4,050 research outputs found
Lineability of non-differentiable Pettis primitives
Let X be an infinite-dimensional Banach space. In 1995, settling a long
outstanding problem of Pettis, Dilworth and Girardi constructed an X-valued
Pettis integrable function on [0; 1] whose primitive is nowhere weakly
differentiable. Using their technique and some new ideas we show that ND, the
set of strongly measurable Pettis integrable functions with nowhere weakly
differentiable primitives, is lineable, i.e., there is an infinite dimensional
vector space whose nonzero vectors belong to ND
Rolewicz-type chaotic operators
In this article we introduce a new class of Rolewicz-type operators in l_p,
. We exhibit a collection F of cardinality continuum of
operators of this type which are chaotic and remain so under almost all finite
linear combinations, provided that the linear combination has sufficiently
large norm. As a corollary to our main result we also obtain that there exists
a countable collection of such operators whose all finite linear combinations
are chaotic provided that they have sufficiently large norm.Comment: 15 page
New insight into cataract formation -- enhanced stability through mutual attraction
Small-angle neutron scattering experiments and molecular dynamics simulations
combined with an application of concepts from soft matter physics to complex
protein mixtures provide new insight into the stability of eye lens protein
mixtures. Exploring this colloid-protein analogy we demonstrate that weak
attractions between unlike proteins help to maintain lens transparency in an
extremely sensitive and non-monotonic manner. These results not only represent
an important step towards a better understanding of protein condensation
diseases such as cataract formation, but provide general guidelines for tuning
the stability of colloid mixtures, a topic relevant for soft matter physics and
industrial applications.Comment: 4 pages, 4 figures. Accepted for publication on Phys. Rev. Let
Eta and Rho invariants on manifolds with edges
We establish existence of eta-invariants as well as of the Atiyah–Patodi–Singer and the Cheeger–Gromov rho-invariants for a class of Dirac operators on an incomplete edge space. Our analysis applies in particular to the signature and the spin Dirac operator. We derive an analogue of the Atiyah–Patodi–Singer index theorem for incomplete edge spaces and their non-compact infinite Galois coverings with edge singular boundary. Our arguments are based on the microlocal analysis of the heat kernel asymptotics associated to the Dirac laplacian of an incomplete edge metric. As an application, we discuss stability results for the two rho-invariants we have defined
Signatures of Witt spaces with boundary
Let M‾ be a compact smoothly stratified pseudomanifold with boundary, satisfying the Witt assumption. In this paper we introduce the de Rham signature and the Hodge signature of M‾, and prove their equality. Next, building also on recent work of Albin and Gell-Redman, we extend the Atiyah-Patodi-Singer index theory established in our previous work under the hypothesis that M‾ has stratification depth 1 to the general case, establishing in particular a signature formula on Witt spaces with boundary. In a parallel way we also pass to the case of a Galois covering M‾Γ of M‾ with Galois group Γ. Employing von Neumann algebras we introduce the de Rham Γ-signature and the Hodge Γ-signature and prove their equality, thus extending to Witt spaces a result proved by Lück and Schick in the smooth case. Finally, extending work of Vaillant in the smooth case, we establish a formula for the Hodge Γ-signature. As a consequence we deduce the fundamental result that equates the Cheeger-Gromov rho-invariant of the boundary ∂M‾Γ with the difference of the signatures of and M‾ and M‾Γ: signdR(M‾,∂M‾)−signdRΓ(M‾Γ,∂M‾Γ)=ρΓ(∂M‾Γ). We end the paper with two geometric applications of our results
Modelling a Particle Detector in Field Theory
Particle detector models allow to give an operational definition to the
particle content of a given quantum state of a field theory. The commonly
adopted Unruh-DeWitt type of detector is known to undergo temporary transitions
to excited states even when at rest and in the Minkowski vacuum. We argue that
real detectors do not feature this property, as the configuration "detector in
its ground state + vacuum of the field" is generally a stable bound state of
the underlying fundamental theory (e.g. the ground state-hydrogen atom in a
suitable QED with electrons and protons) in the non-accelerated case. As a
concrete example, we study a local relativistic field theory where a stable
particle can capture a light quantum and form a quasi-stable state. As
expected, to such a stable particle correspond energy eigenstates of the full
theory, as is shown explicitly by using a dressed particle formalism at first
order in perturbation theory. We derive an effective model of detector (at
rest) where the stable particle and the quasi-stable configurations correspond
to the two internal levels, "ground" and "excited", of the detector.Comment: 13 pages, references added, final versio
Energy transfer in nonlinear network models of proteins
We investigate how nonlinearity and topological disorder affect the energy
relaxation of local kicks in coarse-grained network models of proteins. We find
that nonlinearity promotes long-range, coherent transfer of substantial energy
to specific, functional sites, while depressing transfer to generic locations.
Remarkably, transfer can be mediated by the self-localization of discrete
breathers at distant locations from the kick, acting as efficient
energy-accumulating centers.Comment: 4 pages, 3 figure
A new result on impulsive differential equations involving non-absolutely convergent integrals
AbstractIn this paper we obtain, as an application of a Darbo-type theorem, global solutions for differential equations with impulse effects, under the assumption that the function on the right-hand side is integrable in the Henstock sense. We thus generalize several previously given results in literature, for ordinary or impulsive equations
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