Recent content by WastedGunner

I have a problem that arises in quantum field theory. It involves a problem in combinitorics and about the theory of connected graphs. Essentially, I am trying to prove an identity involving an exponential of an infinite series with the ways to decompose an integer into the sum of integers...

The car is experiencing acceleration due to gravity, therefore it is not in an inertial frame and you cannot use special relativity. Nothing is broken

I don't think this is enough. You can't prove this only using the group properties. Prove instead that (BA-I)b=0 for any nx1 matrix b Then show that the components of BA-I are 0 by choosing specific vectors b

I am pretty sure that is not going to get you the answer. I believe you will be better off showing this lemma: Let A and B be nxn matrices such that AB=I, then (BA-I)b=0 for every b nx1 matrix (a vector) Then you can prove the result easily by considering the components of (BA-I) by...

Ah, I see, very simple. And thanks for the advice.

Could you state one for general f and g?What I would do first is assume we can separate K(x,t)=F(x)G(t) And also assume that f and F are differentiable. Then you find that \frac{f(x)}{F(x)} = \int^R_x G(t)g(t)dt let \hat{f} = \frac{f(x)}{F(x)} and taking the derivative with the FTC you...

Thanks for your reply. I know that the existence of partial derivatives does not guarantee a differentiable function. I have been unable to construct a counter example, the condition that all those function have a uniform Lipschitz constant is a very strong condition. Also, on the note...

Here is a tough one: Say we have a multivariable function f:R^n -> R and for any x, and direction u, the function g:R->R defined as g(t)=f(x+tu) has that g'(t) is Lipschitz with the same Lipschitz constant (say M). For special cases, taking u to be any basis element we see that every partial...