Dabed

@JohnRennie thanks, yes the planet is trailing in both but I had actually my bets on the first one since I thought that when the planets goes over the background star a dip should occur similar as in the transit method (en.wikipedia.org/wiki/…) only that here the planet transits over the background star rather than in its orbit over the leading star but totally unsure on it.

quick question, I'm confused by two microlensing animations, in them the light curves are drawn but they look like mirrored yet the situation being represented looks the same to me so I'm not sure the reason the curves look different or if one of them is wrong.(exoplanets.nasa.gov/resources/2287/gravitational-microlensing) (supernova.eso.org/exhibition/videos/eso50microlensingexo)

@fqq nice thanks again!

@cOnnectOrTR12 I don't know about a technical coverage of their work but in case it is useful for a layman article I was reading about it in quantamagazine.org/…

@fqq @fqq Cool thanks for mentioning it I was just reading about it but as I don't understand much I didn't make the connection between Parisi and the replica trick, putting those terms on google gives some nice looking lectures on arxiv "Replica Theory and Spin Glasses" by Parisi and others authors (arxiv.org/abs/1409.2722) hope someday will put time to try to understand this

thanks @fqq and @ACuriousMind, yes it was the replica trick, the arxiv link is above my level but will bookmark it too, didn't imagine it was related to belief propagation and less that some interpretation could be given with category theory, I was just reading reading about path integrals and statistics in wikipedia and made me recall reading that article it but couldn't find the article after more than one hour looking for it so thanks again

but I think it was an article discussing some kind of trick were instead of calculating the partition Z directly it was easier to take the limit $\lim_{n\to 0}\frac{Z^n}{n}$ were the magic is to forget that n is discrete, does it ring any bell?

Hi, this question surely makes no much sense since I it's about something that I read sometime ago in Wikipedia but I didn't understand it and don't remember what it actually was either so I'm not sure if I'm recalling it correctly or if it's my imagination running wild

at 2m46s but is linked at that time anyway

I was looking at a short video of quanta magazine and in a part the professor mentions a Power law for some hypothetical DM annihilation that looks like P~<σᵥ>ρ²/m, I was wondering if that law maybe has a more known name I can google up or look for in wikipedia, it feels like it could be a law commonly known under some other context.

Quick question, reading wikipedia I came to vacuum bubles where it is written that $Z= \int e^{-S} D\phi = e^{-HT}$ shouldn't it be $Z= \int e^{-S} D\phi = \langle\phi|e^{-HT}|\phi\rangle$?

@Charlie thank you very much, I had tried "fiber optic wikipedia refractive index" in google without luck and since the link you shared mentioned a maximun I tried "fiber optic wikipedia refractive index max" and I think I finally found the relevant wikipedia article en.wikipedia.org/wiki/Numerical_aperture#Fiber_optics

Hi, I was wondering if someone could explain the formula sin(alpha)=[(n1^2-n2^2)^(1/2)]/n0 that appears in a post of physicsfun (instagram.com/p/CKjubnnhBXh), I suppose it is a variation of Snell's law but I dont get how is obtained, what is means and if it has a name of its own

Hi I read this question on math.stackexchange, it looks like something related to the KPZ equation, I read about the Källén–Lehmann representation but couldn't work out how to use it here (if it helps), so I was wondering if someone could be interested to give an answer or provide some hint about it, thanks

@J.M.can'tdealwithit thanks that is the whole thing I only got to spend some time reading on arrays and signing up was a lot easier than I thought so I just used it right away and checked it with mod 4 also, it seems to confirm the second expression from wikipedia, I added the citation needed tag on it and asked the user to provide a citation or proof but it seems to have been edited with a throw-away account so I was thinking of asking on math.stack but wanted to verify it numerically first

@CarlLange Sorry for the delay and thanks, yes in the first link those are the primes I'm interested in wolfram recognizes the verbal expression " first 12 primes congruent to 5 mod 6" as your wrote and also "product of first 12 numbers" but it can't with "product of first 12 primes congruent to 5 mod 6", the second link is only missing the condition of p being prime so it starts at 1 and gives p/p-1=1/0=infinity I had something similar but couldn't fix either of them.

