## Search found 499 matches

- Wed Aug 12, 2015 6:30 pm UTC
- Forum: Mathematics
- Topic: maximization on a function with constraints
- Replies:
**4** - Views:
**1398**

### maximization on a function with constraints

I'm given a function f(x,0) which is f(x,t) at t = 0, and T(x,t) Both of these functions map the [0,1] x R+ to R+ How can I find g(x,t) = d/dt f(x,t) which maximizes f(1,q), for a constant q in R+? Also subject to the constraint that for all t, f(1,t) = ∫ 0 1 g(x,t)/T(x,t) dx I'm not sure if it matt...

- Mon Aug 10, 2015 3:37 pm UTC
- Forum: Mathematics
- Topic: Powertrains
- Replies:
**1** - Views:
**1056**

### Re: Powertrains

yeah if you take that definition of indestructible then 2534 is, but the book specifically mentions the two numbers as fixed points, which 2534 would not be. also reduce doesn't necessarily mean to reduce in size in general, mathematically speaking. you can say P(2534) reduces to 2592 in the same wa...

- Fri Aug 07, 2015 4:48 am UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**7123**

### Re: A million years

Slightly off topic, but would you happen to know how temperature corresponds to intensity or power? http://www.setileague.org/photos/miscpix/waterhol.gif this image seems to suggest that the CMB has an intensity of around 3K, but from what I know, doesn't temperature just specific a specific black b...

- Thu Aug 06, 2015 3:16 pm UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**7123**

### Re: A million years

sure, i just wasnt sure if it might get drowned out by other sources like cmb or exoplanets' magnetospheres or blocked by objects in space. As i said before, it would be nice if there was data somewhere on the "brightness" of space in all frequencies of em

- Thu Aug 06, 2015 2:47 am UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**7123**

### Re: A million years

well then, with an alternate angle of attack, why not launch a new probe every few years to act as relay stations. the planets might not be aligned properly, making probe launch tricky, but that's nothing that can't solved with brute force. OR, just wait a million years, and when the probe has info ...

- Wed Aug 05, 2015 4:10 pm UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**7123**

### Re: A million years

if not elf radiowaves, how about gamma rays. Takes about 1E20 times more energy but if you increase telescope area to 1E9 sq km, you get a manageable 1E7J/photon

- Tue Aug 04, 2015 11:36 pm UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**7123**

### Re: A million years

I haven't been able to find any data on this but are there any EM spectrum wavelengths that just don't appear at all from natural sources? If there is such a frequency, sending just one photon back should be enough to transmit data. For example, ELF radio waves have energy on the order of 1E-32 joul...

- Wed Jul 29, 2015 2:16 am UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3243**

### Re: N-Body Simulation questions

I implemented metric expansion and also leapfrog integration. For some reason, the simulations with leapfrog integration seem to collapse much slowly.When I add metric expansion (linear expansion from 5E23 m to 1E24 m), barely any clusters have time to form. However, when I computed the error in the...

- Thu Jul 23, 2015 11:54 am UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**7123**

### Re: A million years

10^12 kilometers is a fraction of a light-year -- it's nowhere near enough to get to any star. The communication at 10^12 kilometers should be easy -- we could probably do it now. Communication at tens of light-years is harder, but we can simply wait a million years for the technology to get there b...

- Wed Jul 22, 2015 11:32 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3243**

### Re: N-Body Simulation questions

If it's necessary I can try a run with 16384 or 65536 particles. I looked up the zel'dovich approximation and the math seems to be a bit beyond me. By power spectrum do you mean the distribution of the magnitudes of the displacements? Can it be described as a normal/poisson/gamma distribution? Curre...

- Wed Jul 22, 2015 1:14 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3243**

### Re: N-Body Simulation questions

I was actually trying to find the equation for the repulsive/radiation force, but ended up only implementing plummer softening. Since radiation drops off proportional to distance squared, I reasoned modeling it would be equivalent to weakening the gravitational constant a little. Plus, as icicletast...

- Tue Jul 21, 2015 9:28 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3243**

### Re: N-Body Simulation questions

Actually it turned out to be a pretty severe bug in my Barnes Hut implementation which I've fixed. :oops: Here's the corrected simulation , covering just 15 billion years Here's frame four hundred . There's definitely clusters and voids, but I'm not sure about the filaments. With a bit of creative l...

