High orders of Weyl series for the heat content

This article concerns the Weyl series of spectral functions associated with the Dirichlet Laplacian in a $d$-dimensional domain with a smooth boundary. In the case of the heat kernel, Berry and Howls predicted the asymptotic form of the Weyl series characterized by a set of parameters. Here, we concentrate on another spectral function, the (normalized) heat content. We show on several exactly solvable examples that, for even $d$, the same asymptotic formula is valid with different values of the parameters. The considered domains are $d$-dimensional balls and two limiting cases of the elliptic domain with eccentricity $\epsilon$: A slightly deformed disk ($\epsilon\to 0$) and an extremely prolonged ellipse ($\epsilon\to 1$). These cases include 2D domains with circular symmetry and those with only one shortest periodic orbit for the classical billiard. We analyse also the heat content for the balls in odd dimensions $d$ for which the asymptotic form of the Weyl series changes significantly.Comment: 20 pages, 1 figur

High-MgO lavas associated to CFB as indicators of plume-related thermochemical effects: the case of ultra-titaniferous picrite-basalt from the Northern Ethiopian-Yemeni plateau

A comprehensive petrological and geochemical dataset is reported in order to define the thermo-compositional characteristics of Ti (Fe)-enriched picrite-basalt lavas (HT2, TiO2 3-7 wt%), erupted close to the axial zone of the inferred Afar mantle plume, at the centre of the originally continuous Ethiopian-Yemeni CFB plateau (ca. 30Ma) which is zonally arranged with progressively lower Ti basalts (HT1, TiO2 2-4 wt%; LT, TiO2 1-3 wt%) toward the periphery. Integrated petrogenetic modelling based on major and trace element analyses of bulk rocks, minerals and melt inclusions in olivines, as well as Sr-Nd-Pb-He-O isotope compositional variations enables us to make several conclusions. 1) The phase equilibria constraints indicate that HT2 primary picrites were generated at ca. 1570°C mantle potential temperatures (Tp) in the pressure range 4-5 GPa whereas the HT1 and LT primary melts formed at shallower level (< 2 to 3 GPa, Tp 1530 °C for HT1 and 1430°C for LT). Thus the Afar plume head was a thermally and compositionally zoned melting region with maximum excess temperatures of 300-350°C with respect to the ambient mantle. 2) The HT2 primary melts upwelled nearly adiabatically to the base of the continental crust (ca. 1 GPa) where fractionation of olivine, followed by clinopyroxene, led to variably differentiated picritic and basaltic magmas. 3) Trace element modelling requires that the primary HT2 melts were generated - either by fractional or batch melting (F 9-10%) - from a mixed garnet peridotite source (85%) with 15% eclogite (derived from transitional MORB protoliths included in Panafrican terranes) that has to be considered a specific Ti-Fe and incompatible element enriched component entrained by the Afar plume. 4) The LT, HT1 and HT2 lavas have 143Nd/144Nd = 0.5131-0.5128, whereas Sr-Pb isotopes are positively correlated with TiO2, varying from 87 Sr/86Sr 0.7032 and 206Pb/204Pb 18.2 in LT basalts to 87Sr/86Sr 0.7044 and 206Pb/204Pb 19.4 in HT2 picrite-basalts. High 3He/4He (15-20 RA) ratios are exclusively observed in HT2 lavas, confirming earlier evidence that these magmas require a component of deep mantle in addition to eclogite, while the LT basalts may more effectively reflect the signature of the pre-existing mantle domains. The comparison between high-MgO (13-22%) lavas from several Phanerozoic CFB provinces (Karoo, Paranà-Etendeka, Emeishan, Siberia, Deccan, North Atlantic Province) shows that they share extremely high mantle potential temperatures (Tp 1550-1700°C) supporting the view that hot mantle plumes are favoured candidates for triggering many LIPs. However, the high incompatible element and isotopic variability of these high-MgO lavas (and associated CFB) suggest that plume thermal anomalies are not necessarily accompanied by significant and specific chemical effects, which depend on the nature of mantle materials recycled during the plume rise, as well as by the extent of related mantle enrichments (if any) on the pre-existing lithospheric section

Mode Confinement in Photonic Quasi-Crystal Point-Defect Cavities for Particle Accelerators

