This paper makes a contribution to differential elimination and more precisely to the problem of computing a representation of the radical differential ideal generated by a system of differential equations (ordinary or partial). The approach we use here involves characteristic set techniques;‡ these were introduced by J. F. Ritt, the founder of differential algebra. The basic idea is to write t...

saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. because of heterogeneous nature of cell populations, the cell population balance equation (pbe) can be used to capture the dynamic behavior of such cultures. in this work, an unstructured-segregated model is used for d...

The linearization of complex ordinary differential equations is studied by extending Lie’s criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible comp...

in this paper, we introduce a hybrid approach based on neural network and optimization teqnique to solve ordinary differential equation. in proposed model we use heyperbolic secont transformation function in hiden layer of neural network part and bfgs teqnique in optimization part. in comparison with existing similar neural networks proposed model provides solutions with high accuracy. numerica...

BACKGROUND There is a need to have a model to study methadone's losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. AIM To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). METHODOLOGY We conducted a cross-section...

In this paper, the free vibration analysis of sandwich micro beam with piezoelectric layers based on the modified couple stress and surface elasticity theories are investigated. The Hamilton’s principle is employed to derive the sandwich micro beam with piezoelectric based on modified couple stress theory incorporating with Gurtin- Murdoch surface theory. The generalized differential quadrature...

We analyze the stability of Newtonian polytropic static fluid spheres, described by the Lane-Emden equation. In the general case of arbitrary polytropic indices the Lane-Emden equation is a non-linear second order ordinary differential equation. By introducing a set of new variables, the Lane-Emden equation can be reduced to an autonomous system of two ordinary differential equations, which in ...