Free Meixner states

Free Meixner states are a class of functionals on non-commutative polynomials introduced in math.CO/0410482. They are characterized by a resolvent-type form for the generating function of their orthogonal polynomials, by a recursion relation for those polynomials, or by a second-order non-commutative differential equation satisfied by their free cumulant functional. In this paper, we construct an operator model for free Meixner states. By combinatorial methods, we also derive an operator model for their free cumulant functionals. This, in turn, allows us to construct a number of examples. Many of these examples are shown to be trivial, in the sense of being free products of functionals which depend on only a single variable, or rotations of such free products. On the other hand, the multinomial distribution is a free Meixner state and is not a product. Neither is a large class of tracial free Meixner states which are analogous to the simple quadratic exponential families in statistics.Comment: 30 page

Semigroups of distributions with linear Jacobi parameters

We show that a convolution semigroup of measures has Jacobi parameters polynomial in the convolution parameter $t$ if and only if the measures come from the Meixner class. Moreover, we prove the parallel result, in a more explicit way, for the free convolution and the free Meixner class. We then construct the class of measures satisfying the same property for the two-state free convolution. This class of two-state free convolution semigroups has not been considered explicitly before. We show that it also has Meixner-type properties. Specifically, it contains the analogs of the normal, Poisson, and binomial distributions, has a Laha-Lukacs-type characterization, and is related to the $q=0$ case of quadratic harnesses.Comment: v3: the article is merged back together with arXiv:1003.4025. A significant revision following suggestions by the referee. 2 pdf figure

Porosity of closed carbon nanotubes compressed using hydraulic pressure

Experimental data of nitrogen adsorption (T = 77.3 K) from gaseous phase measured on commercial closed carbon nanotubes are presented. Additionally, we show the results of N2 adsorption on compressed (using hydraulic press) CNTs. In order to explain the experimental observations the results of GCMC simulations of N2 adsorption on isolated or bundled multi-walled closed nanotubes (four models of bundles) are discussed. We show that the changes of the experimental adsorption isotherms are related to the compression of the investigated adsorbents. They are qualitatively similar to the theoretical observations. Taking into account all results it is concluded that in the "architecture" of nanotubes very important role has been played by isolated nanotubes

Use of anthropogenic material affects bird nest arthropod community structure: influence of urbanisation, and consequences for ectoparasites and fledging success

Nests are a critically important factor in determining the breeding success of many species of birds. Nevertheless, we have surprisingly little understanding of how local environment helps shape materials used in construction, how this differs among related species using similar nest sites, or if materials used directly or indirectly influence the numbers of offspring successfully reared. We also have little understanding of any potential links between nest construction and the assemblage of invertebrates which inhabit the nest and in particular, with ectoparasites. We addressed these questions by monitoring the success rates of nest-box using Blue Tits Cyanistes caeruleus and Great Tits Parus major, from rural, urban greenspace and urban garden settings. We collected used nests, identified arthropods present, and measured the proportions of highly processed anthropogenic materials used in their construction. Some 25% of Great Tit nest materials were of an anthropogenic source and this was consistent across habitats, while Blue Tits used little (1-2%) except in gardens (~16%), suggesting that Great Tits preferentially sought out these materials. In fledged nests, increasing use of anthropogenic material was associated with lower general arthropod diversity and ectoparasite predator abundance (Blue Tits only) but higher levels of Siphonapterans (fleas). Higher arthropod diversity was associated with lower flea numbers, suggesting that increased diversity played a role in limiting flea numbers. No direct link was found between breeding success and either anthropogenic material usage, or arthropod diversity and abundance. However, breeding success declined with increasing urbanisation in both species and increased with nest weight in Blue Tits. The interplay between urbanisation and bird ecology is complex; our work shows that subtle anthropogenic influences may have indirect and unexpected consequences for urban birds

The Einsteinian T(3)-Gauge Approach and the Stress Tensor of the Screw Dislocation in the Second Order: Avoiding the Cut-off at the Core

A translational gauge approach of the Einstein type is proposed for obtaining the stresses that are due to non-singular screw dislocation. The stress distribution of second order around the screw dislocation is classically known for the hollow circular cylinder with traction-free external and internal boundaries. The inner boundary surrounds the dislocation's core, which is not captured by the conventional solution. The present gauge approach enables us to continue the classically known quadratic stresses inside the core. The gauge equation is chosen in the Hilbert--Einstein form, and it plays the role of non-conventional incompatibility law. The stress function method is used, and it leads to the modified stress potential given by two constituents: the conventional one, say, the `background' and a short-ranged gauge contribution. The latter just causes additional stresses, which are localized. The asymptotic properties of the resulting stresses are studied. Since the gauge contributions are short-ranged, the background stress field dominates sufficiently far from the core. The outer cylinder's boundary is traction-free. At sufficiently moderate distances, the second order stresses acquire regular continuation within the core region, and the cut-off at the core does not occur. Expressions for the asymptotically far stresses provide self-consistently new length scales dependent on the elastic parameters. These lengths could characterize an exteriority of the dislocation core region.Comment: 34 pages, LaTe