1. ### B Bounds for the index of a radical

Hi, I know that, at least formally, the index of a radical should be positive and integer. That is if I introduce \sqrt[x]{2} I need to assume x\in \mathbb N and x>0. However, my calculator has no problem in calculating the radical for any x\neq 0, say x=-\pi. The result it gives is based on...
2. ### Index laws question

Homework Statement we are asked to compare the graphs of 0.5^x with 2^x using index laws Homework Equations I am not sure how the regular index laws apply The Attempt at a Solution All I can say at the moment is the the graph of 2^x is a reflection of 0.5^x in the Y axis. I don't know...
3. ### Fortran How to use Real Array Index in Matrix dimension?

I am developing a FORTRAN code (.f90) which "ll calculate some matrix in some time interval (dt1=0.001) and these matrices have to be integrated in some time steps (dt=0.1). Though I am experience in FORTRAN 77, new to FORTRAN 90. I am unable to make dimension of matrix real (I think that is the...
4. ### Proving that three closed orbits must contain a fixed point

A smooth vector field on the phase plane is known to have exactly three closed orbit. Two of the cycles, C1 and C2 lie inside the third cycle C3. However C1 does not lie inside C2, nor vice-versa. What is the configuration of the orbits? Show that there must be at least one fixed point bounded...
5. ### I Notation (index notation)

I am having trouble converting [D]=[A][ B]T[C] to index notation. I initially thought it would be Dij=AijBkjCkl but I have doubts that this is correct. Would anyone be able to elaborate on this? Regards