Difference between spline and polynomial approximation is that that to some order the splines are only piecewise continuous in derivatives usually some order is discontinuous at the fitting points while a polynomial has continuous derivatives of all orders generally.
Jansen and Boon "Finite groups" 1967 in part esp that part in quotes but some of the other expressions are my own interpretations and questions to ask if others agree eg as to the expression for inversion mainly.
I see by the matrix multiplication how you get that but here is what seems to disagree. Under a rotation about the x-axis a vector along the x-axis does not change ? Using the 3 dimensional R matrices operating on the two dimensional spin, denoting them here as ' vector' ## \sigma ## matrices...
How do the Pauli spin matrices transform under an inversion ? I think I mean to say the 3 dimensional improper rotation which is just in 3 dimensional matrix notation minus the identity - so exactly how are the 2 dimensional Pauli spin matrices changed. And under a 180 rotation do the 'y' and...
Don't need to be concerned with the more recent and advanced subjects like entanglement at this time as you will be kind of 'left in the woods'. It is more important to have a good mathematical functions of the basics like very good understanding of eigenfunctions, eigenvalues, spin, electron...
I assume the issue is that since accelerated charges classically emit radiation and aside from some other rather rare events etc. must therefore continuously loose kinetic energy then they will eventually run into the nucleus at least classically. The answer is that in fact physics is not...
"an infinitely small nonzero number which is at the heart of calculus is also at the heart of quantum physics " In quantum physics it is not an infinitely small number. Plancks constant for example is finite. These two "infinitely small limits" you speak of in mathematics and quantum...
There is also the question of for example
integer*1:: i
integer*1 :: j,k
is same as putting all together in one statement as
integr*1 :: i,j,k
but here has:
type (link), pointer:: next
end type link
type (link), pointer :: first,current
but if do the same there like put them all together...
Yes i mean array of native type say of integers for example I post another more direct program and see if someone can explain some of the observations I have made about it.
----------------------------------------------
integer*1 i
type link
integer*1 i
type (link), pointer:: next
end type link...