Q % E Q # Uscis Form

To explore these numbers, I would start by understanding the following functions: Given two polynomials with integer coefficients [math]P(t), Q(t) \in \mathbb{Z}[t][/math], define[math]\displaystyle f_{P,Q}(x) = \sum_{n=1}^\infty \frac{P(n)}{Q(n)}x^n[/math].Now, the numbers you call “pseudo-rational” are what you get by evaluating [math]f_{P,Q}[/math] at [math]x=1[/math]. This is convenient because now we can explore the functions [math]f_{P,Q}[/math] using tools from analysis, and there’s many more tools available to us than those we can apply directly to the definition of pseudo-rational numbers as infinite sums.For example, we observe that certain special cases of these functions are well known and well studied.[math]\displaystyle f_{1,1}(x) = \sum_{n=1}^\infty x^n = \frac{1}{1-x}[/math][math]\displaystyle f_{1,t}(x) = \sum_{n=1}^\infty \frac{x^n}{n} = -\log(1-x)[/math]More generally, when [math]P=1[/math] and [math]Q[/math] is just [math]t^k[/math] we obtain various polylogarithmic functions:[math]\displaystyle f_{1,t^k}(x) = \sum_{n=1}^\infty \frac{x^n}{n^k} = \text{Li}_k(x)[/math]Now, one cool aspect of switching to functions is that we can “fill up” the numerator [math]P(n)[/math] simply by taking derivatives:[math]\displaystyle x f_{P,Q}'(x) = x \sum_{n=1}^\infty \frac{P(n)}{Q(n)}nx^{n-1} = \sum_{n=1}^\infty \frac{n P(n)}{Q(n)} x^n = f_{tP,Q}[/math]So multiplying the upper polynomial [math]P[/math] by [math]t[/math] is equivalent to a certain differential operator (taking the derivative any multiplying by [math]x[/math]). Iterating this, and observing that [math]f_{P_1+P_2,Q} = f_{P_1,Q}+f_{P_2,Q}[/math], we see that we can understand the functions [math]f_{P,Q}[/math] if we merely understand the functions [math]f_{1,Q}[/math] and their derivatives.We’ve already identified the functions [math]f_{1,t^k}[/math] as polylogarithmic functions. And lo and behold, the derivative of such a function multiplied by [math]x[/math] is also such a function:[math]\displaystyle x \frac{d}{dx}\text{Li}_k(x) = \text{Li}_{k-1}(x)[/math].We still didn’t explain how to handle denominators that are more complex than [math]t^k[/math], but using the method of partial fraction decomposition and shifting the variable by appropriate amounts I think we can identify all of the pseudo-rational numbers as linear combinations of special values of polylogarithmic functions.For example, by their very definition, [math]\text{Li}_k(1) = \zeta(k)[/math] where [math]\zeta[/math] is the Riemann zeta function. This explains why even powers of [math]\pi[/math] are pseudo-rational numbers, since [math]\zeta(2k)[/math] is a rational multiple of [math]\pi^{2k}[/math]. Since very little is known about [math]\zeta(k)[/math] for odd [math]k[/math], I’m afraid very little can be said on which numbers aren’t pseudo-rational. It’s highly unlikely, in my mind, that [math]e[/math] is, but proving that [math]\zeta(7)[/math] isn’t some rational multiple of [math]e[/math] is not something we know how to do.I’m afraid I don’t have time to work this out now in full detail - perhaps others will, or perhaps there’s a better way to view this definition. But I think that’s a reasonable start.

