Can I really pay 0% tax on unlimited long term capital gains if I'm in the 12% federal income tax bracket?
How are long-term capital gains taxed if the gain pushes income into a new tax bracket?
In De Broglie's Explanation for Bohr's Quantization Condition, why do we not use 2πr = n λ/2, why do we use 2πr = n λ? In de Broglie's explanation for Bohr's quantization condition, why do we not use $2\pi r = n\lambda/2$, why do we use $2\pi r = n\lambda$?  We know that in waves on strings, for standing waves creation in a string between two rigid supports, we use "Length of String" $ = n \lambda/2$. Why do we not use a similar concept here? How to include third party Python libraries in Google App Engine? Would a Jedi (Sith) clone be force-full or force-less Just seen a picture of Vader Force-choking a trooper. And then I started wondering: what if they had cloned a Sith (or a Jedi). Would the clones have the Force? Specifically, would they have the same Force as the original? Explain $\iint \mathrm dx\,\mathrm dy = \iint r \,\mathrm \,d\alpha\,\mathrm dr$ Is using std::deque or std::priority_queue thread-safe? Looking for illustrator script to swap all objects with another I have a map with small circles for over 200 cities. I need to change all of the circles into map pins. Is there a way to do this? I think it's a script maybe.   I know how to select all objects of the same appearance and give them a new graphic style but that will only let me change the color, stroke, etc. not replace with a new shape. Problem with Winbind/Samba How to make a HTML Page in A4 paper size page(s)? How to send a header using a HTTP request through a cURL call? I wish to send a header to my Apache server on a Linux box.  How can I achieve this via a cURL call? I have a 230 Gigs HDD on my laptop, i have 50 gigs extended for my linux, i have 80 gigs empty ntfs partition, and 100 gigs ntfs partition where i store all my important data, (i have about 50 gigs of important things) today i mounted the 100 gigs partition took something from it, unmounted it back, and then when i mounted it again it was EMPTY !!! all the data is gone !!!! i used to mount it via the terminal : sudo mount ntfs /dev/sda5 /media/E where E is a dir that i make (when i make it i change the permissions of media to 777 then after creating the dir, i change it back to normal)  Guys you cant imagine how much this data is important to me, Plz HelP,  thnx in advance How can I animate an object fading out? Why is $\omega$ the smallest $\infty$? has a weird case of the mono, while .  Also, that question is missing some content at the end: Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings. I'm trying to do a few proofs about rings: $(1)$ I want to show that for a ring $R$ and the ring of matrices $M_n(R)$, if $I\lhd R\implies M_n(I)\lhd M_n(R)$ and that all ideals of $M_n(R)$ are of the form $M_n(I)$. $(2)$ Prove that if $R$ is a ring with division then $M_n(R)$ is a simple ring.  The relation $I\lhd R$ implies that with $r\in R$ and $x\in I$ we have $rx\in I, xr\in I$. But how can I prove the statement for matrices?, here's what I would do: Consider $\psi \in M_n(R)$, if is given any matrix $\phi\in M_n(I)$ it must be $\psi \phi \in M_n(I),\phi \psi \in M_n(I)$, if we denote the element $(i,j)$ of each matrix by $\phi_{ij}$ and $\psi_{ij}$, then $(\psi \phi)_{ij}=\sum_{k=1}^n \psi_{ik}\phi_{kj}$ and $(\phi \psi)_{ij}=\sum_{k=1}^n \phi_{ik}\psi_{kj}$.  Since $I\lhd R$ is $\psi_{ik}\phi_{kj}\in I$ and $\phi_{ik}\psi_{kj}\in I$, which means that $I\lhd R\implies M_n(I)\lhd M_n(R)$.  To show that every ideal of $M_n(R)$ are of the form $M_n(I)$ with $I$ ideal: Suppose $I$ is not an ideal of $R$, then exists $r\in R$ such that $rx\notin I$ or $xr\notin I$, then with taking a matrix $\phi\in M_n(I)$ such that $x$ is an entry of $\phi$ and a matrix $\psi$ such that $r$ is an entry of $\psi$ we get that the matrices $\phi$ and $\psi$ have an entry $xr$ or $rx$, in either case this is not an element of $I$ then the matrix is not in $M_n(I)$. This concludes my proof (is it?) for $(1)$.  For $(2)$ I'd like to proceed by absurdum . Let's say that $M_n(R)$ is not a simple ring, then it has at least one ideal. Denote by $\varphi$ this ideal in $I$, then for any matrix $\psi$ we have $\varphi\psi \in M_n(I)$ and $\psi \varphi \in M_n(I)$.  Now, can $R$ be a ring with division?.I'm not sure how to prove that it can't. I believe I could use this theorem: "If $I\lhd R$ and $1\in I$ then $I=R$. The case $I\neq R$ implies $1\neq R$ and since $\varphi \psi$ and $\psi \varphi$ are in $M_n(I)$ then there are at entries in the product matrix which belong to $I$ (using $I \lhd R$) but are not $1$ (1\notin I); then there are elements in $I$ (and therefore in $R$ by $I\subset R$) that are not invertible, follows that $R$ is not a ring with division. But if $I=R$?, here I can't see a why $R$ can't be a ring with division. I have seen in American Sniper, Dead-7 and Carrie that when someone is killed, they are laying on the ground with blood leaking out of their back or somewhere else on the body.  