I want to write "P parallely transports"

@0celo7 Did you try to google that?

@ACuriousMind Yes!

Results were inconclusive.

I don't know, mine say "parallelly exists, but is rarely used" pretty conclusively.

that's what mine said.

I don't think that's conclusive at all...

What is inconclusive about it?

There just aren't all that many situations where you have to use "parallel" adverbially

But is my situation acceptable?

Why are you uncertain about that?

Because I'm bad at English?

You want to modify the verb "transport" by "parallel", so you use the adverb. Seems pretty clear to me

I don't know what an adverb is

But if you're sure, then good

Although I think many mathematicians don't care and just write "P parallel transports"

@0celo7 oO

@ACuriousMind What?

What would you call the function of the words that you modify by "-ly" usually?

It hasn't come up, I don't know.

They don't teach grammar in your schools? oO

@ACuriousMind (a) I learned grammar in your schools; (b) yes, they do; (c) I have a poor memory.

Ah, well, maybe I find all those aspects of language just more interesting than others so I tend to remember them

I find 0 aspects of language interesting.

@ACuriousMind Languages are awesome.

They are

I should learn more that are still spoken though

@ACuriousMind I'm going to ask a question, to which the answer will be "no." Can one extend a smooth function on an open set to the whole space?

@ACuriousMind Russian.

It's awesome.

@0celo7 Good luck doing that with $1/x$.

@ACuriousMind Hence the "no."

Do I want to know the answer to why the heck you asked me that question, then?

@ACuriousMind Confirm sanity.

@ACuriousMind If you want to really know, I'll give you the details. But I'm still thinking about them myself.

Depends on how bored you are.

@0celo7 No, I don't

I figured.

(it has to do with geodesics :P)

@ACuriousMind Now, can I ask when one can extend the function?

When its limits to the boundary of the set exist.

Oh, not good. I'm on a manifold.

Limits aren't easy to compute.

Although that might not even be sufficient, but that's definitely necessary

Probably not sufficient.

@ACuriousMind Ok, how about this.

I have $U\subset X$ open, $f:U\to \Bbb R$ smooth. Can I find an open set $V\subset U$ such that $f|V$ may be extended to $X$?

$X$ an open ball of a Banach space.

Ah, yes, I can.

Thanks.

Probably not a general Banach space. But a finite-dim one for sure.

Unless, do there exist partitions of unity on all Banach spaces @ACuriousMind ?

I have no idea

@ACuriousMind so you don't know any geometry or analysis. Those are the two things I thought you were good at

What math do you know really well?

Don't say algebra

@0celo7 I don't know "any geometry or analysis"? Get down from your high horse and learn how to multiply matrices.

Currently representation theory is probably what I know "best"

Guys what's a quick and dirty formula to get the pressure of an impact from the momentum of the object and whatever mechanical property of the target

@Slereah What do you mean by "pressure" of an impact? If you mean what I think you mean, we also need the contact area and the contact time.

Also, this is a highly unusual question for you. What are you and what have you done with the real Slereah? :O

The contact area is known

The contact time is whatever happens

Just imagine a ballistics scenario

A little bullet going to president Kennedy or something

Infinitely rigid object hitting a target

What is the pressure applied to the target

Yeah, okay, so it bounces off, i.e. the impulse is twice the initial momentum $p$. If the contact lasts $\delta t$, the force is $p/\delta t$, and if the contact area is $A$, the pressure should be $\frac{2p}{A\delta t}$, no?

Well yes but how do you determine the contact from the circumstances

I'm pretty sure bullets don't bounce off skulls

That didn't work out so well for Lincoln

What kind of conspiracy theory are you developing here? :D

I am just curious

All things related to ballistics are always using pressures

But they don't seem to specify how we're supposed to derive those pressures

Hm, well, in a "real life collision" where things don't bounce off, I think we probably don't have good "formulae" - I guess we simulate those things?

Are there okay approximations for various types of collisions

But I really don't know, this sounds like material science, which I don't know about

You damn theorists

You'll never increase the GDP

@Slereah Sounds difficult. I mean, the force that acts on the target when the bullet hits it comes from the "matter can't go through matter" electrostatic repulsion/Pauli exclusion, right? I know of no quantitative model for that

Unfortunate

You might try asking that on the site, but I predict it will go the way of your other questions

I dunno

Or maybe some ballistics expert will come out of the woodwork, I don't know

That's probably the closest to a question that could interest the plebs I ever asked

Well, go ask it!

@ACuriousMind What?

I know how to multiply matrices.

Did you know

@ACuriousMind That's an 18 day old quote.

The usual algorithm of matrix multiplication is $O(n^3)$

But there is a $\approx O(n^{2.5})$ one

@Slereah That I knew, but I never wondered what the optimal one is

Is the optimal bound known?

Well $O(n^2)$ is a lower bound, since you need to at least visit every matrix component

But the optimal bound isn't known

Currently

@ACuriousMind how?

@0celo7 What? That it's $O(n^3)$ is obvious - you have $n$ multiplications for each component, and the target has $n^2$ components.

I wouldn't say that's obvious.

I don't know what O(n^3) means.

dtic.mil/dtic/tr/fulltext/u2/a021833.pdf

That seems like something

@0celo7 are you even an engineer

"Terminal ballistics is that part of the science of ballistics that relates to the interaction between a projectile and target. The target could be a tank,truck, command post, aircraft, missile, ship, etc."

No, I think I'm a geometer.

GR needs more tanks

"A simple example of a target is a building that stores munitions "

Military science papers are fun

Lol

@Slereah you could think about a Bingham solid as a weird approximation of human tissue, then you'd have a yield stress at which the bullet hits through; or you could have a look at charpy impact test data for tissue if that has been measured to get an idea?

Apparently for a fair amount of materials, the force/distance is roughly a peak

Although of course that is assuming that the projectile can penetrate the target

What would it be just for a rather simple case, I wonder

Some cylinder hitting an elastic surface

With the edges of the elastic surface remaining at rest, I suppose

To impose some boundary conditions