Hawking radiation and mass annihilation Now, i just heard that the particle anti particle pairs that zip in and out of existence every planck second both have positive mass. if that is so, how does hawking radiation work? black holes lose mass when the particle with negative mass falls into the black hole and cancels out some of the positive mass in it? but, if both particles are positive, the black hole should gain mass instead of losing it. what exactly is going on here?
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?
How can the median number of sexual partners be 6.1 and 3.6? Median number of female sexual partners in lifetime, for men 25-44 years of age, 2006-2008: 6.1  Wouldn't it only be able to be x.5 or x.0? "Failed to download repository information" error I often use Cycles' built in Glass BSDF shader to achieve realistic refraction effects, but in many cases, it seems that Cycles' glass caustics creates an unfortunately large number of fireflies (pixels that are abnormally bright relative to their surroundings). In some models of mine, even when I render for 3000 or more samples/pixel, my final image is still covered in fireflies. While I can improve this in many cases by increasing the total amount of light available in the scene, this loses a lot of the potency of the refractive effects I'm looking for, especially in scenes with low light levels.  So my question is, how can I reduce the amount of fireflies while using Cycles' caustics without sacrificing the quality of the refractive effects?  Note: I am aware that Cycles' caustics will perform much better once Cycles has full support for bidirectional path-tracing, but it looks unlikely that that will become , unfortunately. How to justify the definition of summation $s_n=\sum_{i=1}^n a_i=a_1+\cdots+a_n$? I read  and found that they define summation via recursion, so I decided to formalize the proof that that this definition is actually valid. I've two questions:   Does my proof contain any error? Are there other simple ways to define summation?   Thank you so much!     Suppose that $(a_1,\cdots,a_n)$ is a finite sequence in $\mathbb N$. Show that there is a sequence $(s_1,\cdots,s_n)$ such that $s_1=a_1$ and $s_{i+1}=s_i+a_{i+1}$ for all $1\leq i&lt;n$.   My attempt:  We define mapping $f$ as follows: $f: \mathbb N\times\mathbb N\to\mathbb N\times\mathbb N: (i,a)\mapsto\begin{cases} (i+1,a+a_{i+1})&amp;\text{if }i&lt;n\\ (i+1,a)&amp;\text{if }i\geq n \end{cases}$  By recursion theorem, there is a unique sequence $(p_i\mid i\in\mathbb N)$ such that $p_0=(1,a_1)$ and $p_{i+1}=f(p_i)$. Let $\pi:\mathbb N\times\mathbb N\to\mathbb N$ be the projection to the second co-ordinate i.e. $\pi(i,a)=a$. Let $s_i=\pi(p_i)$ for all $1\leq i\leq n$, then $(s_i\mid 1\leq i\leq n)$ is the required sequence. It's clear from the definition of $s_i$ that $s_{i+1}=s_i+a_{i+1}$ for all $1\leq i&lt;n$. After the last update of TeXLive 2018 (pretest) I get an error with csquotes' macro MakeAutoQuote:  \setcounter{errorcontextlines}{100} \listfiles \documentclass[fontsize=11pt,paper=a4,pagesize,ngerman]{scrartcl} \usepackage[utf8]{inputenc} \usepackage{babel} \usepackage[T1]{fontenc} \usepackage{csquotes} \MakeAutoQuote{»}{«}  \begin{document} ABC \end{document}   The error:  ! Package csquotes Error: Invalid argument.   My versions:  inputenc.sty    2018/04/06 v1.3b Input encoding file babel.sty    2018/02/14 3.18 The Babel package csquotes.sty    2018/02/11 v5.2c context-sensitive quotations (JAW)   I use pdfLaTeX. What is wrong here? Last night I was updating my Ubuntu 10.04 to either 11.04 or 12.04 (I'm not entirely sure which one it was, but I think it was 11.04) and I left it overnight to finish. When I came down in the morning, I noticed that the computer hadn't barely begun installing the updates! The update thing said that my computer was on the installation step, but it was still preparing the libc bin (or whatever its called) . It's like the first part of the step installing the upgrades. So, I stupidly restarted the computer, and when it rebooted, I got five options on a purple screen:  Ubuntu, with Linux 3.0.0-28-generic Ubuntu, with Linux 3.0.0-28-generic (recovery mode) Previous Linux versions Memory test (memtest86+) Memory test (memtest86+, serial console 115200)   Long story short, not matter which way I enter Ubuntu to try and reinstall the updates using the root thing (it's like terminal) after I enter sudo apt-get update it basically said it failed to fetch every url link, and it then says:  W: Some index files have failed to download. They have been ignored, or old ones used instead. W: Not using locking for read only lock file /var/lib/dpkg/lock E: dpkg was interrupted, you must manually run 'sudo dpkg --configure -a' to correct the problem.   