What is meant by the spin of a particle?
What is spin as it relates to subatomic particles?
What does this red icon on my panel mean? This red icon.... It showed up after I upgraded to Ubuntu 12.04LTS; I can't figure out how to ditch it. It seems to be a notification thing.  I am at a loss.  The icon is this one:      I clicked it and read this:     An error occurred, please run Package Manager from the right-click menu or apt-get in a terminal to see what is wrong. The error message was:  'Error: BrokenCount&gt;0'.        This usually means that your installed packages have unmet dependencies. Let $been(x,y)$ denote "person x has been to place y."   Express “Every person has been to 2 or more places” using quantifiers and $been(x, y)$.  This one is completely stumping me. I'm sure that I haven't come across this kind of concept before, and can't wrap my head around how I would approach it. I suspect the quantifiers should be $∀x$, $∀y$, and that it may involve negating the statement "every person has been to one or zero places," but that's as far as I can manage to go. Any help greatly appreciated. How to cut the non-overlapping part of 2 shapes in Illustrator CS6 Does English have any singularia tantum besides mass nouns? and  are, respectively, nouns that have only a singular form and nouns that have only a plural form.  In English, we have a handful of pluralia tantum that are mass nouns which take the plural form (e.g. "riches" and "remains"), a whole load of pluralia tantum that refer to things that come in pairs (e.g. "trousers", "sunglasses", "knickers", or "scissors"), and at least one plurale tantum that fits into neither of the above categories ("clothes", meaning multiple items of clothing - it's clear what the hypothetical singular "clothe" would mean, yet it mysteriously isn't a word). Singularia tantum, on the other hand, seem less varied. As far as I can tell, they are all  - things like "information", "milk", and "racism".  One can imagine there being a singulare tantum that is not a mass noun. For example, we can imagine an alternate universe in which it is still correct English to talk about "a dog", but talking about "dogs" in the plural is incorrect and funny in the same way that it is incorrect and funny to talk about a "scissor". It might seem unintuitive to think that such a noun even could exist - surely, if it is not a mass noun, then people would just pluralise it with an "s" on the end like most other words? But the converse argument could just as well be made about countable pluralia tantum, and I still cannot go to a shop and buy a "clothe". Hence my question: do we have any such countable singularia tantum in the language? Have we in the past? How to run a command that involves redirecting or piping with sudo? How can I know if a process is running? When I get a reference to a System.Diagnostics.Process, how can I know if a process is currently running? Automatic tagging of releases If $f^2$ and $f^3$ are $C^{\infty}(\mathbb R)$ then $f$ is $C^{\infty}(\mathbb R)$ First, this question is motivated by the imprecise question: Is there a sensible notion of parity (evenness and oddness) for real numbers?   Here are some properties a notion of parity for $\mathbb{R}$ should have:    It should be an equivalence relation on $\mathbb{R}$ with exactly two equivalence classes.  Each equivalence class should be dense in $\mathbb{R}$. There should be some kind of symmetry between the two equivalence classes. (This is intentionally imprecise.)   If we divide $\mathbb{R}$ into rationals and irrationals, this lacks symmetry, since the rationals have measure zero and are countable, while the rationals have infinite measure and are uncountable.   So we could require that each equivalence class be uncountable and/or have positive (or infinite) measure. Then take one equivalence class to be the rationals, union with countably many fat cantor sets with positive measure, and the other class its complement. Then both classes are now dense, uncountable, and have infinite measure. But again, symmetry is lacking. One of these classes is "uncountable everywhere" and has "positive measure everywhere" while the other does not.   