Generalized Korn's inequality and conformal Killing vectors

Korn's inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are the infinitesimal rigid-body translations and rotations (Killing vectors). We generalize this inequality by replacing the linearized strain tensor by its trace free part. That is, we obtain a stronger inequality in which the kernel of the relevant operator are the conformal Killing vectors. The new inequality has applications in General Relativity.Comment: 8 page

Salivary gland tumour of the lip: report of two cases and literature review

A research article on rare tumors affecting the salivary gland (SGTS).Salivary gland tumours (SGT'S) are uncommon; they represent 2.4% of head and neck neoplasm and include tumours affecting both major and minor salivary glands. The glands are divided into major and minor salivary gland categories. The major salivary glands are the parotid, submandibular and sublingual glands. The minor glands are dispersed throughout the upper aerodigestive submucosa (palate, tongue, lip, pharynx, nasopharynx, larynx, parapharyngeal space) and anatomical parts; skin, muscle and mucous membrane with numerous salivary glands in the submucosa. Pleomorphic adenomas (benign mixed tumours) are the most common benign SGT and comprise 85% of all salivary gland neoplasms. However, the incidence of SGT'S is claimed to be influenced by geographic and racial factors. African reports suggest a pattern that significantly differs from that of western countries. The ubiquitous deposits of the minor salivary glands complicate the diagnosis and management

Far-infrared vibrational properties of high-pressure-high-temperature C60 polymers and the C60 dimer

We report high-resolution far-infrared transmission measurements of the 2 + 2 cycloaddition C-60 dimer and two-dimensional rhombohedral and one-dimensional orthorhombic high-pressure high-temperature C60 polymers. In the spectral region investigated(20-650 cm(-1)), we see no low-energy interball modes, but symmetry breaking of the linked C-60 balls is evident in the complex spectrum of intramolecular modes. Experimental features suggest large splittings or frequency shifts of some IhC60-derived modes that are activated by symmetry reduction, implying that the balls are strongly distorted in these structures. We have calculated the vibrations of all three systems by first-principles quantum molecular dynamics and use them to assign the predominant IhC60 symmetries of observed modes. Pur calculations show unprecedentedly large downshifts of T-1u(2)-derived modes and extremely large splittings of other modes, both of which are consistent with the experimental spectra. For the rhombohedral and orthorhombic polymers, the T-1u(2)-derived mode that is polarized along the bonding direction is calculated to downshift below any T-1u(1)-derived modes. We also identify a previously unassigned feature near 610 cm(-1) in all three systems as a widely split or shifted mode derived from various silent IhC60 vibrations, confirming a strong perturbation model for these linked fullerene structures

Cooling atoms in an optical trap by selective parametric excitation

We demonstrate the possibility of energy-selective removal of cold atoms from a tight optical trap by means of parametric excitation of the trap vibrational modes. Taking advantage of the anharmonicity of the trap potential, we selectively remove the most energetic trapped atoms or excite those at the bottom of the trap by tuning the parametric modulation frequency. This process, which had been previously identified as a possible source of heating, also appears to be a robust way for forcing evaporative cooling in anharmonic traps.Comment: 5 pages, 5 figure

Obesity, oxidative DNA damage and vitamin D as predictors of genomic instability in children and adolescents

Background/objectives Epidemiological evidence indicates obesity in childhood and adolescence to be an independent risk factor for cancer and premature mortality in adulthood. Pathological implications from excess adiposity may begin early in life. Obesity is concurrent with a state of chronic inflammation, a well-known aetiological factor for DNA damage. In addition, obesity has been associated with micro-nutritional deficiencies. Vitamin D has attracted attention for its anti-inflammatory properties and role in genomic integrity and stability. The aim of this study was to determine a novel approach for predicting genomic instability via the combined assessment of adiposity, DNA damage, systemic inflammation, and vitamin D status. Subjects/methods We carried out a cross-sectional study with 132 participants, aged 10–18, recruited from schools and paediatric obesity clinics in London. Anthropometric assessments included BMI Z-score, waist and hip circumference, and body fat percentage via bioelectrical impedance. Inflammation and vitamin D levels in saliva were assessed by enzyme-linked immunosorbent assay. Oxidative DNA damage was determined via quantification of 8-hydroxy-2′-deoxyguanosine in urine. Exfoliated cells from the oral cavity were scored for genomic instability via the buccal cytome assay. Results As expected, comparisons between participants with obesity and normal range BMI showed significant differences in anthropometric measures (p < 0.001). Significant differences were also observed in some measures of genomic instability (p < 0.001). When examining relationships between variables for all participants, markers of adiposity positively correlated with acquired oxidative DNA damage (p < 0.01) and genomic instability (p < 0.001), and negatively correlated with vitamin D (p < 0.01). Multiple regression analyses identified obesity (p < 0.001), vitamin D (p < 0.001), and oxidative DNA damage (p < 0.05) as the three significant predictors of genomic instability. Conclusions Obesity, oxidative DNA damage, and vitamin D deficiency are significant predictors of genomic instability. Non-invasive biomonitoring and predictive modelling of genomic instability in young patients with obesity may contribute to the prioritisation and severity of clinical intervention measures