So, I entered sudo dpkg --configure -a, and it says:  dpkg: error: unable to access dpkg status area: Read-only file system"   I'm left like wtf, and I really just some guidance here. I just got this laptop, and I can not afford a new one if I broke this one. What are the TeX definitions for the hyphen and dashes -, --, and ---? I've tried latexdef which does not handle --- as the operand. And \texemdash is defined as a character. So that leaves me once again leaning on the collective wisdom of the group :) Android App initial release date When you are viewing an app in Google Play store, it displays the following : Updated, Size, Installs, Current Version, Requires Android, and Rating.  I am trying to do some research and figure out the initial release / publish dates of different apps. Is there a way to get this information from Google Play, or perhaps a website with this information? I heard about nautilus-gksu and would like to install it. Unfortunately, when I try, I get this:  glemi@XPS:~$ sudo apt-get install nautilus-gksu Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package nautilus-gksu   How and where can I get this package? Verb form of "must needs" Then touching the shoulder of a townsman who stood near to him, he addressed him in a formal and courteous manner:      "I pray you, good Sir," said he, "who is this woman? -- and wherefore is she here set up to public shame?"      "You must needs be a stranger in this region, friend," answered the townsman, looking curiously at the questioner and his savage companion, "else you would surely have heard of Mistress Hester Prynne and her evil doings. She hath raised a great scandal, I promise you, in godly Master Dimmesdale's church. "   As far as I know we always use first form of the verb after "must". For instance: "You must go". We never say "You must goes". Also, we never use -s/es with a verb that comes with "You". What are the circumstances in which writer has used "needs" after "You must" in "You must needs to be a stranger in this region."? Negative R squared contradicts ssa/sst? I understand from this question -    that the R squared value of a linear regression model can be negative if the intercept is constrained. And this makes sense if you define R squared as -   $$R^2 = 1-\frac{SSE}{SST}$$  One says $SSE&gt;SST$. But then,  $$SST = SSA + SSE $$ Total Sum of squares  = Sum of squared errors + Sum of squared residual. And with this we get -  $$R^2 = \frac{SSA}{SST}$$ And now it is hard to imagine how $R^2$ can be negative. Aren't SSA and SST >0 always? I have a many-to many relationship between three objects. LGFProducts, PartsinProducts, and Parts. PartsinProducts is the junction object. I want to be able to get data like the names of the parts that are related to the selected LGFProduct.   I understand that parent-child relationship can only traverse one level down while grandchild-grandpa can travel 5 levels at most. What is the parent-child or child-parent in a many-to-many relationship?  I assumed that I should be traversing upwards from Parts to the junction object partsinproduct and then LGFProducts? But my friend who is not a Salesforce expert but has knowledge in CS said that I should do a parent-child query (of LGFProducts to partsinproduct) to child-parent relationship query (PartsinProduct to Parts). Or perhaps both of these options are wrong and another is appropriate.   Also, I am having a little trouble traversing for custom objects. I understand that I need to append the letter r instead of c but get confused. For example, this is my attempt at a three level upward traversal that fails.   SELECT Id, Name, Parts__r.PartsinProducts__r,LGFProducts__r.Name FROM Parts__c   Also if three levels of upward traversal are needed, could one provide an example with custom relationships? As seen above, I am having difficulty successfully querying a three level upward traversal statement for custom objects.  This is my attempt at the parent-child relationship query of LGFProduct to PartsinProducts:  SELECT Name,   (     SELECT Name     FROM PartsinProduct__r   ) FROM LGFProduct__c    I am then given this error: In other words, can I do something like  for() {     for {        for {        }     } }   Except N times? In other words, when the method creating the loops is called, it is given some parameter N, and the method would then create N of these loops nested one in another?  Of course, the idea is that there should be an "easy" or "the usual" way of doing it. I already have an idea for a very complicated one. Please see the following image, where you can find the inconsistency of SO reputation score among different flair themes (one with 7165, while all other three 7265).   