/sci/ - Science & Math

>The uncertainty principle if founded on the fact that to observe an object you must bounce another object off it, thus altering the object you're trying to observe. So all we need is to find some passive way to observe right?
No.

>>4861781
>Retard detected

>>4861755
Only problem is that it's more likely that you survive but become horribly injured.

>>4860660
Essential image.

Last bump

>>4860365
Still no.

Bump.
>>4860172
No. Guess again.

>>4860133
>except for the ones in which she looks like a frog
Dammit I would have preferred to stay ignorant.

>>4860164
By components are isomorphic. I mean that if we consider the components as categories there's an invertible functor between them.

>>4860037
Part of paper I am working on for summer project. Trying to make explicit the information captured by a transform. Long story - very boring.

>>4860071
>Maybe there is no good answer without any information on A and B.
Let me get back to you on that one - I'll see if I can put more in.

It's always amazed me that Stone looks so photogenic at all times.

>>4860096
>What is meant with a component?
Component is just short hand for connected component - in category theory anyway.

>>4859948
I'm aware of the visualisation - it hasn't really helped me.
>>4859962
Him and Zhen Li answer nearly every question I post on stack exchange - they are fucking machines.

>>4859962
I'm well aware of the visualisation - it hasn't really helped me.
>>4859948
Him and Zhen Li answer nearly every question I post on stack exchange - they are fucking machines.

>>4859831
Fuck.

>>4859620
I posted it before (no one answered) - I don't remember implying that though; if anyone's lacking here it's me.
>>4859632
Posted it on stack exchange and they recommend <span class="math">B[/spoiler] being skeletal and connected - I don't see how this is sufficient though...

http://math.stackexchange.com/questions/167264/groupoids-with-all-components-isomorphic

>>4859658
>What about the specific case where A and B have two connected components each, and the connected components of A and B are groups?
What prevents <span class="math">F[/spoiler] mapping one component of <span class="math">A[/spoiler] to one component of <span class="math">B[/spoiler] and the other component of <span class="math">A[/spoiler] to the other component of <span class="math">B[/spoiler]?

>It's hard to even tell what you're looking for.
>Can you give an example of the type of conditions you're looking for for that case?
Firstly, I want the condition to be as weak as possible - keeping <span class="math">A[/spoiler] and <span class="math">B[/spoiler] as general as possible - it's really <span class="math">F[/spoiler] I wanted to restrict. Stuff I would be looking for is; <span class="math">F[/spoiler] defined as a universal functor, full, faithful etc - that kind of shit.
>If not, why do you expect there to be any useful criteria for the general case?
I'm not sure there is any useful criteria at all.

Thanks for the help.

I have a functor <span class="math">F:A \to B [/spoiler] where <span class="math">A[/spoiler] and <span class="math">B[/spoiler] are groupoids and all connected components of <span class="math">A[/spoiler] are isomorphic.

What is a nice canonical sufficient condition for: The (<span class="math">F[/spoiler]-)images of any component of <span class="math">A[/spoiler] are equal.

Any information surrounding this problem would be great. Thanks!

>>4856240
The whole series is rubbish.

Last bump.

Also there is no way to do it without being evil.

bump

Final bump

bump

>>4842976
ty

>>4842746
>>4842808
Nice.

>>4842367
In order:

Commutator of position and momentum operators (Uncertainty principle)
Schrodinger's Wave Equation
Beta decay
Dirac equation
Standard model gauge groups

Newton's Second Law
Principle of least action
Conservation of energy and momentum.
Wave equation
Boltzmann distribution

Maxwell's equations (shitty notation - ever heard of covariant formulation bitch?)

Some shitty space-time metric
General mass energy relationship?
Einstein field equations
Christoffel symbol in terms of metric
Geodesic equation (Should be plus instead?)

>>4842722
Category with all morphisms invertible.

Let <span class="math">A[/spoiler] and <span class="math">B[/spoiler] be groupoids where all components of <span class="math">A[/spoiler] are isomorphic and <span class="math">F:A \to B[/spoiler] be a functor.

What are canonical sufficient conditions for:
All components of <span class="math">A[/spoiler] have the same image (using <span class="math">F[/spoiler]) in <span class="math">B[/spoiler]?

You get +1 internets if you don't use all components are isomorphic.
You get +2 internets if you don't use the groupoids assumption.
You get +10 internets if you find a non-evil condition.

>inb4 hurr durr <span class="math">A[/spoiler] is connected.

http://en.wikipedia.org/wiki/Positive_energy_theorem