For our particular power law utility functions (4), we can give an explicit formula for in terms of : (16).
By using gradient Young measures as a main tool, we can give an explicit form of the "constrained quasiconvexification" of the cost density.
In this paper we find a so-called ( I, J ) similar method which can give some explicit smooth solutions to two-dimensional incompressible Euler equations (see Section 2).
Although RMSD can give an explicit concept of modeling errors, in some cases, a local error (e.g., tail misorientation) can cause a large RMSD value even though the global topology is correct.
A single differential-difference equation, which can be discretized to give explicit finite difference models of wave propagation in elastic block media, is obtained after incorporating continuity conditions of stresses into the equation of motion.
However, specific instances of such problems can be tractable, and we give explicit examples below.
These projects can only go ahead if patients give explicit consent, or when the health secretary grants an exception, for example, to protect people in the event of a large-scale danger to public health.
Finally, we give explicit convergence rates.
However, the authors do not give explicit solutions.
Formulas (7.5) and (7.6) give explicit solution z + ( t, α ).
