On Semi-weakly n-Hyponormal Weighted Shifts

Semi-weak n-hyponormality is defined and studied using the notion of positive determinant partition. Several examples related to semi-weakly n-hyponormal weighted shifts are discussed. In particular, it is proved that there exists a semi-weakly three-hyponormal weighted shift W (alpha) with alpha (0) = alpha (1) < alpha (2) which is not two-hyponormal, which illustrates the gaps between various weak subnormalities.

Quadratically Hyponormal Weighted Shifts with Recursive Tail

We characterize positive quadratic hyponormality of the weighted shift W-alpha(x) associated to the weight sequence alpha(x) : 1, 1, root x, (root u, root v, root w)(Lambda) with Stampfli recursive tail, and produce an interval in x with non-empty interior in the positive real line for quadratic hyponormality but not positive quadratic hyponormality for such a shift. (C) 2013 Elsevier Inc. All rights reserved.

Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality

Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of the shift by prefixing weights to the sequence. We characterize positive quadratic hyponormality and revisit quadratic hyponormality of certain such backward extensions of arbitrary length, generalizing earlier results, and also show that a function apparently introduced as a matter of convenience for quadratic hyponormality actually captures considerable information about positive quadratic hyponormality.

k-Hyponormality and n-Contractivity for Agler-Type Shifts

We consider k-hyponormality and n-contractivity (k, n = 1, 2, ...) as "weak subnormalities" for a Hilbert space operator. It is known that k-hyponormality implies 2k-contractivity; we produce some classes of weighted shifts including a parameter for which membership in a certain n-contractive class is equivalent to k-hyponormality. We consider as well some extensions of these results to operators arising as restrictions of these shifts, or from linear combinations of the Berger measures associated with the shifts.

Comparative Ultrastructure and Molecular Phylogeny of Selenidium melongena n. sp and S. terebellae Ray 1930 Demonstrate Niche Partitioning in Marine Gregarine Parasites (Apicomplexa)

Gregarine apicomplexans are a diverse group of single-celled parasites that have feeding stages (trophozoites) and gamonts that generally inhabit the extracellular spaces of invertebrate hosts living in marine, freshwater, and terrestrial environments. Inferences about the evolutionary morphology of gregarine apicomplexans are being incrementally refined by molecular phylogenetic data, which suggest that several traits associated with the feeding cells of gregarines arose by convergent evolution. The study reported here supports these inferences by showing how molecular data reveals traits that are phylogenetically misleading within the context of comparative morphology alone. We examined the ultrastructure and molecular phylogenetic positions of two gregarine species isolated from the spaghetti worm Thelepus japonicus: Selenidium terebellae Ray 1930 and S. melongena n. sp. The ultrastructural traits of S. terebellae were very similar to other species of Selenidium sensu stricto, such as having vermiform trophozoites with an apical complex, few epicytic folds, and a dense array of microtubules underlying the trilayered pellicle. By contrast, S. melongena n. sp. lacked a comparably discrete assembly of subpellicular microtubules, instead employing a system of fibrils beneath the cell surface that supported a relatively dense array of helically arranged epicytic folds. Molecular phylogenetic analyses of small subunit rDNA sequences derived from single-cell PCR unexpectedly demonstrated that these two gregarines are close sister species. The ultrastructural differences between these two species were consistent with the fact that S. terebellae infects the inner lining of the host intestines, and S. melongena n. sp. primarily inhabits the coelom, infecting the outside wall of the host intestine. Altogether, these data demonstrate a compelling case of niche partitioning and associated morphological divergence in marine gregarine apicomplexans. (C) 2014 Elsevier GmbH. All rights reserved.

A Stable Niche Assumption-Free Test of Ecological Divergence

Understanding the impact of geological events on diversification processes is central to evolutionary ecology. The recent amalgamation between ecological niche models (ENMs) and phylogenetic analyses has been used to estimate historical ranges of modern lineages by projecting current ecological niches of organisms onto paleoclimatic reconstructions. A critical assumption underlying this approach is that niches are stable over time. Using Notophthalmus viridescens (eastern newt), in which four ecologically diverged subspecies are recognized, we introduce an analytical framework free from the niche stability assumption to examine how refugial retreat and subsequent postglacial expansion have affected intraspecific ecological divergence. We found that the current subspecies designation was not congruent with the phylogenetic lineages. Thus, we examined ecological niche overlap between the refugial and modern populations, in both subspecies and lineage, by creating ENMs independently for modern and estimated last glacial maximum (LGM) newt populations, extracting bioclimate variables by randomly generated points, and conducting principal component analyses. Our analyses consistently showed that when tested as a hypothesis, rather than used as an assumption, the niches of N. viridescens lineages have been unstable since the LGM (both subspecies and lineages). There was greater ecological niche differentiation among the subspecies than the modern phylogenetic lineages, suggesting that the subspecies, rather than the phylogenetic lineages, is the unit of the current ecological divergence. The present study found little evidence that the LGM refugial retreat caused the currently observed ecological divergence and suggests that ecological divergence has occurred during postglacial expansion to the current distribution ranges.