While the answer by Bingqing does a good job of explaining how metadynamics works, I would like to add some more important nuances. I will use PMF/FES interchangeably. Start by observing this excellent short clip: The yellow here is the repulsive bias added as a function of the reaction co-ordinate or CV (x-coordinate here). This is done through gaussians. In plain metadynamics the heights of the gaussians stays constant through the simulation. In well-tempered metadynamics, the height decays exponentially depending on the bias already added at a point.In both of these, the bias V eventually diverges. You would then normally recover the FES by looking at -V (in plain metadynamics), or -kV (in well-tempered, where k>1 is a well-defined constant). Since both of these diverge, it is tricky to ascertain convergence. That can be done in 2 ways:1. (especially in plain metadynamics) has the behavior in the CV space become diffusive?2. has the difference between free energies of two points of interest converged?Furthermore, metadynamics allows you to easily recover the PMF as a function of variables other than the CVs already chosen by simple reweighting techniques. This is important given that there is a large variety of abstract CVs becoming increasingly popular that you can use to drive the system out of stable basins. However, typically you might be interested in the FES as a function of more physical variables. That is where reweighting becomes super important.if your CVs can be shown to follow certain properties, then unlike other PMF methods, metadynamics can also give you kinetic rates on the system being studied.I also encourage you to check out PLUMED, which allows doing metadynamics as a simple plugin with most MD codes of your choice.

This is a recent meme that’s getting shared on facebook and elsewhere. Repeating the image from the question source:This is a question that has gone viral recently. Most people answer “G”.But look closely, as the question says. Many of the pipes are blocked - the line that blocks off D from C is not a mistake.To find the real answer (this is assuming a low flow rate, as after all it is shown as a drip in the diagram):From A to B to C is straightforward. None of them can fill before the next one.J is a bit more complex. But as you fill J, as soon as the water rises to the outlet to L it overflows to L. So it can never get any higher. Yes, its level also rises in the outlet tube leading to I, but it can never get high enough to overflow to I.So it flows to L, which in turn fills F.So which fills first, L or F?By the time F is full, L will only be partly full (with the water at the same level for both).So your F is the answer.This video shows the idea, an animation by Nick Rossi using a physics engine, AlgodooIt doesn't quite flow like a real fluid, as he says, but it's enough to get the answer and show how it works.Here is another animation Which will fill first? from THE FLOW... by CorneliaXaosWhich will fill first? by CorneliaXaosThat answers the question, since it shows a dripping tap at a slow flow rate. But let’s go off on a tangent.WHAT HAPPENS IF THE WATER IS POURED INTO A AT A FASTER FLOW RATEIf the flow is very fast then obviously A will fill first. However, could any of the others fill up first before F and before A?It’s’ governed by the Hagen–Poiseuille equation so long asthe flow is due to a pressure difference.the fluid is incompressible and Newtonian (water is, approximately).the flow is laminar (not turbulent) - it is with water if it flows slowly through a narrow pipe.through a pipe of constant circular cross-sectionthat is substantially longer than its diameter,and there is no acceleration of fluid in the pipe.All those conditions seem to apply. The pipes are substantially longer than their diameter which is one of the most important requirements. And they are narrow, and the fluid is water.Under those conditionsIf the outlet is above water, the flow rate is proportional to the height of the head of water above the inlet to the pipe. If the outlet is below water, it’s proportional to the difference in height between the water above the inlet and the water above the outlet.The difference in height of the water here is often called the “head” of water.It is inversely proportional to the length of the pipe.Or in short, the flow rate for laminar flow, in a pipe signNowly longer than its diameter, is proportional to the pressure difference, and so to the head of water, but it is also inversely proportional to the length of the pipe.(it also depends on the radius of the pipe and the viscosity of the water but those are the same for all our pipes).Techy details. The equation is:There L is the length of the pipe and R is its radius.Q is the flow rate (what we are looking for).