One is the explicit function of capillary tube length.
Another is the explicit function of refrigerant mass flow rate.
And xy = sin y)+x2y2 (the magenta curves in the figure at the left) cannot be solved for either y as an explicit function of x or x as an explicit function of y.
Note that this expression can be solved to give x as an explicit function of y by solving a cubic equation, and finding y as an explicit function of x would involve soving a quartic equation, neither of which is in our plan.
In general, if giving the result in terms of x alone were possible, the original expresson could be solved for y as an explicit function of x, and implicit differentiation, while still correct, would not be necessary.
The derived control law, which is an explicit function of the reference states and instantaneous positions of obstacles, allows active spacecraft to avoid collision in real-time.
The flow rate on the other hand is not an explicit function of the bead size, but depends on the overall capillary cross-sectional area.
This result ultimately guarantees a desired exponential decay rate σd while achieving the IR tuning as explicit function of σd and system parameters.
Each of the obtained solutions, namely hyperbolic function solutions, trigonometric function solutions and rational function solutions, contain an explicit function of the variables in the considered equation.
Analytical solutions for the growth of an isolated sphere from zero initial size have been derived with diffusivity an explicit function of concentration.
The Pc was expressed as an explicit function of the radial, in-track, cross-track components of relative position and error covariance.
