What's in the empty space between a nucleus and the electrons?
What is in the space between a nucleus of an atom and its electrons?
Does Change Data Capture (CDC) work in a SQL Server 2012 AlwaysOn Failover Cluster Instances setup? Does  work in a  setup?  There would be two nodes in the AlwaysOn Failover Cluster Instances setup and two Domain Controllers.  We are not using AlwaysOn Availability Groups.  Will CDC work? and will it failover? Target='_blank' to show in new window, NOT new tab, possible? What are irreducibles in the ring $R$ of entire functions? Here's how far I have gone:  I first find the units in $R$. Let $f$ $ \in $ $R$ be a unit. Then $\exists$ $g$ $\in$ $R$ such that $fg=1$, i.e $f(z)g(z)=1$ $\forall$ $z$ $\in$ $\Bbb C$.  Then, $f(z)$ $=$ $\frac 1{g(z)}$ $\forall$ $z \in \Bbb C$. Hence $f(z),g(z) \neq 0$ $\forall$  $z \in \Bbb C$.  Now to find the irreducibles, let $f \in R$ be an irreducible. Hence whenever  $f(z)=g(z)h(z)$ for $g,h \in R$, then $g$ or $h$ is a unit.  Let $h$ be the unit and $\alpha$ be a zero of $f$. Then $f(\alpha)=g(\alpha)h(\alpha)=0$ $\Rightarrow$ $g(\alpha)=0$. Hence $z-\alpha$ is a factor of $g$. So $g(z)=(z-\alpha)^ng_1(z)$ for some $n \in \Bbb N$, where $g_1$ is unit. Since $f$ is irreducible, hence $n=1$.  I'm stuck here. What can be my next step? I opened Cairo-dock in my terminal with: open cairo-dock and that worked but if I close the terminal it goes with it. How can I keep it open regardless of the terminal? How to solve this probability problem analytically (instead of using simulation)? Probability of Bill wins the game if he goes first In particular, I am referring to the Pearson product-moment correlation coefficient. can any one tell me how to write long equation in multline i tried with coding below but some errors of \right and \left appear \begin{multline*} \displaystyle \left \| f  \right \|_{M\dot{K}^{\alpha(\cdot),q}_{p(\cdot), \lambda}(\mathbb{R}^{n})} \approx \max \left\{ \sup_{L\leqslant0,L\in  \mathbb{Z}}2^{-L\lambda}\left ( \sum_{k=-\infty}^{L}2^{k\alpha(0)q}\left \|  f\chi_{k} \right \|^{q}_{L^{p(\cdot)}} \right )^{1/q},\\\sup_{L&gt;0,L\in \mathbb{Z}}\left[ 2^{-L\lambda}\left ( \sum_{k=-\infty}^{-1}2^{k\alpha(0)q} \left \| f\chi_{k} \right \|^{q}_{L^{p(\cdot)}} \right )^{1/q}\\ +2^{-L\lambda}\left ( \sum_{k=0}^{L}2^{k\alpha(\infty)q}\left \|  f\chi_{k} \right \|^{q}_{L^{p(\cdot)}} \right )^{1/q}\right] \right\}  \end{multline*} I have a vector file containing thousands of points. Where points are within x distance from each other, I wish to delete one of the points and keep the other (either by snapping to one point, or simply erasing one of the two points)  However, in Whitebox the vector cleaning tool only works with polygons and lines.  Is there some other way I can do this with my shapefiles? Do tag edits count for Archaeologist? $SU(3)$ irreducible representations with tensor method I am dealing with the tensor product representation of $SU(3)$ and I have some problems in understanding some decomposition.  1) Let's find the irreducible representation of $3\otimes\bar{3}$  we have that this representation trasforms like   $${T^\prime}^i_j=U^i_k {U^{\dagger}}^l_j T^k_l $$  hence I observe that  $$Tr(T)=\delta^j_iT^i_j$$ is an invariant and so  $$T^i_j=\left(T^i_j-\frac{1}{3}\delta^j_iT^i_j\right)+\frac{1}{3}\delta^j_iT^i_j$$  allows me to write $$3\otimes\bar{3}=8\oplus1$$ Here comes my questions: I have heard that this $8$ representation is an "$8_{MA}$" where MA is for "mixed-antisymmetric". The meaning of "mixed-antisymmetric" shold be: "the tensor $\left(T^i_j-\frac{1}{3}\delta^j_iT^i_j\right)$ should be antisymmetric for an exchange of 2 particular indexes but not for a general exchange of 3 indexes". What does this mean? I see only 2 index in that tensor.  2) Consider this representation: $$3\otimes3\otimes3=3\otimes(6\oplus\bar{3})=3\otimes6_S\oplus3\otimes\bar{3}=3\otimes 6_S\oplus8_{MA}\oplus1$$  and now on my notes I have $$3\otimes6_S=10_S\oplus8_{MS}$$  Where "MS" is for "mixed symmetric": symmetric for an exchange of 2 particular indexes but not for a general exchange of 3 indexes.  I could not demonstrate this last decomposition using tensor method. I started noticeing that: $$3\otimes6_S=q^iS^{k,l}$$ where $S^{k,l}$ is a symmetric tensor But then I am not able to proceed in demonstrating the above decomposition (note: I would like to demonstrate this decomposition using only tensor properties, not Young tableaux). I tried to look on Georgi, Hamermesh, Zee and somewhere online but I have not found any good reference which explains well this representatin decomposition...  