- Tue Jul 21, 2015 7:30 pm UTC
- Forum: Science
- Topic: Puzzling artifacts and reasonable reasoning
- Replies:
**79** - Views:
**12804**

### Re: Puzzling artifacts and reasonable reasoning

If you only need a few thousand years and don't mind a bit of futuristic technology, why not encode your message of choice into the genes of a bunch of organisms? You'd need some error resistant encoding, but nothing too complex

- Mon Jul 20, 2015 2:19 am UTC
- Forum: Science
- Topic: Pluto down, next stop...interstellar?
- Replies:
**30** - Views:
**5323**

### Re: Pluto down, next stop...interstellar?

How would planets create interference? I know Jupiter produces radio waves but their wavelength isn't anywhere near 10 km. And if the planets in the destination system do produce radiowaves at that wavelength, we can examine it and pick a different frequency beforehand. If it's really neccessary, wi...

- Sun Jul 19, 2015 6:14 pm UTC
- Forum: Science
- Topic: Pluto down, next stop...interstellar?
- Replies:
**30** - Views:
**5323**

### Re: Pluto down, next stop...interstellar?

cant we just send signals as radio waves, or anything not in the center of the blackbody spectrum. the spectral radiance of a 5790K blackbody is 1.4E-100 W/m^2/sr/m at 10km wavelength, so we shouldn't get any interference from the stars at 4 lightyears and with a 1kW transmitter, the aercibo telesco...

- Sun Jul 19, 2015 12:55 am UTC
- Forum: Mathematics
- Topic: sum and product of natural number
- Replies:
**9** - Views:
**2366**

### Re: sum and product of natural number

I understand it a bit more now -- though thinking about it hurts my brain. I was hoping to compute the pair as a function of the number of times the mathematicians ask each other but that seems out of the question now.

- Sun Jul 19, 2015 12:40 am UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3243**

### Re: N-Body Simulation questions

I tried it out, and it seems to work ok. But I'm still not seeing filaments. The uniform grid seems to collapse, forming some geometric patterns (probably because of the barnes-hut quadtree). Then, large areas of high and low density temporarily appear before the simulation reverts to a more chaotic...

- Fri Jul 17, 2015 11:42 pm UTC
- Forum: Mathematics
- Topic: sum and product of natural number
- Replies:
**9** - Views:
**2366**

### sum and product of natural number

I was reading this post: https://mathoverflow.net/questions/9754/magic-trick-based-on-deep-mathematics/31656#31656 But I'm a bit confused what the apparent "strategy" is. Can anyone explain how the mathematicians can figure out what number it is? I think it may be related to another puzzle...

- Fri Jul 17, 2015 12:56 pm UTC
- Forum: Science
- Topic: Puzzling artifacts and reasonable reasoning
- Replies:
**79** - Views:
**12804**

### Re: Puzzling artifacts and reasonable reasoning

While there may not be another ratio within 1% of the stones, it is relatively likely that the mass of stones were altered after creation by around 10% from erosion or some human activity, meaning any explanatory ratio off by up to 10% is good enough.

- Wed Jul 15, 2015 12:39 pm UTC
- Forum: Science
- Topic: Puzzling artifacts and reasonable reasoning
- Replies:
**79** - Views:
**12804**

### Re: Puzzling artifacts and reasonable reasoning

But you can assign odds to whether time-travel/FTL are possible and it makes sense to assign odds to whether they exist after that. If a rich man had amnesia and forgot how he acquired his wealth, he might reason winning the lottery was highly unlikely, therefore he probably didn't win the lottery. ...

- Tue Jul 14, 2015 10:02 pm UTC
- Forum: Science
- Topic: Puzzling artifacts and reasonable reasoning
- Replies:
**79** - Views:
**12804**

### Re: Puzzling artifacts and reasonable reasoning

Whoever was weighing the stones must have been hallucinating (if that doesn't fall under the hoax category).

- Tue Jul 14, 2015 1:08 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3243**

### Re: Equation for repulsive forces in N-body simulation?

thanks! By the way, a bit off-topic, but would you happen to have any idea on what would be a good initial starting condition? I've read that a lot of large scale simulations use actual cosmological data, but if I just wanted to place the particles, how should I? I was thinking the mass of the parti...

