This paper I am reading has strange notation I have never seen before. It has two potential functions $W$ and $\Phi$ and the partial derivatvies with w are represented normally.
$\frac{\partial W}{\partial y}$ and $\frac{\partial^2 W}{\partial y^2}$.
However, the partial derivatives for $\Phi$ are represented differently:
$\frac{\Phi}{\partial y}$ and $(\frac{^2\Phi}{\partial y^2})$
Is there any significance to this? I have always believed that $\frac{\partial}{\partial x}$ was an operator. I feel like I must be fundamentally miss-understanding something conceptually because the second notation violently disagrees with my intuition. Furthermore, later in the paper the represent a relationship as follows,
$d(f(p,T)) = g(y,t)dt$
Where f is a function of pressure and temperature and g is a function of position and time. I guess this is saying that if we take tiny changes in f (but with respect to what?!?) it is equal to function g over tiny changes in time.
Ive never seen differentiation treated like this and I am very confused!
Here is a link to the article. The weird notation can be seen on pages 24 and 26: https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JB00906