Nobody hass seen cold dark matter. Are ultra-cold (non-relativistic) neutrinos, below 1 fK (femtokelvin), an option for dark matter? This is a question about normal neutrinos - electron neutrinos and muon neutrinos and tau neutrinos - and not any additional, invented neutrino types. This is a question about neutrinos that are not in the cosmic neutrino background, which have a temperature of 1.95K. The question is about cosmological dark matter, not about galactic dark matter. Their density could be large enough to produce the observed cosmological dark matter density. Due to their low temperature and low kinetic energy they would be undetectable. They would be continuously emitted by the cosmological horizon in the same way as black hole radiation is continuously emitted by a black hole. Alternatively, they would arise automatically throughout the universe, whenever space grows in size. Why is this not possible? Or why is it possible? -- Given that the answers below imply that ultra-cold neutrinos cannot be dense enough because of their fermion character, could fermion condensation (via Cooper pairs, as in superconductors) solve the problem?
A number of times I have encountered in text-books and articles that neutrinos might contribute only a small fraction to dark matter. The reason has to do with the fact that if all of the dark matter consisted of neutrinos, then small-scale structures in the Universe could not have formed yet, because, as they say, neutrinos "wash out" small fluctuations. However, none of these texts provided a reference to any specific sources explaining in detail what is meant by "washing out". After all, neutrinos are notorious in their weak interaction with baryonic matter, so if there is a small-scale fluctuation of baryons, then how background neutrinos can prevent it from growing further if they practically do not interact with baryons? I guess the question boils down to calculating cross-sections of interactions at specific temperatures. I would appreciate comments and references to sources addressing this particular issue.
How should we understand the teletransportation thought experiment? A book with two twins and a difficult relation, a room where time flows slower than the outside and a mysterious monster coming from a sink There was this pocket book, back when I was a teenager (20 years ago), with these two twins discovering a room (it was something like a tool shed) where time flowed slower (1 hour inside was equal to 1 minute outside if i remember correctly).   Inside the shed there was a sink and a strange snake-ish metallic monster was slowly coming out from it.  One of the twins, the one with the "less marked" personality, decides to spend one year (during a whole night) inside the room in order to get out older than his twin.  I don't remember what happens with the monster, I think they destroyed the whole shed in the very end. Where should I put  tags in HTML markup? When embedding JavaScript in an HTML document, where is the proper place to put the &lt;script&gt; tags and included JavaScript? I seem to recall that you are not supposed to place these in the &lt;head&gt; section, but placing at the beginning of the &lt;body&gt; section is bad, too, since the JavaScript will have to be parsed before the page is rendered completely (or something like that). This seems to leave the end of the &lt;body&gt; section as a logical place for &lt;script&gt; tags.  So, where is the right place to put the &lt;script&gt; tags?  (This question references , in which it was suggested that JavaScript function calls should be moved from &lt;a&gt; tags to &lt;script&gt; tags. I'm specifically using jQuery, but more general answers are also appropriate.) If every eigenvector of $T$ is also an eigenvector of $T^{*}$ then $T$ is a normal operator Let $V$ be a finite-dimensional inner product space over $\mathbb{C}$ and $T: V \to V$ a linear transformation.   Show that if every eigenvector of $T$ is also an eigenvector of $T^{*}$ then $T$ is a normal.   We need to show that $\forall v \in V,\ TT^*v=T^*Tv$.  I started by picking $v$ to be an eigenvector of $T$, hence $Tv=\lambda_1 v$, and $T^*v=\lambda_2 v$. Therefore: $$TT^*v=T(\lambda_2 v)=\lambda_2 Tv=\lambda_1 \lambda_2 v=...=T^*Tv$$  But I'm stuck when $v$ is not an eigenvector.  (Also, this question is taken from a chapter about Jordan forms, but I can't see how it relates) Convert DOS line endings to Linux line endings in Vim If I open files I created in Windows, the lines all end with ^M. How do I delete these characters all at once? Usually, the equality $\mathfrak{m}^\mathfrak{m} = 2^\mathfrak{m}$ for infinite cardinal $\mathfrak{m}$ is proved like that: $$ 2^\mathfrak{m} \leqslant \mathfrak{m}^\mathfrak{m} \leqslant (2^\mathfrak{m})^\mathfrak{m} = 2^{\mathfrak{m} \cdot \mathfrak{m}} = 2^\mathfrak{m} $$ The last step relies much on the axiom of choice, because the fact $\mathfrak{m}\cdot\mathfrak{m} = \mathfrak{m}$ does. Moreover,  states that in $\sf{ZF}$ this fact is equivalent to $\sf{AC}$.  Note, by a cardinal I mean an equipollence class of an arbitrary set, not necessarily admitting a well-ordering.  That has motivated my question: what can we say about relationship of the initial equality and the axiom of choice in pure $\sf{ZF}$?    To avoid question about definition of cardinals without $\sf{AC}$, we may consider the following statement instead:     For any infinite set $X$ exists a bijection $\; F \, \colon X^X \rightarrow 2^X$   where $X^X$ is the set of all functions from $X$ to $X$, $\; 2^X = \mathcal P(X)$ is the power set, and an infinite set is such that cannot be bijectively mapped onto a finite ordinal. Variance (different definitions) I'm new to statistics and reading stats books I found different definitions for Variance.  