/sci/ - Science & Math

>>8283731
wat

>>8283214
I explained why they're relevant in >>8281121 and >>8282423 and what I'm doing is attempting to put it into a form for which a growth rate can be determined.

>>8282390
Instead of just mindlessly bumping, how about you help?

If we can determine some sort of closed-form answer for the incomplete Bell polynomial at the bottom, the we can remove the last derivative operator. Then we just take [math] \lim_{z \to 1} \lambda_n [/math] and we'll have a simple genral form for the terms in the series, which should make it much easier to analyze, seeing as doing the same for the pre-proceesed cases of [math]n = 1[/math] and [math]n = 2[/math] appear to result in a series expressed in terms of the various Stieltjes gammas.

Here's a few more hours worth of work on it:
https://files.catbox.moe/ri9i0v.pdf
Prove the [math]\lambda_n[/math] sequence is monotonically increasing, and by reference to the fact that [math]\lambda_1 > 0[/math], the result follows by ordinary induction.

>>8280154
So it would seem the theory is more accurate than OP predicted.

>>8279475
Who and what are you quoting?

>>8279843
You clearly need to pay more attention in thermo 101. Even if a single molecule were as hot as the surface of the sun, it would not carry enough energy to initiate the chain reaction of combustion.

Actually, what would happen is that molecule would escape as evaporation, see the Clausius-Claperyon relation.

It depends on what exactly you mean.

If the fire is an isothermal heat source, controlled by some kind of thermostat, then the tank won't rise above 1000C.

If it's actually a constant power source, with an adiabatic flame temperature of 1000C, then the tank will heat up until the thermal input balances the transfer of heat to the ambient air (or the pressure in the vessel causes a rupture).

>>8277158
I've used my knowledge of chemistry for cooking, cleaning, gardening, and various other sundries. It's the sort of thing that's pretty handy to know around the house.

>>8279712
This is /sci/, not /drugs/. Please go and drink them with large glass of [math]\mathrm{HNO}_3[/math].

>>8279753
In pretty much any engineering field, you end up doing a lot of computational physics. I have used very many CPU cycles running various simulations of one kind or another.

>>8279592
>wants to solve perhaps THE greatest mathematical problem of the 20th century
>can't even into LaTeX right
Wonderful. Just, friggin, wonderful.

>>8279422
[math] Li [/math] is usually the logarithmic integral function.

>>8279365
Is that a prediction or a wish?

>>8279239
Right, but the PDF of the distribution of the integral is essentially the CDF of the distribution of the integrand.

>>8279232
I think after that I went into a circuit design phase, which has lasted into the present, seeing as I'm still an EE major.

The 2016 Atlantic hurricane season is heating up:
http://www.noaa.gov/media-release/atlantic-hurricane-season-still-expected-to-be-strongest-since-2012
Take your picks and place your bets, /sci/.

>>8279124
Yes, which is why I said the CDF is the distribution OF that integral.

I did a little more work on it:
https://files.catbox.moe/6atcqt.pdf
Li's criterion says that proving [math]\lambda_n > 0[/math] for all [math] n \in \mathbb{N} [/math] is equivalent to proving the Riemann hypothesis.

>>8279054
It was intended as a simplification, but please explain how it's wrong.

>>8278785
That's exactly what a random walk is called.

Get your head out of the gutter.

I actually did some work on the RH a little while back:
https://files.catbox.moe/1c46nx.pdf
Sorry if it's a bit hard to make sense of. The symbols are basically the ones Mathematica uses.

>>8278414
I used to do a lot of studying of that stuff back when I went through a mathematical finance phase. Unfortunately I've lost all of my notes from that.

Ultimately though they're basically just integrals of random processes. It's seeing what you'd get assuming the process follows a certain distribution. A CDF is essentially the distribution of the Ito integral of the random process that is distributed according to the corresponding PDF.

>>8276901
To summarize:

I remember seeing this exact question asked on /b/ a veeeeery long time ago. And the short answer is, that a perfectly rigid ("Born rigidity") object cannot exist under special relativity. See https://en.wikipedia.org/wiki/Ehrenfest_paradox

The movement of a solid object is a process of sending along information among its constituent particles via the action of a force. This can be seen as analogous to the wave-like pattern of traffic on a congested roadway.

The speed at which this wave of force propagates is also known as the speed of sound. It is mediated by a mixture of classical electrostatic repulsion between electrons, and quantum mechanical processes like Pauli exclusion.

Also note that, unless the rod is kept fairly cold, or the force is applied very quickly and strongly, thermal fluctuations would likely drown out the "signal" sent by the pulse of material strain by the time it finally arrives at the destination.