On the classification and properties of noncommutative duplicates

We give an explicit description of the set of all factorization structures, or twisting maps, existing between the algebras k^2 and k^2, and classify the resulting algebras up to isomorphism. In the process we relate several different approaches formerly taken to deal with this problem, filling a gap that appeared in a recent paper by Cibils. We also provide a counterexample to a result concerning the Hochschild (co)homology appeared in a paper by J.A. Guccione and J.J. Guccione.Comment: 11 pages, no figure

N-complexes as functors, amplitude cohomology and fusion rules

We consider N-complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then to prove that amplitude cohomology only vanishes on injective functors providing a well defined functor on the stable category. For left truncated N-complexes, we show that amplitude cohomology discriminates the isomorphism class up to a projective functor summand. Moreover amplitude cohomology of positive N-complexes is proved to be isomorphic to an Ext functor of an indecomposable N-complex inside the abelian functor category. Finally we show that for the monoidal structure of N-complexes a Clebsch-Gordan formula holds, in other words the fusion rules for N-complexes can be determined.Comment: Final versio

Impact of Grazing Management on the Productivity of Cold Temperate Grasslands of Southern Patagonia - A Critical Assessment

The contention that productivity of cold temperate grasslands of southern Patagonia have been greatly affected by domestic herbivore grazing in the past is fairly widespread. The consequences of spatiotemporal interactions between grazing and abiotic factors on the overall productivity of such systems, however, are still poorly understood. Predictions of both short- and long-term impacts of grazing management strategies on grassland productivity require a better understanding of these interactions. In this paper we make a critical assessment of the impact of grazing management on long-term sustainability of the grass steppes of southern Patagonia (Argentina). We discuss this issue in the context of current understanding of structure and function of these grass steppes, and of present-day global change concerns. We explore the capabilities of present-day tools to integrate biotic and abiotic factors at the landscape level to improve grazing management decisions

Quantum groups and double quiver algebras

For a finite dimensional semisimple Lie algebra ${\frak{g}}$ and a root $q$ of unity in a field $k,$ we associate to these data a double quiver $\bar{\cal{Q}}.$ It is shown that a restricted version of the quantized enveloping algebras $U_q(\frak g)$ is a quotient of the double quiver algebra $k\bar{\cal Q}.$Comment: 15 page

Spin-Boson Hamiltonian and Optical Absorption of Molecular Dimers

An analysis of the eigenstates of a symmetry-broken spin-boson Hamiltonian is performed by computing Bloch and Husimi projections. The eigenstate analysis is combined with the calculation of absorption bands of asymmetric dimer configurations constituted by monomers with nonidentical excitation energies and optical transition matrix elements. Absorption bands with regular and irregular fine structures are obtained and related to the transition from the coexistence to a mixing of adiabatic branches in the spectrum. It is shown that correlations between spin states allow for an interpolation between absorption bands for different optical asymmetries.Comment: 15 pages, revTeX, 8 figures, accepted for publication in Phys. Rev.

Flow equations for Hamiltonians: Contrasting different approaches by using a numerically solvable model

To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered which is structurally similar to impurity models. By this we discuss the question of optimization for the first time. A general truncation scheme is established that produces good results for the Hamiltonian flow as well as for the operator flow. Nevertheless, it is also pointed out that a systematic and feasible scheme for the operator flow on the operator level is missing. For this, an explicit analysis of the operator flow is given for the first time. We observe that truncation of the series of the observable flow after the linear or bilinear terms does not yield satisfactory results for the entire parameter regime as - especially close to resonances - even high orders of the exact series expansion carry considerable weight.Comment: 25 pages, 10 figure

CARBONIZED STARCH MICROCELLULAR FOAM-CELLULOSE FIBER COMPOSITE STRUCTURES

The production of microporous carbon foams from renewable starch microcellular foam-fiber (SMCF-Fiber) composites is described. Carbon foams are used in applications such as thermal insulation, battery electrodes, filters, fuel cells, and medical devices. SMCF-Fiber compos-ites were created from an aquagel. The water in the aquagel was exchanged with ethanol and then dried and carbonized. Higher amylose content starches and fiber contents of up to 4% improved the processability of the foam. The SMCF structure revealed agglomerates of swollen starch granules connected by a web of starch with pores in the 50-200 nanometer range. Heating the SMCF-fiber in a nitrogen atmosphere to temperatures between 350-700˚C produced carbon foams with a three-dimensional closed cell foam structure with cell diameters around 50 microns and pore walls around 1-3 microns. The stress versus strain compression data for carbonized samples displayed a linear elastic region and a plateau indicative of brittle crushing, typical of an elastic-brittle foam. The carbon foam products from these renew-able precursors are promising carbon structures with moderate strength and low density

Covering functors without groups

Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation finite algebra by Riedtmann and later for finite dimensional algebras by Bongartz and Gabriel, R. Martinez-Villa and de la Pe\~na. The best understood class covering functors is that of Galois covering functors F: A -> B determined by the action of a group of automorphisms of A. In this work we introduce the balanced covering functors which include the Galois class and for which classical Galois covering-type results still hold. For instance, if F:A -> B is a balanced covering functor, where A and B are linear categories over an algebraically closed field, and B is tame, then A is tame.Comment: Some improvements have been made; in particular, the proof of Theorem 2 has been restructured and clarifie

The first Hochschild cohomology group of a schurian cluster-tilted algebra

Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type Ã.Fil: Assem, Ibrahim. University of Sherbrooke; CanadáFil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Reciprocal effects of silicon supply and endophytes on silicon accumulation and Epichloë colonization in grasses

Cool season grasses associate asymptomatically with foliar Epichloë endophytic fungi in a symbiosis where Epichloë spp. protects the plant from a number of biotic and abiotic stresses. Furthermore, many grass species can accumulate large quantities of silicon (Si), which also alleviates a similar range of stresses. While Epichloë endophytes may improve uptake of minerals and nutrients, their impact on Si is largely unknown. Likewise, the effect of Si availability on Epichloë colonization remains untested. To assess the bidirectional relationship, we grew tall fescue (Festuca arundinacea) and perennial ryegrass (Lolium perenne) hydroponically with or without Si. Grasses were associated with five different Epichloë endophyte strains [tall fescue: AR584 or wild type (WT); perennial ryegrass: AR37, AR1, or WT] or as Epichloë-free controls. Reciprocally beneficial effects were observed for tall fescue associations. Specifically, Epichloë presence increased Si concentration in the foliage of tall fescue by at least 31%, regardless of endophyte strain. In perennial ryegrass, an increase in foliar Si was observed only for plants associated with the AR37. Epichloë promotion of Si was (i) independent of responses in plant growth, and (ii) positively correlated with endophyte colonization, which lends support to an endophyte effect independent of their impacts on root growth. Moreover, Epichloë colonization in tall fescue increased by more than 60% in the presence of silicon; however, this was not observed in perennial ryegrass. The reciprocal benefits of Epichloë-endophytes and foliar Si accumulation reported here, especially for tall fescue, might further increase grass tolerance to stress