Sentence examples for equations holds from inspiring English sources
As a result, a single set of fluid dynamics equations holds at all points of the domain and there are no internal boundaries.
As a result, one set of equations holds in the entire computational domain, eliminating the need to apply boundary conditions on the surface of suspended objects.
It turns out that if the following set of equations holds: Rleft( q right Aleft( q right) + Kleft( q right)Sleft( q right) = A^{d} left( q right) Kleft( q right Tleft( q right) = K^{d} left( q right) Rleft( q right Kleft( q right) = Kleft( q right Rleft( q right)then policy rules (12) can ensure that open-loop system (10) will be matched to the desired one.
These equations hold for any nonlinearity.
Thus making those equations hold guarantees optimality.
Similar equations hold for the higher order terms.
Thus, this means that the following equations hold: Set.
Hence, by, for sufficiently large, the following equations hold: (3.10).
Elementary algebra fixes some domain, typically the reals or complex numbers, and works with the equations holding within that domain.
The approximate field variables are selected such that all equilibrium equations hold in strong form.
Indeed, from (2.4) we deduce that the following equations hold: (3.14).
