A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems

In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some reference

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

Average sex ratio and population maintenance cost

The ratio of males to females in a population is a meaningful characteristic of sexual species. The reason for this biological property to be available to the observers of nature seems to be a question never asked. Introducing the notion of historically adapted populations as global minimizers of maintenance cost functions, we propose a theoretical explanation for the reported stability of this feature. This mathematical formulation suggests that sex ratio could be considered as an indirect result shaped by the antagonism between the size of the population and the finiteness of resources.Comment: 18 pages. A revised new version, where all the text was improved to become more clear for the reade

On invariant sets in Lagrangian graphs

In this exposition, we show that a Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are smooth enough. We also provide some counterexamples for the case that the Hamiltonians are not smooth enough.Comment: 4 page

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