q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials

We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace operator. This allows to construct q-deformed Schroedinger equations in higher dimensions. The equivalence of these Schroedinger equations with those defined on q-Euclidean space in quantum variables is shown. We also define the m-dimensional q-Clifford-Hermite polynomials and show their connection with the q-Laguerre polynomials. These polynomials are orthogonal with respect to an m-dimensional q-integration, which is related to integration on q-Euclidean space. The q-Laguerre polynomials are the eigenvectors of an su_q(1|1)-representation

Operator identities in q-deformed Clifford analysis

In this paper, we define a q-deformation of the Dirac operator as a generalization of the one dimensional q-derivative. This is done in the abstract setting of radial algebra. This leads to a q-Dirac operator in Clifford analysis. The q-integration on R(m), for which the q-Dirac operator satisfies Stokes' formula, is defined. The orthogonal q-Clifford-Hermite polynomials for this integration are briefly studied

Interacting effects of temperature, habitat and phenotype on predator avoidance behaviour in <i>Diadema antillarum</i>: implications for restorative conservation

Caribbean long-spined sea urchin Diadema antillarum populations crashed following a mass mortality event in 1983-1984 with cascading effects on reef health. Population restoration efforts may be hampered by unknown effects of short- and long-term elevated sea surface temperature (SST). We investigated how a key behavioural trait, predator avoidance behaviour (PAB; percentage of long defensive spines that moved in response to shadow stimuli), was affected by elevated SST in 180 individuals from 2 contrasting Honduran reefs: Utila (flattened reef structure, dearth of predation refugia) and Banco Capiro (complex reef structure, abundant refugia). Initiation of PAB is mediated by melanin, which breaks down at elevated water temperatures; thus, as SST rises, D. antillarum may become vulnerable to predation. We compared local current SST (CSST; 29.7°C) with 2 IPCC predicted long-term climate change scenarios under laboratory conditions. PAB decreased by 13.98-15.37% at CSST +1.4°C and 31.67-42.44% at CSST +3.1°C. Trial temperatures were similar to maxima recorded in the Caribbean during the 2016 El Niño, so our results also represent likely responses to worst-case short-term acute temperature anomalies. Juveniles maintained higher PAB than adults, indicating increased reliance on anti-predation behaviours. White-spined phenotypes from Utila’s flattened reef maintained higher PAB than black-spined counterparts, likely due to increased conspicuousness to visual predators. Habitat complexity may mitigate temperature-driven losses in natural behavioural defences. D. antillarum may be resilient to near-term (D. antillarum populations must be coupled to augmented reef complexity to improve future resilience

Energy of Isolated Systems at Retarded Times as the Null Limit of Quasilocal Energy

We define the energy of a perfectly isolated system at a given retarded time as the suitable null limit of the quasilocal energy $E$. The result coincides with the Bondi-Sachs mass. Our $E$ is the lapse-unity shift-zero boundary value of the gravitational Hamiltonian appropriate for the partial system $\Sigma$ contained within a finite topologically spherical boundary $B = \partial \Sigma$. Moreover, we show that with an arbitrary lapse and zero shift the same null limit of the Hamiltonian defines a physically meaningful element in the space dual to supertranslations. This result is specialized to yield an expression for the full Bondi-Sachs four-momentum in terms of Hamiltonian values.Comment: REVTEX, 16 pages, 1 figur

Boundary effects on the local density of states of one-dimensional Mott insulators and charge density wave states

We determine the local density of states (LDOS) for spin-gapped one-dimensional charge density wave (CDW) states and Mott insulators in the presence of a hard-wall boundary. We calculate the boundary contribution to the single-particle Green function in the low-energy limit using field theory techniques and analyze it in terms of its Fourier transform in both time and space. The boundary LDOS in the CDW case exhibits a singularity at momentum 2kF, which is indicative of the pinning of the CDW order at the impurity. We further observe several dispersing features at frequencies above the spin gap, which provide a characteristic signature of spin-charge separation. This demonstrates that the boundary LDOS can be used to infer properties of the underlying bulk system. In presence of a boundary magnetic field mid-gap states localized at the boundary emerge. We investigate the signature of such bound states in the LDOS. We discuss implications of our results on STM experiments on quasi-1D systems such as two-leg ladder materials like Sr14Cu24O41. By exchanging the roles of charge and spin sectors, all our results directly carry over to the case of one-dimensional Mott insulators.Comment: 28 page

Spatial and temporal variability of biogenic isoprene emissions from a temperate estuary

