Atoms: boson or fermion? The spin of fundamental particles determines if they are bosons or fermions. The atoms also have bosonic or fermionic behavior, for example $\require{mhchem}\ce{^4He}$ has bosonic and $\ce{^3He}$ has fermionic statistics. Which quantity of atom determines its statistics?
Huge confusion with Fermions and Bosons and how they relate to total spin of atom I am supremely confused when something has spin or when it does not. For example, atomic Hydrogen has 4 fermions, three quarks to make a proton, and 1 electron. There is an even number of fermions, and each fermion has a 1/2 spin. Since there are an even number of fermions, the total spin value is an integer. This spin number is the "intrinsic" spin number that cannot be changed, but its orientation "up" or "down" can be changed.  For atomic Hydrogen, it is a Boson because it has integer spin, however it also has a single electron. I read on physics forums, , that the spin of atom comes from the electrons and not its nucleus. I also read on here, , that the spin of atomic Hydrogen is 1/2! The answer says atomic Hydrogen has spin 1/2 because it ignores the nuclear spin.  This is one thing that is confusing me. Shouldn't atomic Hydrogen have an integer spin because of the nuclear component? So does atomic Hydrogen have spin and is affected by a magnetic field? Nuclear spins are affected by magnetic fields, but they aren't as affected as electrons according to the discussion on physics forums.  Why do we ignore nuclear spin sometimes? Also, can someone help me out here with all the possibilities?  Is there a Boson with an half integer spin value? (Surely, there must not be) However atomic Hydrogen is one of those cases! (It seems...) (Why don't we cancel out the nuclear spin with the electron spin?)  Say we have another atom that is a Boson, It has unpaired electrons in different orbitals, so what determines whether or not electrons fill in orbitals as spin up or down? Does spin down nuclear spin cancel out a electron up spin?
How to ignore certain files in Git Before, the concept of imaginary numbers, the number $i = \sqrt{-1}$ was shown to have no solution among the numbers that we had. So we declared $i$ to be a new type of number. How come we don't do the same for other "impossible" equations, such as $x = x + 1$, or $x = 1/0$?  Edit: OK, a lot of people have said that a number $x$ such that $x = x + 1$ would break the rule that $0 \neq 1$. However, let's look at the extension from whole numbers to include negative numbers (yes, I said that I wasn't going to include this) by defining $-1$ to be the number such that $-1 + 1 = 0$. Note that this breaks the "rule" that "if $x \leq y$, then $ax \leq ay$", which was true for all $a, x, y$ before the introduction of negative numbers. So I'm not convinced that "That would break some obvious truth about all numbers" is necessarily an argument against this sort of thing. Why is a conservative force defined as the negative gradient of a potential? I'm learning about work in my dynamics class right now. We have defined the work on a particle due to the force field from point A to point B as the curve Integral over the force field from point A to B. From math I know that if a vector field has a potential, we only need to evaluate the potential at point B minus the potential at point A to get the result of the curve Integral. In the text that I'm reading, it's explained that if the integral over a force-field is path-independent, then the force field $F = -{\rm grad}(V)$, where $V$ is the potential. Why is it defined as the negative gradient? Doesn't one determine the potential from $F$ mathematically. Why do we impose the sign on the potential? How can I get a command block? How to join a LAN / IPX game on Diablo 1? Recently some of my friends and I grew nostalgic about the original Diablo and realized we've never truly tried the multiplayer aspect of that game. So we set up a modern VPN LAN solution via tuungle (using the appropriate IPX Wrappers) but the problem is, while any of us can manage to create session in Diablo FULL, others cannot find a way to join my IPX/LAN game.  There are no "join" buttons in the game itself.  I've read somewhere that Spawn version is a trial version but can be used to join Multiplayer games. If they can, is it possible for them to play the entire game on LAN or is trial restricted from choosing some classes/accessing some areas?  Or are there some other ways to join? How do I start a process from C#? I am teaching myself information about groups, but don't really understand how to work through this problem. Here is what I have been thinking so far (please note that I do not need to work through showing any closure): $\mathbb{Z}^*$ denotes the nonzero integers. Prove or disprove: $(\mathbb{Z}^*, \cdot)$ and/or $(\mathbb{Z}^*, \div)$ is a group.  