How do black hole jets form?
Where do the bipolar jets of black holes come from?
$(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$? Well i tried to prove it but failed. They are both commutative and have the same set of units. So i can't see a property of one ring which the other ring does not possess. Thank you for any help. Installing Ubuntu on a single partition I’m trying to install Ubuntu 16.04 alongside with Windows 7. My HDD supports only 4 partitions. Three of the partitions are taken up by windows. The fourth one is labelled as free space.   Now, how do I make root, swap and home partitions? Should I format my free space as primary with EXT4 first (if so, what should be the mount point?) and then create logical partitions for root/Home/swap? How do I go about this?  Edit: I tried to use the automatic installation option for dual boot. However I got the error ubi partman exit code 141. Probably because it tried to create two separate partitions for root and swap.   $ sudo parted -l Model: ATA ST1000DM003-1CH1 (scsi) Disk /dev/sda: 1000GB Sector size (logical/physical): 512B/4096B Partition Table: msdos Disk Flags:   Number  Start   End    Size   Type     File system  Flags  1      1049kB  106MB  105MB  primary  ntfs         boot  2      106MB   277GB  277GB  primary  ntfs  3      277GB   903GB  627GB  primary  ntfs When does System.gc() do something? The Matching Problem/Derangements - n letters to n people There are n letters addressed to n eople at different addresses. The n addresses are typed on n envelopes.  A disgruntled secretary shuffles the letters and puts them in the envelopes in random order, one letter per envelope.  Find the probability that at least one letter is put in a correctly addressed envelope. [Hint: use the inclusion-exclusion formula.] What is the probability approximately, for large n ?    My attempt at a solution:  P(all correct) = $\frac{1}{n!}$  P(n-1 correct) = ${n \choose n-1} \frac{1}{n!} = \frac{1}{1!(n-1)!}$  ${n \choose n-1}$ ways of selecting n-1 correct letters.  P(n-2 correct) = ${n \choose n-2} \frac{1}{n!} = \frac{1}{2!(n-2)!}$  ...  P(n-n correct) = ${n \choose n-n} \frac{1}{n!} = \frac{1}{n!(n-n)!} = \frac{1}{n!}$  This all looks ok to me, but I tested this for a case of 4 people, (I think the theoretical value should be $\frac{9}{24}$ but obviously that is not what I got. Can someone correct my logic please? Also, with regards to the hint about inclusion/exclusion - where would that come in?  I read about derangements on Wikipedia but it did not make total sense to me (the derivation).  I would appreciate any advice whatsoever including references to other material. Time travel short story where dinosaur doesn't taste like chicken During The Great Battle of the Last Alliance, there were an estimated 100,000 elves that fought with the armies of Isildur. This was one of the first scenes in the first LOTR movie. However, in the trilogy, it appears that only a small number of elves show up to Helms Deep and overall left the majority of the fighting to the humans. Why did the elves not participate during the rest of the war? I read about Java's type erasure .  When does type erasure occur? At compile time or runtime? When the class is loaded? When the class is instantiated?  A lot of sites (including the official tutorial mentioned above) say type erasure occurs at compile time. If the type information is completely removed at compile time, how does the JDK check type compatibility when a method using generics is invoked with no type information or wrong type information?  Consider the following example: Say class A has a method, empty(Box&lt;?&nbsp;extends&nbsp;Number&gt;&nbsp;b). We compile A.java and get the class file A.class.  public class A {     public static void empty(Box&lt;? extends Number&gt; b) {} }     public class Box&lt;T&gt; {}   Now we create another class B which invokes the method empty with a non-parameterized argument (raw type): empty(new Box()). If we compile B.java with A.class in the classpath, javac is smart enough to raise a warning. So A.class has some type information stored in it.  public class B {     public static void invoke() {         // java: unchecked method invocation:         //  method empty in class A is applied to given types         //  required: Box&lt;? extends java.lang.Number&gt;         //  found:    Box         // java: unchecked conversion         //  required: Box&lt;? extends java.lang.Number&gt;         //  found:    Box         A.empty(new Box());     } }   My guess would be that type erasure occurs when the class is loaded, but it is just a guess. So when does it happen? Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$ Find the maximum value of $f(x)$ when $0 \leq x \leq 1$ and $$ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$$   I'm guessing that the Fundamental Theorem of Calculus can't be used because the integrand is a function of $x$.  