[1] Isoprene is important for its atmospheric impacts and the ecophysiological benefits it affords to emitting organisms; however, isoprene emissions from marine systems remain vastly understudied compared to terrestrial systems. This study investigates for the first time drivers of isoprene production in a temperate estuary, and the role this production may play in enabling organisms to tolerate the inherently wide range of environmental conditions. Intertidal sediment cores as well as high and low tide water samples were collected from four sites along the Colne Estuary, UK, every six weeks over a year. Isoprene concentrations in the water were significantly higher at low than high tide, and decreased toward the mouth of the estuary; sediment production showed no spatial variability. Diel isoprene concentration increased with light availability and decreased with tidal height; nighttime production was 79% lower than daytime production. Seasonal isoprene production and water concentrations were highest for the warmest months, with production strongly correlated with light (r2 = 0.800) and temperature (r2 = 0.752). Intertidal microphytobenthic communities were found to be the primary source of isoprene, with tidal action acting as a concentrating factor for isoprene entering the water column. Using these data we estimated an annual production rate for this estuary of 681 μmol m−2 y−1. This value falls at the upper end of other marine estimates and highlights the potentially significant role of estuaries as isoprene sources. The control of estuarine isoprene production by environmental processes identified here further suggests that such emissions may be altered by future environmental change

Solutions for the General, Confluent and Biconfluent Heun equations and their connection with Abel equations

In a recent paper, the canonical forms of a new multi-parameter class of Abel differential equations, so-called AIR, all of whose members can be mapped into Riccati equations, were shown to be related to the differential equations for the hypergeometric 2F1, 1F1 and 0F1 functions. In this paper, a connection between the AIR canonical forms and the Heun General (GHE), Confluent (CHE) and Biconfluent (BHE) equations is presented. This connection fixes the value of one of the Heun parameters, expresses another one in terms of those remaining, and provides closed form solutions in terms of pFq functions for the resulting GHE, CHE and BHE, respectively depending on four, three and two irreducible parameters. This connection also turns evident what is the relation between the Heun parameters such that the solutions admit Liouvillian form, and suggests a mechanism for relating linear equations with N and N-1 singularities through the canonical forms of a non-linear equation of one order less.Comment: Original version submitted to Journal of Physics A: 16 pages, related to math.GM/0002059 and math-ph/0402040. Revised version according to referee's comments: 23 pages. Sign corrected (June/17) in formula (79). Second revised version (July/25): 25 pages. See also http://lie.uwaterloo.ca/odetools.ht

A pilot study of performance among hospitalised elderly patients on a novel test of visuospatial cognition: the letter and shape drawing (LSD) test.

peer-reviewedObjectives. Conventional bedside tests of visuospatial function such as the clock drawing (CDT) and intersecting pentagons tests (IPT) are subject to considerable inconsistency in their delivery and interpretation. We compared performance on a novel test – the letter and shape drawing (LSD) test –with these conventional tests in hospitalised elderly patients. Methods. The LSD, IPT, CDT and the Montreal Cognitive Assessment (MoCA) were performed in 40 acute elderly medical inpatients at University Hospital Limerick The correlation between these tests was examined as well as the accuracy of the visuospatial tests to identify significant cognitive impairment on the MoCA. Results. The patients (mean age 81.0±7.71; 21 female) had a median MoCA score of 15.5 (range = 1–29). There was a strong, positive correlation between the LSD and both the CDT (r = 0.56) and IPT (r = 0.71). The correlation between the LSD and MoCA (r = 0.91) was greater than for the CDT and IPT (both 0.67). The LSD correlated highly with all MoCA domains (ranging from 0.54 to 0.86) and especially for the domains of orientation (r = 0.86), attention (0.81) and visuospatial function (r = 0.73). Two or more errors on the LSD identified 90% (26/29) of those patients with MoCA scores of ⩽20, which was substantially higher than for the CDT (59%) and IPT (55%). Conclusion. The LSD is a novel test of visuospatial function that is brief, readily administered and easily interpreted. Performance correlates strongly with other tests of visuospatial ability, with favourable ability to identify patients with significant impairment of general cognition.PUBLISHEDpeer-reviewe

An Algebraic Construction of Generalized Coherent States for Shape-Invariant Potentials

Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary to establish a connection between classical and quantum formulations of a given system (continuity of labeling, resolution of unity, temporal stability, and action identity); b) reproduce results already known for shape-invariant systems, like harmonic oscillator, double anharmonic, Poschl-Teller and self-similar potentials and; c) point to a formalism that provides an unified description of the different kind of coherent states for quantum systems.Comment: 14 pages of REVTE

Uniqueness of the Trautman--Bondi mass

It is shown that the only functionals, within a natural class, which are monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth ``piece'' of conformal null infinity Scri, are those depending on the metric only through a specific combination of the Bondi `mass aspect' and other next--to--leading order terms in the metric. Under the extra condition of passive BMS invariance, the unique such functional (up to a multiplicative factor) is the Trautman--Bondi energy. It is also shown that this energy remains well-defined for a wide class of `polyhomogeneous' metrics.Comment: latex, 33 page