ΔP is the difference in pressure between the two ends of the pipe, which for water is proportional to the difference in height of the inlet and the outlet.Finally μ is the dynamic viscosityAll of those are constant (the pipes are all the same radius, and the viscosity is constant) except for L, the length of the pipe, Q which we are interested in and ΔP.So our equation simplifies to Q = c ΔP / L, where c is a constant which is the same for all the pipes in our example because they are all the same radius.Double the length of the pipe and you halve the flow rate. Double the head and you double the flow rate.So now for instance, can L fill at any flow rate?Its outlet is a very long pipe. Even if L is nearly full of water ,the head of water in F will mean the difference in heads between L and F is quite small even if F is nearly full and L is likewise.Its inlet is a much shorter pipe. Whether L can fill will depend on whether we can get J to have a high head to increase the flow rate of L's inlet pipe to more than that of its outlet pipe. But, at least at first sight, it would seem that such a high flow rate could mean that one of the other tanks earlier in the chain could fill firstSo - it’s quite a finely balanced question, and hard to answer.A obviously can fill first with a very fast flow rate, just fill it faster than it can empty.Well we can actually try this out with a real world experiment :).Well we can actually try this out with a real world experiment :).Prozix has made a 3D printed version of the puzzle. If you have a 3D printer you can download it here and print it out and test it yourself: Answer to the question Which one fill First / water equilibrium system by prozixI don’t have a 3D printer but he has uploaded some videos.First this is what happens with a slow flow rateNote that at 22 seconds in, J nearly fills briefly.If you look closely, you see that a bubble forms in the outlet from J to L, which makes sense, it’s a downward pipe and air is buoyant. The bubble then gets pushed out into L and then bursts.This shows the bubble just before it bursts (you can show the video at 1080p from the Settings)So - if the pipes are very thin - or the flow is just right - that might lead to J filling right there, if you can arrange it to fill before the bubble disperses.So even at a slow rate we have something anomalous already, though its because of a bubble.But what happens at faster flow rates? I asked in a comment to the video, and Prozix was interested and answered with a new videoAt 28 seconds in, at one of the flow rates, then L and F fill at the same time.Here, it all makes sense up to J. J can’t fill (apart from that possibility due to the bubble) at this stage because the pipe from C to J has only a tiny head above its inlet. It’s outlet is about twice as long as its inlet, perhaps more.Aside: If C was nearly full, J would start to fill, and if we could have the level of water stay below the outlet into L while J fills, then C with its shorter pipe could continue to fill J even when it is nearly full. But as it is now, there is no chance of J filling.So that makes sense. But how can F fill at the same time as L? That's more mysterious.The pipe from L to F is three times the length of the pipe from J to L. Meanwhile, in the situation shown here, the head from J to L is about double the head from L to F.So by the Hagen Pousseville equation again, the flow rate from L to F should be about two thirds of the flow rate from J to L in this situation where J is half full and both L and F are almost full.So you expect L to fill faster than F.So, I don’t think they can get into this situation at all, with a steady flow into L. There must be something going on that doesn’t fit our assumptions of laminar flow, or something else such as a bubble forming.Let’s look at what lead up to this. If you look at the video, L fills faster than F to start with, keeping nearly the same head from L to F as from J to L.L is clearly filling faster than F and is on track to beat it. There is no sign of any bubbles in the inlet to L.But then a little while later you get this (25 seconds in)Now F is filling faster than J. Something has happened to reduce the flow rate into L, which then permits the two levels between L and F to equalize.But the head going into L hasn’t changed. Also the input pipe to L is full and there are no bubbles. I think the only possible answer is turbulence.You can see waves forming in J so maybe that means there’s a bit of turbulence impeding the flow from J to L, especially since the water level for J is exactly at the level for the outlet to L. What are your thoughts?This is what happened with a moderately fast flow rate:Here is the video starting at that point.All of A, B, C, J, L and F are just about full. B, L and F started to overflow first and I think L just about beat the other two though it was almost simultaneous. In this frame you can see L just about to overflow and the other two though they have the water raised above the level of the top, haven’t yet actually started to flow down the side.So how do we understand that as a possible state in terms of the flow rates? Back to our diagram againWith A, B, C, J, L and F all filled, then A to B to C to J all have the same length of pipe and same head (height difference of the water in the tanks above inlet and outlet) so have the same flow rate. J to L has around 2.5 times the head of C to J, and the pipe is around 2.5 times the length, so the flow out of J is about the same as the flow into it, and the difference in head between the top of J and the outlet to I is small. From L to F, the difference in head is about the same as for C to J (which we already know is about the same as the flow from J to L) but the pipe is far longer, so L shouldn’t be able to empty as fast as it fills, and the water flows out of J faster than it flows out of L, so L should fill before J.From L to F, the difference in head is about the same as for C to J but the pipe is far longer, so L shouldn’t be able to empty as fast as it