Foliations of Isonergy Surfaces and Singularities of Curves

It is well known that changes in the Liouville foliations of the isoenergy surfaces of an integrable system imply that the bifurcation set has singularities at the corresponding energy level. We formulate certain genericity assumptions for two degrees of freedom integrable systems and we prove the opposite statement: the essential critical points of the bifurcation set appear only if the Liouville foliations of the isoenergy surfaces change at the corresponding energy levels. Along the proof, we give full classification of the structure of the isoenergy surfaces near the critical set under our genericity assumptions and we give their complete list using Fomenko graphs. This may be viewed as a step towards completing the Smale program for relating the energy surfaces foliation structure to singularities of the momentum mappings for non-degenerate integrable two degrees of freedom systems.Comment: 30 pages, 19 figure

Hypoxic Pulmonary Vasoconstriction in Humans:Tale or Myth

Hypoxic Pulmonary vasoconstriction (HPV) describes the physiological adaptive process of lungs to preserves systemic oxygenation. It has clinical implications in the development of pulmonary hypertension which impacts on outcomes of patients undergoing cardiothoracic surgery. This review examines both acute and chronic hypoxic vasoconstriction focusing on the distinct clinical implications and highlights the role of calcium and mitochondria in acute versus the role of reactive oxygen species and Rho GTPases in chronic HPV. Furthermore it identifies gaps of knowledge and need for further research in humans to clearly define this phenomenon and the underlying mechanism

An epidemic model with a time delay in transmission

summary:We study a mathematical model which was originally suggested by Greenhalgh and Das and takes into account the delay in the recruitment of infected persons. The stability of the equilibria are also discussed. In addition, we show that the introduction of a time delay in the transmission term can destabilize the system and periodic solutions can arise by Hopf bifurcation