Projective dynamics and first integrals

We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami's theorem about projectively flat Riemannian manifolds. We set the ground for a new and simple theory of the integrable systems having only quadratic first integrals. This theory begins with two centered quadrics related by central projection, each quadric being a model of a space of constant curvature. Finally, we present an extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure

Renal Denervation for Treating Hypertension: Current Scientific and Clinical Evidence

Initial studies of catheter-based renal denervation (RDN) for uncontrolled HTN using radiofrequency ablation in the main renal arteries showed that RDN was effective in lowering office blood pressure (BP). However, the first randomized sham-controlled trial, SYMPLICITY-HTN-3, did not show significantly lower office or 24-h ambulatory systolic BP compared with sham treatment. Subsequent studies in both animals and humans demonstrated the potential importance of more distal and branch renal artery radiofrequency ablation, and a second-generation multielectrode system became available. Two recent randomized sham-controlled trials in patients not taking antihypertensive drugs (SPYRAL HTN-OFF MED) or continuing to take drugs (SPYRAL HTN-ON MED) performed RDN with the second-generation radiofrequency ablation system using an ablation protocol that included treatment of the distal renal artery as well as the branch renal arteries. These studies showed that RDN significantly reduced office and 24-h ambulatory BP compared with sham treatment. Another recent randomized sham-controlled trial in patients not receiving medications showed that RDN with catheter-based ultrasound (RADIANCE-HTN SOLO) applied in just the main renal arteries significantly lowered daytime ambulatory and office BP compared with sham treatment. These trials have renewed clinical and scientific interest in defining the appropriate role of RDN in hypertension treatment. In addition, other important issues will need to be addressed in the future such as the development of tests to determine the extent of RDN at the time of the procedure and the potential of renal nerve fibers to regain their patency at some later stage following the ablation procedure. © 2019 American College of Cardiology Foundatio