fills, so it should fill long before J fills,So if the flow rate is high enough for J to fill like this, L should fill before J and F doesn’t get a look in.So how could it happen? Well it could be the bubble from J to L, slows down the flow out of J so that J fills first before L.As for F filling, how did that happen? Let’s look at it again:The head from J to L is far higher than from L to F and the pipe is shorter, so the flow into L should be a lot more than the flow out of L to F. So it seems impossible for F to fill like this. It's not the bubble - the two tanks fill up reasonably steadily at the same rate. You can watch the video at quarter speed to check. Click the Settings icon in the lower-right corner, then click the Speed selector.Perhaps at this flow rate, its the double kink in the pipe from J to L causing more turbulence and so slowing down the input to L? What do you think? That could also help explain why J fills at this flow rate, if the pipe from J to L, has a slower flow rate than you’d expect from its length and head. What do you think? Do say in the comments.Even K can fill, though it is pretty hard to do. This is with a very strong flow into A, and several of the others have been overflowing for some time. They have turned off the inlet pipe at this point.Amusingly, in the real world, E ends up half full too after some time of running it at a high flow rate with the water overflowing from A.Here is the complete videoSo far the only confirmed alternatives to F are A (obviously) and L (pretty sure it wins at the moderate flow rate).That’s just a start. There are many other things to tryVarying flow rate. Can you get, J, say, to fill first or even K by turning the flow rate up and down at critical points during the filling process? This could cause bubbles to form, as well as adjust the heads of the various tanks.What happens if you scale the whole model up, or scale it down to a very small size? Scaling it down could make the flow rates out of some of the pipes very slow. It could also mean that bubbles like the one from J to L take a long time to disperse too. Scaling up could lead to more possibility of turbulent flow through the pipes.Try adding sugar for viscosityWhat if it is really hot, and you use a slow flow rate so that the water evaporates quickly?What if it is really cold so that the water freezes? That would seem to be a way to fill even B first, if the water freezes by the time it gets to B to C but remains unfrozen as far as the flow from A to B.NOTEIf you see anything in this to correct, however small or important it is, please either suggest an edit for my answer or say in a comment. Thanks!

A potato and a cucumber are in a boat. The potato starts rocking the boat. The cucumber’s annoyed: “Hey, that’s annoying. Stop rocking the boat.” So, the potato stops rocking the boat.A couple minutes later, the potato gets bored again, so he starts rocking the boat. The cucumber is a bit angry: “Didn't we go over this? Stop rocking the boat.” So, the potato stops rocking the boat.Ten minutes later, the potato gets bored again, so he starts rocking the boat. Now the cucumber is furious. “For the last time, stop rocking the boat. If you rock the boat again I’ll push you off.”After another half hour, the potato is bored yet again. So, he starts rocking the boat. The cucumber pushes the potato off!(Stupid, yet funny, amiright? no?)A sailor met a pirate in a bar, and the sailor couldn't help but notice that the pirate was pretty badly the worse for wear. He had a peg leg, a hook, and an eye patch.So, the sailor asked the pirate how he got the peg leg, and the pirate answered, "Well mate, I got washed up overboard one night while we were in a fierce storm. and dern me if a shark didn't go and bite off me leg."Then the sailor asked, "So, how'd you get the hook?" and the pirate answered, "Well, we was in a fierce fight while boarding a ship one time, and that's when I got me hand cut off."Finally, the sailor asked, "So, how'd you get the eye patch?" and the pirate responded, "A seagull pooped in me eye.""You mean to tell me you lost an eye just because a seagull pooped in it?""Well, it was the first day with me hook..."(OK, you gotta admit this one’s actually good)What’s the dumbest animal in the jungle?..........The polar bear.(This one takes some people a while)Our heroes are two young lovers, a guy and a girl. They decide they want to get married, and even buy engagement rings.Unfortunately, their country is at war, and the guy gets drafted.While he’s away fighting, the parents of the lovers get into a huge fight, and decide that the lovers can’t get married.After the war ends, they meet. They still love each other, but determine they can’t go against the wishes of their parents. Instead, they decide that, once per year, they will meet on a specific dock.Every year, they meet, and they grow older. Eventually, the guy develops Alzheimer's. One year, he forgets, and goes to the wrong dock. He’s at one dock, fishing as he waits.Meanwhile, the girl is at the correct dock, waiting. And waiting. Eventually, she gives up, and thinks “he must not love me anymore.” She throws her ring into the water and leaves.The guy is fishing, oblivious. He hasn’t caught anything today, but then suddenly feels a tug on his line. He begins to reel it in. He pulls his prize out of the water. What is it he catches?..........It is the potato!(I’m sorry.)

