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, $1 \le p < \infty$. 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

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

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

Pair production in a strong slowly varying magnetic field: the effect of a background gravitational field

The production probability of an $e^--e^+$ pair in the presence of a strong, uniform and slowly varying magnetic field is calculated by taking into account the presence of a background gravitational field. The curvature of the spacetime metric induced by the gravitational field not only changes the transition probabilities calculated in the Minkowski spacetime but also primes transitions that are strictly forbidden in absence of the gravitational field.Comment: 56 pages, no figure

Differentiation of an additive interval measure with values in a conjugate Banach space

We present a complete characterization of finitely additive interval measures with values in conjugate Banach spaces which can be represented as Henstock-Kurzweil-Gelfand integrals. If the range space has the weak Radon-Nikodym property (WRNP), then we precisely describe when these integrals are in fact Henstock-Kurzweil-Pettis integrals

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

A full descriptive definition of the BV-integral

summary:We present a Cauchy test for the almost derivability of additive functions of bounded BV sets. The test yields a full descriptive definition of a coordinate free Riemann type integral

Occurrence and diversity of arbuscular mycorrhizal fungi colonising off‐season and in‐season weeds and their relationship with maize yield under conservation agriculture

Weeds are responsible for major crop losses worldwide but can provide beneficial agroecosystem services. This study aimed to elucidate how arbuscular mycorrhizal fungi (AMF) in weeds respond to host identity and conservation agricultural practices. The study was carried out at two locations in Southern Africa during off-season and in-season maize cultivation. Off-season AMF root colonisation, diversity indices and community composition significantly differed among weed species at both locations. Glomus sp. VTX00280 explains most of the AMF community differences. In-season, implementation of conventional tillage with mulching alone (CT + M) or together with crop rotation (CT + M + R) resulted in a 20% increase in AMF colonisation of the constantly occurring weed species, Bidens pilosa (BIDPI) and Richardia scabra (RCHSC), com- pared with conventional tillage plus rotations (CT + R). The diversity of AMF was highest under no-tillage plus mulching (NT + M). Off-season and in-season AMF structures of both BIDPI and RCHSC were not related, but 39% of the taxa were shared. Structural equation modelling showed a significant effect of the cropping system on weed AMF diversity parameters and weed and maize root colonisation, but no significant influence of weed root AMF traits and maize colonisation was detected on maize yield. This may be explained by the improvement in weed competitive ability, which may have offset the AMF-mediated benefits on yield. Our findings highlight that implementing M and CR to CT and NT positively affected weed AMF colonisation and diversity. The similarity between the off-season and in-season AMF composition of weeds supports the fact that weeds functionally host AMF during the non-crop period

Dynamics of a tunable superfluid junction

We study the population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics. At barriers higher than the chemical potential, we observe slow oscillations well described by a Josephson model. In the limit of low barriers, the fundamental frequency agrees with a simple hydrodynamic model, but we also observe a second, higher frequency. A full numerical simulation of the Gross-Pitaevskii equation giving the frequencies and amplitudes of the observed modes between these two limits is compared to the data and is used to understand the origin of the higher mode. Implications for trapped matter-wave interferometers are discussed.Comment: 8 pages, 7 figures; v3: Journal reference added, minor changes to tex