- Tue Jul 14, 2015 12:52 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3243**

### Re: Equation for repulsive forces in N-body simulation?

Just for fun, I'm trying to simulate the large scale structure of the universe by placing a bunch of particles and hoping they collapse into filaments and clusters and such. I wanted a repulsive force both to prevent everything from clumping together and to prevent force from going to infinity as ra...

- Sun Jul 12, 2015 3:22 am UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3243**

### Re: Equation for repulsive forces in N-body simulation?

Thank you. Just to be clear, u is the speed of the stellar wind?

- Sat Jul 11, 2015 7:00 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3243**

### N-Body Simulation questions

I'm trying to model an N-body system, and in addition to gravity, I want to have a force which models the repulsive forces of stellar wind, star formation, and other phenomenon. Hopefully something of the form F(m1, m2, distance). I tried using PV = nRT to solve for T, then using Stefan-Boltzmann, b...

- Thu Jul 09, 2015 12:15 pm UTC
- Forum: Mathematics
- Topic: variance of weighed sum of random variables
- Replies:
**7** - Views:
**1899**

### Re: variance of weighed sum of random variables

Thanks, that's the word I was looking for, and http://stats.stackexchange.com/a/16609 gives a nice expression for it.

- Thu Jul 09, 2015 3:40 am UTC
- Forum: Mathematics
- Topic: variance of weighed sum of random variables
- Replies:
**7** - Views:
**1899**

### Re: variance of weighed sum of random variables

I just realized what I really needed wasn't what I thought I was looking for here. What I actually want is the variance of the weighed average of two probability mass functions X and Y. In other words, the variance of the probability mass function Z = aX+bY, given a+b = 1. I'm not exactly sure what ...

- Wed Jul 08, 2015 11:04 pm UTC
- Forum: Mathematics
- Topic: Prove that 25+8*(n!)) is not square
- Replies:
**10** - Views:
**3097**

### Re: Prove that 25+8*(n!)) is not square

Somewhat related to this https://en.wikipedia.org/wiki/Brocard%27s_problem

I tested up to n = 20000 without finding any squares

I tested up to n = 20000 without finding any squares

- Tue Jul 07, 2015 10:01 pm UTC
- Forum: Mathematics
- Topic: Wanted: Elegant proof of sin(x)/x limit
- Replies:
**49** - Views:
**6830**

### Re: Wanted: Elegant proof of sin(x)/x limit

If you can use area of circle = pi r^2, then you can show the area of a sector as a ratio of the circle area: pi r^2 * (theta/2pi) = theta r^2 /2

- Mon Jul 06, 2015 9:45 pm UTC
- Forum: Mathematics
- Topic: variance of weighed sum of random variables
- Replies:
**7** - Views:
**1899**

### Re: variance of weighed sum of random variables

let sum = 2*A = A + A if variances linearly add var(sum) = var(A) + var(A) = 2*var(A) but if weights scale standard deviation std(sum) = std(A) + std(A) = 2*std(A) var(sum) = sqrt(std(sum)) = sqrt(2)*sqrt(std(A)) = sqrt(2)*var(A) this is a contradiction though edit: whoops i see where i messed up no...

- Mon Jul 06, 2015 5:09 pm UTC
- Forum: Mathematics
- Topic: variance of weighed sum of random variables
- Replies:
**7** - Views:
**1899**

### variance of weighed sum of random variables

how do i find the variance of a weighed sum of random variables? http://stats.stackexchange.com/questions/5392/variance-of-two-weighted-random-variables the question in this link suggests it's the sum of the (w_i*std_i)^2 given that correlation is 0 the first answer suggests it's the square of the s...

