Recent content by e(ho0n3

The last chapter of the book "Fundamentals of Quantum Optics and Quantum Information" by Peter Lambropoulos and David Petrosyan has information about this.

The derivative f' is the distribution defined by (f', g) = -(f, g'), where g is any test function.

I believe integration does not exist for distributions so that will not work.

Homework Statement Let f be a distribution on R and suppose that its kth derivative is 0. Prove that f is a polynomial. 2. The attempt at a solution I honestly haven't a clue how to start. If I could treat f like a "regular" function, this would so easy.

You have narrowed down the list of choices to just E, so E must be the answer. Is there anything more you need to know?

Can you prove that R is reflexive, symmetric and transitive?

By area, do you mean the surface area of triangular prism or the area of the triangle?

It looks right to me.

That's what many books say too, but I don't see how it immediately follows. For example, I don't see how it rules out that three subsimplices can share a common facet.

First, some definitions: An n-simplex is defined as the convex hull of n+1 affinely independent vectors in Rd (its vertices). A face of a simplex is defined to be the convex hull of any subset of its vertices. A facet of a n-simplex is a face that is an (n-1)-simplex. A triangulation T of an...

There are no constraints on an. I do know of a couple that might shed some light on this general situation. As you previously mentioned, if the an are all 0 (or are eventually all 0), then the limit exists for all n. If the an are eventually all some nonzero constant, then we know the limit...

Homework Statement Let an be a sequence of real numbers. For what values of x does lim anxn exist? The attempt at a solution Let us suppose that lim anxn exist and is equal to b. What can we say about x? Hmm...there is a monotonic subsequence that converges to b, say a_{k_n}x^{k_n}. If...

Thank you for the suggestions. I'm a little rusty on this stuff.

Homework Statement Prove lim na^n = 0 when 0 < a < 1. The attempt at a solution Without danger, we change from the discrete n to the continuous x so that now we have to prove that lim xa^x = 0. Let e > 0. We have to find an N such that xa^x < e for all x > N. Now if xa^x < e is the same as...

You have a good point there. Thanks for your help.