Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes

Kinetic theory model predictions compared with low-thrust axisymmetric nozzle plume data

A system of nonlinear integral equations equivalent to the steady-state Krook kinetic equation was used to model the flow from a low-thrust axisymmetric nozzle. The mathematical model was used to numerically calculate the number density, temperature, and velocity of a simple gas as it expands into a near vacuum. With these quantities the gas pressure and flow directions of the gas near the exit plane were calculated and compared with experimental values for a low-thrust nozzle of the same geometry and mass flow rate

Pulmonary fissure integrity and collateral ventilation in COPD patients

Purpose: To investigate whether the integrity (completeness) of pulmonary fissures affects pulmonary function in patients with chronic obstructive pulmonary disease (COPD). Materials and Methods: A dataset consisting of 573 CT exams acquired on different subjects was collected from a COPD study. According to the global initiative for chronic obstructive lung disease (GOLD) criteria, these subjects (examinations) were classified into five different subgroups, namely non-COPD (222 subjects), GOLD-I (83 subjects), GOLD-II (141 subjects), GOLD-III (63 subjects), and GOLD-IV (64 subjects), in terms of disease severity. An available computer tool was used to aid in an objective and efficient quantification of fissure integrity. The correlations between fissure integrity, and pulmonary functions (e.g., FEV1, and FEV1/FVC) and COPD severity were assessed using Pearson and Spearman's correlation coefficients, respectively. Results: For the five sub-groups ranging from non-COPD to GOLD-IV, the average integrities of the right oblique fissure (ROF) were 81.8%, 82.4%, 81.8%, 82.8%, and 80.2%, respectively; the average integrities of the right horizontal fissure (RHF) were 62.6%, 61.8%, 62.1%, 62.2%, and 62.3%, respectively; the average integrities of the left oblique fissure (LOF) were 82.0%, 83.2%, 81.7%, 82.0%, and 78.4%, respectively; and the average integrities of all fissures in the entire lung were 78.0%, 78.6%, 78.1%, 78.5%, and 76.4%, respectively. Their Pearson correlation coefficients with FEV1 and FE1/FVC range from 0.027 to 0.248 with p values larger than 0.05. Their Spearman correlation coefficients with COPD severity except GOLD-IV range from -0.013 to -0.073 with p values larger than 0.08. Conclusion: There is no significant difference in fissure integrity for patients with different levels of disease severity, suggesting that the development of COPD does not change the completeness of pulmonary fissures and incomplete fissures alone may not contribute to the collateral ventilation. © 2014 Pu et al