Analytic trigonometry combines the use of a coordinate system, such as the Cartesian coordinate system used in analytic geometry, with algebraic manipulation of the various trigonometry functions to obtain formulas useful for scientific and engineering applications.
As a consequence, we obtain formulas for certain Bergman kernels on the complex group G (Theorems 5, 6).
We derive the system stability condition, and obtain formulas for the system state probabilities, blocking probabilities, starvation probability, stockout probability, system availability in the steady state.
Finally, let us obtain formula (7).
The fluid model allows us to obtain formulas that only depend on the distance to the serving BS.
With the aid of techniques from combinatorial group theory, we obtain formulas for the Nielsen numbers of the selfmaps of.
In this subsection, we will obtain formulas of the solutions of homogeneous singular linear matrix difference equations.
Simulations show a traveling wave in which the time of the first k-fold mutant, Tk, is approximately linear in k and heuristics are used to obtain formulas for ETk.
By using matrix pencil theory, we obtain formulas for the solutions and we give necessary and sufficient conditions for existence and uniqueness of solutions.
Wu et al. (2013) did numerical computations for a fixed population size N. Here, we will instead let the strength of selection [Formula: see text] where c is fixed and let [Formula: see text] to obtain formulas for the invadability probabilities [Formula: see text] that determine the rankings.
