Why does Hawking radiation cause black holes to die? If a particle is being expelled from a black hole and an antiparticle is being driven into it, shouldn't the opposite occur as well and in the same frequencies?  I mean, black holes should emit antiparticle radiation as well and gather energy from it and the black hole energy shouldn't change, right?  What am I missing?
Black holes and positive/negative-energy particles I was reading Brian Greene's "Hidden Reality" and came to the part about Hawking Radiation. Quantum jitters that occur near the event horizon of a black hole, which create both positive-energy particles and negative-energy particles, produce the so-called Hawking radiation. However, I do not understand why only the negative-energy particles are being absorbed into the black hole, while the positive-energy particles shoot outward. Shouldn't there be 50/50 chance that each type of particle is being absorbed by the black hole? Also, the book mentions that a negative-energy particle would appear to an observer inside the black hole as positive. Why?
Can we calculate the standard error of prediction just based on simple linear regression output? The standard error of prediction in simple linear regression is $\hat\sigma\sqrt{1/n+(x_j-\bar{x})^2/\Sigma{(x_i-\bar{x})^2}}$.  My question is to calculate the standard error of prediction for $pop=1029$ just based on the following regression output. I can get all except $\bar{x}$. And I also know how to calculate the approximate standard error of prediction based on the standard errors of intercept and coefficient of $pop$, ignoring their correlation. Forward vs Forwards Why isn't $V= V_1 + V_2$? $V=V_a - V_c = V_a - V_b + V_b - V_c$, $V_a - V_b= V_1$ and $V_b - V_c = V_2$ Doesn't that prove that $V = V_1 + V_2$? Regardless of $V_3$, If i'm wrong , is there a way to obtain $V$ in terms of $V_1$, $V_2$ and $V_3$ Testing pointers for validity (C/C++) Is there any way to determine (programatically, of course) if a given pointer is "valid"? Checking for NULL is easy, but what about things like 0x00001234? When trying to dereference this kind of pointer an exception/crash occurs.  A cross-platform method is preferred, but platform-specific (for Windows and Linux) is also ok.  Update for clarification: The problem is not with stale/freed/uninitialized pointers; instead, I'm implementing an API that takes pointers from the caller (like a pointer to a string, a file handle, etc.). The caller can send (in purpose or by mistake) an invalid value as the pointer. How do I prevent a crash? Let $A$ and $B$ be two sets of real numbers. Define the distance from $A$ to $B$ by $$\rho (A,B) = \inf \{ |a-b| : a \in A, b \in B\} \;.$$ Give an example to show that the distance between two closed sets can be $0$ even if the two sets are disjoint. I want to update my sources.list file with the fastest server from the command line in a fresh Ubuntu Server install. I know this is trivially easy with the GUI, but there doesn't seem to be a simple way to do it from from the command line? If just a single photon hit a single slit interferometer, what would happen? Would you just see a dot on the screen, or would there be a diffraction pattern? Furthermore, if you had a double slit interferometer but also had which-path information would there still be a diffraction pattern even though there is no interference? How to put GeoServer layers behind authentication? Why Java needs Serializable interface? We work heavily with serialization and having to specify Serializable tag on every object we use is kind of a burden. Especially when it's a 3rd-party class that we can't really change.  The question is: since Serializable is an empty interface and Java provides robust serialization once you add  implements Serializable - why didn't they make everything serializable and that's it?    What am I missing? Force applied off center on an object I'm messing around with python for the first time.  I'm making my own changes to the interface, just because..  How can I move the text inside the buttons down and to the left? The left image is what I have now and the right one it's what I want to do..  Please have in mind that I have zero python knowledge. But I'm willing to learn.. Cantrips seem to be the only type of spell that cares only about your class level. However, in the multiclassing section they are not mentioned, does this mean that cantrips use your character level, instead of your class level?  Does this mean a Warlock 2 / Fighter 15 can cast an Eldritch Blast with 4 beams just like a level 17 Warlock? From some comments in the answers for  (now deleted, 10k only), there's confusion around the usage of I vs. me:  While the sentence, "the other attendees are myself and Steve," is agreed to be incorrect, there's confusion about whether the correct form is "the other attendees are me and Steve" or "the other attendees are Steve and I."  (I've always used the heuristic of removing the other people from the sentence, so I always thought "the other attendee is me" would be correct, instead of "the other attendee is I." Is this true, or am I using a flawed heuristic?) Approximating a $\sigma$-algebra by a generating algebra Theorem. Let $(X,\mathcal B,\mu)$ a finite measure space, where $\mu$ is a positive measure. Let $\mathcal A\subset \mathcal B$ an algebra generating $\cal B$. Then for all $B\in\cal B$ and $\varepsilon&gt;0$, we can find $A\in\cal A$ such that $$\mu(A\Delta B)=\mu(A\cup B)-\mu(A\cap B)&lt;\varepsilon.$$  I don't think there is a proof in this site. It's a useful result for several reasons:  We know what the algebra generated by a collection of sets is, but not what the generated $\sigma$-algebra is. The map $\rho\colon \cal B\times\cal B\to \Bbb R_+$, $\rho(A,A')=\mu(A\Delta A')$ gives a pseudo-metric on $\cal B$. This makes a link between generating for an algebra and dense for the pseudo-metric. We say that a $\sigma$-algebra is separable if it's generated by a countable class of sets. In this case, the algebra generated by this class is countable. An with the mentioned result, we can show that $L^p(\mu)$ is separable for $1\leq p&lt;\infty$, which makes a link between the two notions. In ergodic theory, we have to test mixing conditions only an a generating algebra, not on all the $\sigma$-algebra. If two vectors $a$ and $b$ make angle $\alpha$ and $\beta$ with the $x$-axis, prove, using vectors, that:   $$\cos(\beta - \alpha) = \cos \alpha \cos\beta + \sin\alpha \sin\beta$$   I tried taking components of each vector along the plane, but that didn't get me anywhere. I tried taking component of vector $b$ along vector $a$, but I also got stuck there. Can anyone point me in the right direction? How to print line numbers to the log. Say when outputting some information to the log, I also want to print the line number where that output is in the source code. As we can see in the stack trace, it displays the line number where the exception has occurred. Stack trace is available on the exception object.  Other alternative could be like manually including the line number when printing to the log. Is there any other way? This question was recently split into different questions for each workaround. See   meta posts for more information.   Can you use NBT tags in commands? I’ve tried commands that normally work in Java Edition like: give @s minecraft:planks 30 1 {display:{Lore:[&quot;Wooden planks&quot;]}} give @s stone_pickaxe{Unbreakable:1b} give @s item_frame{EntityTag:{Invisible:1b}} summon villager ~ ~ ~ {Offers:{Recipes:[{buy:{id:&quot;emerald&quot;,Count:5b},sell:{id:&quot;diamond_sword&quot;}}]}} summon tnt ~ ~ ~ {Fuse:20s} Is there a way to unlock PDF documents? I realize most PDF documents are locked for a reason, but I spend several hours a week editing datasheets provided directly from my vendors to be sent to customers. Obviously it's very annoying and somewhat of a show-stopper when I download a datasheet in PDF format, then I am not able to draw boxes, add comments, or draw arrows to the supplied product.  One of our vendors told us the way around that was to print a physical copy, then scan it in as a PDF - not the most technological or aesthetically pleasing solution I have found.  I at least would like to be able to print the PDF to another PDF so that the new copy is unlocked for editing. Is there any way around this? Anbox snap installation fails I'm trying to install Anbox in my new Ubuntu 16.04 using instructions from  . It seemed to work, but I got no icon in my dash, so I suspect that the installation is not complete. With Synaptic  Package Manager I can see that anbox-common &amp; anbox-modules-dkms are installed, but I have no icon in my dash, so I tried running   sudo snap install --edge --devmode anbox   and got this error:  error: cannot install "anbox": Get    https://search.apps.ubuntu.com/api/v1/snaps/details/core?channel=stable&amp;fields=anon_download_url%2Carchitecture%2Cchannel%2Cdownload_sha3_384%2Csummary%2Cdescription%2Cdeltas%2Cbinary_filesize%2Cdownload_url%2Cepoch%2Cicon_url%2Clast_updated%2Cpackage_name%2Cprices%2Cpublisher%2Cratings_average%2Crevision%2Cscreenshot_urls%2Csnap_id%2Csupport_url%2Ccontact%2Ctitle%2Ccontent%2Cversion%2Corigin%2Cdeveloper_id%2Cprivate%2Cconfinement%2Cchannel_maps_list:    dial tcp: lookup search.apps.ubuntu.com on [::1]:53: read udp    [::1]:54255-&gt;[::1]:53: read: connection refused   What am I doing wrong? Why was the connection refused? According to the instructions, it seems this is the correct command to install it.  ps: I'm not that familiar with Linux, I'm more of a Windows guy, trying to learn Linux. How can I select first occurrence between two patterns including them. Preferably using sed or awk.  I have:  text something P1 something content1 content2 something P2 something text something P1 something content3 content4 something P2 something text   I want the first occurrence of the lines between P1 and P2 (including P1 line and P2 line):  something P1 something content1 content2 something P2 something