At the same time, considerations of construction of such an element receded : the theorem becomes an existence theorem.
12.
This activity resulted in the first major core existence theorem for a large class of cooperative games without side payments.
13.
Together with Poincar?s existence theorem, this proves the theorem on ( 1, 1 )-classes.
14.
For first order initial value problems, the Peano existence theorem gives one set of circumstances in which a solution exists.
15.
A continuation of the above work leads to another result in relativity proved by Yau, an existence theorem for black holes.
16.
As noted above, the axiom of choice ( AC ) is used in the general existence theorem of discontinuous linear maps.
17.
In addition to working on mathematical statistical mechanics, he also proved existence theorems on nonlinear hyperbolic differential equations describing fluid flow.
18.
The existence theorems for quantum fields can be expected to be very difficult to find, if indeed they are possible at all.
19.
Even more general is Carath�odory's existence theorem, which proves existence ( in a more general sense ) under weaker conditions on.
20.
For example, John Nash's original proof of the existence of a Nash equilibrium, from 1951, was such an existence theorem.
