The symmetries of octupolar tensors

Octupolar tensors are third order, completely symmetric and traceless tensors. Whereas in 2D an octupolar tensor has the same symmetries as an equilateral triangle and can ultimately be identified with a vector in the plane, the symmetries that it enjoys in 3D are quite different, and only exceptionally reduce to those of a regular tetrahedron. By use of the octupolar potential that is, the cubic form associated on the unit sphere with an octupolar tensor, we shall classify all inequivalent octupolar symmetries. This is a mathematical study which also reviews and incorporates some previous, less systematic attempts

Assessment of production and qualitative characteristics of different populations of Salvia sclarea L. found in Sicily (Italy)

Salvia sclarea L. is an important industrial crop, valued for its herbal-aromatic properties and high quality essential oils, that is used in food, pharmaceuticals and cosmetics. In this study, carried out from 2009 to 2010, the morphological and production characteristics and essential oil content and composition of three Sicilian populations were studied. In particular, the composition of essential oils extracted from primary and secondary inflorescences using steam distillation was assessed. Morphological, production and qualitative data from the three populations were subjected to analysis of variance and cluster analysis. Regarding the quality of the oils, only the most prevalent compounds were taken into consideration in this study. The three populations were linalyl acetate/ linalool chemotypes. Highly significant variations were found for the effective local population and inflorescence type in the composition of the essential oil principal components. In particular, the primary inflorescences were found to be accumulation sites favoured by monoterpenes, and secondary inflorescences were favoured by sesquiterpenes and sclareol. Populations “S. Stefano Quisquina” and “Alcara Li Fusi” performed best on a morphological and production level, whereas populations “Prizzi”and “Alcara Li Fusi” performed best in terms of quality. Population “S. Stefano Quisquina” produced high levels of sclareol. Biotype selection from within the populations should be based on both morphological, production and quality analyses

Four-year study on the bio-agronomic response of biotypes of Capparis spinosa L. on the island of Linosa (Italy)

The caper plant is widespread in Sicily (Italy) both wild in natural habitats and as specialized crops, showing considerable morphological variation. However, although contributing to a thriving market, innovation in caper cropping is low. The aim of the study was to evaluate agronomic and production behavior of some biotypes of Capparis spinosa L. subsp. rupestris, identified on the Island of Linosa (Italy) for growing purposes. Two years and seven biotypes of the species were tested in a randomized complete block design. The main morphological and production parameters were determined. Phenological stages were also observed. Analysis of variance showed high variability between the biotypes. Principal component analysis and cluster analysis highlighted a clear distinction between biotypes based on biometric and production characteristics. Production data collected in the two-year period 2007–2008 showed the greatest production levels in the third year following planting in 2005. In particular, biotype SCP1 had the highest average value (975.47 g) of flower bud consistency. Our results permitted the identification of biotypes of interest for the introduction into new caper fields. Further research is needed in order to characterize caper biotypes in terms of the chemical composition of the flower buds and fruits

Drug-eluting balloons for the treatment of the superficial femoral artery in-stent restenosis: 2-year follow-up.

OBJECTIVES: The aim of this prospective registry was to evaluate the safety and efficacy at 2-year follow-up of the use of drug-eluting balloons (DEBs) for the treatment of superficial femoral artery (SFA) in-stent restenosis (ISR). BACKGROUND: The use of DEBs for the treatment of SFA ISR is associated with a satisfactory primary patency rate at 1 year, but no data are available for longer follow-up. Unfortunately, when DEBs were used to treat SFA de novo lesions, the occurrence of restenosis increased by 50% between the first and the second years of follow-up. METHODS: From December 2009 to December 2010, 39 consecutive patients underwent percutaneous transluminal angioplasty of SFA ISR at our institution (Clinica Montevergine, Mercogliano, Italy). All patients underwent conventional SFA percutaneous transluminal angioplasty and final post-dilation with paclitaxel-eluting balloons (IN.PACT, Medtronic Inc., Minneapolis, Minnesota). Patients were evaluated for up to 24 months. RESULTS: During follow-up, 1 patient died of heart failure and another of sudden death, for a 2-years rate of cardiovascular mortality rate of 5.12 %. The primary patency rate at 2 years was 70.3% (11 of 37 patients experienced restenosis recurrence at 2-year follow-up). The treatment of complex ISR lesions (classes II and III) was associated with an increased rate of recurrent restenosis compared with class I (33.3 % and 36.3 % vs. 12.5%; p = 0.05). CONCLUSIONS: The data suggest that adjunctive use of DEBs for the treatment of SFA ISR is a safe and effective therapeutic strategy up to 2 years of follow-up

The Symmetries of Octupolar Tensors

Octupolar tensors are third order, completely symmetric and traceless tensors.Whereas in 2D an octupolar tensor has the same symmetries as an equilateral triangle andcan ultimately be identified with a vector in the plane, the symmetries that it enjoys in 3D arequite different, and only exceptionally reduce to those of a regular tetrahedron. By use of theoctupolar potential, that is, the cubic form associated on the unit sphere with an octupolartensor, we shall classify all inequivalent octupolar symmetries. This is a mathematical studywhich also reviews and incorporates some previous, less systematic attempts

Timo

Il genere Thymus appartiene alla famiglia delle Lamiacaee e comprende numerose specie distribuite nell’area mediterranea. Il nome deriva dal greco “δίμοσ” (profumo) per sottolineare l’intenso e gradevole aroma che la pianta produce. Secondo altri autori il nome trae origine dalla parola egiziana “tham”, che si riferisce ad una pianta profumata usata per le imbalsamazioni. In Italia il Pignatti descrive 17 specie di timo, delle quali quelle maggiormente interessanti da un punto di vista erboristico sono: T. vulgaris L. (timo comune), T. capitatus (L.) Hoffman et Link (timo capitato), T. serpyllum L. (timo serpillo) e T. zygis L. (timo rosso). Allo stato spontaneo sono presenti varie forme di timo, differenti, oltre che per le caratteristiche morfologiche, anche per la variabilità nella composizione degli oli essenziali. Sulla base delle caratteristiche degli oli vengono generalmente classificati 7 chemiotipi di timo, non interamente riconosciuti dalla F.U. Il timo è una specie tipica degli ambienti caldo-temperati mediterranei, ma è presente anche nelle zone orientali dell’Europa e nel centro-sud dell’arcipelago delle Baleari. In Italia, si trova allo stato spontaneo lungo le zone costiere, nelle pendici assolate e rocciose e in luoghi aridi in prossimità del mare. Si ritrova in ambienti con altitudine variabile da 0 a 1.500 metri s.l.m.

A review on octupolar tensors

In its most restrictive definition, an octupolar tensor is a fully symmetric traceless third-rank tensor in three space dimensions. So great a body of works have been devoted to this specific class of tensors and their physical applications that a review would perhaps be welcome by a number of students. Here, we endeavour to place octupolar tensors into a broader perspective, considering non-vanishing traces and non-fully symmetric tensors as well. A number of general concepts are recalled and applied to either octupolar and higher-rank tensors. As a tool to navigate the diversity of scenarios we envision, we introduce the octupolar potential, a scalar-valued function which can easily be given an instructive geometrical representation. Physical applications are plenty; those to liquid crystal science play a major role here, as they were the original motivation for our interest in the topic of this review