Arlington School District and Arlington Teachers Association

In the matter of the fact-finding between the Arlington School District, employer, and the Arlington Teachers Association, union. PERB case no. M2014-156. Before: Robert J. Rabin, fact finder

Serre Duality, Abel's Theorem, and Jacobi Inversion for Supercurves Over a Thick Superpoint

The principal aim of this paper is to extend Abel's theorem to the setting of complex supermanifolds of dimension 1|q over a finite-dimensional local supercommutative C-algebra. The theorem is proved by establishing a compatibility of Serre duality for the supercurve with Poincare duality on the reduced curve. We include an elementary algebraic proof of the requisite form of Serre duality, closely based on the account of the reduced case given by Serre in Algebraic Groups and Class Fields, combined with an invariance result for the topology on the dual of the space of repartitions. Our Abel map, taking Cartier divisors of degree zero to the dual of the space of sections of the Berezinian sheaf, modulo periods, is defined via Penkov's characterization of the Berezinian sheaf as the cohomology of the de Rham complex of the sheaf D of differential operators, as a right module over itself. We discuss the Jacobi inversion problem for the Abel map and give an example demonstrating that if n is an integer sufficiently large that the generic divisor of degree n is linearly equivalent to an effective divisor, this need not be the case for all divisors of degree n.Comment: 14 page

Bosonic p-brane and A--D--M decomposition

A master action for the bosonic p-brane, interpolating between the Nambu--Goto and Polyakov formalisms, is discussed. The fundamental arbitrariness of extended structures (p-brane) embeded in space time manifold has been exploited to build an independent metric in the brane world volume. The cosmological term for the generic case follows naturally in the scheme. The dynamics of the structure leads to a natural emergence of the A--D--M like split of this world volume. The role of the gauge symmetries vis-\`{a}-vis reparametrization symmetries is analyzed by a constrained Hamiltonian approach.Comment: LaTeX, 14 pages, Title changed, paper extended, references added, this version is to appear in Phys. Rev.

D-modules on 1|1 Supercurves

It is known that to every 1|1 dimensional supercurve X there is associated a dual supercurve \hat{X}, and a superdiagonal \Delta in their product. We establish that the categories of D-modules on X, \hat{X}, and \Delta are equivalent. This follows from a more general result about D-modules and purely odd submersions. The equivalences preserve tensor products, and take vector bundles to vector bundles. Line bundles with connection are studied, and examples are given where X is a superelliptic curve.Comment: 18 page

Chaplygin Gravitodynamics

We consider a new approach for gravity theory coupled to Chaplygin matter in which the {\it{relativistic}} formulation of the latter is of crucial importance. We obtain a novel form of matter with dust like density $(\sim (volume)^{-1})$ and negative pressure. We explicitly show that our results are compatible with a relativistic generalization of the energy conservation principle, derived here.Comment: Title changed, Revised version,N o change in conclusions, Journal ref.: MPL A21 (2006)1511-151

Autoxidation of lipids in parchment

Historic parchment is a macromolecular material, which is complex due to its natural origin, inhomogeneity of the skin structure, unknown environmental history and potential localised degradation. Most research into its stability has so far focussed on thermal and structural methods of analyses. Using gas chromatographic analysis of the atmosphere surrounding parchment during oxidation, we provide the experimental evidence on the production of volatile aldehydes, which can be the products of lipid autoxidation. Oxidation of parchment with different aldehyde emissions was additionally followed in situ using chemiluminometry and the same techniques were used to evaluate the oxidation of differently delipidised parchment. It was shown that the production of peroxides and the emission of aldehydes from the material decrease with lower lipid content. Building on this evidence, we can conclude that the presence of lipids (either initially present in the skin or resulting from conservation intervention) leads to oxidative degradation of collagen and that the non-destructive analysis of the emission of volatiles could be used as a quick tool for evaluation of parchment stability