@rhermans thanks, as it seems there is no easy command I guess I will need an array and if condition which would exclude wolfram alpha and leave wolfram mathematica as my best bet, wolfram cloud sounds easier so will try signing up later with more calm and if I still not able to do it then I will ask again as a formal question, thanks again and best regards

@rhermans thanks, I have never used it but I can access mathematica trough uni so either is fine really I only thought wolfram alpha would be enough to do it and yes probably without wikipedia it can be stated simpler equivalent problem mainly what I know to do is how to multiply the first n primes $\prod_{p \in \mathbb{P} }p$ but what I want to achieve is to multiply only those that are equal to 5 mod 6 $\prod_{p \equiv 5 \pmod{6},\atop p \in \mathbb{P} }p$

Hi, I have a question but it is about wolfram alpha rather than mathematica so I ask just in case is still of interest and sorry for being off topic, the problem is that I'm trying to check a formula from wikipedia but I don't know how to write the mod condition it is the second expression here en.wikipedia.org/wiki/…, any help would be appreciated, thanks

@CarlLange great! thank you very much once again

now I realize that if I understand correctly the code should be using your own space that I suppose you pay for on wolfram so if you need to save it please just do it, I have bookmarked the permalink to your message so that I can access the code later and try to reproduce the it myself if not on mathematica maybe octave

@CarlLange Is opaque to me too but as you say it may be difficult to prove but is easy to understand so it got me relatively hooked, I had thought about it sometime ago and then forgotten about it and now it came back to my mind once again, I'm just trying my luck before someone solve it.

thank you very much this is very helpful

wow that was pretty fast just 6 mins after and yes exactly I was thinking in that question, I made another one asking about how to prove the known result that [1,1/1,1/2,1/3,1/4,..] =pi/2 where the terms are the reciprocals on the natural numbers I received two proofs and I was trying to see if I could adapt the second one to the case of the reciprocals of the primes

I wanted to calculate the continued fraction of $[1/2,1/3,1/5,1/7,...]=? $ where the terms are the prime numbers, from another question I found that I need to write FromContinuedFraction[{1/2, 1/3, 1/5, 1/7}] but haven't found how I could add the first n primes automatically instead of manually, is that possible in wolframalpha?

Hi, I don't have mathematica I was just playing with wolframalpha.com so I don't think posting a question is in place but was wondering if maybe here I could get a little help

quick question, any suggestion about what free software could I use to calculate a functional derivative?

@StudySmarterNotHarder nice to meet you, yes but I don't study harder neither smarter=) lowly user only 617 and first time in this chat, did you cross a comment of mine that caught your attention because there is a lot of daniel d math.stackexchange.com/users?search=daniel+d

$\sum_{n \in \mathbb{N} } \frac{n } {\phi(n)} (1-\frac{n}{x})=\frac{A}{2}(w) x-\frac12\log x+\frac{(1-D)}{2}+o(x^{-1/5} )\tag{2}$, so I was wondering if someone could help me understand how does one go from (2) to (1) (as I understand $w(n/x)=(1-\frac{n}{x})$ )

Hi, I was reading a question where OP stars by mentioning the asymptotic $\sum_{n \in \mathbb{N} } \frac{\phi(n) } {n} w(n/x)=c_0(w) x+c_1(w) (\log^2 x ) +o(\log^2 x )\tag{1}$, I don't know much so I asked for a reference to see If I could understand further and he linked a paper mentioning equation number 9 which is

@MikeMiller Oh sorry my bad I was not careful, thanks

(sorry had a little problem rendering it)

$\sum_{n \in \mathbb{N} } \frac{n } {\phi(n)} (1-\frac{n}{x})=\frac{A}{2}(w) x-\frac12\log x+\frac{(1-D)}{2}+o(x^{-1/5} )\tag{°} $, so I was wondering if someone could help me understand how does one go from (*) to (°) (as I understand $w(n/x)=(1-\frac{n}{x})$ )

$\sum_{n \in \mathbb{N} } \frac{n } {\phi(n)} (1-\frac{n}{x})=\frac{A}{2}(w) x-\frac12\log x+\frac{(1-D)}{2}+o(x^{-1/5} )\tag{}$, so I was wondering if someone could help me understand how does one go from () to (*) (as I understand $w(n/x)=(1-\frac{n}{x})$ )

Hi, I was reading a question where OP stars by mentioning the asymptotic $\sum_{n \in \mathbb{N} } \frac{\phi(n) } {n} w(n/x)=c_0(w) x+c_1(w) (\log^2 x ) +o(\log^2 x )\tag{*}$, I don't know much so I asked for a reference to see If I could understand further and he linked a paper mentioning equation number 9 which is:

yes, ok thank you

Hi: can I ask a tech support-like question in the Google-Chrome tag?