In this Letter, we present a study of the confinement properties of point-defect resonators in finite-size photonic-bandgap structures composed of aperiodic arrangements of dielectric rods, with special emphasis on their use for the design of cavities for particle accelerators. Specifically, for representative geometries, we study the properties of the fundamental mode (as a function of the filling fraction, structure size, and losses) via 2-D and 3-D full-wave numerical simulations, as well as microwave measurements at room temperature. Results indicate that, for reduced-size structures, aperiodic geometries exhibit superior confinement properties by comparison with periodic ones.Comment: 4 pages, 4 figures, accepted for publication in Applied Physics Letter

Survival probability (heat content) and the lowest eigenvalue of Dirichlet Laplacian

We study the survival probability of a particle diffusing in a two-dimensional domain, bounded by a smooth absorbing boundary. The short-time expansion of this quantity depends on the geometric characteristics of the boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue of the Dirichlet Laplacian defined on the domain. We present a simple algorithm for calculation of the short-time expansion for an arbitrary "star-shaped" domain. The coefficients are expressed in terms of powers of boundary curvature, integrated around the circumference of the domain. Based on this expansion, we look for a Pad\'e interpolation between the short-time and the long-time behavior of the survival probability, i.e. between geometric characteristics of the boundary and the lowest eigenvalue of the Dirichlet Laplacian.Comment: Accepted in IJMP

Post-stroke depression increases disability more than 15% in ischemic stroke survivors: a case-control study

We performed a retrospective, case-control study in consecutive ischemic stroke patients admitted to our stroke rehabilitation unit. Patients were matched for severity of neurological impairment (evaluated with the Canadian Neurological Scale, CNS), age (difference within 1 year), and onset admission interval (difference within 3 days). Participants were divided into two subgroups according to the presence or absence of PSD. Aim was to assess the specific influence of post-stroke depression (PSD) and antidepressant treatment on both basal functional status and rehabilitation outcomes. All PSD patients were treated primarily with serotoninergic antidepressants (AD). The final sample included 280 patients with depression (out of 320 found in a whole case series of 993 ischemic patients, i.e., 32.25%) and 280 without depression. Forty patients with depression were excluded because they had a history of severe psychiatric illness or aphasia, with a severe comprehension deficit. On one hand, PSD patients obtained lower Barthel Index (BI) and Rivermead Mobility Index (RMI) scores at both admission and discharge, with minor effectiveness of rehabilitative treatment and longer length of stay; on the other hand, this group had a lower percentage of dropouts. Lastly, PSD patients showed a different functional outcome, based on their response to antidepressant therapy, that was significantly better in responders than in non-responders (13.13%). Our results confirm the unfavorable influence of PSD on functional outcome, despite pharmacological treatment

Mogućnosti i izazovi održivog razvoja ovčarstva Srbije

This paper analyzes the present state of sheep farming in Serbia and provide guidance for sustainable development in the future. It also discusses the challenges of the modern age that may affect the viability of sheep production. Today in Serbia grows less than 1.5 million sheep. In terms of breed structures, most of the population makes indigenous Pramenka sheep (80%), while the remaining 20% are: Tsigai, Merinolandschaf, Ile de France, Pirot improved, Mis sheep, and other less important population, as well as the crossbreed with foreign and local domestic sheep. However, due to the intense process of industrialization, from the second half of the twentieth century until today there is a trend of depopulation, demographic discharge of the village, which has resulted in reducing the farms so that the number of sheep in the past two decades fell by about 30%. The greatest reduction in the number of sheep registered in the nineties. After stabilization, a large decrease in the number of sheep was followed by the 2010th year and by 6% compared to 2008 year. Genetical improvement is significantly increased level of production of all species of domestic animals. However, animals selected for high and efficient production are exposed to greater risk. This primarily refers to the physiological and immunological problems, but would generally be said that all this leads to distortion of harmony between the organism and the environment and the repercussions on the molecular level. Sustainable development of sheep breeding in Serbia must be kept in mind this reality. New challenges facing the sheep breeding of Serbia, stems from a political orientation toward membership in the European Union. Sheep Serbia must find its place in this new challenge.Ovaj rad analizira sadašnje stanje ovčarstva u Srbiji i daje smernice za održivi razvoj u budućnosti. On takođe raspravlja o izazovima modernog doba koji mogu uticati na održivost ovčarske proizvodnje. Srbija danas raspolaže sa nešto manje od 1,5 miliona ovaca. U pogledu rasne strukture, većinu čini pramenkalokalne autohtone ovce, dok preostalih 15- 20% su: Cigaja, Merinolandschaf, Ile de France, Pirotska oplemenjena, novo proizvedena Mis ovca, i druge manje važne populacije, kao i melezi sa inostranim rasama. Međutim, zbog intenzivnog procesa industrijalizacije, od druge polovine dvadesetog veka do danas postoji trend smanjenja seoskog stanovništva i pražnjenja sela, što je rezultiralo smanjenjem farmi, tako da je broj ovaca u poslednje dve decenije opao za oko 30%. Najveći pad broja ovaca registrovan je tokom devedesetih. Posle stabilizacije, veliki pad u broju ovaca je usledio 2010. godine za 6% u odnosu na 2008. godinu. Genetsko unapređenje je poslednjih decenija znatno povećalo nivo proizvodnje svih vrsta domaćih životinja. Međutim, životinje selekcionisane za visoku i efikasnu proizvodnju izloženi su većem riziku. Ovo se prvenstveno odnosi na fiziološke i imunološke probleme, ali bi se generalno moglo reći da je sve to dovelo do narušavanja harmonije između organizma i sredine i posledica na molekularnom nivou. Održivi razvoj ovčarstva Srbije mora imati u vidu ovu realnost. Novi izazovi sa kojima se suočava ovčarstvo Srbije, proističu i iz političke orijentacije ka članstvu u Evropskoj uniji. Zbog svih pomenutih razloga ovčarstvo Srbije mora naći svoje pravo mesto u svetlu novih izazova

