On simplicial commutative algebras with Noetherian homotopy

In this paper, a strategy is developed studying a simplicial commutative algebra A whose zeroth homotopy group is a Noetherian ring B and whose higher homotopy groups are finite over B. The strategy replaces A with a connected simplicial supplemented k(q)-algebra, for each prime ideal q in B, which preserves much of the Andre-Quillen homology of A. The methods for this construction involves a mixture of methods of homotopy theory (e.g. Postnikov towers) with methods of commutative algebras (e.g. completions, Cohen factorizations). We finish by indicating how these methods resolve a more general form of a conjecture posed by Quillen.Comment: 10 page

Simplicial commutative algebras with vanishing Andre-Quillen homology

In this paper, we study the Andr\'e-Quillen homology of simplicial commutative $\ell$-algebras, $\ell$ a field, having certain vanishing properties. When $\ell$ has non-zero characteristic, we obtain an algebraic version of a theorem of J.-P. Serre and Y. Umeda that characterizes such simplicial algebras having bounded homotopy groups. We further discuss how this theorem fails in the rational case and, as an application, indicate how the algebraic Serre theorem can be used to resolve a conjecture of D. Quillen for algebras of finite type over Noetherian rings, which have non-zero characteristic.Comment: 11 page

Large-angle slewing maneuvers for flexible spacecraft

A new class of closed-form solutions for finite-time linear-quadratic optimal control problems is presented. The solutions involve Potter's solution for the differential matrix Riccati equation, which assumes the form of a steady-state plus transient term. Illustrative examples are presented which show that the new solutions are more computationally efficient than alternative solutions based on the state transition matrix. As an application of the closed-form solutions, the neighboring extremal path problem is presented for a spacecraft retargeting maneuver where a perturbed plant with off-nominal boundary conditions now follows a neighboring optimal trajectory. The perturbation feedback approach is further applied to three-dimensional slewing maneuvers of large flexible spacecraft. For this problem, the nominal solution is the optimal three-dimensional rigid body slew. The perturbation feedback then limits the deviations from this nominal solution due to the flexible body effects. The use of frequency shaping in both the nominal and perturbation feedback formulations reduces the excitation of high-frequency unmodeled modes. A modified Kalman filter is presented for estimating the plant states

Higher homotopy operations and cohomology

We explain how higher homotopy operations, defined topologically, may be identified under mild assumptions with (the last of) the Dwyer-Kan-Smith cohomological obstructions to rectifying homotopy-commutative diagrams.Comment: 28 page

Historical Calibration of a Water Account System

Models that are used for future based scenarios should be calibrated with historical water supply and use data. Historical water records in Australia are discontinuous, incomplete and often incongruently disaggregated. We present a systematic method to produce a coherent reconstruction of the historical provision and consumption of water in Victorian catchments. This is demonstrated using WAS: an accounting and simulation tool that tracks the stocks and flows of physical quantities relating to the water system. The WAS is also part of, and informed by, an integrated framework of stocks and flows calculators for simulating long-term interactions between other sectors of the physical economy. Both the WAS and related frameworks consider a wide scope of inputs regarding population, land use, energy and water. The physical history of the water sector is reconstructed by integrating water data with these information sources using a data modelling process that resolves conflicts and deduces missing information. The WAS allows strategic exploration of water and energy implications of scenarios of water sourcing, treatment, delivery and end use cognisant of historical records.water accounting, stocks and flows, historical time series, data modelling, calibration