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

Control of Hamiltonian chaos as a possible tool to control anomalous transport in fusion plasmas

It is shown that a relevant control of Hamiltonian chaos is possible through suitable small perturbations whose form can be explicitly computed. In particular, it is possible to control (reduce) the chaotic diffusion in the phase space of a Hamiltonian system with 1.5 degrees of freedom which models the diffusion of charged test particles in a turbulent electric field across the confining magnetic field in controlled thermonuclear fusion devices. Though still far from practical applications, this result suggests that some strategy to control turbulent transport in magnetized plasmas, in particular tokamaks, is conceivable. The robustness of the control is investigated in terms of a departure from the optimum magnitude, of a varying cut-off at large wave vectors, and of random errors on the phases of the modes. In all three cases, there is a significant region of maximum efficiency in the vicinity of the optimum control term.Comment: 17 pages, 21 figure

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

Biological Characteristics and Medical Treatment of Breast Cancer in Young Women—A Featured Population: Results from the NORA Study

Background. The present paper described the biological characteristics and clinical behavior of young women in the cohort NORA study Patients and Methods. From 2000–2002, patients (N > 3500) were enrolled at 77 Italian hospitals. Women aged ≤50 years (N = 1013) were stratified into age groups (≤35, 36–40, 41–45, and 46–50 years). The relationship between age and patient characteristics, cancer presentation, and treatment was analyzed. Results. Younger women more frequently had tumors with ER/PgR-negative(χ2 = 7.07; P = .008), HER2 amplification (χ2 = 5.76; P = .01), and high (≥10%) Ki67 labelling index (χ2 = 9.53; P = .002). Positive nodal status, large tumors, and elevated Ki67 all associated with the choice for chemotherapy followed by endocrine therapy in hormone receptor-positive patients (P < .0001). At univariate analysis, ER-ve status, chemotherapy and age resulted as the only statistically significant variables (HR = 2.02, P = .004, and >40 versus ≤40, P < .0001, resp.). At multivariate analysis, after adjustment for significant clinical and pathological factors, age remains a significant prognostic variable (HR = 0.93, P = .0021). Conclusion. This cohort study suggests that age per sè is an important prognostic factor. The restricted role of early diagnosis and the aggressive behavior of cancer in this population make necessary the application of targeted medical strategies crucial