Recent content by Lodeg

I want to clarify my question. In fact, a linear system is caracterised by a linear operator H shch that Ao = H Ai, where Ai and Ao are respectively the input and output. A mode of this linear system should satisfy Ao = λ Ai, so that H Ai = λ Ai. However, in the case of helmholtz equation ∆E...

In the book "Fundamentals of photonics", the authors defined waveguide modes using the notion of linear systems, where they said: "Every linear system is characterized by special inputs that are invariant to the system, i.e., inputs that are not altered (except for a multiplicative constant)...

Hi, Is there any solution manual for Tu's "Introduction to manifolds", available in the net?

Thank you very much

This allows simplifying some expressions. Are there any criteria to judge the validity of such a condition? Are there any reference that mention different gauge conditions other than Coulomb and Lorenz conditions?

More generally, could a condition like ∫∫ L(A) x F(r,t) dS = 0 be a gauge, where L is a linear operator?

In that case, would a condition like ∫∫ A x F(r,t) dS = 0 , be acceptable as a guage?

How do we verify whether a condition on the magnetic vector potential A constitutes a possible gauge choice ? Specifically, could a relation in the form: A x F(r,t) = 0, be a gauge , where F is an arbitrary vector field?

How do we verify whether a condition on the magnetic vector potential A constitutes a possible gauge choice ? Specifically, could a relation in the form A x F(r,t) be a gauge , where F is an arbitrary vector field?

Indeed, directions at each point.

I mean: to each point p in R2 is associsted a line Lp. The family Lp depends smoothly on p. It is somewhat a smooth subbundle of TR2

Hi, Given a smooth distribution of lines in R2, could we assert that there is a unique distribution of curves such that: - the family of curves "fill in" R2 completely - every curve is tangent at every point to one of the smooth distribution of lines