On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded eigenvalues

A virial theorem is established for the operator proposed by Brown and Ravenhall as a model for relativistic one-electron atoms. As a consequence, it is proved that the operator has no eigenvalues greater than $\max(m c^2, 2 \alpha Z - \frac{1}{2})$, where $\alpha$ is the fine structure constant, for all values of the nuclear charge $Z$ below the critical value $Z_c$: in particular there are no eigenvalues embedded in the essential spectrum when $Z \leq 3/4 \alpha$. Implications for the operators in the partial wave decomposition are also described.Comment: To appear in Letters in Math. Physic

Dirac-Sobolev inequalities and estimates for the zero modes of massless Dirac operators

The paper analyses the decay of any zero modes that might exist for a massless Dirac operator H:= \ba \cdot (1/i) \bgrad + Q, where $Q$ is $4 \times 4$-matrix-valued and of order O(|\x|^{-1}) at infinity. The approach is based on inversion with respect to the unit sphere in $\R^3$ and establishing embedding theorems for Dirac-Sobolev spaces of spinors $f$ which are such that $f$ and $Hf$ lie in $(L^p(\R^3))^4, 1\le p<\infty.$Comment: 11 page

Ectodermal Influx and Cell Hypertrophy Provide Early Growth for All Murine Mammary Rudiments, and Are Differentially Regulated among Them by Gli3

Mammary gland development starts in utero with one or several pairs of mammary rudiments (MRs) budding from the surface ectodermal component of the mammalian embryonic skin. Mice develop five pairs, numbered MR1 to MR5 from pectoral to inguinal position. We have previously shown that Gli3Xt-J/Xt-J mutant embryos, which lack the transcription factor Gli3, do not form MR3 and MR5. We show here that two days after the MRs emerge, Gli3Xt-J/Xt-J MR1 is 20% smaller, and Gli3Xt-J/Xt-J MR2 and MR4 are 50% smaller than their wild type (wt) counterparts. Moreover, while wt MRs sink into the underlying dermis, Gli3Xt-J/Xt-J MR4 and MR2 protrude outwardly, to different extents. To understand why each of these five pairs of functionally identical organs has its own, distinct response to the absence of Gli3, we determined which cellular mechanisms regulate growth of the individual MRs, and whether and how Gli3 regulates these mechanisms. We found a 5.5 to 10.7-fold lower cell proliferation rate in wt MRs compared to their adjacent surface ectoderm, indicating that MRs do not emerge or grow via locally enhanced cell proliferation. Cell-tracing experiments showed that surface ectodermal cells are recruited toward the positions where MRs emerge, and contribute to MR growth during at least two days. During the second day of MR development, peripheral cells within the MRs undergo hypertrophy, which also contributes to MR growth. Limited apoptotic cell death counterbalances MR growth. The relative contribution of each of these processes varies among the five MRs. Furthermore, each of these processes is impaired in the absence of Gli3, but to different extents in each MR. This differential involvement of Gli3 explains the variation in phenotype among Gli3Xt-J/Xt-J MRs, and may help to understand the variation in numbers and positions of mammary glands among mammals

Mechanism of gallic acid biosynthesis in bacteria (Escherichia coli) and walnut (Juglans regia)

Gallic acid (GA), a key intermediate in the synthesis of plant hydrolysable tannins, is also a primary anti-inflammatory, cardio-protective agent found in wine, tea, and cocoa. In this publication, we reveal the identity of a gene and encoded protein essential for GA synthesis. Although it has long been recognized that plants, bacteria, and fungi synthesize and accumulate GA, the pathway leading to its synthesis was largely unknown. Here we provide evidence that shikimate dehydrogenase (SDH), a shikimate pathway enzyme essential for aromatic amino acid synthesis, is also required for GA production. Escherichia coli (E. coli) aroE mutants lacking a functional SDH can be complemented with the plant enzyme such that they grew on media lacking aromatic amino acids and produced GA in vitro. Transgenic Nicotianatabacum lines expressing a Juglans regia SDH exhibited a 500% increase in GA accumulation. The J. regia and E. coli SDH was purified via overexpression in E. coli and used to measure substrate and cofactor kinetics, following reduction of NADP+ to NADPH. Reversed-phase liquid chromatography coupled to electrospray mass spectrometry (RP-LC/ESI–MS) was used to quantify and validate GA production through dehydrogenation of 3-dehydroshikimate (3-DHS) by purified E. coli and J. regia SDH when shikimic acid (SA) or 3-DHS were used as substrates and NADP+ as cofactor. Finally, we show that purified E. coli and J. regia SDH produced GA in vitro

The experience of living with chronic heart failure: a narrative review of qualitative studies

<p>Abstract</p> <p>Background</p> <p>Chronic heart failure (CHF) is the leading cause of all hospitalisations and readmissions in older people, accounting for a large proportion of developed countries' national health care expenditure. CHF can severely affect people's quality of life by reducing their independence and ability to undertake certain activities of daily living, as well as affecting their psychosocial and economic capacity. This paper reports the findings of a systematic narrative review of qualitative studies concerning people's experience of living with CHF, aiming to develop a wide-ranging understanding of what is known about the patient experience.</p> <p>Methods</p> <p>We searched eight relevant electronic databases using the terms based on the diagnosis of 'chronic heart failure', 'heart failure' and 'congestive heart failure' and qualitative methods, with restrictions to the years 1990-May 2008. We also used snowballing, hand searching and the expert knowledge of the research team to ensure all relevant papers were included in the review. Of 65 papers collected less than half (n = 30) were found relevant for this review. These papers were subsequently summarised and entered into QSR NVivo7 for data management and analysis.</p> <p>Results</p> <p>The review has identified the most prominent impacts of CHF on a person's everyday life including social isolation, living in fear and losing a sense of control. It has also identified common strategies through which patients with CHF manage their illness such as sharing experiences and burdens with others and being flexible to changing circumstances.</p> <p>Finally, there are multiple factors that commonly impact on patients' self care and self-management in the disease trajectory including knowledge, understanding and health service encounters. These health service encounters encompass access, continuity and quality of care, co-morbid conditions, and personal relationships.</p> <p>Conclusions</p> <p>The core and sub-concepts identified within this study provide health professionals, service providers, policy makers and educators with broad insights into common elements of people's experiences of CHF and potential options for improving their health and wellbeing. Future studies should focus on building a comprehensive picture of CHF through examination of differences between genders, and differences within age groups, socioeconomic groups and cultural groups.</p

STAGES IN THE ORIGIN OF VERTEBRATES: ANALYSIS BY MEANS OF SCENARIOS

Vertebrates lack an epidermal nerve plexus. This feature is common to many invertebrates from which vertebrates differ by an extensive set of shared-derived characters (synapomorphies) derived from the neural crest and epidermal neurogenic placodes. Hence, the hypothesis that the developmental precursor of the epidermal nerve plexus may be homologous to the neural crest and epidermal neurogenic placodes. This account attempts to generate a nested set of scenarios for the prevertebrate-vertebrate transition, associating a presumed sequence of behavioural and environmental changes with the observed phenotypic ones. Toward this end, it integrates morphological, developmental, functional (physiological/behavioural) and some ecological data, as many phenotypic shifts apparently involved associated transitions in several aspects of the animals. The scenarios deal with the origin of embryonic and adult tissues and such major organs as the notochord, the CNS, gills and kidneys and propose a sequence of associated changes. Alternative scenarios are stated as the evidence often remains insufficient for decision. The analysis points to gaps in comprehension of the biology of the animals and therefore suggests further research.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72629/1/j.1469-185X.1989.tb00471.x.pd