Symbolic parametrization of curves

If algebraic varieties like curves or surfaces are to be manipulated by computers, it is essential to be able to represent these geometric objects in an appropriate way. For some applications an implicit representation by algebraic equations is desirable, whereas for others an explicit or parametric representation is more suitable. Therefore, transformation algorithms from one representation to the other are of utmost importance.We investigate the transformation of an implicit representation of a plane algebraic curve into a parametric representation. Various methods for computing a rational parametrization, if one exists, are described. As a new idea we introduce the concept of working with classes of conjugate (singular or simple) points on curves. All the necessary operations, like determining the multiplicity and the character of the singular points or passing a linear system of curves through these points, can be applied to such classes of conjugate points. Using this idea one can parametrize a curve if one knows only one simple point on it. We do not propose any new method for finding such a simple point. By classical methods a rational point on a rational curve can be computed, if such a point exists. Otherwise, one can express the coordinates of such a point in an algebraic extension of degree 2 over the ground field.     

Providing security and fault tolerance in P2P connections between clouds for mHealth services

The mobile health (mHealth) and electronic health (eHealth) systems are useful to maintain a correct administration of health information and services. However, it is mandatory to ensure a secure data transmission and in case of a node failure, the system should not fall down. This fact is important because several vital systems could depend on this infrastructure. On the other hand, a cloud does not have infinite computational and storage resources in its infrastructure or would not provide all type of services. For this reason, it is important to establish an interrelation between clouds using communication protocols in order to provide scalability, efficiency, higher service availability and flexibility which allow the use of services, computing and storage resources of other clouds. In this paper, we propose the architecture and its secure protocol that allows exchanging information, data, services, computing and storage resources between all interconnected mHealth clouds. The system is based on a hierarchic architecture of two layers composed by nodes with different roles. The routing algorithm used to establish the connectivity between the nodes is the shortest path first (SPF), but it can be easily changed by any other one. Our architecture is highly scalable and allows adding new nodes and mHealth clouds easily, while it tries to maintain the load of the cloud balanced. Our protocol design includes node discovery, authentication and fault tolerance. We show the protocol operation and the secure system design. Finally we provide the performance results in a controlled test bench.     

Linear complete differential resultants and the implicitization of linear DPPEs

The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of n$n$ linear differential polynomial parametric equations in n−1$n-1$ differential parameters. We give necessary conditions to ensure properness of the system of differential polynomial parametric equations.     

Radical parametrizations of algebraic curves by adjoint curves

We present algorithms for parametrizing by radicals an irreducible curve, not necessarily plane, when the genus is less than or equal to 4 and the curve is defined over an algebraically closed field of characteristic zero. In addition, we also present an algorithm for parametrizing by radicals any irreducible plane curve of degree d having at least a point of multiplicity d−r, with 1≤r≤4 and, as a consequence, every irreducible plane curve of degree d≤5 and every irreducible singular plane curve of degree 6.     

Identification of New Coloured Anthocyanin–Flavanol Adducts in Pressure-Extracted Pomegranate (<Emphasis Type="BoldItalic">Punica granatum</Emphasis> L.) Juice by High-Performance Liquid Chromatography/Electrospray Ionization Mass Spectrometry

Pomegranate (Punica granatum L.) juice, obtained by pressure extraction of the whole fruit, contains coloured flavanol–anthocyanin adducts (the flavanol occupies the upper part of the dimmer) from the direct condensation between anthocyanidins delphinidin, cyanidin and pelargonidin and flavan-3-ols (epi)gallocatechin, (epi)catechin and (epi)afzelechin. The presence of adducts between these same flavanols and anthocyanidins, but belonging to the coloured anthocyanin–flavanol adduct type (anthocyanin occupies the upper part of the dimmer) has been revealed by reversed-phase liquid chromatography coupled to tandem mass spectrometry (ion trap), with positive electrospray ionization (LC–ESI/MS ⁿ ). These new adducts are isotopic with their corresponding counterparts (flavanol–anthocyanin adducts) and indistinguishable from them by comparison of the mass spectra from the MS² of the isotopic parent ions. However, they can be distinguished by comparison of the mass spectra from the MS³ of their corresponding isotopic aglycons. Hence, the MS³ of the aglycon from a given flavanol–anthocyanin adduct always yields a mass spectrum containing five characteristic ions, the three with smaller m/z being only dependent on the anthocyanidin and the other two on both the anthocyanidin and the flavanol. In contrast, the mass spectrum from the MS³ of the aglycon of its counterpart anthocyanin–flavanol adduct gives only two of the above five characteristic ions, where the ion with smaller m/z only depends on the anthocyanidin and the other on both the anthocyanidin and the flavanol. Ten 3-hexoside derivatives of coloured anthocyanin–flavanol adducts were detected in pomegranate juice being reported for the first time this type of adducts from a natural source.     

“Arbequina” Olive Oil Composition Is Affected by the Application of Regulated Deficit Irrigation during Pit Hardening Stage

Three new regulated deficit irrigation (RDI) treatments were applied to “Arbequina” olive orchards during pit hardening. Oil quality was determined by measuring analytical parameters for olive oil grading, antioxidant activity, total phenol content, fatty acid profile, volatile compounds profile, and sensory analysis. Oils from RDI were classified as “extra virgin olive oil” and their quality was improved due to their higher antioxidant potential (ABTS⁺ [increased ~75%] and DPPH^˙ [increased ~25%] assays) and phenols (increased ~53%) than control. Concentration of total volatile compounds decreased (~27%) but RDI olive oils showed a more balanced profile (alcohols, aldehydes, and esters). Monounsaturated fatty acid content increased (~5%) and atherogenic and thrombogenic indexes decreased (~8.5%) in RDI olive oil. Regarding sensory analysis, RDI provided more balanced oils with higher fruit aroma than control. Other benefits of RDI olive oil, when compared with oil from full irrigated orchards are reduced use of water and improved functional and sensory quality.     

Information content of the kernel matrix for the phase function retrieval problem

We investigate the information content of the radiation measurements to be used in the retrieval of the scattering properties of the atmosphere with the perturbation technique that we previously introduced. Applying this technique to different sets of data, we obtained solutions with varying accuracy. An analysis of these solutions shows that selecting linearly independent data in directions corresponding to small values of the scattering angle increases the number of pieces of information. (This result is in accord with conclusions reached by other researchers, based on a variety of criteria.) This information content should be largely independent of the method or methods employed to perform the inversion procedure.