Bumblebee

@MagnusAlexander would a substitution of $\sin^{2}(x)$ work?

@MagnusAlexander I was just curios to see if it were possible.

Is it possible to evaluate this integral without a substitution? $$\int \frac{\sin(x) \cos(x)}{\sin^{4}(x) + \cos^{4}(x)} \, dx$$

Nvm, I solved it

But i'm having trouble finding the appropriate simplification

cos(2x) + cos(x) = 1 + sin(2x) - sin(x)

I need to solve for x over the range [-pi,pi]

I am in need of assistance please.

@Koro How does a banana with a hole illustrate the fixed point theorem?

I need some ideas. Basically, I wrote a paper on the Banach Fixed Point Theorem and its application to fractal image compression. To celebrate my school has allowed us to dress up as our Papers. What outfits would represent the Banach Fixed Point Theorem well?

Got it. Thanks :)

Yes

Yes

Yes

I figured out that the mediating particle has to be a W+ boson

No, i'm still not quite sure

I understand now

Oh, so it's an anti-muon.

Ohhhh

Yes

How do you know that it is an anti-muon?

Yes

I'm not sure how to do this question.

@JohnRennie Hello:) Are you available to discuss a problem now?

Is it possible to transform this equation to the one given in my notes? If so, how?

And I got $$M_J = \frac{3 N k_B T r}{2 G m}$$

I worked from the equation $$\frac{G M_J m}{r} = \frac{3}{2} N k_{B} T$$

However I do not know how this is derived

my notes set gives the Jeans mass as $$M_{J} = \frac{3 k_{B} T R}{2 G m}$$

I have a question regarding the derivation of the jeans mass

@JohnRennie Hello:) Been a while.

Being able to harness that kind of energy at room temperature would be increadible

Well i'm glad it's making a comeback

Ok, but how did Stanley Pons and Martin Fleischmann obtain the data which suggested that they achieved cold fusion? I mean, fusion usually occurs in the sun, and they are trying to achieve it within a test tube at room temperature which seems impossible

Ah ok.

Wait, so has cold fusion been achieved?

I suppose they hypothesised that fusion could be achieved at room temperature, and they set out to design some experiment to prove this was the case.

I wanted to know more about it in the context of the scientific method.

Yes, the idea that fusion can be achieved at room temperature.

I was hoping I could talk to you about cold fusion

@JohnRennie Hello :)

Hi @JohnRennie :)

so the replication of results

ah

@j I was just wondering because usually in the Natural Sciences, it seems that something needs to be "sufficiently" proven in order to count as scientific knowledge. I'm just trying to gauge where that "sufficiently" is.

hmmm ok

Are you available to discuss my question from earlier?

Hi @JohnRennie

@JohnRennie As you are a scientist who has been working in the natural sciences for many years, I wanted to ask if you knew the answer to this question: what conditions must something pass in order to be classified as scientific knowledge?