Avoidance Control on Time Scales

We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent's actions. Leitmann's avoidance conditions are proved to be valid for dynamic systems evolving on an arbitrary time scale.Comment: Revised edition in JOTA format. To appear in J. Optim. Theory Appl. 145 (2010), no. 3. In Pres

Hahn's Symmetric Quantum Variational Calculus

We introduce and develop the Hahn symmetric quantum calculus with applications to the calculus of variations. Namely, we obtain a necessary optimality condition of Euler-Lagrange type and a sufficient optimality condition for variational problems within the context of Hahn's symmetric calculus. Moreover, we show the effectiveness of Leitmann's direct method when applied to Hahn's symmetric variational calculus. Illustrative examples are provided.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 06-Sept-201

The Hahn Quantum Variational Calculus

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory and Application

A Stochastic Optimal Control Model of Pollution Abatement

Link alla rivista: http://www.e-ndst.kiev.ua/v10n2.ht

Necessary optimality conditions for infinite horizon variational problems on time scales

We prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems of the calculus of variations on time scales. Here the Lagrangian depends on the independent variable, an unknown function and its nabla derivative, as well as a nabla indefinite integral that depends on the unknown function

Progress in Classical and Quantum Variational Principles

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis Principle is the classical limit of Schr\"{o}dinger's variational principle of wave mechanics, and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems

Noninvasive monitoring of cardiac function in a chronic ischemic heart failure model in the rat: Assessment with tissue Doppler and non-Doppler 2D strain echocardiography

<p>Abstract</p> <p>Objectives</p> <p>Feasibility of noninvasive monitoring of cardiac function after surgically induced ischemic cardiomyopathy with tissue Doppler and non-Doppler 2D strain echocardiography in rats.</p> <p>Background</p> <p>The optimal method for quantitative assessment of global and regional ventricular function in rats with chronic heart failure for research purposes remains unclear.</p> <p>Methods</p> <p>20 rats underwent suture ligation of the left anterior descending coronary artery via a left thoracotomy to induce ischemic cardiomyopathy. Echocardiographic examination with estimation of left ventricular wall thickness, diameters, fractional shortening, ejection fraction, wall velocities as well as radial strain were performed before and 4 weeks after surgery.</p> <p>Results</p> <p>Mean LVEF decreased from 70 ± 6% to 40 ± 8% (p < 0.0001) one month after the operation. LVEDD increased from 7 ± 1 mm to 9 ± 1 mm (p < 0.0001), systolic anterior velocity decreased from 0.79 ± 0.25 cm/s to 0.18 ± 0.19 cm/s (p < 0.0001). Radial 2D strain was significantly reduced after myocardial infarction of the septal (18.2 ± 6.6% vs 7.0 ± 5.9%, p < 0.001), anteroseptal (17.3 ± 5.2% vs 4.6 ± 3.0%, p < 0.0001), anterior (18.9 ± 5.9% vs 5.6 ± 2.5%, p < 0.0001), lateral (21.4 ± 4.9% vs 8.1 ± 3.5%, p < 0.0001) as well as posterior myocardial segments (19.3 ± 5.2% vs 15.4 ± 5.5%, p < 0.01). Inferior segments (19.2 ± 7.9% vs 17.8 ± 7.9%, ns) did not change at all.</p> <p>Conclusion</p> <p>It is feasible to assess dimensions, global function, and regional contractility with echocardiography in rats suffering from chronic heart failure after myocardial infarction. Particularly regional function can be exactly evaluated if tissue Doppler and 2D strain is used.</p