Contractions: Nijenhuis and Saletan tensors for general algebraic structures

Generalizations in many directions of the contraction procedure for Lie algebras introduced by E.J.Saletan are proposed. Products of arbitrary nature, not necessarily Lie brackets, are considered on sections of finite-dimensional vector bundles. Saletan contractions of such infinite-dimensional algebras are obtained via a generalization of the Nijenhuis tensor approach. In particular, this procedure is applied to Lie algebras, Lie algebroids, and Poisson structures. There are also results on contractions of n-ary products and coproducts.Comment: 25 pages, LateX, corrected typo

Construction of completely integrable systems by Poisson mappings

Pulling back sets of functions in involution by Poisson mappings and adding Casimir functions during the process allows to construct completely integrable systems. Some examples are investigated in detail.Comment: AmsTeX, 9 page

Completely integrable systems: a generalization

We present a slight generalization of the notion of completely integrable systems to get them being integrable by quadratures. We use this generalization to integrate dynamical systems on double Lie groups.Comment: Latex, 15 page

Generalized n-Poisson brackets on a symplectic manifold

On a symplectic manifold a family of generalized Poisson brackets associated with powers of the symplectic form is studied. The extreme cases are related to the Hamiltonian and Liouville dynamics. It is shown that the Dirac brackets can be obtained in a similar way.Comment: Latex, 10 pages, to appear in Mod. Phys. Lett.

A variational principle for volume-preserving dynamics

We provide a variational description of any Liouville (i.e. volume preserving) autonomous vector fields on a smooth manifold. This is obtained via a ``maximal degree'' variational principle; critical sections for this are integral manifolds for the Liouville vector field. We work in coordinates and provide explicit formulae

Examining the efficacy of a genotyping-by-sequencing technique for population genetic analysis of the mushroom Laccaria bicolor and evaluating whether a reference genome is necessary to assess homology

Given the diversity and ecological importance of Fungi, there is a lack of population genetic research on these organisms. The reason for this can be explained in part by their cryptic nature and difficulty in identifying genets. In addition the difficulty (relative to plants and animals) in developing molecular markers for fungal population genetics contributes to the lack of research in this area. This study examines the ability of restriction-site associated DNA (RAD) sequencing to generate SNPs in Laccaria bicolor. Eighteen samples of morphologically identified L. bicolor from the United States and Europe were selected for this project. The RAD sequencing method produced anywhere from 290 000 to more than 3 000 000 reads. Mapping these reads to the genome of L. bicolor resulted in 84 000-940 000 unique reads from individual samples. Results indicate that incorporation of non-L. bicolor taxa into the analysis resulted in a precipitous drop in shared loci among samples, suggests the potential of these methods to identify cryptic species. F-statistics were easily calculated, although an observable "noise" was detected when using the "All Loci" treatment versus filtering loci to those present in at least 50% of the individuals. The data were analyzed with tests of Hardy-Weinburg equilibrium, population genetic statistics (FIS and FST), and population structure analysis using the program Structure. The results provide encouraging feedback regarding the potential utility of these methods and their data for population genetic analysis. We were unable to draw conclusions of life history of L. bicolor populations from this dataset, given the small sample size. The results of this study indicate the potential of these methods to address population genetics and general life history questions in the Agaricales. Further research is necessary to explore the specific application of these methods in the Agaricales or other fungal groups

Multiscale description of carbon-supersaturated ferrite in severely drawn pearlitic wires

AbstractA multiscale simulation approach based on atomistic calculations and a discrete diffusion model is developed and applied to carbon-supersaturated ferrite, as experimentally observed in severely deformed pearlitic steel. We employ the embedded atom method and the nudged elastic band technique to determine the energetic profile of a carbon atom around a screw dislocation in bcc iron. The results clearly indicate a special region in the proximity of the dislocation core where C atoms are strongly bound, but where they can nevertheless diffuse easily due to low barriers. Our analysis suggests that the previously proposed pipe mechanism for the case of a screw dislocation is unlikely. Instead, our atomistic as well as the diffusion model results support the so-called drag mechanism, by which a mobile screw dislocation is able to transport C atoms along its glide plane. Combining the C-dislocation interaction energies with density-functional-theory calculations of the strain dependent C formation energy allows us to investigate the C supersaturation of the ferrite phase under wire drawing conditions. Corresponding results for local and total C concentrations agree well with previous atom probe tomography measurements indicating that a significant contribution to the supersaturation during wire drawing is due to dislocations

Reduction of Lie-Jordan Banach algebras and quantum states

A theory of reduction of Lie-Jordan Banach algebras with respect to either a Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared with the standard reduction of C*-algebras of observables of a quantum system in the presence of quantum constraints. It is shown that the later corresponds to the particular instance of the reduction of Lie-Jordan Banach algebras with respect to a Lie-Jordan subalgebra as described in this paper. The space of states of the reduced Lie-Jordan Banach algebras is described in terms of equivalence classes of extensions to the full algebra and their GNS representations are characterized in the same way. A few simple examples are discussed that illustrates some of the main results

Jacobi structures revisited

Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra associated with a vector bundle which satisfy a property similar to that of the Jacobi brackets, are introduced. They turn out to be equivalent to generalized Lie algebroids in the sense of Iglesias and Marrero and can be viewed also as odd Jacobi brackets on the supermanifolds associated with the vector bundles. Jacobi bialgebroids are defined in the same manner. A lifting procedure of elements of this Grassmann algebra to multivector fields on the total space of the vector bundle which preserves the corresponding brackets is developed. This gives the possibility of associating canonically a Lie algebroid with any local Lie algebra in the sense of Kirillov.Comment: 20 page

Technical Note: Trend estimation from irregularly sampled, correlated data

Estimation of a trend of an atmospheric state variable is often performed by fitting a linear regression line to a set of data of this variable sampled at different times. Often these data are irregularly sampled in space and time and clustered in a sense that 5 error correlations among data points cause a similar error of data points sampled at similar times. Since this can affect the estimated trend, we suggest to take the full error covariance matrix of the data into account. Superimposed periodic variations can be jointly fitted in a straight forward manner, even if the shape of the periodic function is not known. Global data sets, particularly satellite data, can form the basis to estimate 10 the error correlations