Re: f(x,y) * f(y,z) = f(x,z)
- From: Narasimham <mathma18@xxxxxxxxxxx>
- Date: Sun, 16 Sep 2007 07:34:30 -0000
On Sep 15, 11:47 pm, "Jon Slaughter" <Jon_Slaugh...@xxxxxxxxxxx>
wrote:
"Narasimham" <mathm...@xxxxxxxxxxx> wrote in message
news:1189877998.942637.181890@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Find general solutions for f from f(x,y) * f(y,z) = f(x,z). Only the
division and some division based functions comes to mind, like f(u,v)
= u/v, (u/v)^2, log(u) / log(v) etc. So what is the fullest basis?
TIA.
Narasimham
well, an obvious solution is if f is separable. f(x,y) = g(x)/g(y), then
f(x,z) = g(x)/g(z)
for arbitrary g.
This sorta generalizes what you were getting at. I'm not sure about the most
general case though.
The chain rule of differentiation operates much the same way,dy/dx =
(dy/dt)/(dx/dt) etc. even at the level of differentials, so I thought
perhaps some ODEs for f can be set up.Also similar is the case for
implicit functions using partial derivatives. But not able to go any
further in an attempt even to formulate generalization.
Regards,
Narasimham
.
- References:
- f(x,y) * f(y,z) = f(x,z)
- From: Narasimham
- Re: f(x,y) * f(y,z) = f(x,z)
- From: Jon Slaughter
- f(x,y) * f(y,z) = f(x,z)
- Prev by Date: Re: JSH: Your funeral
- Next by Date: Re: Topology with topological property.
- Previous by thread: Re: f(x,y) * f(y,z) = f(x,z)
- Next by thread: Re: f(x,y) * f(y,z) = f(x,z)
- Index(es):
Relevant Pages
|
