The solution of a system of n-th-order differential equations using Lie series

Solution to system of n-th order differential equations using Lie serie

Solution of ordinary differential equations by means of Lie series

Solution of ordinary differential equations by Lie series - Laplace transformation, Weber parabolic-cylinder functions, Helmholtz equations, and applications in physic

Lie series for celestial mechanics, accelerators, satellite stabilization and optimization

Lie series applications to celestial mechanics, accelerators, satellite orbits, and optimizatio

Anomalous diffusion as a signature of collapsing phase in two dimensional self-gravitating systems

A two dimensional self-gravitating Hamiltonian model made by $N$ fully-coupled classical particles exhibits a transition from a collapsing phase (CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical point of view, the two phases are characterized by two distinct single-particle motions : namely, superdiffusive in the CP and ballistic in the HP. Anomalous diffusion is observed up to a time $\tau$ that increases linearly with $N$. Therefore, the finite particle number acts like a white noise source for the system, inhibiting anomalous transport at longer times.Comment: 10 pages, Revtex - 3 Figs - Submitted to Physical Review

Predictive value of heidelberg retina tomograph parameters for the development of glaucoma in the European glaucoma prevention study

PURPOSE: To determine whether baseline Heidelberg Retina Tomograph (HRT) measurements of the optic disc are associated with the development of open-angle glaucoma (OAG) in individuals with ocular hypertension in the European Glaucoma Prevention Study (EGPS). DESIGN: Retrospective analysis of a prospective, randomized, multicenter, double-masked, controlled clinical trial. METHODS: There were 489 participants in the HRT Ancillary Study to the EGPS. Each baseline HRT parameter was assessed in univariate and multivariate proportional hazards models to determine its association with the development of OAG. Proportional hazards models were used to identify HRT variables that predicted which participants in the EGPS had developed OAG. Development of OAG was based on visual field and/or optic disc changes. RESULTS: At a median follow-up time of about 5 years, 61 participants developed OAG. In multivariate analyses, adjusting for randomization arm, age, baseline IOP, central corneal thickness, pattern standard deviation, and HRT disc area, the following HRT parameters were associated with the development of OAG: the "outside normal limits" classification of the Frederick Mikelberg (FSM) discriminant function (hazard ratio [HR] 2.51, 95% confidence interval [CI]: 1.45-4.35), larger mean cup depth (HR 1.64, 95% CI: 1.21-2.23), cup-to-disc area ratio (HR 1.43, 95% CI: 1.14-1.80), linear cup-to-disc ratio (HR 1.43, 95% CI: 1.13-1.80), cup area (HR 1.33, 95% CI: 1.08-1.64), smaller rim area (HR 1.33, 95% CI: 1.07-1.64), larger cup volume (HR 1.30, 95% CI: 1.05-1.61), smaller rim volume (HR 1.25, 95% CI: 1.01-1.54), larger maximum cup depth (HR 1.18, 95% CI: 1.01-1.36), and cup shape measure (HR 1.18, 95% CI: 1.01-1.36). CONCLUSIONS: Several baseline HRT parameters, alone or in combination with baseline clinical and demographic factors, were significantly associated with the development of OAG among the EGPS participants