Recent content by mathplease

going to have to say the mythbuster's crew (especially jamie) for this one. have you heard of peter beach?

ah i see. if the conductivity of the material is low can i assume it to be lossless material?

not relating to any specific homework question: how can i go about calculating the relative phase of reflected / transmitted fields for normally incident plane waves? for example, i know how to calculate the relative amplitude of the reflected field from the reflection coefficient...

actually i think y = ek where dk = max |d| works

Homework Statement Let D be a nxn diagonal matrix and T:Rn -> Rn be the linear operator associated with D. ie., Tx = Dx for all x in Rn. Show that: llTll = max ldl where d1, ..., dn are the entries on the diagonal of DHomework Equations the smallest M for which llTxll <= M*llxll is the norm...

haha, thanks guys. much clearer now.

i see, yes. so in general, to show that something is a bounded linear operator from X to Y, you need to show the inequality, prove linearity and show that its a mapping from X to Y?

a linear operator T: X -> Y is bounded if there exists M>0 such that: ll Tv llY \leq M*ll v llX for all v in X conversely, if i know this inequality is true, is it always true that T: X ->Y and is linear?

The instantaneous energy density of a region of space of an EM wave is: u = \epsilon0E2 [J/m^3] hence the average energy density is: uavg = (1/2)\epsilon0E02 [J/m^3] uavg = <S> / c [J/m^3] Is this equal to the wave's average http://en.wikipedia.org/wiki/Radiation_pressure"...

thanks for checking

I would like a second opinion on my answer to this question as I'm confusing myself thinking about my proof. Any input is appreciated Homework Statement "Let (X, ||.||) be a complete normed linear space and Y \subsetX be a non-empty subspace of X. Then (Y, ||.||) is a normed linear...

without any context behind the question it's reasonable to interpret it in another popular way. although i still don't think it works with this particular question you posted here, but consider the similar type: (AB + 1) / (CBA + A + B) = 0.138 now instead of treating AB as A multiplied...

the example was simplified; i assumed there were only two individual particle states ("on the left" or "on the right"). more generally, http://en.wikipedia.org/wiki/Entropy_%28statistical_thermodynamics%29#Counting_of_microstates" is not so easy, although in certain situations you can make a...

entropy, S, is defined to be: S = k * ln(W) k is the Boltzmann constant, approximately 1.38*10^-23 J/K W is the number of ways to arrange the system //===================================================================...

not if he doesn't pour it in front of them?