A neuro-heuristic scheme is design to solve nonlinear singular second order system based on Thomas-Fermi equation using the strength of universal approximation capabilities of feedforward artificial neural networks supported with optimization power of genetic algorithms and sequential quadratic programming.
The strength of universal function approximation capabilities of ANNs is exploited in formulation of mathematical model of the problem based on an unsupervised error.
Mathematical model of transformed system is constructed by exploiting the strength of universal function approximation ability of ANNs and an unsupervised error function is formulated for the system in a least mean square sense.
This is achieved by a suitable interpolation of the buckling strength approximations of the two limiting cases mentioned above, and using the effective section method to relate the loading on a silo or tank to the circumferential compressive stress at the inner edge of the ringbeam.
To normalize for differences in thickness and diameter of the implants in the push-out specimens, the load data were converted to strength by approximation of the implant surface area (implant diameter × height × π).
Alas, for all the moments that their strengths shone through, there were other moments of approximation, carelessness, uncertainty or simple screaming out of high notes, as in the number "Odissea".
The strengths of the proposed approximation rely on the generic spatial discretization of the model equations using a continuous finite element type approximation technique, while avoiding the solution of a large linear system with a sparse mass matrix which would come along with any standard ODE solver in a classical finite element approach to advance the solution in time.
WHAT THIS STUDY ADDS TO OUR KNOWLEDGE ☑ The developed placebo model could describe the data of this new population to a very good approximation, showing the strength of a population systems pharmacology approach.
I use the analytical approximation of [ 13], to jointly estimate the strength of selection (s) and the rate of adaptive substitution per site per generation.
Finally, based on the proposed method, an acceptable approximation for the ultimate strength of the NC is predicted.
