UNIVERSAL COVERING OF DRIFTLESS CONTROL SYSTEMS

Let M be a finite-dimensional manifold and Sigma be a driftless control system on M of full rank. We prove that for a given initial state x epsilon M, the covering space Gamma(Sigma, x) for a monotonic homotopy of trajectories of Sigma which is recently constructed in [1] coincides with the simply connected universal covering manifold of M and that the terminal projection epsilon(x) : Gamma(Sigma, x) -> M given by epsilon(x) ([alpha]) = alpha(1) is a covering mapping.

Vanadium Pentoxide Nanostructures: An Effective Control of Morphology and Crystal Structure in Hydrothermal Conditions

A systematic study was made of the synthesis of V(2)O(5)center dot nH(2)O nanostructures, whose morphologies, crystal structure, and amount of water molecules between the layered structures were regulated by strictly controlling the hydrothermal treatment variables. The synthesis involved a direct hydrothermal reaction between V(2)O(5) and H(2)O(2), without the addition of organic surfactant or inorganic ions. The experimental results indicate that high purity nanostructures can be obtained using this simple and clean synthetic route. Oil the basis of a study of hydrothermal treatment variables such as reaction temperature and time, X-ray diffraction (XRD) and scanning transmission electron microscopy (STEM) revealed that it was possible to obtain nanoribbons of the V(2)O(5)center dot nH(2)O monoclinic phase and nanowires or nanorods of the V(2)O(5)center dot nH(2)O orthorhombic phase. Thermal gravimetric analysis (TGA) shows also that the water content in the Structure call be controlled at appropriate hydrothermal conditions. Concerning the oxidation state of the vanadium atoms of as-obtained samples, a mixed-valence state composed of V(4+) and V(5+) was observed ill the V(2)O(5)center dot nH(2)O monoclinic phase, while the valence of the vanadium atoms was preferentially 5+ in the V(2)O(5)center dot nH(2)O orthorhombic phase. The X-ray absorption near-edge structure (XANES) results also indicated that the local structure of vanadium possessed a higher degree of symmetry in the V(2)O(5)center dot nH(2)O monoclinic phase.