For $(\mathbb{Z}^*, \cdot)$:  Group. Associative Law: Let $a,b,c \in \mathbb{Z}^*$. Then $(a\cdot b)\cdot c=a\cdot (b \cdot c)$, and the associative law holds. Existence of Identity: Let $a \in \mathbb{Z}^*$, then $a \cdot 1 = 1 \cdot a = a$, and the identity holds. Existence of Inverses: Let $a \in \mathbb{Z}^*$. Then the inverse of $a^{-1}=-a$, and the inverse holds. Note that this only works because we are ommitting zero.  Hopefully this looks like I am on the right track. I don't know to what extent I can explain logic vs showing it with mathematical operations, so I would appreciate guidance in this respect.  For $(\mathbb{Z}^*, \div)$: Not a group. Disprove by counterexample.  Yeah, I dunno about this one. I don't think it's true, because we will be introduction rational expressions that won't allow this to hold, but I'm not sure where I can use this information to disprove the statement. how to left justify comments to indent same as other text in Algorithmic How do I left justify my comments in the algorithm.  I am using algorithmicx package.  What I want is: to pull the comment to left as shown in the attached snapshot.  The code for my algorithm is       \documentclass[a4paper]{article}     \pagestyle{empty}     \usepackage{algorithm}     \usepackage{algpseudocode}     \usepackage[caption=false,font=footnotesize]{subfig}     \begin{document}     \begin{algorithm} \label{algoQ}     \caption{Algorithm to check quality of methods}     \begin{algorithmic}     \For{\textbf{each} $msd$ in$msdList$}  \Comment { \% for each MSD \%}     \Statex   \Comment { \% get MSDs referenced method service \%}     \EndFor \textbf{endFor}     \end{algorithmic}     \end{algorithm}     \end{document} Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$ How to convert string to byte array in Python the converse of Pythagoras Theorem Find the value of $a^2-b^2+c^2$ Meta's tag pages inaccessible due to self-redirect loop Tag pages (route /questions/tagged/tagname) redirect to themselves indefinitely:  $ curl -D - http://meta.stackexchange.com/questions/tagged/featured HTTP/1.1 302 Found Cache-Control: private Content-Type: text/html; charset=utf-8 Location: /questions/tagged/featured X-Frame-Options: SAMEORIGIN Date: Fri, 05 Jul 2013 16:47:42 GMT Content-Length: 143  &lt;html&gt;&lt;head&gt;&lt;title&gt;Object moved&lt;/title&gt;&lt;/head&gt;&lt;body&gt; &lt;h2&gt;Object moved to &lt;a href="/questions/tagged/featured"&gt;here&lt;/a&gt;.&lt;/h2&gt; &lt;/body&gt;&lt;/html&gt;   This only happens on Meta, so far, but only applies to any meta-tag that doesn't have a dash in it; those with a dash seem to be exempt, as do invalid tags:    redirects.  does not.  does not. The new ask page is now live on the network! Mysql: Select all data between two dates I am creating a query that finds the shortest path from dangerous crossing nodes to hospitals (many-to-many). I have the proper output from pgr_dijkstra, with output as follows  seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost  -----+----------+-----------+---------+------+------+------+----------    1 |        1 |         2 |       3 |    2 |    4 |    1 |        0    2 |        2 |         2 |       3 |    5 |    8 |    1 |        1    3 |        3 |         2 |       3 |    6 |    9 |    1 |        2    4 |        4 |         2 |       3 |    9 |   16 |    1 |        3    5 |        5 |         2 |       3 |    4 |    3 |    1 |        4    6 |        6 |         2 |       3 |    3 |   -1 |    0 |        5    7 |        1 |         2 |       5 |    2 |    4 |    1 |        0    8 |        2 |         2 |       5 |    5 |   -1 |    0 |        1   I am trying to use st_makeline to create seperate lines for each individual node path, however thus far the function has been creating one big line SELECT  st_transform(st_makeline(t1.the_geom),4326)         FROM pgr_dijkstra(                 'SELECT osm_id as id, source, target, cost FROM spatial.melbourne_edges',                 array(select hospital_id from hospitals_in_vicinity),                  array(select crossing_id from dangerous_crossing_nodes), false) as route                 inner join spatial.melbourne_nodes t1 on route.node = t1.id --);  How am i able to make a column of all the different paths? How do I take great HDR photos of moving objects? By moving objects, I mean cities with cars, ocean with moving water, malls with people moving by.  I tried it on moving people and had noticeable ghosting, using bracketed shots at + and - 2ev.  What's the basic technique on getting sharp looking HDR photos in areas that are moving? I'm assuming it's not bracketed shots but a single shot with exposure editing? What are irreducibles in the ring $R$ of entire functions? How add 14 days on end date I have End Date column and I want to add 14 Days on it auto when created, can I do it by workflow? Can I do it via jQuery. If yes how? if no how I can do it? What's the difference between "Service" and "/etc/init.d/"?