Weak KAM for commuting Hamiltonians

For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax-Oleinik semi-groups, a result of Barles and Tourin ([BT01]), using a direct geometrical method (Stoke's theorem). We also obtain a "generalization" of a theorem of Maderna ([Mad02]). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton-Jacobi equation) for G and for H are the same. As a corrolary we obtain the equality of the Aubry sets, of the Peierls barrier and of flat parts of Mather's $\alpha$ functions. This is also related to works of Sorrentino ([Sor09]) and Bernard ([Ber07b]).Comment: 23 pages, accepted for publication in NonLinearity (january 29th 2010). Minor corrections, fifth part added on Mather's $\alpha$ function (or effective Hamiltonian

Incidence and predisposing factors of cognitive disorders following off-pump coronary artery bypasses graft surgery

Patients and Methods: A total of 171 patients who had undergone off-pump CABG without any history of psychiatric disorders were enrolled. Samples were selected according to a purposive sampling method. The Mini-Mental State Examination (MMSE) questionnaire was given to each patients to assess the incidence of cognitive disorder during the first 24 hours of surgery in ICU. To compare creatinine, erythrocytes sedimentation rate, extubation time, and patients’ age between those with and those without postoperative cognitive disorder, independent-samplest test was employed. To compare two groups in terms of any history of diseases such as diabetes, hypertension, and hyperlipidemia, and qualitative C-reactive protein (CRP), Chi square test was used. Results: Results showed that 75% of patients had postoperative cognitive disorder. There was a significant association between the history of hypertension, CRP, and preoperative creatinine levels in both cognitive disorder and control groups. Background: Cognitive disorder, which is a common problem for the hospitalized patients, is a fluctuating cognitive destruction that leads to the loss of consciousness. It is usually accompanied by increased mortality, prolonged hospital stay, and decreased rehabilitation. Objectives: The purpose of this study was to determine the risk factors associated with cognitive disorder after coronary artery bypasses graft surgery (CABG). Conclusions: Given the significant prevalence of postoperative cognitive disorder and significant association between the history of hypertension, CRP, and preoperative creatinine and cognitive disorder, the detection of patient’s clinical symptoms may improve diagnosis, treatment, and even prevention of cognitive disorder. © 2014, Iranian Society of Regional Anesthesia and Pain Medicine (ISRAPM); Published by Kowsar

Arnold diffusion in the dynamics of a 4-machine power system undergoing a large fault

We focus on the seemingly complicated dynamics of a four-machine power system which is undergoing a sudden fault. Adopting a Hamiltonian (energy) formulation, we consider the system as an interconnection of (one degree of freedom) subsystems. Under certain configuration (a star network) and parameter values we establish the presence of Arnold diffusion which entails periodic, almost periodic, and complicated nonperiodic dyanmics all simultaneously present; and erratic transfer of energies between the subsystems. In section 1 we introduce the transient stability problem in a mathematical setting and explain what our results mean in the power systems context. Section 2 provides insights into Arnold diffusion and summarizes its mathematical formulation as in [8], [1]. Section 3 gives conditions for which Arnold diffusion arises on certain energy levels of the swing equations. These conditions are verified analytically in the case when all but one subsystem (machine) undergo relatively small oscillations

Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation

Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact and connected manifold and let u be a semi-concave function defined on M. If E (u) is the set of all the super-differentials of u and (\phi t) the Hamiltonian flow of H, we prove that for t > 0 small enough, \phi-t (E (u)) is an exact Lagrangian Lipschitz graph. This provides a geometric interpretation/explanation of a regularization tool that was introduced by P.~Bernard to prove the existence of C 1,1 subsolutions

Improving Complementary Methods to Predict Evapotranspiration for Data Deficit Conditions and Global Applications Under Climate Change

A reliable estimate of evapotranspiration (ET) in river basins is important for the purpose of water resources planning and management. ET represents a significant portion of rainfall in the water budget; therefore, the uncertainty in estimating ET can lead to the inaccurate prediction of water resources. While remote sensing techniques are available to estimate ET, such methods are expensive and necessary data may not be readily available. Classical methods of estimating ET require detailed land use/cover information that are not readily available in rural river basins. Complementary methods provide simple and reliable approaches to estimate ET using meteorological data only. However, these methods have not been investigated in detail to assess the overall applicability and the needs for revisions if any. In this work, an improved approach to use the complementary methods using readily available meteorological data is presented. The methodology is validated using 34 global FLUXNET sites with heterogeneous land use/cover, climatic, and physical conditions. The method was compared with classical methods using Ghana as a study area where original pioneering studies of ET have been performed. The work was extended to develop global maps of ET and water surplus (precipitation - ET) for the 20th century followed by climate change-induced 21st century estimates for 2040-2069 and 2070-2099 periods. The emission scenario used was the moderate A1B with the global climate models CGCM3.1 and HADGEM1. The results were assessed at different scales from global to regional such as for potential outcomes of climate change on ET and water surplus

Periodic orbits of period 3 in the disc

Let f be an orientation preserving homeomorphism of the disc D2 which possesses a periodic point of period 3. Then either f is isotopic, relative the periodic orbit, to a homeomorphism g which is conjugate to a rotation by 2 pi /3 or 4 pi /3, or f has a periodic point of least period n for each n in N*.Comment: 7 page

Optimization of the Electronic Driver and Thermal Management of LEDs Lighting Powered by Solar PV

AbstractThe developments of efficient photovoltaic (PV) standalone systems requires advanced technology for PV cells and modules for high performance but also the application of components or loads of use with low energy consumption. In this context, the development of lighting systems using solar energy and electroluminescent components like high power white Light Emitting Diodes (LEDs) is proposed. The integration of the light fixture with the choice of best technologies for high efficiency LEDs and the design of an ultra-economic driver as the PWM driver permit us to obtain a high lighting efficiency. Our study has taken in consideration thermal aspect and the choice of adequate heat sinks for thermal management. This study, allowed us to consider both effects of thermal and electronic order and allowed us to the achievement of a high efficiency lighting powered by solar energy. With the implementation of the PWM electronic controls, we should reach an energy efficiency of the LEDs Driver from 85 to 90%