Quaternionic integrable systems

Standard (Arnold-Liouville) integrable systems are intimately related to complex rotations. One can define a generalization of these, sharing many of their properties, where complex rotations are replaced by quaternionic ones. Actually this extension is not limited to the integrable case: one can define a generalization of Hamilton dynamics based on hyperKahler structures.Comment: 10 pages. To appear in the proceedings of the SPT2002 conference, edited by S. Abenda, G. Gaeta and S. Walcher, World Scientifi

Michel theory of symmetry breaking and gauge theories

We extend Michel's theorem on the geometry of symmetry breaking [L. Michel, {\it Comptes Rendus Acad. Sci. Paris} {\bf 272-A} (1971), 433-436] to the case of pure gauge theories, i.e. of gauge-invariant functionals defined on the space ${\cal C}$ of connections of a principal fiber bundle. Our proof follows closely the original one by Michel, using several known results on the geometry of ${\cal C}$. The result (and proof) is also extended to the case of gauge theories with matter fields.Comment: 24 pages. An old paper posted for archival purpose

On the geometry of lambda-symmetries, and PDEs reduction

We give a geometrical characterization of $\lambda$-prolongations of vector fields, and hence of $\lambda$-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal one-form $\mu$, and we speak of $\mu$-prolongations of vector fields and $\mu$-symmetries of PDEs. We show that these are as good as standard symmetries in providing symmetry reduction of PDEs and systems, and explicit invariant solutions

Weierstrass's criterion and compact solitary waves

Weierstrass's theory is a standard qualitative tool for single degree of freedom equations, used in classical mechanics and in many textbooks. In this Brief Report we show how a simple generalization of this tool makes it possible to identify some differential equations for which compact and even semicompact traveling solitary waves exist. In the framework of continuum mechanics, these differential equations correspond to bulk shear waves for a special class of constitutive laws.Comment: 4 page

Pancreatic cystosis in cystic fibrosis. Sometimes a bike ride can help you decide

Pancreatic cystosis (PC) is an uncommon manifestation of pancreas involvement in cystic fibrosis (CF), characterized by the presence of multiple macrocysts partially or completely replacing pancreas. Only few reports are available from literature and management (surgery vs follow up) is commonly based on the presence of symptoms or complications due to local mass effect, although evidence-based recommendations are still not available. We here report the case of a young adult CF patient with PC, in which cardiopulmonary exercise testing (CPET) provided important information to be integrated to the radiological finding of inferior vena cava compression by the multicystic pancreas complex. Through the analysis of oxygen kinetic cardiodynamic phase pattern, CPET may be helpful to safely exclude significant mass effects on blood venous return and to improve the decision-making process on whether to consider surgery or not in patients with PC

Innovative Soil Management and Micro-Climate Modulation for Saving Water in Peach Orchards

Microclimatic and soil management studies emphasize that roofing above the canopy or soil mulching contributes to reduce water losses from horticultural cropping systems and, at the same time, to increase water use efficiency. The aim of this 2-year on-farm study, carried out on a late ripening peach (cv. California) orchard, was to investigate the combined effect of water supply (full or deficit irrigation, DI), incoming light (hail or shading net), and soil management (tilling or mulching) on: microclimate; fruit growth; yield; irrigation water use productivity (WPI); and soil water stress coefficient (Ks). Shading hail net reduced air temperature (−1°C), wind speed (−57%), solar radiation (−32%), while increased relative air humidity (+9.5%). Compared to the control treatment (hail net coverage, soil tillage, and full irrigation), the innovative management (DI + shading hail net + mulching) reduced seasonal volumes of irrigation water (−25%) and increased both final yield (+36%) and WPI (+53%). Saving water resources without losing yield is an achievable goal by peach orchards growing under the Mediterranean climate if the DI agro-technique is adopted conjointly with shading hail net and soil mulching

Local and nonlocal solvable structures in ODEs reduction

Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable structures even though finding them in general could be a very difficult task. In practice a noteworthy simplification may come by computing solvable structures which are adapted to some admitted symmetry algebra. In this paper we consider solvable structures adapted to local and nonlocal symmetry algebras of any order (i.e., classical and higher). In particular we introduce the notion of nonlocal solvable structure

Orchard floor management affects tree functionality, productivity and water consumption of a late ripening peach orchard under semi-arid conditions

Semi-arid conditions are favorable for the cultivation of late ripening peach cultivars; however, seasonal water scarcity and reduction in soil biological fertility, heightened by improper soil management, are jeopardizing this important sector. In the present two-year study, four soil managements were compared on a late ripening peach orchard: (i) completely tilled (control); (ii) mulched with reusable reflective plastic film; (iii) mulching with a Leguminosae cover-crop flattened after peach fruit set; (iv) completely tilled, supplying the water volumes of the plastic mulched treatment, supposed to be lower than the control. Comparison was performed for soil features, water use, tree functionality, fruit growth, fruit quality, yield and water productivity. Even receiving about 50% of the regular irrigation, reusable reflective mulching reduced water loss and soil carbon over mineralization, not affecting (sometimes increasing) net carbon assimilation, yield, and fruit size and increasing water productivity. The flattening technique should be refined in the last part of the season as in hot and dry areas with clay soils and low organic matter, soil cracking increased water evaporation predisposing the orchard at water stress. The development and implementation of appropriate soil management strategies could be pivotal for making peach production economically and environmentally sustainable

On the relation between standard and μ\mu-symmetries for PDEs

We give a geometrical interpretation of the notion of $\mu$-prolongations of vector fields and of the related concept of $\mu$-symmetry for partial differential equations (extending to PDEs the notion of $\lambda$-symmetry for ODEs). We give in particular a result concerning the relationship between $\mu$-symmetries and standard exact symmetries. The notion is also extended to the case of conditional and partial symmetries, and we analyze the relation between local $\mu$-symmetries and nonlocal standard symmetries.Comment: 25 pages, no figures, latex. to be published in J. Phys.