6,691 research outputs found
On axiom schemes for T-provably Δ1 formulas
This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and least number axiom schemes to formulas which are Δ1 provably in an arithmetic theory T. In particular, we determine the provably total computable functions of this kind of theories. As an application, we obtain a reduction of the problem whether IΔ0+¬exp implies BΣ1 to a purely recursion-theoretic question.Ministerio de Ciencia e Innovación MTM2008–0643
Existentially Closed Models in the Framework of Arithmetic
We prove that the standard cut is definable in each existentially closed model of IΔ0 + exp by a (parameter free) П1–formula. This definition is optimal with respect to quantifier complexity and allows us to improve some previously known results on existentially closed models of fragments of arithmetic.Ministerio de Educación y Ciencia MTM2011–2684
The Bias and Mass Function of Dark Matter Halos in Non-Markovian Extension of the Excursion Set Theory
The excursion set theory based on spherical or ellipsoidal gravitational
collapse provides an elegant analytic framework for calculating the mass
function and the large-scale bias of dark matter haloes. This theory assumes
that the perturbed density field evolves stochastically with the smoothing
scale and exhibits Markovian random walks in the presence of a density barrier.
Here we derive an analytic expression for the halo bias in a new theoretical
model that incorporates non-Markovian extension of the excursion set theory
with a stochastic barrier. This model allows us to handle non-Markovian random
walks and to calculate perturbativly these corrections to the standard
Markovian predictions for the halo mass function and halo bias. Our model
contains only two parameters: kappa, which parameterizes the degree of
non-Markovianity and whose exact value depends on the shape of the filter
function used to smooth the density field, and a, which parameterizes the
degree of stochasticity of the barrier. Appropriate choices of kappa and a in
our new model can lead to a closer match to both the halo mass function and
halo bias in the latest N-body simulations than the standard excursion set
theory.Comment: 10 pages, 1 figure, MNRAS, in press. Minor change
An approximate model for the adhesive contact of rough viscoelastic surfaces
Surface roughness is known to easily suppress the adhesion of elastic
surfaces. Here a simple model for the contact of \emph{viscoelastic} rough
surfaces with significant levels of adhesion is presented. This approach is
derived from our previous model [E. Barthel and G. Haiat {\em Langmuir}, 18
9362 2002] for the adhesive contact of viscoelastic spheres. For simplicity a
simple loading/unloading history (infinitely fast loading and constant pull-out
velocity) is assumed. The model provides approximate analytical expressions for
the asperity response and exhibits the full viscoelastic adhesive contact
phenomenology such as stress relaxation inside the contact zone and creep at
the contact edges. Combining this model with a Greenwood-Williamson statistical
modeling of rough surfaces, we propose a quantitative assessment of the
adhesion to rough viscoelastic surfaces. We show that moderate viscoelasticity
efficiently restores adhesion on rough surfaces over a wide dynamic range
Partial regularity for manifold constrained p(x)-harmonic maps
We prove that manifold constrained -harmonic maps are
-regular outside a set of zero -dimensional Lebesgue's measure,
for some . We also provide an estimate from above of the
Hausdorff dimension of the singular set
The Erdos-Moser sum-free set problem
We show that if A is a finite set of integers then it has a subset S of size
\log^{1+c} |A| (c>0 absolute) such that s+s' is never in A when s and s' are
distinct elements of S.Comment: 47 pages. Corrections and clarification
A Framework for Robust Assessment of Power Grid Stability and Resiliency
Security assessment of large-scale, strongly nonlinear power grids containing
thousands to millions of interacting components is a computationally expensive
task. Targeting at reducing the computational cost, this paper introduces a
framework for constructing a robust assessment toolbox that can provide
mathematically rigorous certificates for the grids' stability in the presence
of variations in power injections, and for the grids' ability to withstand a
bunch sources of faults. By this toolbox we can "off-line" screen a wide range
of contingencies or power injection profiles, without reassessing the system
stability on a regular basis. In particular, we formulate and solve two novel
robust stability and resiliency assessment problems of power grids subject to
the uncertainty in equilibrium points and uncertainty in fault-on dynamics.
Furthermore, we bring in the quadratic Lyapunov functions approach to transient
stability assessment, offering real-time construction of stability/resiliency
certificates and real-time stability assessment. The effectiveness of the
proposed techniques is numerically illustrated on a number of IEEE test cases
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