Symmetries of Helmholtz forms and globally variational dynamical forms

Invariance properties of classes in the variational sequence suggested to Krupka et al. the idea that there should exist a close correspondence between the notions of variationality of a differential form and invariance of its exterior derivative. It was shown by them that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form, so that the latter is locally the Euler--Lagrange form of a Lagrangian. We show that the corresponding local system of Euler--Lagrange forms is variationally equivalent to a global Euler--Lagrange form.Comment: Presented at QTS7 - Quantum Theory and Symmetries VII, Prague 7-13/08/201

The Prolongation Problem for the Heavenly Equation

We provide an exact regular solution of an operator system arising as the prolongation structure associated with the heavenly equation. This solution is expressed in terms of operator Bessel coefficients.Comment: 9 pages, Proc. SIGRAV Conference (Bari 1998

Integrable nonlinear field equations and loop algebra structures

We apply the (direct and inverse) prolongation method to a couple of nonlinear Schr{\"o}dinger equations. These are taken as a laboratory field model for analyzing the existence of a connection between the integrability property and loop algebras. Exploiting a realization of the Kac-Moody type of the incomplete prolongation algebra associated with the system under consideration, we develop a procedure with allows us to generate a new class of integrable nonlinear field equations containing the original ones as a special case.Comment: 13 pages, latex, no figures

The Lie derivative of spinor fields: theory and applications

Starting from the general concept of a Lie derivative of an arbitrary differentiable map, we develop a systematic theory of Lie differentiation in the framework of reductive G-structures P on a principal bundle Q. It is shown that these structures admit a canonical decomposition of the pull-back vector bundle i_P^*(TQ) = P\times_Q TQ over P. For classical G-structures, i.e. reductive G-subbundles of the linear frame bundle, such a decomposition defines an infinitesimal canonical lift. This lift extends to a prolongation Gamma-structure on P. In this general geometric framework the concept of a Lie derivative of spinor fields is reviewed. On specializing to the case of the Kosmann lift, we recover Kosmann's original definition. We also show that in the case of a reductive G-structure one can introduce a "reductive Lie derivative" with respect to a certain class of generalized infinitesimal automorphisms, and, as an interesting by-product, prove a result due to Bourguignon and Gauduchon in a more general manner. Next, we give a new characterization as well as a generalization of the Killing equation, and propose a geometric reinterpretation of Penrose's Lie derivative of "spinor fields". Finally, we present an important application of the theory of the Lie derivative of spinor fields to the calculus of variations.Comment: 28 pages, 1 figur

Cryotomography of budding influenza a virus reveals filaments with diverse morphologies that mostly do not bear a genome at their distal end

Influenza viruses exhibit striking variations in particle morphology between strains. Clinical isolates of influenza A virus have been shown to produce long filamentous particles while laboratory-adapted strains are predominantly spherical. However, the role of the filamentous phenotype in the influenza virus infectious cycle remains undetermined. We used cryo-electron tomography to conduct the first three-dimensional study of filamentous virus ultrastructure in particles budding from infected cells. Filaments were often longer than 10 microns and sometimes had bulbous heads at their leading ends, some of which contained tubules we attribute to M1 while none had recognisable ribonucleoprotein (RNP) and hence genome segments. Long filaments that did not have bulbs were infrequently seen to bear an ordered complement of RNPs at their distal ends. Imaging of purified virus also revealed diverse filament morphologies; short rods (bacilliform virions) and longer filaments. Bacilliform virions contained an ordered complement of RNPs while longer filamentous particles were narrower and mostly appeared to lack this feature, but often contained fibrillar material along their entire length. The important ultrastructural differences between these diverse classes of particles raise the possibility of distinct morphogenetic pathways and functions during the infectious process

Musculoskeletal Physical Therapy During the COVID-19 Pandemic: Is Telerehabilitation the Answer?

The coronavirus disease 2019 (COVID-19) pandemic has induced worldwide governments to adopt severe rules limiting individual freedom and imposing social distancing (eg, closing school, mandatory quarantine, restricting entertainments)1 in order to prevent the collapse of national health care systems. In addition to the goal of reducing the COVID-19 pandemic, this paradigm shift brings a different allocation of resources within diagnosis-related groups toward high-intensity levels of care (eg, intensive care units) needed for patients suffering of severe COVID-19. Although these measures are necessary in this pandemic, they constitute a barrier for health care professionals who are usually in close contact with patients needing low-intensity care, such as musculoskeletal (MSK) physical therapists

Carbon sequestration in a Mediterranean olive orchard managed sustainably over a 20-year period

Olive is a widespread crop within Mediterranean area and Italy is one of the biggest producer of olives and oil in the world. From an environmental point of view, centered on carbon (C) sequestration, managing olive orchards sustainably is an urgent and actual issue. This trial was done in a 2-ha olive orchard (Olea europaea L., cv. ‘Maiatica’; 70-year-old plants, with a distance of 8 × 8 m and NE orientation) located in Ferrandina (Southern Italy, Basilicata region; N 40°29’; E 16°28’). The soil is a sandy loam (Haplic Calcisol - WRB), with a mean bulk density of 1.30 g cm–3 and sediment as parental material. The major landform is plain, the slope form is classified as convex-straight and the gradient class as gently sloping (2-5%). Half of the orchard has been managed using sustainable agricultural practices (sustainable management, Sung) for 20 years (2000-2020). Trees were drip-irrigated from March to October with urban wastewater. A light pruning was carried out every year during winter. The soil was permanently covered by spontaneous self-seeding weeds, mowed twice a year. Cover crop residues and prunings were shredded and left along the row as mulch. The other half of the orchard was kept as ‘control’ plot. It was rainfed and conducted with a locally conventional management (Cmng), according to the practices usually adopted by farmers. The Cmng was managed by tillage performed 2-3 times per year to control weeds. Intensive pruning was carried out every two years, but pruned residues were removed from the orchard. A mineral fertilization was carried out once per year, during the fruit set and pit hardening phase (early spring). The average value (n = 5; 0-100 cm soil depth) of baseline soil organic carbon (SOC) stock (related to the Cmng) in the 20-year period was 4.79 t SOC ha–1, with an average additional SOC storage potential because of the adoption of the Smng of 0.15 t SOC ha–1 yr–1, and a SOC stock after 20 years of Smng of 7.75 t SOC ha–1 yr–1. In the Smng system, soil acted as a significant sink for C, especially due to the supplies of the organic resources internal to the system. The Smng system, made up of mature olive trees, was also able to fix in its aboveground and belowground components, a > 2-times higher total amount of C than the Cmng. Spontaneous vegetation was the most important pool, sequestering about 35% of the total fixed C. Also pruning material had a substantial importance in C fixation. Emissions of CO2 eq per kg of olives, calculated according to the Life Cycle Assessment (LCA), were 0.08 kg in the Smng system and 0.11 kg in the Cmng system. Besides C sequestration, the application of the Smng markedly improved physical, chemical, and biological soil fertility, with benefits on plants and production. The application of a sustainable soil and plant management makes olive growing a multifunctional rural activity, not only aimed at production, but including many other objectives, such as environmental, landscaping cultural, social and recreational