Description and molecular phylogeny of a new and one known needle nematode of the genus Paralongidorus (Nematoda: Longidoridae) from grapevine in Portugal

A new and a known longidorid nematode, Paralongidorus lusitanicus n. sp. and Paralongidorus plesioepimikis, are described and illustrated from populations extracted from soil associated with grapevine (Vitis vinifera L.) from Escaroupim and Pó (central-Western Portugal), respectively. The new needle nematode P. lusitanicus n. sp. is characterised by a very large body size (8072–12,022 μm), an expanded and rounded lip region, ca 30 μm wide, with a clear constriction followed by a depression posterior to the amphidial aperture, amphidial fovea very large (11.0–19.0 μm), stirrup-shaped, with conspicuous slit-like aperture as shown in scanning electron microscopy studies, a very long and flexible odontostyle (180.0–223.0 μm), guiding ring located at 28.0–41.5 μm from anterior end, vulva anterior to the mid-body (34–41%), a dorsally convex-conoid tail with rounded terminus (29–42 μm long), bearing two or three pairs of caudal pores and males common (ratio 1:1.6 females) with spicules ca 80 μm long. Morphological and morphometric traits for P. plesioepimikis fit well with the original description, and is reported for the first time in Portugal. Integrative diagnosis of both species was completed with molecular data obtained using D2-D3 expansion segments of 28S rDNA, ITS1-rDNA and partial 18S–rDNA. The phylogenetic relationships of these species with other Paralongidorus spp. using these three molecular markers indicated that P. lusitanicus n. sp. clustered together with other Paralongidorus spp. forming a sister clade with P. plesioepimikis, both of them sharing a large body, long odontostyle, an anteriorly located vulva and an expanded and rounded lip region with a clear constriction followed by a depression posterior to the amphidial aperture

Harnack's inequality for a class of non-divergent equations in the Heisenberg group

We prove an invariant Harnack's inequality for operators in non-divergence form structured on Heisenberg vector fields when the coefficient matrix is uniformly positive definite, continuous, and symplectic. The method consists in constructing appropriate barriers to obtain pointwise-to-measure estimates for supersolutions in small balls, and then invoking the axiomatic approach from [DGL08] to obtain Harnack's inequality

Primordial black hole evolution in two-fluid cosmology

Several processes in the early universe might lead to the formation of primordial black holes with different masses. These black holes would interact with the cosmic plasma through accretion and emission processes. Such interactions might have affected the dynamics of the universe and generated a considerable amount of entropy. In this paper we investigate the effects of the presence of primordial black holes on the evolution of the early universe. We adopt a two-fluid cosmological model with radiation and a primordial black hole gas. The latter is modelled with different initial mass functions taking into account the available constraints over the initial primordial black hole abundances. We find that certain populations with narrow initial mass functions are capable to produce significant changes in the scale factor and the entropy.Comment: 8 pages, 7 figures. Modified to match the published versio