Carotenoid-based skin ornaments reflect foraging propensity in a seabird, Sula leucogaster

Carotenoid-based ornaments are common signalling features in animals. It has long been proposed that such ornaments communicate information about foraging abilities to potential mates. However, evidence linking foraging with ornamentation is largely missing from unmanipulated, free-ranging populations. To investigate this relationship, we studied a coastal population of brown booby (Sula leucogaster brewsteri), a seabird with a carotenoid-based gular skin ornament. δ13C values from both feathers and blood plasma were negatively correlated with male gular colour, indicating birds that consumed more pelagic prey in offshore locations had more ornamented skin than those that fed on nearshore, benthic prey. This relationship was supported by our GPS tracking results, which revealed longer, more offshore foraging trips among highly ornamented males. Our data show that brown booby ornaments are honest indicators of foraging propensity; a link consistent with the rarity hypothesis and potentially driven by the concentration of carotenoids found in phytoplankton versus benthic algae. Carotenoid-based ornaments may reflect foraging tendencies in animals such as coastal predators that use food webs with distinct carotenoid profiles

Size-structured populations: immigration, (bi)stability and the net growth rate

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net reproduction function. In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero, i.e. when linearisation does not decide stability. This allows us to demonstrate, through a concrete example, how immigration might be beneficial to the population. In particular, we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates. In fact, the linearised system exhibits bistability, for a certain range of values of the external inflow, induced potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin

Evaluation of pyrolysis chars derived from marine macroalgae silage as soil amendments

Sections PDFPDF Tools Share Abstract Pyrolysis char residues from ensiled macroalgae were examined to determine their potential as growth promoters on germinating and transplanted seedlings. Macroalgae was harvested in May, July and August from beach collections, containing predominantly Laminaria digitata and Laminaria hyperborea ; naturally seeded mussel lines dominated by Saccharina latissima ; and lines seeded with cultivated L. digitata . Material was ensiled, pressed to pellets and underwent pyrolysis using a thermo‐catalytic reforming (TCR) process, with and without additional steam. The chars generated were then assessed through proximate and ultimate analysis. Seasonal changes had the prevalent impact on char composition, though using mixed beach‐harvested material gave a greater variability in elements than when using the offshore collections. Applying the char at 5% (v/v)/2% (w/w) into germination or seedling soils was universally negative for the plants, inhibiting or delaying all parameters assessed with no clear advantage in harvesting date, species or TCR processing methodology. In germinating lettuce seeds, soil containing the pyrolysis chars caused a longer germination time, poorer germination, fewer true leaves to be produced, a lower average plant health score and a lower final biomass yield. For transplanted ryegrass seedlings, there were lower plant survival rates, with surviving plants producing fewer leaves and tillers, lower biomass yields when cut and less regrowth after cutting. As water from the char‐contained plant pots inhibited the lettuce char control, one further observation was that run‐off water from the pyrolysis char released compounds which detrimentally affected cultivated plant growth. This study clearly shows that pyrolysed macroalgae char does not fit the standard assumption that chars can be used as soil amendments at 2% (w/w) addition levels. As the bioeconomy expands in the future, the end use of residues and wastes from bioprocessing will become a genuine global issue, requiring consideration and demonstration rather than hypothesized use

BIO Logical Agents: Norms, Beliefs, Intentions in Defeasible Logic

In this paper we follow the BOID (Belief, Obligation, Intention, Desire) architecture to describe agents and agent types in Defeasible Logic. We argue, in particular, that the introduction of obligations can provide a new reading of the concepts of intention and intentionality. Then we examine the notion of social agent (i.e., an agent where obligations prevail over intentions) and discuss some computational and philosophical issues related to it. We show that the notion of social agent either requires more complex computations or has some philosophical drawbacks