Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids

We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri-Morosi and describe a double complex which computes the holomorphic Poisson cohomology. A holomorphic Lie algebroid structure on a vector bundle $A\to X$ is shown to be equivalent to a matched pair of complex Lie algebroids $(T^{0,1}X,A^{1,0})$, in the sense of Lu. The holomorphic Lie algebroid cohomology of $A$ is isomorphic to the cohomology of the elliptic Lie algebroid $T^{0,1}X\bowtie A^{1,0}$. In the case when $(X,\pi)$ is a holomorphic Poisson manifold and $A=(T^*X)_\pi$, such an elliptic Lie algebroid coincides with the Dirac structure corresponding to the associated generalized complex structure of the holomorphic Poisson manifold.Comment: 29 pages, v2: paper split into two, part 1 of 2, v3: two references added, v4: final version to appear in International Mathematics Research Notice

The effects of nitrogen and potassium nutrition on the growth of nonembryogenic and embryogenic tissue of sweet orange (Citrus sinensis (L.) Osbeck)

<p>Abstract</p> <p>Background</p> <p>Mineral nutrients are one of the most basic components of plant tissue culture media. Nitrogen in the form of NH₄⁺and NO₃^-is the dominant mineral nutrient in most plant tissue culture formulations, with effects dependent on both the proportion and the amount of NH₄⁺and NO₃^-. The effects of nitrogen nutrition on the growth of nonembryogenic and embryogenic cell lines of sweet orange (<it>C. sinensis </it>(L.) Osbeck cv. 'Valencia'), tissues routinely used in citrus horticultural and plant improvement research, was explored using an experimental approach free of ion confounding that included a 2-component mixture (NH₄⁺:K⁺) and a quantitative factor [NO₃^-] crossed by the mixture, thereby providing ion-specific estimates of proportional and amount effects.</p> <p>Results</p> <p>First, the linear mixture component, though only a comparison of the design space vertices, was highly significant for both tissue types and showed that NH₄⁺was required by both tissues. Second, the NH₄⁺* K⁺mixture term was highly significant for both tissue types, revealing that NH₄⁺and K⁺exhibit strong synergistic blending and showed that growth was substantially greater at certain blends of these two ions. Third, though the interaction between the NH₄⁺:K⁺mixture and NO₃^-amount on fresh weight accumulation for both tissue types was significant, it was substantially less than the main effect of the NH₄⁺:K⁺mixture. Fourth, a region of the design space was identified where fresh weight growth was increased 198% and 67% over the MS medium controls for nonembryogenic and embryogenic tissues.</p> <p>Conclusion</p> <p>By designing a mineral nutrient experiment free of ion confounding, a direct estimation of ion-specific proportional and amount effects on plant tissue growth is possible. When the ions themselves are the independent factors and/or mixture components, the resulting design space can be systematically explored to identify regions where the response(s) is substantially improved over current media formulations. In addition, because the response is over a defined experimental region, a specific medium formulation is more accurately interpreted as a coordinate in the specified design geometry.</p

Mapping the Fundamental Niches of Two Freshwater Microalgae, Chlorella vulgaris

The fundamental niche defined by five ions, NO3 −, PO4 3−, K+, Na+, and Cl−, was mapped for Chlorella vulgaris (Trebouxiophyceae) and Peridinium cinctum (Dinophyceae) growth rates and maximum cell densities in batch cultures. A five dimensional ion-mixture experimental design was projected across a total ion concentration gradient of 1 to 30 mM to delineate the ion-based, “potential” niche space, defined as the entire n-dimensional hypervolume demarcated by the feasible ranges of the independent factors under consideration. The growth rate-based, fundamental niche volumes overlapped for ca. 94% of the ion mixtures, although the regions of maximal growth rates and cell densities were different for each alga. Both C. vulgaris and P. cinctum exhibited similar positive responses to cations and negative responses to anions. It was determined that total ion concentration for these five ions, from 1 to 30 mM, did not directly affect either growth rate or maximal cell density for either alga, although it did play an interactive role with several ions. This study is the first that we are aware of to attempt the mapping of a multivariate, ion-based, fundamental niche volume. The implications of the experimental design utilized and the potential utility of this type of approach are discussed

Modular classes of Poisson-Nijenhuis Lie algebroids

The modular vector field of a Poisson-Nijenhuis Lie algebroid $A$ is defined and we prove that, in case of non-degeneracy, this vector field defines a hierarchy of bi-Hamiltonian $A$-vector fields. This hierarchy covers an integrable hierarchy on the base manifold, which may not have a Poisson-Nijenhuis structure.Comment: To appear in Letters in Mathematical Physic

On localization in holomorphic equivariant cohomology

We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.Comment: 16 pages. Completely rewritten, new title. v3: Minor changes in the exposition. v4: final version to appear in Centr. Eur. J. Mat

Sub-aggregator Business Models for Demand Response

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Formal Hecke algebras and algebraic oriented cohomology theories

In the present paper we generalize the construction of the nil Hecke ring of Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology theory of Levine-Morel and Panin-Smirnov, e.g. to Chow groups, Grothendieck's K_0, connective K-theory, elliptic cohomology, and algebraic cobordism. The resulting object, which we call a formal (affine) Demazure algebra, is parameterized by a one-dimensional commutative formal group law and has the following important property: specialization to the additive and multiplicative periodic formal group laws yields completions of the nil Hecke and the 0-Hecke rings respectively. We also introduce a deformed version of the formal (affine) Demazure algebra, which we call a formal (affine) Hecke algebra. We show that the specialization of the formal (affine) Hecke algebra to the additive and multiplicative periodic formal group laws gives completions of the degenerate (affine) Hecke algebra and the usual (affine) Hecke algebra respectively. We show that all formal affine Demazure algebras (and all formal affine Hecke algebras) become isomorphic over certain coefficient rings, proving an analogue of a result of Lusztig.Comment: 28 pages. v2: Some results strengthened and references added. v3: Minor corrections, section numbering changed to match published version. v4: Sign errors in Proposition 6.8(d) corrected. This version incorporates an erratum to the published versio

Integral Grothendieck-Riemann-Roch theorem

We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.Comment: 24 page

Hamilton-Jacobi formalism for Linearized Gravity

In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit

The Next Big Match: Convergence, Competition and Sports Media Rights

Using examples from a number of different European countries, this article analyses the increasingly prominent position of traditional telecommunications companies, such as British Telecom (UK), Deutsche Telekom (Germany), France Telecom/Orange (France) and Telefonica (Spain), in the contemporary sports media rights market. The first part of the article examines the commercial strategies of telecommunications operators and highlights how their acquisition of sports rights has been driven by the need to ensure a competitive position within an increasingly converged communications market. The second part of the article then moves on to consider the regulation of the sports media rights market. Most significantly, this section emphasises the need for further regulatory intervention to ensure that increased competition for sports rights leads to improved services and lower prices for consumers, rather than merely endlessly spiralling fees for the exclusive ownership of premium rights that are then passed on to sports channel and/or broadband subscribers