Modified hyperspheres algorithm to trace homotopy curves of nonlinear circuits composed by piecewise linear modelled devices.

We present a homotopy continuation method (HCM) for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL) representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this proposal, four nonlinear circuits composed of piecewise linear modelled devices are analysed to determine their multiple operating points. The results show that HCM can find multiple solutions within a single homotopy trajectory. Furthermore, we take advantage of the fact that homotopy trajectories are PWL curves meant to replace the multidimensional interpolation and fine tuning stages of the path tracking algorithm with a simple and highly accurate procedure based on the parametric straight line equation.

Knigth's Move in the Periodic Table, From Copper to Platinum, Novel Antitumor Mixed Chelate Copper Compounds, Casiopeinas, Evaluated by an in Vitro Human and Murine Cancer Cell Line Panel.

We synthesized a novel anticancer agents based on mixed chelate copper (II) complexes, named Casiopeínas((R)) has of general formula [Cu(N-N)(N-O)H(2)O]NO(3) (where, N-N = diimines as 1,10- phenanthroline, 2,2-bipyridine, or substituted and N-O=aminoeidate or [Cu(N-N)(O-O)H(2)O]NO(3) (where NN= diimines as 10-phenanthroline, 2,2-bipyridine or substituted Casiopeínas I, II, IV, V, VI, VII VIII and O-O=acetylacetonate, salicylaldehidate Casiopínas III). We evaluated the in vitro antitumor activity using a human cancer cell panel and some nurine cancer cells. Eleven Casiopeinas are evaluated in order to acquire some structure-activity correlations and some monodentated Casiopeinäs analogues; cisplatinum was used as control drug. The 50% growth inhibition observed is, in all cases reach with concentrations of Casiopeina's 10 or 100 times lower than cisplatinum. In a previous work we reported the induction of apoptosis by Casiopeina II. The results indicate that Casiopeinass are a promising new anticancer drug candidates to be developed further toward clinical trials.