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Probabilistic analysis presented here is carried out using mainly the stochastic perturbation technique provided by the common application of the traditional FEM commercial code ABAQUS and the symbolic computations package MAPLE.
The cell problem is solved for the first case by the plane strain homogenization-oriented code MCCEFF and, in the 3D case, using the system ABAQUS® (8-node linear brick finite elements C3D8), where the uniform deformations are imposed on specific outer surfaces of the composite cell; probabilistic part is carried out in the symbolic computations package MAPLE®.
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This method of asymptotics is simple to implement using a symbolic computation package (like Maple).
This algorithm has been implemented with the symbolic computation package Maple.
The sensitivity analysis presented in this paper is performed via the provided semi-analytical technique using the commercial FEM code ABAQUS and the symbolic computation package MAPLE.
The system was viewed in two different 2D geometries which were used to develop capacitance models both theoretically and by using a finite element computation package, COMSOL Multiphysics® [3].
The data were analyzed using the statistical method of PROBIT analysis with the aid of the SPSS 11.5 computation package (SPSS Inc., Chicago, Illinois, USA).
The concentration that killed 50% of the nauplii (LC50 in μg/mL and Confidence Intervals 95%) was determined using the statistical method of PROBIT analysis with the aid of the SPSS 11.5 computation package (SPSS Inc., Chicago, IL, USA) [ 22].
The coefficients are obtained in a similar manner as stability analysis of geometrically nonlinear structures, where symbolic computation software package is used for analytical derivation of equations.
We construct successfully a series of some exact solutions including the elliptic doubly periodic solutions with the aid of computerized symbolic computation software package such as Maple or Mathematica.
The maximum specific growth rate (μmax) and maximum specific substrate-consumption rate (νmax) were calculated by nine-dimension polynomial approximations using the numerical computation software package MATLAB (MathWorks, Natick, MA).
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