TITLE: What is $\circeq$ used for?
QUESTION [5 upvotes]: I was looking for a way to put 'des' over the equals sign in latex and stumbled upon this symbol 
$\circeq$
What are mathematicians using it for?

REPLY [2 votes]: A quick Google search shows a few uses of $\circeq$ to represent a binary relation. Examples:

If $\Sigma, \Delta$ are sets of sentences, say that
  $\Sigma \circeq \Delta$ iff they have the same models.

and

Let $\circeq$ be the relation on the set $P(\mathbb R)$ of all polynomials with real coefficients defined by $f \circeq g$ iff $f$ and $g$ have a root in common.

The character is also known as "ring equal to".