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In cloud computing, analytical queueing formulas are often integrated in optimization programs, where they are repeatedly evaluated across what-if scenarios.
The force constants and vibrational frequencies were determined by computing analytical frequencies on the stationary points obtained after the optimization to check if there were true minima.
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In Section 3, we compute analytical expressions for the asymptotic and the approximate BERs when BSs use a single antenna.
These series can be used to compute analytical formulae for the stochastic properties of nonlinear equations, in analogy to the standard approach for linear equations.
The package Phoretic allows to compute analytical (and also numerical) expressions for forces and torques stemming from elastic and diffusive scattering processes parameterized by an accommodation coefficient.
As part of the model simulation, a number of vehicles of interest are selected and applied to the models to compute analytical DFs.
This computed analytical model gives a practical possibility for investigation of experimental data from measurements of galactic cosmic rays and their anomalous component.
Using simulations of the master equation as a reference, we show that, far from a bifurcation, the Langevin approach provides a reliable tool to compute analytical expressions for time correlation functions.
This work couples a nonlinear shell model to an unsteady vortex lattice solver, and then computes analytical design gradients: the derivative of aerodynamic force/power quantities with respect to a large vector of thickness variables.
where γ S j R ( i ) = γ 0 | h S j R ( i ) | 2, and γ RD ( i ) = γ 0 | h RD ( i ) | 2. γ RD ( i ) = γ 0 | h RD ( i ) | 2. It is also difficult here to compute analytical expressions for the PDF and the MGF of γ BA) at the destination node.
The model is designed for multilocus genomic sequence alignments, with one sequence sampled from each of the three species, and is formulated using a Markov chain representation that allows use of matrix exponentiation to compute analytical expressions for the probability density of coalescent histories.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com