Dynamical symmetries and the Ermakov invariant

Ermakov systems possessing Noether point symmetry are identified among the Ermakov systems that derive from a Lagrangian formalism and, the Ermakov invariant is shown to result from an associated symmetry of dynamical character. The Ermakov invariant and the associated Noether invariant, are sufficient to reduce these systems to quadratures

Comment on "A note on the construction of the Ermakov-Lewis invariant"

We show that the basic results on the paper referred in the title [J. Phys. A: Math. Gen. v. 35 (2002) 5333-5345], concerning the derivation of the Ermakov invariant from Noether symmetry methods, are not new

On the Lie symmetries of a class of generalized Ermakov systems

The symmetry analysis of Ermakov systems is extended to the generalized case where the frequency depends on the dynamical variables besides time. In this extended framework, a whole class of nonlinearly coupled oscillators are viewed as Hamiltonian Ermakov system and exactly solved in closed form

On the generalized Hamiltonian structure of 3D dynamical systems

The Poisson structures for 3D systems possessing one constant of motion can always be constructed from the solution of a linear PDE. When two constants of the motion are available the problem reduces to a quadrature and the structure functions include an arbitrary function of them

Physical features of soil quality under an agroforestry system

Os sistemas agroflorestais são uma alternativa sustentável de produção agropecuária. O objetivo deste trabalho foi avaliar a qualidade de um solo sob sistema agroflorestal, mediante a quantificação dos seguintes atributos físicos do solo: densidade, porosidade, resistência à penetração e estabilidade dos agregados. O solo sob sistema agroflorestal apresentou qualidade superior, quando comparado ao mesmo solo cultivado em sistema convencional, apresentando menor densidade, maior porosidade, menor resistência à penetração e maior agregação. __________________________________________________________________________________________ ABSTRACTAgroforestry systems seem to be a sustainable alternative for agricultural production. The objective of this work was to evaluate the quality of a soil used under an agroforestry system by the quantification of the following soil physical attributes: density, porosity, resistance to penetration and aggregate stability. The soil under agroforestry exhibited a superior quality compared to the same soil cultivated by a conventional system, reflected by smaller soil density, higher porosity, lesser resistance to penetration and higher aggregate stability

Diversity and Composition of the Adult Fecal Microbiome Associated with History of Cesarean Birth or Appendectomy: Analysis of the American Gut Project

AbstractBackgroundCesarean birth is associated with altered composition of the neonate's microbiota and with increased risk for obesity and other diseases later in life. The mechanisms of these associations, and whether cesarean birth is associated with an altered adult microbiota, are unknown.MethodsIn 1097 adult volunteers without diabetes, inflammatory bowel disease, or recent antibiotic use, fecal microbiome metrics were compared by history of cesarean birth (N=92) or appendectomy (N=115). Associations with potential confounders, microbiome alpha diversity, and individual microbial taxa were estimated by logistic regression. Permutation tests assessed differences in microbial composition (beta diversity) based on Jensen–Shannon divergence.FindingsCesarean birth history was associated with younger age; appendectomy with older age and higher body mass index. Neither was associated with fecal microbiome alpha diversity. Microbial composition at all taxonomic levels differed significantly with cesarean birth (P≤0.008) but not with appendectomy (P≥0.29). Relative abundance differed nominally for 17 taxa with cesarean birth and for 22 taxa with appendectomy, none of which was significant with adjustment for multiple comparisons.InterpretationAdults born by cesarean section appear to have a distinctly different composition of their fecal microbial population. Whether this distinction was acquired during birth, and whether it affects risk of disease during adulthood, are unknown.FundingSupported by the Intramural Research Program, National Cancer Institute, National Institutes of Health (Z01-CP-010214)

On the Hamiltonian structure of Ermakov systems

A canonical Hamiltonian formalism is derived for a class of Ermakov systems specified by several different frequency functions. This class of systems comprises all known cases of Hamiltonian Ermakov systems and can always be reduced to quadratures. The Hamiltonian structure is explored to find exact solutions for the Calogero system and for a noncentral potential with dynamic symmetry. Some generalizations of these systems possessing exact solutions are also identified and solved