I propose some definitions: A subset $A \subset \mathbb{R}$ is uncountable everywhere if for any open interval $(a,b)$, the intersection $A \cap (a,b)$ is uncountable. A subset $A \subset \mathbb{R}$ has positive measure everywhere if for every open interval $(a,b)$, the intersection $A \cap (a,b)$ has positive measure. We can see immediately that having positive measure everywhere implies being uncountable everywhere, since a positive measure set must be uncountable.   Finally, my questions:    Is there a partition of $\mathbb{R}$ into two sets that are both uncountable everywhere?  Is there a partition of $\mathbb{R}$ into two sets that both have positive measure everywhere?  Is there a partition of $\mathbb{R}$ into two sets that split each interval $(a,b)$ into two parts of equal measure?   Potential generalizations for extra credit: What about partitions of $\mathbb{R}$ with $n$ equivalence classes, where $n \in \mathbb{N}$, or even with countably many, or even uncountably many equivalence classes?  Note: If you've seen these definitions of uncountable everywhere or positive measure everywhere somewhere under a different name, please let me know. I've never found anything where other people were thinking about these notions.  EDIT: By "measure," I mean Lebesgue outer measure, so we don't have to worry about anything being measurable. How do I make a redirect in PHP? Overriding !important style Title pretty much sums it up.  The external style sheet has the following code:  td.EvenRow a {   display: none !important; }   I have tried using:  element.style.display = "inline";   and  element.style.display = "inline !important";   but neither works. Is it possible to override an !important style using javascript.  This is for a greasemonkey extension, if that makes a difference. After the downfall of Voldemort, what happened to the Death Eaters?  They committed many crimes, including mass murder and torture. Nothing in the books made mention of their punishments. What happened? I have a small Problem that occurs from time to time.   Sometimes, when I copy things or when I put an object from the symbol library on my page, the whole file gets messed up. The screenshot shows it. I make the graphic on the right, Illustrator the ones on the left.   I have pixel snapping checked. Is there a way to tell Illustrator to align everything to pixels no matter what? Rails: Could not find bcrypt-ruby-3.0.1 in any of the sources Computing determinant without expansion $$\begin{align}\mathrm D &amp;= \left|\begin{matrix} (b+c)^2 &amp; a^2 &amp; a^2 \\ b^2 &amp; (a+c)^2 &amp; b^2 \\ c^2 &amp; c^2 &amp; (a+b)^2 \end{matrix}\right|\\ &amp;= (a+b+c)\left|\begin{matrix} b+c - a &amp; a^2 &amp; a^2 \\ b - a -c &amp; (a+c)^2 &amp; b^2 \\ 0 &amp; c^2 &amp; (a+b)^2 \end{matrix}\right| \\ &amp;= (a+b+c)^2\left|\begin{matrix} b+c - a &amp; 0 &amp; a^2 \\ b - a -c &amp; a+c - b &amp; b^2 \\ 0 &amp; c - a-b &amp; (a+b)^2 \end{matrix}\right|\\ &amp;= (a+b+c)^2\left|\begin{matrix} b+c - a &amp; 0 &amp; a^2 \\ 0 &amp; a+c - b &amp; b^2 \\ c - a-b &amp; c - a-b &amp; (a+b)^2 \end{matrix}\right|\end{align}$$  Can $\rm D$ be further simplified without expanding ?  I feel it should be because this was competition question. Was The Empire in Star Wars inspired by Nazi Germany? I have some plasterboard screws like this:     However, without a drill I have a job getting them into the wall. Am I safe to use normal screws on hangings that aren't going to be taking a great deal of weight? In this case it is a rack of coat hooks. STI vs STD vs Sexually Transmitted Virus Where to get 2010 Census Block data? I would like to download 2010 Census Block Data for several towns and I can't seem to find it on American Factfinder.   Is it there? And if not, does anyone know where I could find it? I want to calculate the derivative of $|x|^\alpha$ with respect to $x$, where $1&lt;\alpha&lt;2$.  $\frac{d|x|^\alpha}{dx}=\alpha|x|^{\alpha-1}\mathrm{sign}(x)$  Is it correct?  And is it true that  $\lim_{x \to 0} \alpha|x|^\alpha\mathrm{sign}(x)=0$?  What with the following derivative $|x|^\alpha\rm{sign}(x)$. I would be grateful for any hints.