Sentence examples for are defined everywhere from inspiring English sources

It is only necessary that the enclosure forms a closed surface and that its properties are defined everywhere.

So, this only works if F and its derivatives are defined everywhere in the region, R. Otherwise, we are in trouble.

Continuous/stochastic models involve continuous distributions, or fields, that are defined everywhere in space and evolve according to a random process.

Then, well, f is not defined at the origin, but it's defined everywhere else.

If the curl is zero, and if the field is defined everywhere, then it's going to be conservative.

But for now let's just say if it is defined everywhere and it satisfies this criterion then it is a gradient field.

OK, so in particular, if you have a vector field that's defined everywhere the plane, then you take any closed curve.

So, OK, so a consequence of Green's theorem is that if F is defined everywhere in the plane -- -- and the curl of F is zero everywhere, then F is conservative.

But, for the right-hand side to make sense, and therefore for the equality to make sense, we need the vector field to be defined everywhere inside the region.

Well, if you know that your vector field is defined everywhere in a simply connected region, then you don't have to worry about this question of, can I apply Green's theorem to the inside?

So, one thing to know is if the curl of F, which is an x minus My happens to be zero, well, and now I can say, and the domain is simply connected, or if the field is defined everywhere, then F is actually a gradient field.