Recent content by Aslet

Hi everyone! I'm approaching the physics of stochastic processes. In particular I am studying from "Handbook of stochastic processes - Gardiner". This book defines a stationary process like: $$ p(x_1, t_1; x_2, t_2; ...; x_n, t_n) = p(x_1, t_1 + \epsilon; x_2, t_2 + \epsilon; ...; x_n, t_n +...

Ok, I made a drawing and I realized my mistake. :sorry: I will also try to demonstrate the two inclusions, thank you for the big help! :biggrin:

Sorry, I was ambiguous! I meant that I don't understand $$ A_1 \cup A_2 = A_1 \cup [ A_2 \setminus ( A_1 \cap A_2 ) ] $$ It seems like ## A_2 = A_2 \setminus ( A_1 \cap A_2 ) ##. Thank you again. :)

Thank you very much! I only need the hypothesis in writing the difference, and obviously ## A_1 \cap A_2 \subseteq A_2 ##. I also get that ## A_1 \cap [ A_2 \setminus ( A_1 \cap A_2 ) ] = \emptyset ##. I still don't get the first relation that you wrote. :(

I understand that if ## A_2 \subseteq A_1 ##, then the equation it's easy to understand, more or less. Unfortunately the book doesn't give me this hypothesis. :frown: Is it possible that the authors forgot about it or is this hypothesis not necessary?

Hello everyone! I'm studying the physics of complex systems and I'm approaching probability theory. I understand that we need a ## \sigma-algebra ## and the Kolmogorov axioms in order to define a probability space but then I bumped into the following relation: $$ p(A_1 \cup A_2 ) = p( A_1 ) + p(...

Thank you very much! I know about quadratic potentials and the curve you showed me reminds me of a mirrored diagram of the electronic energy of a diatomic molecule in function of the distance between atoms. :smile: :dademyday: , you do a similar thing when you want to study a termodynamic...

3) I call ## R_M ( \theta ) ## the position of the mass at a certain angle ## \theta ##. From the geometry of the system I find: $$ R_M ( \theta ) = 2 R cos ( \theta ) \qquad ( R_M ( \theta ) )_y = 2R \cos ^2 ( \theta ) $$ The potential energy in function of the angle thus is: $$ 2 m g R \cos...

Hello! Sorry, i don't know about these diagrams. In which book can I find a brief explanation about those?

Yep! I'm also going to post the answer to the third point. :wink:

1 ) ## k = ( 3 + 2 \sqrt 2 ) \dfrac { mg } { R } ## 2 ) ## N = ( 1 + \sqrt 2 ) m g \qquad a = \sqrt 2 g ##

Haruspex, yeah sure. Then if this is the only problem I will semplify the equations and as soon as I have the time I will write it here! Thank!

Mmm, ok! Thanks! I am thinking. :sorry:

No, because i don't understand what you mean saying that. From what i rember the elastic force is proportional to the compression or the lenghtening of the spring from its rest position. :frown:

Counterclockwise?