EDIT: the demonstration should not include the use of Young diagrams...my professor started the demonstration by writing $\epsilon_{\rho,i,k}q^i S^{k,l}=T'^l_\rho=8_{MS}$ and then stopped the demonstration. Java ReentrantReadWriteLocks - how to safely acquire write lock? I am using in my code at the moment a  to synchronize access over a tree-like structure.  This structure is large, and read by many threads at once with occasional modifications to small parts of it - so it seems to fit the read-write idiom well.  I understand that with this particular class, one cannot elevate a read lock to a write lock, so as per the Javadocs one must release the read lock before obtaining the write lock.  I've used this pattern successfully in non-reentrant contexts before.  What I'm finding however is that I cannot reliably acquire the write lock without blocking forever.  Since the read lock is reentrant and I am actually using it as such, the simple code  lock.getReadLock().unlock(); lock.getWriteLock().lock()  can block if I have acquired the readlock reentrantly.  Each call to unlock just reduces the hold count, and the lock is only actually released when the hold count hits zero.    EDIT to clarify this, as I don't think I explained it too well initially - I am aware that there is no built-in lock escalation in this class, and that I have to simply release the read lock and obtain the write lock.  My problem is/was that regardless of what other threads are doing, calling getReadLock().unlock() may not actually release this thread's hold on the lock if it acquired it reentrantly, in which case the call to getWriteLock().lock() will block forever as this thread still has a hold on the read lock and thus blocks itself.  For example, this code snippet will never reach the println statement, even when run singlethreaded with no other threads accessing the lock:  final ReadWriteLock lock = new ReentrantReadWriteLock(); lock.getReadLock().lock();  // In real code we would go call other methods that end up calling back and // thus locking again lock.getReadLock().lock();  // Now we do some stuff and realise we need to write so try to escalate the // lock as per the Javadocs and the above description lock.getReadLock().unlock(); // Does not actually release the lock lock.getWriteLock().lock();  // Blocks as some thread (this one!) holds read lock  System.out.println("Will never get here");   So I ask, is there a nice idiom to handle this situation?  Specifically, when a thread that holds a read lock (possibly reentrantly) discovers that it needs to do some writing, and thus wants to "suspend" its own read lock in order to pick up the write lock (blocking as required on other threads to release their holds on the read lock), and then "pick up" its hold on the read lock in the same state afterwards?  Since this ReadWriteLock implementation was specifically designed to be reentrant, surely there is some sensible way to elevate a read lock to a write lock when the locks may be acquired reentrantly?  This is the critical part that means the naive approach does not work. Is there a canonical explanation for how Ant-Man's weight works when he shrinks down that's consistent with the various events depicted in the film?    I think the explanation given in the film is roughly "the suit compresses the space in-between atoms, so your size decreases, your density increases, and your total mass stays the same", however it seems to be portrayed in contradictory ways.  For instance:   He can float in water, and even be sent shooting through the air by a relatively gentle flow of water filling a bathtub.  This wouldn't happen if he retained his original mass, as he'd essentially be the densest thing on the planet and should sink like a stone even in a vat of molten lead. Upon landing after being ejected from the bathtub, the ceramic tile underneath him shatters.  That takes a significant amount of force, and similar effects are used at other points in the movie where he falls onto (or straight through) various things. He's able to get sucked into a vacuum-cleaner.  One that didn't even appear to be a high-end, extra powerful vacuum-cleaner, let alone one capable of sucking up a 200 pound piece of dust.   He can run along the barrel of a gun as someone shoots it, apparently without causing them to drop the weapon or even have trouble continuing to aim it.     Does a more consistent explanation exist in other media, that would fit with the above examples?  Or is this simply a case of the power being made to do whatever happened to be most convenient at the time? Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$ Prove that (a) gcd(a, b) = gcd (a, b – a) (b) Let r be the remainder if we divide b by a. Then gcd(a, b) = gcd(a, r).  I solved part a like: Assume a=pcommonpa b=pcommonpb gcd (a,b) = pcommon b-a = pcommon*(pb-pa)  So: gcd(a, b-a) = common again But I need help for part b guys I can solve it but I need a mathematical expression. tags of mundanity that are gratuitously applied to posts It's an additional unnecessary burden to the honest stacker during suggested edit duty. A question presents some code then the minor editor adds a tag like 'for-loop' or 'forms'.  These tags are so general that they only have a handful of followers. They serve no useful purpose and are the cause of many too minor edits. Why not permit culling of generic tags? The Android app crashes when trying to upload a picture from my phone Characterization convex function. Is it correct to use the word "birthday" for the deceased, or is there a better alternative? How does one refer to the birthdate of someone who is no more, we usually say  Today is my uncle's 80th birth anniversary (Common in Indian English, not sure if it's correct)  or  Today would have been my uncle's 80th birthday   Is it right to say  "Today is my uncle's 80th birthday" for an uncle who is dead? Donating winning lottery ticket to 501(c)3 Private Foundation: cost-basis deduction + full tax free redemption for foundation? US 501(c)3 Private Foundations are typically controlled by the primary donator, so that is a nice perk, but in exchange for that perk I realize the tax deductions for donating are significantly lowered than for charities. Aside from being lower, the tax code doesn't recognize appreciated property and only allows for a deduction based on the donating taxpayer's cost-basis: ie. the price they paid for the property no matter its current market value.  When there is a significant delta of price paid vs current redeemable value, it seems this can still be a perk for the donating taxpayer in some circumstances, such as with lottery tickets that are known winners already.  If the donating taxpayer pays $1 for the ticket. Their cost basis is $1. If the ticket is now worth $100,000,000 but has not been redeemed, is it accurate that the donating taxpayer can donate this to their private foundation for a deduction at cost basis, and the private foundation can redeem the $100,000,000 ticket completely exempt from all lottery withholding income taxes?   (Other taxes unique to private foundations are known and outside the scope of this question.)  Most literature I can find is about appreciated marketable securities, and occasionally real estate. It doesn't seem that the tax code specifies any distinction between property, but it also doesn't seem the answer to this question is part of the general collective conscious even if it really is that obvious if my understanding is already correct. How can't install a 338KB app when I have 474MB free? I have a Motorola phone, with 8GB of internal memory.  To my surprise, in a few days, I had 474MB of free space, but couldn't install a 338KB app!! So, clearly the limit of ~25MB referred to in some comments ( and ) are not always the case. A user just told me the following:     Actually it's "25MB or 10% of the storage", whichever is hit first. So   with e.g. 10 GB internal storage, it would hit you as soon as you drop   below 1 GB free. Crazy, but that's what it is.   Actually, that's not correct, because I didn't have to free up 1GB of internal memory. But anyway, half a gigabyte is enough to run a full operational system. I've seen similar complaints of hundreds of MB not enough to install apps ~ 1MB or similar small operations ( and ).  What's wrong here? WinDirStat shows 244GB unknown space on external drive I recently noticed that one of my external hard drive seems to be missing a lot of space. It was recommended that I try WinDirStat, as it could help identify how much space each file was taking up. This is the result:     As you can see, there is about 244.7GB "unknown" usage.  Doing a bit of research online, the most common suggestion was (a) Recycle Bin and (b) System Volume Information.  (a) As you can see, empty. To double check, I ran Disk Cleanup. It confirmed that it was empty. (Note that a new file appeared by the time I took this screenshot, but it's only 129 Bytes.)  (b) Harder to tell. However, according to various forums, the most common reason for System Volume Information to grow large is due to System Restore Files. I had a look, and it is definitely turned off for this drive, as seen here:     What else could be causing this issue? It is an enormous amount of storage to have gone missing!