We answer a question of Schwede on the existence of global Picard spectra associated to his ultra-commutative global ring spectra;given an ultracommutative global ring spectrum R, we show there exists a global spectru...
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Let M = G/H be a Riemannian homogeneous space, where G is a compact Lie group with closed subgroup H. Classical intersection theory states that the de Rham cohomology ring of M describes the signed count of intersecti...
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Given an ∞-category C with pullbacks, its (∞, 2)-category Span(C) of spans has the universal property of freely adding right adjoints to morphisms in C satisfying a Beck–Chevalley condition. We show that this unive...
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We show that the ∞-category of normed algebras in genuine Gspectra, as introduced by Bachmann–Hoyois, is modelled by strictly commutative algebras in G-symmetric spectra for any finite group G. We moreover provide a...
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In order to derive a result such as the Alpern-Schneider theorem safety and liveness properties of concurrent program executions, it is shown that all that is needed is a V-preserving map phi between complete Boolean ...
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In order to derive a result such as the Alpern-Schneider theorem safety and liveness properties of concurrent program executions, it is shown that all that is needed is a V-preserving map phi between complete Boolean algebras. Every property becomes a conjunction of a safety and a liveness property and safety properties can be characterized by sets of configurations that are to be ''avoided''. Aside from the original result of B. Alpern and F.B Schneider we also provide a new application by considering transition systems with a UNITY-style logic. Safety properties are characterized by a set of forbidden pairs of successive states and progress properties are those allowing all possible state-successor pairs. Every property of a transition system is shown to be a conjunction of a safety and a progress property.
A matrix or a linear operator A is said to possess an UV-displacement structure if rank(AU - VA) is small compared with the rank of A. Estimates for tbe rank of A(dagger)V - UA(dagger) and more general displacements o...
A matrix or a linear operator A is said to possess an UV-displacement structure if rank(AU - VA) is small compared with the rank of A. Estimates for tbe rank of A(dagger)V - UA(dagger) and more general displacements of A(dagger) are presented, where A(dagger) is the pseudoinverse of A. The general results are applied to close-to-Toeplitz, close-to-Vandermonde, and generalized Cauchy matrices, Bezoutians, Toeplitz and Hankel operators, singular integral operators, and integral operators with displacement kernel. This leads to formulas for At which can be used for the fast computation of pseudosolutions. For Vandermonde matrices the exact displacement rank of A(dagger) is evaluated. It turns out that this rank is not always small.
We show that a complex structure on a nilpotent almost abelian real Lie algebra is unique if it exists. As a consequence, we get full control over the cohomology and deformations of almost abelian complex *** Codes 32...
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For the parallelization of implicit Runge-Kutta methods for stiff ODE's a parallel computation of the stages is obvious. In this paper we consider the parallelization of the stages of linearly-implicit Runge-Kutta...
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For the parallelization of implicit Runge-Kutta methods for stiff ODE's a parallel computation of the stages is obvious. In this paper we consider the parallelization of the stages of linearly-implicit Runge-Kutta methods. The construction and implementation of a parallel linearly-implicit Runge-Kutta method is described. The numerical results are compared with the code PSODE of van der Houwen/Sommeijer [6] and a straightforward parallelization of RADAU5 [5]. All methods are based on the S-stage implicit Radau-IIA method.
An induced subgraph G of a graph H is a retract of H if there is an edge-preserving map f from H onto G such that f | G is the identity map on G . A median graph is a connected graph such that for any three vertices u...
An induced subgraph G of a graph H is a retract of H if there is an edge-preserving map f from H onto G such that f | G is the identity map on G . A median graph is a connected graph such that for any three vertices u,v and w , there exists a unique vertex x which lies simultaneously on some shortest ( u,v )-, ( v,w )-, and ( w,u )-paths. It is shown that a graph G is a retract of some hypercube if and only if G is a median graph.
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