create. Up to now, it seems there is no such tool. How is light emitted by an incandescent lamp $\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$ I've already see a  by Marko Riedel which I list it follows:     The standard way to treat these sums is to integrate   $$ f(z) = \frac{1}{(z+\alpha)^2} \pi \cot(\pi z)$$   along a contour consisting of a circle of radius $R$ and with $R$ going to infinity and hence being larger than $\alpha$, where the circle does not pass through the poles on the real axis.   Now along the semicircle in the upper half plane we have   $$|f(z)| \le \frac{1}{(R-|\alpha|)^2}\pi \left|\frac{e^{i\pi R\exp(i\theta)} + e^{-i\pi R\exp(i\theta)}} {e^{i\pi R\exp(i\theta)} - e^{-i\pi R\exp(i\theta)}}\right|= \frac{1}{(R-|\alpha|)^2} \pi  \left|\frac{e^{2i\pi R\exp(i\theta)}+1}{e^{2i\pi R\exp(i\theta)}-1}\right| &lt; \frac{1}{(R-|\alpha|)^2} \pi   \frac{1+e^{-2\pi R\sin(\theta)}e^{2i\pi R\cos(\theta)}} {1-e^{-2\pi R\sin(\theta)}e^{2i\pi R\cos(\theta)}}$$   This last term is clearly $O(1/R^2)$ as $R$ goes to infinity as the quotient of the two exponentials goes to one since $\exp(-R)$ vanishes and there is no singularity when $\theta = 0$ or $\theta = \pi$ as $R\cos\theta = \pm R$, which is not an integer by the assumption that the circle avoids the poles and hence cannot be one.     My question: It is clear that for each $z=Re^{i \theta}$ , $f(z)=O(1/R^2)$ ，but can this guarantee that the last term on RHS is uniform bounded ? Since $\theta$ varies on a compact interval $[0, \pi]$ , I want to show that for each $ \theta \in [0, \pi]$ , and a fixed positive number $M \gt 1 $ there exist an open ball contains $\theta$ and a fixed $R_{\theta}\gt 0$ , for every $R \ge R_{\theta}$ and $x \in $ the open ball $$\frac{1+e^{-2\pi R\sin(x)}e^{2i\pi R\cos(x)}} {1-e^{-2\pi R\sin(x)}e^{2i\pi R\cos(x)}} \le M$$  For $\theta \neq 0,\pi$ , it is easy to find the desired $R_{\theta}$ and the open ball , but if $\theta = 0$ or $ \theta = \pi$ , for every open ball containing $\theta$ , it behave erratically near $\theta$ , I have no idea how to deal with this . Let $g(x)\in \mathbb{Z}[x]$, a nonconstant polynomial. Show that the set of primes $p$ such that $p\mid g(n)$ for some $n\in \mathbb{Z}$ is infinite.  I don't know how to start. I have tried asuming that the set is finite but i haven't reached any contradiction. This seems to be quite a trivial problem, but after some searching I can't stil figure out the answer. One can run tcpdump using "any" as the interface description, ie:   # tcpdump -i any -n host 192.168.0.1   Is there any way to force tcpdump to show on which interface displayed packet was captured?  Update:  As more people confirmed this is probably not possible with vanilla tcpdump, can someone propose a solution to mentioned problem? Perhaps different sniffer?   General issue is as follows: On a system with 50 interfaces determine what is inbound interface for packets coming from specific ip address. Downgrading from SQL Server 2008 to 2005 Markdown code snippets don't allow trailing spaces Show that any bounded linear functional on a normed linear space is continuous Show that any bounded linear functional on a normed linear space is continuous.   Can we say that it is uniformly continuous ?   Also, is it true, if we reverse the statement    any continuous  linear functional on a normed linear space is bounded ?? Word: how to show hidden ribbon tabs? How can I control which tabs are available to be opened in the MS Word 2010 ribbon?  Under Word Options > Customize Ribbon > Main Tabs there are several groups checked (Blog Post, Insert (Blog Post), Outlining, Background Removal), but they don't appear on the ribbon even though there is space for them. How is one supposed to turn them on or get to them?  The one in particular I'm after today is the Blog Post tab, which I know I can get to in a round about way via File > New > Blog Post Template. However I don't want a new post, rather an old one, which means File > New > Blog Post Template > Open existing > [select from list] > [close new blog post window] > [slap No I don't to save darn it]. Extra work for nothing is irritating; how do I get Blog Post (or Outlining or ...) to show up in that nice empty space next to AddIns? What is the default root password? I installed  (Precise Pangolin), 64 bit. Nowhere was I asked to set password for root.  