Hybrid photonic-bandgap accelerating cavities

In a recent investigation, we studied two-dimensional point-defected photonic bandgap cavities composed of dielectric rods arranged according to various representative periodic and aperiodic lattices, with special emphasis on possible applications to particle acceleration (along the longitudinal axis). In this paper, we present a new study aimed at highlighting the possible advantages of using hybrid structures based on the above dielectric configurations, but featuring metallic rods in the outermost regions, for the design of extremely-high quality factor, bandgap-based, accelerating resonators. In this framework, we consider diverse configurations, with different (periodic and aperiodic) lattice geometries, sizes, and dielectric/metal fractions. Moreover, we also explore possible improvements attainable via the use of superconducting plates to confine the electromagnetic field in the longitudinal direction. Results from our comparative studies, based on numerical full-wave simulations backed by experimental validations (at room and cryogenic temperatures) in the microwave region, identify the candidate parametric configurations capable of yielding the highest quality factor.Comment: 13 pages, 5 figures, 3 tables. One figure and one reference added; minor changes in the tex

The impact on disability of initial treatment with methotrexate in patients with rheumatoid arthritis: results from the MARI study

The study aimed to assess in a population of subjects with rheumatoid arthritis (RA) treated with methotrexate (MTX) how the initial approach to the treatment influenced subsequent disability. We performed a cross-sectional analysis of data collected during the baseline visit of the MARI study, a multicenter observational study on patients with RA on treatment with MTX for at least 12 months. Subjects who fulfilled the Health Assessment Questionnaire (HAQ) were included in the evaluation. For every patient we retrospectively evaluated the disease duration, the duration of symptoms before the diagnosis, the time elapsed before first MTX treatment, the initial MTX dose, and the concomitant medications in the first six months of therapy. Disability was defined as a DI-HAQ score ≥1. The study population included 1015 subjects. Patients with a DI-HAQ score ≥1 had a longer duration of symptoms before diagnosis, a higher delay in treatment initiation, a lower initial dose of MTX and a more frequent co-treatment with symptomatic drugs. Disability was found less frequently in subjects treated with other concomitant disease modifying anti-rheumatic drugs (DMARDs) but not with biological agents. Logistic regression analysis identified as significant predictors of disability: older age, female sex, a longer time to complete diagnosis, a delay in starting MTX treatment higher than 6 months, and a concomitant treatment with symptomatic drugs, while a combination therapy with other DMARDs was associated with a lower risk of disability. A late diagnosis and a delay in starting a treatment with MTX are associated with poorer functional outcomes in patients with RA

A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

Immune genotypes, immune responses, and survival in a wild bird population

ACKNOWLEDGEMENTS We thank the Tsawout and Tseycum bands for allowing us to conduct research on Mandarte Island, and to the many contributors to long-term monitoring, especially L. Keller, P. Nietlisbach, and J. Krippel. We also thank C. Ritland, A. Miscampbell, and G. Huber for their assistance in the laboratory. All work was conducted under permit of the Canadian Wildlife Service and UBC Animal Care Committee. Funding Information: This study was generously supported by the Natural Sciences and Engineering Research Council of Canada via a Post‐doctoral Fellowship award to MJNF (PDF‐2014–454522) and a Discovery Grant to EAMS.Peer reviewedPublisher PD