Solution of a quadratic quaternion equation with mixed coefficients

A comprehensive analysis of the morphology of the solution space for a special type of quadratic quaternion equation is presented. This equation, which arises in a surface construction problem, incorporates linear terms in a quaternion variable and its conjugate with right and left quaternion coefficients, while the quadratic term has a quaternion coefficient placed between the variable and its conjugate. It is proved that, for generic coefficients, the equation has two, one, or no solutions, but in certain special instances the solution set may comprise a circle or a 3-sphere in the quaternion space $\mathbb{H}$. The analysis yields solutions for each case, and intuitive interpretations of them in terms of the four-dimensional geometry of the quaternion space $\mathbb{H}$.Comment: 19 pages, to appear in the Journal of Symbolic Computatio

Zeros of slice functions and polynomials over dual quaternions

This work studies the zeros of slice functions over the algebra of dual quaternions and it comprises applications to the problem of factorizing motion polynomials. The class of slice functions over an alternative $*$-algebra $A$ was defined by Ghiloni and Perotti in 2011, extending the class of slice regular functions introduced by Gentili and Struppa in 2006. Both classes strictly include the polynomials over $A$. We focus on the case when $A$ is the algebra of dual quaternions $\mathbb{DH}$. The specific properties of this algebra allow a full characterization of the zero sets, which is not available over general alternative $*$-algebras. This characterization sheds some light on the study of motion polynomials over $\mathbb{DH}$, introduced by Heged\"us, Schicho, and Schr\"ocker in 2013 for their relevance in mechanism science.Comment: 37 pages, to appear in Trans. Amer. Math. So

An Experience on Environmental Education based on Respect-Reduce-Reuse-Recycle in a Village Primary School in the Marche Region, in Italy

T he importance of environmental educatio n is widely recognized worldwide: an important objective is that the citizens are accustomed to apply the best available practices in their life , while ask ing the administration and the government to gradually enforce measures lead ing to a reduction of the environmental impact and to a more sustainable lifestyle. This requires a formation starting at an early age: however, in Italy the relevant indications from the National Curriculum are still limited and do not suggest explicitly the performance of any pr actical activity , tailored on the specific school setting . This inadequacy of the Curriculum becomes particularly apparent in cases where other concerns are present, for example the areas in the Marche region affected by the 2016 earthquake : here, the need to resum e a day by day routine put a kind of \u201cdamper\u201d on other questions, such as environmental issues . This had an effect also i n children\u2019s life on this question, school needs to take a stand , which is the objective of this study . This work concerns an approach to environmental education in a multi classes primary school context (age 6 10) in a small village school, located in the Central Apennine in Italy. This is performed through an experience carried out by investigating the behavior towards waste p roduction of the community, as perceived by children at school. It is therefore articulated through the application of 4R (Respect, which encompasses Reduce, Reuse and Recycle) applying and extending the indications from the Italian National Curriculum. Th e project leads also to an experience of self production of objects by the use of waste, to improve their awareness of the possibilities included in their upcycling. Feedback on the experience is finally acquired from the children and discussed, especially in the sense of creating future citizens with a more sensible and reasonable behavior towards the environment and leading possibly to zero waste strategies in their family and work setting. The data were analy z ed using thematic analysis and different them es about waste production were singled out

An Experience on Environmental Education Based on Respect-Reduce-Reuse-Recycle in a Village Primary School in the Marche Region, in Italy

The importance of environmental education is widely recognized worldwide: an important objective is that the citizens are accustomed to apply the best available practices in their life, while asking the administration and the government to gradually enforce measures leading to a reduction of the environmental impact and to a more sustainable lifestyle. This requires a formation starting at an early age: however, in Italy the relevant indications from the National Curriculum are still limited and do not suggest explicitly the performance of any practical activity, tailored on the specific school setting. This inadequacy of the Curriculum becomes particularly apparent in cases where other concerns are present, for example the areas in the Marche region affected by the 2016 earthquake: here, the need to resume a day-by-day routine put a kind of “damper” on other questions, such as environmental issues. This had an effect also in children’s life: on this question, school needs to take a stand, which is the objective of this study. This work concerns an approach to environmental education in a multi-classes primary school context (age 6-10) in a small village school, located in the Central Apennine in Italy. This is performed through an experience carried out by investigating the behavior towards waste production of the community, as perceived by children at school. It is therefore articulated through the application of 4R (Respect, which encompasses Reduce, Reuse and Recycle) applying and extending the indications from the Italian National Curriculum. The project leads also to an experience of self-production of objects by the use of waste, to improve their awareness of the possibilities included in their upcycling. Feedback on the experience is finally acquired from the children and discussed, especially in the sense of creating future citizens with a more sensible and reasonable behavior towards the environment and leading possibly to zero-waste strategies in their family and work setting. The data were analyzed using thematic analysis and different themes about waste production were singled out

