350 research outputs found
Geometricity for derived categories of algebraic stacks
We prove that the dg category of perfect complexes on a smooth, proper
Deligne-Mumford stack over a field of characteristic zero is geometric in the
sense of Orlov, and in particular smooth and proper. On the level of
triangulated categories, this means that the derived category of perfect
complexes embeds as an admissible subcategory into the bounded derived category
of coherent sheaves on a smooth, projective variety. The same holds for a
smooth, projective, tame Artin stack over an arbitrary field.Comment: 31 page
Development of a non-linear simulation for generic hypersonic vehicles - ASUHS1
A nonlinear simulation is developed to model the longitudinal motion of a vehicle in hypersonic flight. The equations of motion pertinent to this study are presented. Analytic expressions for the aerodynamic forces acting on a hypersonic vehicle which were obtained from Newtonian Impact Theory are further developed. The control surface forces are further examined to incorporate vehicle elastic motion. The purpose is to establish feasible equations of motion which combine rigid body, elastic, and aeropropulsive dynamics for use in nonlinear simulations. The software package SIMULINK is used to implement the simulation. Also discussed are issues needing additional attention and potential problems associated with the implementation (with proposed solutions)
Uncapacitated Flow-based Extended Formulations
An extended formulation of a polytope is a linear description of this
polytope using extra variables besides the variables in which the polytope is
defined. The interest of extended formulations is due to the fact that many
interesting polytopes have extended formulations with a lot fewer inequalities
than any linear description in the original space. This motivates the
development of methods for, on the one hand, constructing extended formulations
and, on the other hand, proving lower bounds on the sizes of extended
formulations.
Network flows are a central paradigm in discrete optimization, and are widely
used to design extended formulations. We prove exponential lower bounds on the
sizes of uncapacitated flow-based extended formulations of several polytopes,
such as the (bipartite and non-bipartite) perfect matching polytope and TSP
polytope. We also give new examples of flow-based extended formulations, e.g.,
for 0/1-polytopes defined from regular languages. Finally, we state a few open
problems
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