Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

The "Pulse Time Index of Norm" highly correlates with the left ventricular mass index in patients with arterial hypertension

Igor N Posokhov,1 Natalya N Kulikova,2 Irina V Starchenkova,2 Elena A Grigoricheva,3 Vitaly V Evdokimov,3 Artemy V Orlov,4 Anatoly N Rogoza5 On behalf of The BPLab-Vasotens Registry Collaborators 1Hemodynamic Laboratory Ltd, Nizhny Novgorod, Russia; 23rd Republican Hospital, Saransk, Russia; 3Chelyabinsk State Medical Academy, Chelyabinsk, Russia; 4National Research Nuclear University MEPhl, Moscow, Russia; 5Cardiology Research Center, Moscow, Russia Background: Arterial stiffness, as measured by the pulse wave velocity (PWV), is recommended for routine use in clinical practice as an important parameter for the evaluation of cardiovascular risk.1 New 24-hour monitors (eg, with Vasotens® technology; Petr Telegin Company, Nizhny Novgorod, Russian Federation) provide single PWV measurements as well as several PWV measurements over a period of 24 hours.2 Such 24-hour pulse wave analysis led to the development of the novel Pulse Time Index of Norm (PTIN), which is defined as the percentage of a 24-hour period during which the PWV does not exceed the 10 m/second PWV threshold. The aim of this study is to test the new PTIN for correlation with the left ventricular mass index (LVMI). Methods: Oscillometrically generated waveform files (n=137) used for clinical research studies were reanalyzed using the new 2013 version of the Vasotens technology program, which enables PTIN calculations. Results: A good correlation (r=−0.72) between the PTIN and the LVMI was shown, which was significantly above the blood pressure load (r=0.41). Conclusion: The PTIN generated by the Vasotens technology can be recommended as an indicator of end organ damage via hypertension. Keywords: pulse wave velocity, ambulatory, 24-hour, monitoring, PTIN, arterial stiffness, LVM