Minkowski products of unit quaternion sets

The Minkowski product of unit quaternion sets is introduced and analyzed, motivated by the desire to characterize the overall variation of compounded spatial rotations that result from individual rotations subject to known uncertainties in their rotation axes and angles. For a special type of unit quaternion set, the spherical caps of the 3-sphere $S^3$ in $\mathbb{R}^4$, closure under the Minkowski product is achieved. Products of sets characterized by fixing either the rotation axis or rotation angle, and allowing the other to vary over a given domain, are also analyzed. Two methods for visualizing unit quaternion sets and their Minkowski products in $\mathbb{R}^3$ are also discussed, based on stereographic projection and the Lie algebra formulation. Finally, some general principles for identifying Minkowski product boundary points are discussed in the case of full-dimension set operands.Comment: 29 pages, 1 figur

Defoliation of common ragweed by Ophraella communa beetle does not affect pollen allergenicity in controlled conditions

Ragweed allergy is one of the primary causes of seasonal allergies in Europe and its prevalence is expected to rise. The leaf beetle Ophraella communa, recently and accidentally established in N-Italy and S-Switzerland, represents a promising approach to control ragweed, but negative side effects should be excluded before its use. Since biotic and abiotic stresses are known to influence the allergenicity of pollen, we set out to assess the effect of sub-lethal defoliation by O. communa on the quantity and quality of ragweed pollen. Seventeen sister pairs (including six clones) of ragweed plants were grown in controlled conditions. One of each pair was exposed to O. communa as soon as the plant started to produce reproductive structures. After 10 weeks of exposure, plant traits were measured as a proxy for pollen quantity. Pollen quality was assessed by measuring its viability and allergenicity. Generally, plants produced very few male flowers and little amount of pollen. Damage by the beetle was severe with most of the leaf tissue removed, but no treatment effect was found on any of the quantitative and qualitative traits assessed. In conclusion, O. communa did not increase the amount or allergenicity of ragweed pollen grains in our experimental conditions

Schur functions and their realizations in the slice hyperholomorphic setting

we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization in terms of the associated de Branges-Rovnyak space

Corrigendum: Synergistic exploitation of hyper- and multi-spectral precursor sentinel measurements to determine phytoplankton functional types (SynSenPFT) [Front. Mar. Sci,(203),4] DOI: 10.3389/fmars.2017.00203

This is the final version. Available on open access from Frontiers Media via the DOI in this recordThe article to which this is the corrigendum is in ORE at http://hdl.handle.net/10871/38250In the original article, we neglected, but would like to acknowledge the North-German Supercomputing Alliance (HLRN) for providing HPC resources that have contributed to the research results reported in this paper. The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way

Synergistic exploitation of hyper- and multi-spectral precursor sentinel measurements to determine phytoplankton functional types (SynSenPFT)

This is the final version. Available from Frontiers Media via the DOI in this record.The corrigendum to this article is in ORE at http://hdl.handle.net/10871/38256We derive the chlorophyll a concentration (Chla) for three main phytoplankton functional types (PFTs) - diatoms, coccolithophores and cyanobacteria - by combining satellite multispectral-based information, being of a high spatial and temporal resolution, with retrievals based on high resolution of PFT absorption properties derived from hyperspectral satellite measurements. The multispectral-based PFT Chla retrievals are based on a revised version of the empirical OC-PFT algorithm applied to the Ocean Color Climate Change Initiative (OC-CCI) total Chla product. The PhytoDOAS analytical algorithm is used with some modifications to derive PFT Chla from SCIAMACHY hyperspectral measurements. To combine synergistically these two PFT products (OC-PFT and PhytoDOAS), an optimal interpolation is performed for each PFT in every OC-PFT sub-pixel within a PhytoDOAS pixel, given its Chla and its a priori error statistics. The synergistic product (SynSenPFT) is presented for the period of August 2002 March 2012 and evaluated against PFT Chla data obtained from in situ marker pigment data and the NASA Ocean Biogeochemical Model simulations and satellite information on phytoplankton size. The most challenging aspects of the SynSenPFT algorithm implementation are discussed. Perspectives on SynSenPFT product improvements and prolongation of the time series over the next decades by adaptation to Sentinel multi- and hyperspectral instruments are highlighted.ESA SEOM SY-4Sci Synergy projectSFB/TR 172 (AC)3 “Arctic Amplification” subproject C03DFG-Priority Program SPP 1158 “Antarktis” PhySyn BU2913/3-1Helmholtz Climate Initiative REKLIMHelmholtz Association of German Research Centres (HGF

Le dimensioni psicologiche nel monitoraggio del paziente diabetico in terapia con microinfusore: stato attuale e prospettive.

SUMMARY Psychological aspects in the evaluation of the diabetic patient treated with infusion pump-therapy: current state and perspectives This article aim is to offer a close examination of up-to-date theoretical contributions referring to the following subject: psychological aspects in CSII therapy. This close examination was made considering two different researches: the first by regarding the evaluation of the post implant period, and the second concerning the study of drop out causes. It was possible to find out problems and psychosocial changes caused by the implant, but also to specify critical points, useful to build necessary protocols, to support diabetological valuations and to suggest psychoeducational interventions