In this paper a control law for stabilizing an underactuated surface vessel is presented. We propose a timevarying controller that provides semi-global practical asymptotic stability. The method combines nested saturation techniques by Tee1 [lo] and backstepping approach. The stability analysis involves the averaging theory.

In this work, we conducted a QSAR study on 18 molecules using descriptors from the Density Functional Theory (DFT) in order to predict the inhibitory activity of hydroxamic acids on histone deacetylase 7. This study is performed using the principal component analysis (PCA) method, the Ascendant Hierarchical Classification (AHC), the linear multiple regression method (LMR) and the nonlinear multiple regression (NLMR). DFT calculations were performed to obtain information on the structure and information on the properties on a series of hydroxamic acids compounds studied. Multivariate statistical analysis yielded two quantitative models (model MLR and model MNLR) with the quantum descriptors: electronic affinity (AE), vibration frequency of the OH bond (ν(OH)) and that of the NH bond (ν(NH)). The LMR model gives statistically significant results and shows a good predictability R 2 = 0.9659, S = 0.488, F = 85 and p-value < 0.0001. Electronic affinity is the priority descriptor in predicting the activity of HDAC7 inhibitors in this study. The results obtained suggest that the descriptors derived from the DFT could be useful to predict the activity of histone deacetylase 7 inhibitors. These models were evaluated according to the criteria of Tropsha et al.

Several studies have been carried out on the structure of hydroxamic acids as histone deacetylase inhibitors. Scientists discovered that the (-CONHOH) moiety of hydroxamic acids was responsible for the chelation of the zinc ion into the active site of histone deacetylases thereby inhibiting the activity of these. In this work, we conducted a study using the new dual descriptor from the conceptual DFT to determine the atoms responsible for zinc chelation in order to propose new, more active molecules. The calculations were performed to determine the local reactivity of the hydroxamic acids studied using Fukui functions by the Hirshfeld method. Global parameters were also determined to predict the relative stability and reactivity of hydroxamic acids. The work was conducted at computational level B3LYP / 6-311G (d, p). The most polarizable compound has an energy gap of 3.933 eV. The analysis of the local indices of reactivity as well as the dual descriptors revealed that an oxygen of these compound is the most favorable site vis-à-vis electrophilic attack.

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This Quantitative Structure-Activity Relationship (QSAR) study was conducted using a series of twenty (20) chalcone derivatives with inhibitory activities against Plasmodium falciparum 3D7. The molecules were optimized at the B3LYP/LanL2DZ computational level, to obtain the molecular descriptors. This work was performed using the Linear Multiple Regression (LMR) method, the NonLinear Regression (NLMR) and the Artificial Neural Network (ANN) method. These tools allowed us to obtain three (3) quantitative models from the quantum descriptors that are, the overall softness (S), the bond lengths l(c=o) and l(c=c), and the polarizability (α). These models have good statistical performance. Among them, the ANN has a significantly better predictive ability R 2 =0.997; RMCE = 0.035; F= 3571.499. The external validation tests verify all the criteria of Tropsha et al. and Roy et al. Also, the applicability domain of this model determined from the levers shows that a prediction of the pIC50 of new chalcone derivatives is acceptable when its lever value is lower than 1.07. For the ANN method, the Ch19 molecule is certainly outside the applicability domain, but it is not an influential point for the model, because this derivative belongs to the validation set, and therefore was not used in the model development. The behavior of this molecule could be explained by its structural diversity.