I always thought that these four themes are based on the same data until now. Is this a bug? Are different flair themes really updated individually?    P.S.: The inconsistency only shows on my mobile, no problem from my desktop. What does this residuals versus fitted plot mean about my model? Prove by induction that $n^2<n!$ How to divide two 64-bit numbers in Linux Kernel? Some code that rounds up the division to demonstrate (C-syntax):  #define SINT64 long long int #define SINT32 long int  SINT64 divRound(SINT64 dividend, SINT64 divisor) {   SINT32 quotient1 = dividend / divisor;    SINT32 modResult = dividend % divisor;   SINT32 multResult = modResult * 2;   SINT32 quotient2 = multResult / divisor;    SINT64 result = quotient1 + quotient2;    return ( result ); }   Now, if this were User-space we probably wouldn't even notice that our compiler is generating code for those operators (e.g. divdi3() for division). Chances are we link with libgcc without even knowing it. The problem is that Kernel-space is different (e.g. no libgcc). What to do?  Crawl Google for a while, notice that pretty much everyone addresses the unsigned variant:  #define UINT64 long long int #define UINT32 long int  UINT64 divRound(UINT64 dividend, UINT64 divisor) {   UINT32 quotient1 = dividend / divisor;    UINT32 modResult = dividend % divisor;   UINT32 multResult = modResult * 2;   UINT32 quotient2 = multResult / divisor;    UINT64 result = quotient1 + quotient2;    return ( result ); }   I know how to fix this one: Override udivdi3() and umoddi3() with do_div() from asm/div64.h. Done right? Wrong. Signed is not the same as unsigned, sdivdi3() does not simply call udivdi3(), they are separate functions for a reason.  Have you solved this problem? Do you know of a library that will help me do this? I'm really stuck so whatever you might see here that I just don't right now would be really helpful.  Thanks, Chad So, I'm working on a control station that has buttons. It is a one-mesh creation, that means, I don't want to create buttons and things like that separated from the main mesh, but as you can see, I have problems. I would like to make the highlighted parts to be one with the main part around them. I've tried everything, and I have this problem on multiple creations. Any idea?  Update: I've added another example of the problem. I want them to be one face, instead of two. (2nd picture) How to do relative imports in Python? Imagine this directory structure:  app/    __init__.py    sub1/       __init__.py       mod1.py    sub2/       __init__.py       mod2.py   I'm coding mod1, and I need to import something from mod2. How should I do it?    I tried from ..sub2 import mod2 but I'm getting an "Attempted relative import in non-package".  I googled around but found only "sys.path manipulation" hacks. Isn't there a clean way?      Edit: all my __init__.py's are currently empty    Edit2: I'm trying to do this because sub2 contains classes that are shared across sub packages (sub1, subX, etc.).  Edit3: The behaviour I'm looking for is the same as described in  (thanks John B) How does this wiring work? I have a Trane XV90 and XL 14i. The wiring looks a little strange as in the picture bellow.                    _____________                   |           |   BK W2  W1   R  G  Y  B/C  YLO O     |___||   |__|  ||   |          |   |     ||   |_____>|----------|         |   |     ||_________>|other wire|         |   |     |           ------------         V   V     V     ---------------     |thermostat   |     ---------------  The R and G are jumpered together and the G wire is connected on the board  but is actually not connecting to the thermostat on the other end. So people told me that means the furnace fan is always on! (In my diagram above, I switched the location of Y and B/C to make diagram easier to draw. You can refer to the photo added below to see the details) My questions are the following  is the jumper between O and Y doing anything? I don't think I have heat pump I need to install Honeywell wifi thermostat and I am thinking of doing either one of the following:   remove jumper between R and G, and use G to connect B/C and then to thermostat C and put jumper between G and Y  leave jumper between R and G, and use G to connect B/C and then to thermostat C and put jumper between G and Y  remove jumper between R and G, connect G on control board to thermostat G, and finally have the spare wire to connect B/C and then thermostat C  leave jumper between R and G, does not connect G to thermostat,  and just use a spare wire to connect B/C on board to thermostat C   Can anyone comment on those plans? Thanks a lot!