In my lab class we performed an experiment, in which we 'determined' the value of Planck's constant (value of h/e actually) by measuring the turn-on voltage for light emitting diodes of various colors. The idea is:
Given a light emitting diode that emits light with a maximum wavelength of...
Hello, I am also having an export problem in Mathematica when trying to export pdf format. Namely, I can't get it to export pdf images at all!
Anything I try to export, such as the image:
sinplot=Plot[Sin[x],{x,0,1}]
will export perfectly fine to .jpg or .png file types...
Ok, for 2), I've got the formula
\left[\mathbb{Q}\left(e^{ik\pi/n}\right) \, : \, \mathbb{Q} \right] = \phi\left(\frac{n}{\gcd(n,k)}\right)
,
where phi is Euler's totient funciton.
Is that right?
Now I just have to prove it...
Two problems from my abstract algebra class...
1)
Let K be the algebraic closure of a fi eld F and suppose E is a field such that F F \subseteq E \subseteq K. Then is K the algebraic closure of E?
2)
Let n be a natural number with n\geq2, and suppose that \omega is a complex nth...
Ok, I thought about it a little more. Hn-1 might not necessarily be positive, since it might not be possible to go from i to j in exactly n-1 steps, but it would be possible for some k, 1<k<n-1. Also, the diagonal entries of Hn-1 would not necessarily be positive (if for some node you have to...
If H is a nxn primitive, irreducible matrix, is it always true that Hn-1 > 0? That is, every entry in Hn-1 is positive.
From my class notes, the definition of H primitive is that there exists some k>0 such that Hk > 0. And a matrix is irreducible if its digraph is strongly connected (that...
Ok, I'm started off with a different approach to see if I could understand this a bit better... and it only leads me to believe that the problem must be wrong.
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Assume K=1 (since that is the smallest it can be). Then S is the set of functions on [0,1] such that |f(x)| < ||f|| for all x in...
Still at a loss...
So: Assume {u1, ..., um} is an orthonormal basis of S.
I'm trying the function f= u1 + ... + um. Is this the right one to consider? It certainly is the nicest.
Then ||f|| = sqrt(m).
I still don't know where exactly to apply the Bessels inequality. If I do, all I keep...
Let S be a subspace of L^{2}(\left[0,1\right]) and suppose \left|f(x)\right|\leq K \left\| f \right\| for all f in S.
Show that the dimension of S is at most K^{2}
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The prof hinted us to use Bessel's inequality.
Namely, let \left\{ u_1,\dots, u_m \right\} be a set of...
Last year, I was also a homework grader and tutor for Calculus 2. I'll probably put them in my application, alongside my 6 semesters of research.
Also, I really love to teach, and I really want to be a professor mostly because theoretical physics is interesting to me and beable to teach it...
I am the president of the SPS at my school, and we organize tutoring sessions for the intro level physics classes. So, I volunteer 4 hours a week to tutor college physics. Also, I volunteer at a local high school to tutor math. Do these kind of "volunteering extracurricular activities" help...
Let A be a matrix and \mu be an eigenvalue of that matrix. Suppose that for some k, \tex{ker}\left(A-\mu I\right)^k=\tex{ker}\left(A-\mu I\right)^{k+1}. Then show that \tex{ker}\left(A-\mu I\right)^{k+r}=\tex{ker}\left(A-\mu I\right)^{k+r+1} for all r\geq0.
Prove that a normal operator with real eigenvalues is self-adjoint
Seems like a simple proof, but I can't seem to get it.
My attempt: We know that a normal operator can be diagonalized, and has a complete orthonormal set of eigenvectors.
Let A be normal. Then A= UDU* for some...
Hmm.. after a bit more thinking...
I think that the sequence only needs to converge pointwise (not uniformly) to a function in order for the limit function to also be in LipC([a,b]).
So, my proof for (i) pretty much works. (I think) Please tell me if I am wrong?!
Also, interestingly, I...