The algebraic structure of cohomological field theory

The algebraic foundation of cohomological field theory is presented. It is shown that these theories are based upon realizations of an algebra which contains operators for both BRST and vector supersymmetry. Through a localization of this algebra, we construct a theory of cohomological gravity in arbitrary dimensions. The observables in the theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. As such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization approach, different moduli spaces are obtained by introducing curvature singularities on codimension two submanifolds via a puncture operator. This puncture operator is constructed from a naturally occuring differential form of co-degree two in the theory, and we are led to speculate on connections between this continuum quantum field theory, and the discrete Regge calculus.     

Scheduling precedence graphs of bounded height

The existence of a schedule for a partially ordered set of unit length tasks on m identical processors is known to be NP-complete (J. D. Ullman, NP-complete scheduling problems, J. Comput. System Sci., 10 (1975), 384–393). The problem remains NP-complete even if we restrict the precedence graph to be of height bounded by a constant. (J. K. Lenkstra and A. H. G. Rinnooy Kan, Complexity of scheduling under precedence constraints, Operations Res., 26 (1978), 22–35; D. Dolev and M. K. Warmuth, “Scheduling Flat Graphs,” IBM Research Report RJ 3398, 1982). In these NP-completeness proofs the upper bound on the number of available processors varies with the problem instance. We present a polynomial algorithm for the case where the upper bound on the number of available processors and the height of the precedence graph are both constants.     

Oxoneptunium(v) as part of the framework of a polyoxometalate

(NH4)14Na4[(Np3W4O15)(H2O)3(BiW9O33)3].62H2O (1) and (NH4)14.5Na3.5[(Np3W4O15)(H2O)3(SbW9O33)3].40.5H2O (2) each contain three neptunyl(v) moieties encapsulated within heteropolyoxotungstate frameworks in which axial {NpO2}+ oxygens form one face of a WO6 octahedron.     

Avoided-crossing-based liquid-crystal photonic-bandgap notch filter

We demonstrate a highly tunable deep notch filter realized in a liquid-crystal photonic-bandgap (LCPBG) fiber. The filter is realized without inducing a long-period grating in the fiber but simply by filling a solid-core photonic-crystal fiber with a liquid crystal and exploiting avoided crossings within the bandgap of the LCPBG fiber. The filter is demonstrated experimentally and investigated using numerical simulations. A high degree of tuning of the spectral position of the deep notch is also demonstrated.     

Injective dimension of sheaves of rational vector spaces

The Cantor–Bendixson rank of a topological space X is a measure of the complexity of the topology of X. We will be interested primarily in the case that the space is profinite: Hausdorff, compact and totally disconnected. In this paper, we prove that the injective dimension of the abelian category of sheaves of $\mathbb{Q}$-modules over a profinite space X is determined by the Cantor–Bendixson rank of X.     

Experimental and numerical investigation of a stagnation pulverised coal flame

A multi-stream Flamelet Progress Variable (FPV) model, specifically developed for coal combustion, is proposed. The model accounts for the different fuel streams associated with the volatile and char burnout products. The applicability of the new FPV model is investigated in a laminar stagnation pulverized coal flame. The flame considered is a premixed mixture of CH₄, O₂ and N₂, carrying pulverized coal particles, stabilized in an impinging wall. Spontaneous emissions of OH*, CH* and C${}_2^{*}$ are measured to identify the flame. The 1D numerical simulations of the experimental conditions are able to reproduce the main features of the flame. The applicability of the multi-stream FPV model to coal combustion is further evaluated with the a posteriori analysis of the FPV results, comparing the results with a reference model, where the species are fully transported and the chemistry directly evaluated. Then, with the budget analysis, the influence of the control variables used to build the look-up table is assessed by examining the conditional contributions to the overall transport terms of scalar quantities (e.g. species, temperature). The results of both analyses show that the proposed multi-stream FPV model can accurately predict the main features of coal combustion, with only minor issues related to the manifold used to build the look-up table.