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

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

Braids of entangled particle trajectories

In many applications, the two-dimensional trajectories of fluid particles are available, but little is known about the underlying flow. Oceanic floats are a clear example. To extract quantitative information from such data, one can measure single-particle dispersion coefficients, but this only uses one trajectory at a time, so much of the information on relative motion is lost. In some circumstances the trajectories happen to remain close long enough to measure finite-time Lyapunov exponents, but this is rare. We propose to use tools from braid theory and the topology of surface mappings to approximate the topological entropy of the underlying flow. The procedure uses all the trajectory data and is inherently global. The topological entropy is a measure of the entanglement of the trajectories, and converges to zero if they are not entangled in a complex manner (for instance, if the trajectories are all in a large vortex). We illustrate the techniques on some simple dynamical systems and on float data from the Labrador sea.Comment: 24 pages, 21 figures. PDFLaTeX with RevTeX4 macros. Matlab code included with source. Fixed an inconsistent convention problem. Final versio

Workplace Stressors and Coping Strategies Among Public Hospital Nurses in Medan, Indonesia

Background: Nursing is considered as a stressful job when compared with other jobs. Prolonged stress without effective coping strategies affects not only nurses\u27 occupational life but also their nursing competencies. Medan is the biggest city in Sumatera Island of Indonesia. Two tertiary public hospital nurses in this city hold the responsibility in providing excellent care to their patients. Objective: To investigate the relationships between the nurse\u27s workplace stressors and the coping strategies used. Method: The descriptive correlational study was conducted to examine the relationships between workplace stressors and the coping strategies used in nurses of two public hospitals in Medan. The sample size of 126 nurses was drawn from selected in-patient units. Data were collected by using self-report questionnaires and focus group interview. The majority of subjects experienced low workplace stressors, where death/dying was the most commonly reported workplace stressor followed by workload. Religion was the most commonly used coping strategy. Result: Significant correlations were found between subscales of workplace stressors and coping strategies. Most of subjects used emotion-focused and dysfunctional coping strategies rather than problem-focused coping strategies. Conclusion: The nurse administrators in the hospitals need to advocate their in order to use problem-focused coping strategies more frequent than emotion-focused and dysfunctional coping strategies when dealing with workplace stressors