I just installed  software. It was installed under the /root folder by default. Now I try do something on that folder. I tried with su to switch to root, but I don't know its password.   Should I always use sudo or get the default root password, if any?  How do I create a  for software installed inside the /root directory? Interval preserving transformations are linear in special relativity In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity:  Prove that any spacetime transformation $\left(y^0,y^1,y^2,y^3\right)\leftrightarrow \left(x^0,x^1,x^2,x^3\right)$ that preserves intervals, that is, such that  $$\left(dy^0\right)^2-\left(dy^1\right)^2-\left(dy^2\right)^2-\left(dy^3\right)^2=\left(dx^0\right)^2-\left(dx^1\right)^2-\left(dx^2\right)^2-\left(dx^3\right)^2$$  is linear (assuming that the origins of both coordinates coincide). That is, show that $\frac{\partial y^i}{\partial x^j}=L_j^i$ is constant throughout spacetime (that is, show that $\frac{\partial L_j^i}{\partial x^k}=0$).  Thus far all I've been able to prove is that $g_{ij}L_p^iL_q^j=g_{pq}$ (where $g_{ij}$ is the metric tensor of special relativity) and that $\frac{\partial L_j^i}{\partial x^k}=\frac{\partial L_k^i}{\partial x^j}$. Any further ideas? I won a Samsung Galaxy S6 Edge, signed into it with my Google account, played around with it, wiped it, and sold it.  Now the person can't get past setup because it's saying he must login with an account previously synced to the phone.   Is there anything I can do from my side to remove this lock? Search for a string and print everything before and after within a range I have this file:  sometext1{ string1 }  sometext2{ string2 string3 }  sometext3{ string4 string5 string6 }   I want to search this file for a specific string and print everything before this string up to the opening { and everything after this string up to the closing }. I tried to achieve this with sed but if I try to print everything in the range /{/,/string2/ for example sed prints this:  sometext1{ string1 }  sometext2{ string2 sometext3{ string4 string5 string6 }   If I search for the string "string2" I need the output to be:   sometext2{ string2 string3 }   Thanks. Set a polygon's normal's orientation as the objects local rotation orientation (if every polygon is an object) Asking distant cousins for DNA? In my family we have a DNA contradiction – two cousins (at about the 4th cousin level) took a Y-DNA test, but did not match and had two completely different haplogroups.   Since then, I have traced living cousins with the same surname – the only ones left living that I am aware of – and I would love to pay to have them tested to see if we can figure out where the non-paternity event (NPE) or other event happened (i.e. this new cousin could help us determine which line the NPE occurred in depending on which cousin he matches).   Does anyone have a sample letter, or know the best way to go about asking a distant cousin for DNA?   I have their address and am planning to write a letter, but I can't imagine receiving such a letter, so I am not quite sure how to ask without scaring them off. Can not update Bash on Debian 6.0 (Squeeze) I can not update  on a Debian 6.0 (Squeeze) server to get rid of the discovered vulnerability:  bash --version GNU bash, version 4.1.5(1)-release (x86_64-pc-linux-gnu)  apt-get update apt-get install bash Reading package lists... Done Building dependency tree Reading state information... Done bash is already the newest version. 0 upgraded, 0 newly installed, 0 to remove and 7 not upgraded.   Can I use Squeeze-LTS for this server just to update Bash? After one week I will be on another server, so I will not make any other updates.  uname -m x86_64  lsb_release -a No LSB modules are available. Distributor ID: Debian Description:    Debian GNU/Linux 6.0.5 (squeeze) Release:        6.0.5 Codename:       squeeze Map a function across a list conditionally Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ . I'm looking for a simple proof that up to isomorphism every group of order 2p (p prime) is either $\mathbb{Z}_{2p}$ or $D_{p}$ (The Dihedral group of order 2p).  I should note that by simple I mean short and elegant and not necessarily elementary. So feel free to use tools like Sylow Theorems, Cauchy Theorem and similar stuff.  Thanks a lot!