The puddle continuously grows with few signs of slowing down. This is obviously not CGI because it is a real liquid (may not be real blood as that would spark an emergency in real life).   I have seen in American Sniper that when the protagonist kills yet another enemy, they are filmed hitting the ground and blood starts pooling around their body.  In Carrie: In the dance room where Carrie sets her powers loose and kills a lot of teenagers in the process, there are a few that hit the ground with blood pooling under their bodies. Sometimes they would be on their side with blood coming out.  In Dead 7: Kimono and the other six killed lots of zombies. Some of the six were killed in the process as well before they came to Apocalypta to kill her. They were filmed hitting the ground dead with blood pooling around them.  I am not sure how they film this as they are wearing thin shirts for these scenes, and not only that, but the characters also have blood (obviously fake) only just dripping out of the side of their mouths (an indicator they have a ruptured and wounded stomach or lung (in this case the blood would be pink and frothy).  What is the film technique that allows this to happen? When I have my external monitor hooked up, I access it by mousing off the left hand side of my Macbook display. Can I switch this so that I can access the external by mousing off to the right of My Macbook display?   The reason I ask, is my monitor is on the right side of my macbook, and it's unintuitive to mouse left to get to a screen on the right. In follow up to , it appears that some numbers cannot be represented by floating point at all, and instead are approximated.  How are floating point numbers stored?  Is there a common standard for the different sizes?  What kind of gotchas do I need to watch out for if I use floating point?  Are they cross-language compatible (ie, what conversions do I need to deal with to send a floating point number from a python program to a C program over TCP/IP)? Insert a full page image How can I insert a full page image?  No blank space left in the page.  Bonus:  How can I add some text over the image? How to apply for a UK standard visitor visa as a family? I am an Indian citizen residing in the United States. My wife and I are planning to travel to the UK for a week. We plan to apply for the UK standard visitor visa from the US. I was filling out the application and I have a few questions.   Travel History - The application asks for travel history to the United States, Canada, Australia and New Zealand. Considering that we're resident aliens in the United States, should we consider all the times we've traveled back to the US from India? Travel History - Should we also list out the times we've traveled to India from the US? Cost of the trip - Hypothetically if we plan to spend a total of ~4,000 USD on this trip, should I split up the cost and write down 2,000 USD on my application and 2,000 USD on my wife's application? Income - From what I've read on the forum, my wife must say that "someone else" i.e. me - is paying for her costs and mention my GWF number in the remarks on her application. Would that be sufficient considering that I'll be sending all income documents with my application? Savings - We have joint savings accounts. Should I mention the same amount on both our applications? Posting the documents - Is the up-to-date advice to send all documents in one packet? Or would sending them in separate packets at the same time be better? My thought was to annotate my wife's packet with my GWF number if we were to send them separately. Bank statements - We get e-statements. Would printing those out be enough? How to create local total counters? I would like to write page numbers like this '7/9' in all minted environments of my document. The first number ('7') is the current page and the second number ('9') is the maximum number of page breaks the source file has been split into.  I was planning to use the package totcount but I realized that it was only considering the last value of the counter at the end of the document and it couldn't manage counters locally to an environment.  Here is a totally stupid example, but it illustrate the problem:  \documentclass{report}  \usepackage{totcount} \newtotcounter{sectnum}  \let\oldsection\section \renewcommand{\section}{%   \setcounter{sectnum}{0}%   \regtotcounter{sectnum}%   \oldsection% }  \let\oldsubsection\subsection \renewcommand{\subsection}{%   \stepcounter{sectnum}%   \oldsubsection% }  \begin{document}  \section*{One}  \subsection*{SectionOne} \thesectnum / \total{sectnum}  \subsection*{SectionTwo} \thesectnum / \total{sectnum}  \subsection*{SectionThree} \thesectnum / \total{sectnum}  \subsection*{SectionFour} \thesectnum / \total{sectnum}   \section*{Two}  \subsection*{SectionOne} \thesectnum / \total{sectnum}  \subsection*{SectionTwo} \thesectnum / \total{sectnum}  \end{document}   Gives:    Where we would have liked to have: '1/4', '2/4', '3/4', '4/4' and '1/2', '2/2'.  So, is there a way to get this kind of feature ?