- Sun Jul 05, 2015 2:23 pm UTC
- Forum: Mathematics
- Topic: Mancala game and factorization of big numbers
- Replies:
**7** - Views:
**1398**

### Re: Mancala game and factorization of big numbers

Dixon's factorization algorithm factorizes in O(exp(2*sqrt(2)*log(n)*log(log(n)))) compared to at least O(sqrt(2

Äsymptotically, 2*sqrt(2)*log(n)*log(log(n)) < n*log(2)/2

^{n})) = O(2^{n/2}) = O(exp(n*log(2)/2)) for this.Äsymptotically, 2*sqrt(2)*log(n)*log(log(n)) < n*log(2)/2

- Tue Jun 30, 2015 11:43 pm UTC
- Forum: Mathematics
- Topic: Attrition population model and Laplace transform
- Replies:
**1** - Views:
**1212**

### Attrition population model and Laplace transform

I was trying to come up with a population model for attrition today. Each member of the population has a risk of death per unit of time, so that you have a distribution A(r,t) which describes the distribution of the population across the axis of risk at a certain time t. Then dA/dt = -rA, by seperat...

- Mon Jun 22, 2015 5:37 pm UTC
- Forum: Mathematics
- Topic: A Diophantine equation related to happy bases
- Replies:
**3** - Views:
**1309**

### Re: A Diophantine equation related to happy bases

by https://en.m.wikipedia.org/wiki/Fermat's_theorem_on_sums_of_two_squares we know any counter example has b^2+1 = 1 mod 4. by http://mathworld.wolfram.com/SumofSquaresFunction.html we know the number of ways we can write a 1 mod 4 prime as a sum of squares is 1, and since 1+b^2 works, there are no ...

- Mon Jun 15, 2015 1:40 pm UTC
- Forum: Mathematics
- Topic: standard deviation on number of events.
- Replies:
**15** - Views:
**2685**

### Re: standard deviation on number of events.

with some algebra i think you can find it for e > u. let e be epsilon, t be time (20), u be mu. t/(u+e) = t/u + [ - t/u + t/(u+e) ] = t/u + [tu - t (u+e)]/(ue+u^2) = t/u - te/(u^2+ue) so std = ts/(u^2 + us) where s is the original std. which is remarkably similar to the other answer, ts/u^2, other t...

- Sat Jun 13, 2015 5:01 pm UTC
- Forum: Mathematics
- Topic: standard deviation on number of events.
- Replies:
**15** - Views:
**2685**

### Re: standard deviation on number of events.

Yes, that's what I was looking for -- thank you.

edit: what happens if i have a large standard deviation making ε > μ

this makes (20/μ)*(1- ε/μ + (ε/μ)2 - ...) diverge and you end with ???

edit: what happens if i have a large standard deviation making ε > μ

this makes (20/μ)*(1- ε/μ + (ε/μ)2 - ...) diverge and you end with ???

- Sat Jun 13, 2015 3:21 pm UTC
- Forum: Mathematics
- Topic: standard deviation on number of events.
- Replies:
**15** - Views:
**2685**

### Re: standard deviation on number of events.

Yes, that's what I was looking for -- thank you.

- Sat Jun 13, 2015 1:09 am UTC
- Forum: Mathematics
- Topic: Numbers representable by successive exponentiation
- Replies:
**13** - Views:
**1853**

### Re: Numbers representable by successive exponentiation

On a tangential note, would it be impossible to do much better than just a decimal system from an information theory standpoint? You might as well do (10*n1+n2)*10^(10*n3+n4) and now you can have, within a magnitude of 1E57 10*10^55 11*10^55 ... 99*10^56 10*10^57 which is certainly a lot more accuracy

- Sat Jun 13, 2015 12:36 am UTC
- Forum: Mathematics
- Topic: standard deviation on number of events.
- Replies:
**15** - Views:
**2685**

### Re: standard deviation on number of events.

I'm not sure I understand.

I understand vaguely/intuitively why the standard deviation of the harmonic mean would help -- but once I have it, what do I do with it?

I understand vaguely/intuitively why the standard deviation of the harmonic mean would help -- but once I have it, what do I do with it?

- Fri Jun 12, 2015 3:03 am UTC
- Forum: Mathematics
- Topic: standard deviation on number of events.
- Replies:
**15** - Views:
**2685**

### Re: standard deviation on number of events.

I'm afraid I wasn't making myself clear enough. If I knew the times between the events had a mean of say, 5 and a standard deviation of 3, then the standard error of the mean would tell me that the average of the times between nine events would have a deviation of 3/sqrt(9) = 1. But I want to know, ...