Any help would be greatly appreciated. Why is "No new release found" when upgrading from a LTS to the next? I'm following the , but on launching the upgrade tool I get this response:  Checking for a new ubuntu release No new release found   Am I doing something wrong? Is there a workaround? Default Class Accessibility in C# by default is a class:   private ? internal ?  sealed ? What are the assumptions for applying a quantile regression model? The question has been asked (one time) on CV before, but the answer is really imprecise and does not really answer the question in my opinion.  So: What are the assumptions for estimating a linear regression model via quantile regression?  To my understanding (and as several CV users have mentioned), quantile regression does not assume any specific distribution of the error terms - does that mean that, in a time series model, autocorrelation and heteroscedasticity do not have to be accounted for?  What about the other Gauss-Markov assumptions? I would assume that the assumption of no perfect multicollinearity has to be met when applying quantile regression, but do the parameters have to be linear? The linearity assumption only has to hold for the specific quantile I would assume.  Anyways - I do not find any backup for any of my thoughts in the scientific literature and I would appreciate a comprehensive answer. Thank you! Is  purely conceptual or does it represent some real "thing"?  Said another way, is superposition thought to have some tangible physical manifestation or is it simply the lack of physical determinism, except as defined by a wave function?  It seems like my question might be semantic.  For example, it is said that   superposition is obeyed, like a law superposition can be observed, like a phenomena superposition describes behavior   I guess my question is, can superposition be measured like an electrical charge, or is it simply the lack of knowable position. "Authoring" versus "Writing" In my area of work the word author as a verb has become quite common. However, it seems to have a subtly different meaning than plain vanilla write. For example, one does not write software unit tests; one authors them.  Can anyone offer a clear distinction between the two words? Has author as a verb become a common usage outside of the field of computer software? What are bitwise operators? 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. My awk program to change spaces into tabs doesn't work How to write a shell script which uses awk to read in the data file students.txt and output the data in the tabbed format as shown:  Surname Forename MSc Stream Date of Birth Smith John IT 15.01.1986 Taylor Susan IT 04.05.1987 Thomas Steve MIT 19.04.1986    Do not worry if tabbed columns don’t line up. The distance between each of (Surname, Forename, MSc Stream and Date of Birth) column is one tab.   Question:  Why this bellow code doesn't work for me?  awk 'BEGIN {IFS=" "} {OFS="\t"} {print $1,$2,$3,$4}' students.txt Is it possible to do something like this  #ifdef SOMETHING #define foo // #else #define foo MyFunction #endif   The idea is that if SOMETHING is defined, then calls to foo(...) become comments (or something that doesn't get evaluated or compiled), otherwise it becomes a call to MyFunction.  I've seen __noop used, but I don't believe I can use that.  EDIT(s):  I don't think I can really use a macro here, because MyFunction takes a variable number of arguments.  Also, I'd like to make it so the arguments are NOT evaluated!  (So doing something like commenting out the body of MyFunction doesn't really give me what I need, as the arguments will still be evaluated) How do I execute for a player wearing armor with a colored name I am working on a command block contraption on my server that involves armor giving you certain potion effects.  /execute if entity @p[nbt={Inventory[{Slot:100b,id:"minecraft:leather_boots",tag:{display:{Name:"{\"text\":\"Frog Boots\"}"}}}]}] run effect give @s jump_boost 1 1 true  However, it only works if the boots are named in an anvil. How would I write the command if I wanted to test if the player was wearing boots named "Frog Boots" in bold and green text? How to convert a column number (e.g. 127) into an Excel column (e.g. AA) How do you convert a numerical number to an Excel column name in C# without using automation getting the value directly from Excel.  Excel 2007 has a possible range of 1 to 16384, which is the number of columns that it supports. The resulting values should be in the form of excel column names, e.g. A, AA, AAA etc. If $\sigma_n=\frac{s_1+s_2+\cdots+s_n}{n}$ then $\operatorname{{lim sup}}\sigma_n \leq \operatorname{lim sup} s_n$ This is a question from the book Methods of Real Analysis by R. R. Goldberg.     If $(s_n)$ is a sequence of real numbers and if $$\sigma_n=\frac{s_1+s_2+\cdots+s_n}{n}$$ then prove that: $\operatorname{{lim sup}}\sigma_n \leq \operatorname{lim sup} s_n$.   I don't have any idea how to start working on this problem. Please help. Thanks.