Fully representable and *-semisimple topological partial *-algebras

We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the scope of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome is that, for an appropriate order relation, one recovers the \M-bounded elements introduced in previous works.Comment: 26 pages, Studia Mathematica (2012) to appea

Family history in the Aetiology of Gestational Diabetes Mellitus and Type 2 Diabetes

The aetiology of Type 2 diabetes [NIDDM] is assumed to involve a multiplicity of causal factors involving both genetic and environmental, including intrauterine, components. Aim: To identify the relationship of various aspects of family history and hence the possible role of genetic influence in the development of Type 2 DM in the Maltese population. Methods: The family history details of a study population undergoing an oGTT during pregnancy was assessed during pregnancy and at follow-up eight years postpartum. The findings were related to previous national epidemiological studies. Results: The study showed a definite statistical correlation between a maternal and sibling family history of diabetes with the onset of GDM/GIGT and later Type 2 DM. No such correlation was shown with a paternal or grandparent family history. Conclusions: The findings suggest that genetic factors are poor determinants for adult-onset GDM or Type 2 DM, the major role player being apparently alterations in the intrauterine environment of the fetus.peer-reviewe

Geological indicators for impact: The anomalous case of the Vredefort structure, South Africa

The Vredefort Dome is located within and almost central to the Witwatersrand basin in its presently known extent. It exposes a central Archean granite core which is surrounded by a collar of supracrustal rocks. These collar rocks outline a strong polygonal geometry. The Archean core is comprised of two concentric zones, the Outer Granite Gneiss (OGG), and the core central Inlandsee Leucogranofels (ILG). The rocks of the inner core display granulite facies metamorphism, while the OGG is in amphibolite facies. The inner core is believed from recent drill hole information to be underlain by mafic and ultramafic gneisses, the extent of which cannot be assessed at present. A fairly broad zone of charnockites separates the OGG and ILG domains. This zone is characterized by a high concentration of pseudotachylite and ductile shearing. Whereas a number of other domical structures are located within or surrounding the Witwatersrand basin, the Vredefort structure is anomalous, in that it has: a partly polygonal geometry; extensive alkali intrusives in the northwestern sector; granophyre dykes (ring-dykes peripheral to the contact collar-basement and NW-SE or NE-SW trending dykes within the Archean basement); contact metamorphism of the collar supracrustal rocks; the overturning of collar supracrustals in the northern sectors; deformation phenomena widely regarded as representing shock metamorphism (pseudotachylite, (sub)planar microdeformation features in quartz, shatter cones and occurrences of high-P quartz polymorphs); a positive 30 mgal gravity anomaly; and high amplitude magnetic anomalies. Recent geophysical, structural and petrological evidence pertinent for the identification of the processes that led to the formation of the Vredefort structure are summarized

The Theorem of Jentzsch--Szeg\H{o} on an analytic curve. Application to the irreducibility of truncations of power series

The theorem of Jentzsch--Szeg\H{o} describes the limit measure of a sequence of discrete measures associated to the zeroes of a sequence of polynomials in one variable. Following the presentation of this result by Andrievskii and Blatt in their book, we extend this theorem to compact Riemann surfaces, then to analytic curves over an ultrametric field. The particular case of the projective line over an ultrametric field gives as corollaries information about the irreducibility of the truncations of a power series in one variable.Comment: 16 pages; the application to irreducibility and the final example have been correcte

Rotationally-invariant slave-boson formalism and momentum dependence of the quasiparticle weight

We generalize the rotationally-invariant formulation of the slave-boson formalism to multiorbital models, with arbitrary interactions, crystal fields, and multiplet structure. This allows for the study of multiplet effects on the nature of low-energy quasiparticles. Non-diagonal components of the matrix of quasiparticle weights can be calculated within this framework. When combined with cluster extensions of dynamical mean-field theory, this method allows us to address the effects of spatial correlations, such as the generation of the superexchange and the momentum dependence of the quasiparticle weight. We illustrate the method on a two-band Hubbard model, a Hubbard model made of two coupled layers, and a two-dimensional single-band Hubbard model (within a two-site cellular dynamical mean-field approximation).Comment: added figures, improved discussio

Dynamic regulation of quaternary organization of the M1 muscarinic receptor by subtype-selective antagonist drugs

Although rhodopsin-like G protein-coupled receptors can exist as both monomers and non-covalently associated dimers/oligomers, the steady-state proportion of each form and whether this is regulated by receptor ligands is unknown. Herein we address these topics for the M1 muscarinic acetylcholine receptor, a key molecular target for novel cognition enhancers, by employing Spatial Intensity Distribution Analysis. This method can measure fluorescent particle concentration and assess oligomerization states of proteins within defined regions of living cells. Imaging and analysis of the basolateral surface of cells expressing some 50 molecules.microm-2 of the human muscarinic M1 receptor identified an ~75/25 mixture of receptor monomers and dimers/oligomers. Both sustained and shorter-term treatment with the selective M1 antagonist pirenzepine resulted in a large shift in the distribution of receptor species to favor the dimeric/oligomeric state. Although sustained treatment with pirenzepine also resulted in marked upregulation of the receptor, simple mass-action effects were not the basis for ligand-induced stabilization of receptor dimers/oligomers. The related antagonist telenzepine also produced stabilization and enrichment of the M1 receptor dimer population but the receptor subtype non-selective antagonists atropine and N-methylscopolamine did not. In contrast, neither pirenzepine nor telenzepine altered the quaternary organization of the related M3 muscarinic receptor. These data provide unique insights into the selective capacity of receptor ligands to promote and/or stabilize receptor dimers/oligomers and demonstrate that the dynamics of ligand regulation of the quaternary organization of G protein-coupled receptors is markedly more complex than previously appreciated. This may have major implications for receptor function and behavior