We first extend the Peierls algebra of gauge invariant functions from the space S of classical solutions to the space H of histories used in path integration and some studies of decoherence. We then show that it may be generalized in a number of ways to act on gauge dependent functions on H. These generalizations (referred to as class I) depend on the choice of an “invariance breaking term,” wh...

A paradigm for describing dynamical systems that have both Hamiltonian and dissipative parts is presented. Features of generalized Hamiltonian systems and metric systems are combined to produce what are called metriplectic systems. The phase space for metriplectic systems is equipped with a bracket operator that has an antisymmetric Poisson bracket part and a symmetric dissipative part. Flows a...

In this paper we show that the moduli space of twisted polygons in G/P , where G is semisimple and P parabolic, and where g has two coordinated gradations, has a natural Poisson bracket that is directly linked to G-invariant evolutions of polygons. This structure is obtained by reducing the quotient twisted bracket on GN defined in [23] to the moduli space GN/PN . We prove that any Hamiltonian ...

introduction: the aim of this study was to assess the galvanic behavior of different bracket and archwire combinations that are commonly used in orthodontic treatments. methods: three types of orthodontic archwires with a diameter of 0.016×0.022 inch and 80 standard edgewise maxillary central incisor brackets were selected. three groups consisted of different wire-bracket couples and one group ...

Soils support an enormous microbial diversity, but the ecological drivers of this diversity are poorly understood. Interactions between the roots of individual grass species and the arbuscular mycorrhizal (AM) fungi and bacteria in their rhizoplane were studied in a grazed, unimproved upland pasture. Individual root fragments were isolated from soil cores, DNA extracted and used to identify pla...

A number of studies have shown that an association with mycorrhizal fungi can alter the outcome of interactions between plants and their enemies. While the directions of these effects vary, their strength suggests the need for greater attention to multispecies interactions among plant enemies, plants, and mycorrhizal fungi. We recognize that mycorrhizal fungi could effect plant enemies by impro...

While the effects of habitat size and isolation have been successfully studied for macro-organisms, there is currently debate about their relative importance in explaining patterns of microbial species richness. In this study, we examine the species richness of a dominant group of eukaryotic soil microbes, ectomycorrhizal fungi, on 'tree islands' of constant age and host composition that range ...

We introduce the concept of a relative Tutte polynomial. We show that the relative Tutte polynomial can be computed in a way similar to the classical spanning tree expansion used by Tutte in his original paper on this subject. We then apply the relative Tutte polynomial to virtual knot theory. More specifically, we show that the Kauffman bracket polynomial (hence the Jones polynomial) of a virt...

We consider the Gelfand-Dickey (GD) structure defined by the Moyal ⋆-product with parameter κ, which not only defines the bi-Hamiltonian structure for the generalized Moyal KdV hierarchy but also provides a W (κ) n algebra containing the Virasoro algebra as a subalgebra with central charge κ2(n3 − n)/3. The free-field realization of the W (κ) n algebra is given through the Miura transformation ...