Name This Binary Operation on $Bbb N$

It looks like $aominus b=|a-b|$, or the distance between $a$ and $b$

1. Perform an operation on an array in O(n)

The following algorithm is $O(n)$ and uses a stack, the stack have the elements that have not found an answer to the problem, the idea is to iterate the array backwards and in each iteration while the i-th element is greater than the popped element from the stack then the i-th element is the closest greater element (to the left) to the element that was popped.These are the steps:First initialize the $P$ array with these values:That initialization is the "worst possible case" where there is no element greater to the left, in other words when a strictly increasing array is given as an input.The algorithm:CorrectnessThe loop invariant is that in the stack there is always the element for whom the algorithm has not found answer yet, so we keep pushing and if we found a element that is greater than the popped element we assign the answer as shown. In this sense we can say that this is a Greedy Algorithm, because it relies on as soon as we found a element greater than the popped element we put the answer "locally" without comparing further (Which of course would make it $O(n^2)$), is guaranteed that it is the correct answer because as we are going backwards the first time we see a element that is greater than the elements in the stack is going to correspond to number of times that the element has to be moved. If after the main loop of the algorithm is done there still elements in the stack it means that those elements are greater than all the elements to their left, and since we initialized $P$ with the "worst possible case", then the algorithm is correct.Running timeFor each element there is only 4 possible operations: The first insertion into the stack, pop the element in order to check if $current$ is greater than $prev$, put the element back if $prev$ > $current$, and finally pop the element when the answer is found. That would give us $4n$ in the worst case and indeed that is $O(n)$.Last but not least, some python code

2. Will Operation Fast and Furious be Obama's Watergate?

Do you even know what 'Watergate' was about?

3. Using a CT to measure the current in home electronic devices

The ratio of 50/5A indicates that the transformer will give 5A secondary current with the rated current of 50A through the core and assumes that the secondary is shorted. The 1.5VA rating says that you can take up to 1.5VA of apparent power from the secondary without affecting the accuracy. This corresponds to a voltage of 0. 3V across the secondary at 5A. It sounds like you really need a voltage output proportional to the current which you will get with a higher resistance across the secondary (since the line frequency is constant) but this is not the normal mode of operation. The ratio of secondary voltage to primary current (the transimpedance) depends on the secondary inductance which is not known but you could measure the output voltage with a range of known primary currents to determine this. If you get too little output, you could wrap the primary cable through the core several times to increase the sensitivity. I doubt that you will get much output with this transformer though since there are too few secondary turns.You could try experimenting with a 12V toroidal mains transformer, passing one or two turns of your neutral line through the core and loading the original primary (now the secondary) with a resistor of a few k$Omega$. This should give linear results as long as the current is sinusoidal. And yes, you should pass only one wire through the core

4. Was 9/11 a Mossad operation?

False flag operations are par for the course with most modern governments. As someone said, "cui bono" or "follow the money." Who stood to benefit/profit immensely from this spectacle? Bush, as a "war president" got re-elected. The petro-banking-military complex made trillions off the taxpayers with the Iraq and Afghanistan invasions. A permanent "cold war" has been in place in the Middle East since the late 1940's between Israel and oil-producing countries. Israel, the US's unofficial 51st state and enforcer of oil deliveries in the region has nukes and a well-disciplined and well-armed military in place, ready to act at a moment's notice. This state of tension maintains oil-supply lines open and cooperative, oil-producing allies well-armed. Mossad does not need any more funds. It gets more than enough. Always has. Note, a majority of the "identified" hijackers were Saudis. Not a single Afghan or Iraqi in the bunch. It is likely that the Saudis indirectly funded the hijackers. It is also likely that the jealousy between American intelligence units kept them from sharing isolated bits of information that could have led to the "big picture." Most US intel agencies have been politicized and like most bureaucracies focus on "low-hanging fruit" and "sting-operations" to justify their bloated budgets, their fancy paneling, bookshelves and perks. Note the Boston Marathon crazies and the Times Square idiot with explosives in his van whose incompetence led to his capture. Not James Bond-type efforts. Bureaucratic incompetence by US intel agencies was at least a factor in the 9/11 episode coming to fruition. This is a long way of saying that without a smoking gun, it may be tough to pin this operation on any one actor or set of actors working in conspiracy beyond those inside the planes. Be well.