The h Bar

0celo7

21:00

I want to write "P parallely transports"

ACuriousMind

21:51

@0celo7 Did you try to google that?

0celo7

@ACuriousMind Yes!

Results were inconclusive.

ACuriousMind

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

0celo7

that's what mine said.

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

ACuriousMind

What is inconclusive about it?

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

0celo7

But is my situation acceptable?

ACuriousMind

21:55

Why are you uncertain about that?

0celo7

Because I'm bad at English?

ACuriousMind

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

0celo7

I don't know what an adverb is

But if you're sure, then good

ACuriousMind

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

@0celo7 oO

0celo7

@ACuriousMind What?

ACuriousMind

21:58

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

0celo7

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

ACuriousMind

They don't teach grammar in your schools? oO

0celo7

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

ACuriousMind

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

0celo7

I find 0 aspects of language interesting.

DanielSank

22:06

@ACuriousMind Languages are awesome.

ACuriousMind

They are

I should learn more that are still spoken though

0celo7

@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?

DanielSank

@ACuriousMind Russian.

It's awesome.

ACuriousMind

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

0celo7

@ACuriousMind Hence the "no."

ACuriousMind

22:11

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

0celo7

@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.

ACuriousMind

@0celo7 No, I don't

0celo7

I figured.

(it has to do with geodesics :P)

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

ACuriousMind

When its limits to the boundary of the set exist.

0celo7

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

Limits aren't easy to compute.

ACuriousMind

22:17

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

0celo7

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 ?

ACuriousMind

I have no idea

0celo7

@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

ACuriousMind

22:34

@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"

Slereah

22:56

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

ACuriousMind

@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

Slereah

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

ACuriousMind

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?

Slereah

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

ACuriousMind

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

Slereah

23:03

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

ACuriousMind

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?

Slereah

Are there okay approximations for various types of collisions

ACuriousMind

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

Slereah

You damn theorists

You'll never increase the GDP

ACuriousMind

@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

Slereah

23:06

Unfortunate

ACuriousMind

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

Slereah

I dunno

ACuriousMind

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

Slereah

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

ACuriousMind

Well, go ask it!

0celo7

23:09

@ACuriousMind What?

I know how to multiply matrices.

ACuriousMind

Aug 13 at 23:14, by 0celo7

I was going to troll and say I don't remember how to multiply matrices

Aug 13 at 23:14, by 0celo7

But I really don't.

Slereah

Did you know

0celo7

@ACuriousMind That's an 18 day old quote.

Slereah

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

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

ACuriousMind

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

Is the optimal bound known?

Slereah

23:11

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

0celo7

@ACuriousMind how?

ACuriousMind

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

0celo7

I wouldn't say that's obvious.

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

Slereah

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."

0celo7

No, I think I'm a geometer.

Slereah

23:17

GR needs more tanks

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

Military science papers are fun

0celo7

Lol

Sanya

@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?

Slereah

"The deceleration of a nondeforming projectile is given by the ratio of
the total force on the projectile to the mass of the projectile. A convenient
form for the specification of the total force on the projectile is a correlation
of total force to the distance traveled into the barrier."

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

Slereah

23:40

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

To impose some boundary conditions

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