We derive analytic expressions for the long-run probabilities of the server states.
We derive analytic expressions of the fractal form and structure factors, and we show how to determine the fractal dimensions and scaling factors at each structural level.
Several other applications considered the flow of non-Newtonian nanofluids in the presence of magnetohydrodynamics, radiation and porous media to derive analytic solutions to describe them.
Then, according to the MPR model, we derive analytic expressions for the system state probabilities of the finite Markov chain that represents the FF-NDMA protocol.
Within this context, we derive analytic expressions to approximate patient waiting times and wastage costs, allowing management to see the tradeoff between these two metrics for different policies.
We show that the problem can be formulated as a minimax optimization problem and derive analytic lower bounds for the computational cost.
Here, we extend the conventional PITT method to account for finite interfacial reaction kinetics and derive analytic equations for electric current under PITT operations.
In this study, we derive analytic expressions for the elliptical truncated moment generating function (MGF), the zeroth-, first-, and second-order moments of quadratic forms of the multivariate normal, Student's t, and generalized hyperbolic distributions.
The approach, while being very simple, is able to derive analytic models of execution time as a function of parameters, such as processor speed, network latency, or bandwidth without even looking at the application source.
We also derive analytic axisymmetric solutions for the case of a single locomoting sphere and ellipsoid based on spherical and ellipsoidal harmonics, and compare our numerical results to these.