I live in Germany. I got an invite to the Quora partner program the day I landed in USA for a business trip. So from what I understand, irrespective of the number of views on your answers, there is some additional eligibility criteria for you to even get an email invite.If you read the terms of service, point 1 states:Eligibility. You must be located in the United States to participate in this Program. If you are a Quora employee, you are eligible to participate and earn up to a maximum of $200 USD a month. You also agree to be bound by the Platform Terms (https://www.quora.com/about/tos) as a condition of participation.Again, if you check the FAQ section:How can other people I know .participate?The program is invite-only at this time, but we intend to open it up to more people as time goes on.So my guess is that Quora is currently targeting people based out of USA, who are active on Quora, may or may not be answering questions frequently ( I have not answered questions frequently in the past year or so) and have a certain number of consistent answer views.Edit 1: Thanks to @Anita Scotch, I got to know that the Quora partner program is now available for other countries too. Copying Anuta’s comment here:If you reside in one of the Countries, The Quora Partner Program is active in, you are eligible to participate in the program.” ( I read more will be added, at some point, but here are the countries, currently eligible at this writing,) U.S., Japan, Germany, Spain, France, United Kingdom, Italy and Australia.11/14/2018Edit 2 : Here is the latest list of countries with 3 new additions eligible for the Quora Partner program:U.S., Japan, Germany, Spain, France, United Kingdom, Italy, Canada, Australia, Indonesia, India and Brazil.Thanks to Monoswita Rez for informing me about this update.

I’ve noticed that a lot of people have asked this question in various ways and, through research and experience, I’ve found out why.Quora API can find your profile details from your existing accounts like Google, Facebook and/or other places and automatically make you an account on Quora without you ever consenting to it or realizing it.When you finally ‘join’ Quora officially, you log in to an account that was probably made ages before you even actually joined.It is likely that you searched up something on a search engine that associated to Quora somehow and you logged in with one of your social media accounts, generally speaking, Facebook.Many of Quora’s website traffic is from people searching things on the internet and to find answers, looked in Quora.To disconnect social media accounts that have connected, you can go to Your profile picture > Settings from the drop down menu > Account from the side menu > and scroll down to see Connected Accounts. Disconnect all or some as desired and done! Those accounts now have no connection to Quora whatsoever.You can also completely delete your Quora account : Your profile picture > Settings > Privacy > Delete Account.

Make it compellingQuickly and clearly make these points:Who you are and why you are doing thisHow long it takesWhats in it for me -- why should someone help you by completing the surveyExample: "Please spend 3 minutes helping me make it easier to learn Mathematics. Answer 8 short questions for my eternal gratitude and (optional) credit on my research findings. Thank you SO MUCH for helping."Make it convenientKeep it shortShow up at the right place and time -- when people have the time and inclination to help. For example, when students are planning their schedules. Reward participationOffer gift cards, eBooks, study tips, or some other incentive for helping.Test and refineTest out different offers and even different question wording and ordering to learn which has the best response rate, then send more invitations to the offer with the highest response rate.Reward referralsIf offering a reward, increase it for referrals. Include a custom invite link that tracks referrals.

A simple API was announced on January 7, 2011, supporting the Quora extensions for Google Chrome and Firefox. It enables applications to retrieve notifications for a logged in user, as well as the number of unread messages in the user's inbox and the number of people they follow and who follow them.More information is at: Quora Extension API