/sci/ - Science & Math

I'll instead give you the face when I see another 80% Tao specializing in higher algebraic topology

>mfw I know a math professor who's rather difficult to handle
>mfw I KNOW he's lurking /sci

I won't tell. He would know. But I know there are professors among us.

>>8594969
I disagree. Riemannian geometry became Italian school mathematics and physicists didn't know anything about it.
The formulation of special relativity using a metric was also the work of Minskowski, and Einstein head to learn it.

>>8594953
Lots of people worked in that direction.
The first metric theory of gravitiy was that of Nordstrom
https://en.wikipedia.org/wiki/Nordstr%C3%B6m's_theory_of_gravitation

There is also a famous Einstein-Hilbert dispute
https://en.wikipedia.org/wiki/Relativity_priority_dispute#General_relativity_4
Hilbert was done with the theory earlier than Einstein, and he was the one who knew the math, but Einstein came up with the general field equations.

And generally, there are articles from a decade after GR came out that make it clear they don't get the math (or it's implications) of coordinate transformations vs. curved spaces.

It's like with spin, the early physicists working this out had no insight into Lie-algebra homomorphisms, everything was foggy

>>8165469
>>8165630
The multiplication is supposed to be over the index i (not n).

For each i, we have that [math] p_i(t) [/math] is a function and I take it to be smooth.
Let's be more specific, although these are not fixed rules:
[math] p_i(t) [/math] should to be a function that is zero until a time [math] t=T_i^{introduction} [/math] and grows to some value in [math](0,1)[/math], e.g. 0.2

Background:
There are driver assistance systems [math]i[/math] (like Automatic parking for cars) that that ought to reduce the number of car accidents.
https://en.wikipedia.org/wiki/Advanced_driver_assistance_systems

People in this industry assign pretty random numbers, called potentials [math]p_i[/math], to those systems that ought to capture their effectiveness in doing so, and thus their value. Not all cars will have all systems implemented, and that's why one must make a choice/subset of the available ones.
For a fixed time span, say a month, the idea is that if there wasn't the system i, then there would be [math]n_z[/math] accidents, and with the system, [math]n_i[/math] (with [math]n_z < n_i[/math] because lives are saved etc.) of those would be prevented.
The basic deal is to define
[math] p_i = \dfrac{n_i}{n_z} [/math]
If e.g. [math] p_i = \dfrac{1}{10} [/math] or [math] n_i = n_z/10 [/math], then it means the system i prevents 1/10's of all the accidents.

What's empirically available is the number [math] n_r [/math] of real accidents that happened.
I have the police data for Austria, there are about 5 accidents per hour recorded or whatever.
We don't know [math] n_z [/math], the number of accidents in the world without i's.
For the prevented accidents, we should have
[math] n_i = n_z - n_r [/math].
So
[math] p_i = 1 - \dfrac{n_r}{n_z} [/math]
[math] 1 - p_i = \dfrac{n_r}{n_z} [/math]
[math] n_z = \dfrac{n_r}{1 - p_i} [/math]
for i.
cont.

I'm finishing my PhD at an Aerospace agency, computational chemistry. This job is cool, but somewhat of a niche and I don't know what happens after.
I'm currently reading Kierkegaard in hope to get some perspective. Truth is I'd like to end up with some 20 hour job and keep on reading for the next 11 years.

If the local mean at k for a function f is defined as

<span class="math"> \langle f(k) \rangle := \int_{k}^{k+1} f(k') dk' [/spoiler]

what's a simple rational approximation for

<span class="math"> \sum_{k=0}^\infty ( k \, z^k - \langle k \, z^k \rangle ) [/spoiler]

when <span class="math"> z = 0.99999 [/spoiler]?