### On the degree of nilpotency of the radical of relatively free algebras.

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In this paper a geometrical link between partial differential equations (PDE) and special coordinate nets on two-dimensional smooth manifolds with the a priori given curvature is suggested. The notion of G-class (the Gauss class) of differential equations admitting such an interpretation is introduced. The perspective of this approach is the possibility of applying the instruments and methods of non-Euclidean geometry to the investigation of differential equations. The equations generated by the...

Two new applications of ${\Lambda}^{2}$-representations of PDEs are presented: 1. Geometric algorithms for numerical integration of PDEs by constructing planimetric discrete nets on the Lobachevsky plane ${\Lambda}^{2}$. 2. Employing ${\Lambda}^{2}$-representations for the spectral-evolutionary problem for nonlinear PDEs within the inverse scattering problem method.

A computational framework for testing the effects of cytotoxic molecules, specific to a given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The model is based on a cellular automaton to describe tumour cell states transitions from proliferation to death. It is coupled with a model describing the tumour vasculature and its adaptation to the blood rheological constraints when alterations are induced by VDAs treatment....

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