Definition1: $ s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2 $  Definition2: $ s^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \bar{x})^2 $  I would like to know why is used different definition for same thing? How to check if a row exists in MySQL? (i.e. check if an email exists in MySQL) Avoid trailing zeroes in printf() After a company has issued shares, why should it care if the value of the shares fluctuate? Since the shares are now publicly traded, if the value fluctuates, that is strictly a transaction between buyer and seller, none of whom are directly related to the company. E.g. if I sell X an iPhone for $100, why should I care if X is selling the iPhone to Y for 1 dollar or 1000 dollars? I have got my $100, so I need not bother. No? Move the Add Favorite / Ignored Tags boxes to the top It seems that most people who use the ignored tags feature end up with a fairly long list of those tags.  Although , it is sometimes necessary to add new ignored tags manually (typically when adding some-tag*).  It would be a lot easier if the add box was above the long list of ignored tags rather than below. I suppose the same would apply to the favorites tags for consistency's sake. Understanding slice notation I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it. How to catch and print the full exception traceback without halting/exiting the program? Label and caption without float I’d like to have an environment that works much like a float, except that it doesn’t float.  That is, in fact, I’d like to be able to define an environment that has a label and a caption.  I explicitly do not want to use a floating environment, though. For one thing, floats do many things fancy which I just don’t need, nor want (such as spacing) and for another, floats have their share of problems (for example consider the problem of ).  Is there a ready-made way to achieve this? Of course, I could always write my own based on the result of the other answer, i.e. harnessing \refstepcounter. But I’m not sure how to use that, documentation is scarce, and I’d prefer an existing solution. Does $\sum\limits_{k=1}^n 1 / k ^ 2$ converge when $n\rightarrow\infty$? I can prove this sum has a constant upper bound like this: $$\sum_{k=1}^n \frac1{k ^ 2} \lt 1 + \sum_{k=2}^n \frac 1  {k (k - 1)} = 2 - \frac 1 n \lt 2$$ And computer calculation shows that sum seems to converge to 1.6449.  But I still want to know:  Does this sum converge? Is there a name of this sum (or the series $\frac{1}{k^2} $)? How to close (kill) ssh ControlMaster connections manually stop Ipod from asking for old Apple ID password Recently, I've changed my Apple ID because my old E-mail has been hacked. Now that I set the new one as my apple ID, the old Apple account still appears when I open almost all my apps on my Ipod Touch (4th Gen.), asking for the password to my old Apple ID. When I put in the old password to my old Apple ID, it'll keep asking for it no matter how many times I type it in. How do I fix this while keeping my account secure? Any suggestions would help! I just learned about the C++ construct called "placement new".  It allows you to exactly control where a pointer points to in memory.  It looks like this:   #include &lt;new&gt;        // Must #include this to use "placement new"  #include "Fred.h"     // Declaration of class Fred   void someCode()  {    char memory[sizeof(Fred)];    void* place = memory;     Fred* f = new(place) Fred();   // Create a pointer to a Fred(),                                   // stored at "place"     // The pointers f and place will be equal     ...  }    (example from ) In this example, the this pointer of Fred will be equal to place.    I've seen it used in our team's code once or twice.  In your experience, what does this construct enable?  Do other pointer languages have similar constructs?  To me, it seems reminiscent of equivalence in FORTRAN, which allows disparate variables to occupy the same location in memory. As I understand it, anything created with an alloc, new, or copy needs to be manually released. For example:  int main(void) {     NSString *string;     string = [[NSString alloc] init];     /* use the string */     [string release]; }   My question, though, is wouldn't this be just as valid?:  int main(void) {     NSAutoreleasePool *pool;     pool = [[NSAutoreleasePool alloc] init];     NSString *string;     string = [[[NSString alloc] init] autorelease];     /* use the string */     [pool drain]; } The rule says if the order of two actions/events is clear then the past perfect is not necessary, i.e. you can use past simple. So if the sentence has before or after then the order is clear and therefore the rule applies.  says the first sentence is incorrect. Is he/she right? If so, how do you explain what appears, to me, to be contradictory?     If the Past Perfect is not referring to an action at a specific time,   Past Perfect is not optional. Compare the examples below. Here Past   Perfect is referring to a lack of experience rather than an action at   a specific time. For this reason, Simple Past cannot be used.      Examples:      She never saw a bear before she moved to Alaska. Not Correct      She had never seen a bear before she moved to Alaska. Correct   They say "a lack of experience rather than an action". Saying that just does not solve the problem I have which is the past simple fits the rule of order of events. Not seeing is a negative event with the verb "to see".  I hope the answer won't be this is how we speak or this is how English works or since when languages are logical!