6,720 research outputs found
Nilpotence and descent in equivariant stable homotopy theory
Let be a finite group and let be a family of subgroups of
. We introduce a class of -equivariant spectra that we call
-nilpotent. This definition fits into the general theory of
torsion, complete, and nilpotent objects in a symmetric monoidal stable
-category, with which we begin. We then develop some of the basic
properties of -nilpotent -spectra, which are explored further
in the sequel to this paper.
In the rest of the paper, we prove several general structure theorems for
-categories of module spectra over objects such as equivariant real and
complex -theory and Borel-equivariant . Using these structure theorems
and a technique with the flag variety dating back to Quillen, we then show that
large classes of equivariant cohomology theories for which a type of
complex-orientability holds are nilpotent for the family of abelian subgroups.
In particular, we prove that equivariant real and complex -theory, as well
as the Borel-equivariant versions of complex-oriented theories, have this
property.Comment: 63 pages. Revised version, to appear in Advances in Mathematic
Constructive Provability Logic
We present constructive provability logic, an intuitionstic modal logic that
validates the L\"ob rule of G\"odel and L\"ob's provability logic by permitting
logical reflection over provability. Two distinct variants of this logic, CPL
and CPL*, are presented in natural deduction and sequent calculus forms which
are then shown to be equivalent. In addition, we discuss the use of
constructive provability logic to justify stratified negation in logic
programming within an intuitionstic and structural proof theory.Comment: Extended version of IMLA 2011 submission of the same titl
An isomorphism of motivic Galois groups
In characteristic 0 there are essentially two approaches to the conjectural
theory of mixed motives, one due to Nori and the other one due to,
independently, Hanamura, Levine, and Voevodsky. Although these approaches are
apriori quite different it is expected that ultimately they can be reduced to
one another. In this article we provide some evidence for this belief by
proving that their associated motivic Galois groups are canonically isomorphic.Comment: 56 pages, published versio
Active damping of a DC network with a constant power load: an adaptive passivity-based control approach
This paper proposes a nonlinear, adaptive controller to increase the stability margin of a direct-current (DC) small-scale electrical network containing a constant power load, whose value is unknown. Due to their negative incremental impedance, constant power loads are known to reduce the effective damping of a network, leading to voltage oscillations and even to network collapse. To tackle this problem, we consider the incorporation of a controlled DC-DC power converter between the feeder and the constant power load. The design of the control law for the converter is based on the use of standard Passivity-Based Control and Immersion and Invariance theories. The good performance of the controller is evaluated with numerical simulations.Postprint (author's final draft
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