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

Fosfomycin Pharmacokinetic Profile in Plasma and Urine and Quantitative Estimation in Prostate and Seminal Vesicles after One and Two Consecutive Doses of Oral Fosfomycin Trometamol in Healthy Male Volunteers

The present Phase I study investigated, for the first time, fosfomycin pharmacokinetics in humans after two 3 g doses of fosfomycin trometamol administered 27 h apart, according to the dose regimen recommended for the prophylactic indication for transrectal prostate biopsy in adult men. Plasma, urine and seminal plasma concentrations were measured after one and two consecutive doses in 24 healthy men, representative of the target population of the prophylactic indication. Prostate and seminal vesicle concentrations were estimated based on seminal plasma concentrations using a one-step regression method. The exposure to fosfomycin was very similar in rate (C-max, t(max)) after one and two doses. The AUC showed a minimal increment. On average, the apparent volume of distribution was high (>100 L), and the mean clearance had an intermediate value. The total amount and dose fraction of fosfomycin excreted in urine showed a small increment after two doses. The renal clearance was about 5 L/h. The fosfomycin concentration in the prostate and seminal vesicles showed that the antibiotic increased on average after two consecutive doses. This result confirmed the ability of fosfomycin to distribute into the prostate and into seminal vesicles after one single dose and that a two consecutive dose regimen increases the antibiotic availability inside these peripheral tissues

The Prognostic Role of Procalcitonin in Critically Ill Patients Admitted in a Medical Stepdown Unit: A Retrospective Cohort Study

Procalcitonin (PCT) is a a marker of bacterial infection. Its prognostic role in the critically-ill patient, however, is still object of debate. Aim of this study was to evaluate the capacity of admission PCT (aPCT) in assessing the prognosis of the critically-ill patient regardless the presence of bacterial infection. A single-cohort, single-center retrospective study was performed evaluating critically-ill patients admitted to a stepdown care unit. Age, sex, Simplified Acute Physiology Score II (SAPS-II), shock, troponin-I, aPCT, serum creatinine, cultures and clinical endpoints (in-hospital mortality or Intensive Care Unit (ICU) transfer) were collected. Time free from adverse event (TF-AE) was defined as the time between hospitalization and occurrence of one of the clinical endpoints, and calculated with Kaplan-Meier curves. We engineered a new predictive model (POCS) adopting aPCT, age and shock.We enrolled 1063 subjects: 450 reached the composite outcome of death or ICU transfer. aPCT was significantly higher in this group, where it predicted TF-AE both in septic and non-septic patients. aPCT and POCS showed a good prognostic performance in the whole sample, both in septic and non-septic patients. aPCT showed a good prognostic accuracy, adding informations on the rapidity of clinical deterioration. POCS model reached a performance similar to SAPS-II

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