Some notions of subharmonicity over the quaternions

This works introduces several notions of subharmonicity for real-valued functions of one quaternionic variable. These notions are related to the theory of slice regular quaternionic functions introduced by Gentili and Struppa in 2006. The interesting properties of these new classes of functions are studied and applied to construct the analogs of Green's functions.Comment: 16 page

Regular vs. classical M\"obius transformations of the quaternionic unit ball

The regular fractional transformations of the extended quaternionic space have been recently introduced as variants of the classical linear fractional transformations. These variants have the advantage of being included in the class of slice regular functions, introduced by Gentili and Struppa in 2006, so that they can be studied with the useful tools available in this theory. We first consider their general properties, then focus on the regular M\"obius transformations of the quaternionic unit ball B, comparing the latter with their classical analogs. In particular we study the relation between the regular M\"obius transformations and the Poincar\'e metric of B, which is preserved by the classical M\"obius transformations. Furthermore, we announce a result that is a quaternionic analog of the Schwarz-Pick lemma.Comment: 14 page

A Phragm\'en - Lindel\"of principle for slice regular functions

The celebrated 100-year old Phragmen-Lindelof principle is a far reaching extension of the maximum modulus theorem for holomorphic functions of one complex variable. In some recent papers there has been a resurgence of interest in principles of this type for functions of a hypercomplex variable and for solutions of suitable partial differential equations. In the present article we obtain a Phragmen-Lindelof principle for slice regular functions, a class of quaternion-valued functions of a quaternionic variable which has been recently introduced.Comment: 10 page

Semi-continuous Chlorella vulgaris Cultivation Using Anaerobic Digestate Liquid Fraction Pre-treated by Ultrasonic Cavitation to Improve Carbon Dioxide Solubilization

Nutrients-enriched effluents such as digestate can represent a suitable and economically appealing substrate for microalgae growth since they combine the effluent treatment with biomass production. Then, microalgae biomass can be exploited to produce several bio-based compounds. However, the use of digestate for microalgae cultivation can be challenging due to its high levels of ammonia nitrogen and its low C/N ratio. For this reason, an ultrasonic cavitation (UC) process combined with carbon dioxide (CO2) insufflation was tested on digestate, in order to obtain a faster solubilization of the CO2 in the medium and thus an increase in the C/N ratio. The test was carried out growing Chlorella vulgaris on both digestate (mixotrophic condition) and BG-11 medium (autotrophic condition) in 1 L photobioreactors. For the first 14 days of the experiment the reactors were maintained in batch conditions to acclimatize microalgae. Then, they were switched to semi-continuous for 32 days. The reactors were fed three times a week, with an HRT (Hydraulic Retention Time) of 10.5 d as weekly average. Regarding the test on digestate, both UC pre-treated and untreated conditions reached the highest biomass production at the end of the batch (4.8 and 4.1 g L-1 respectively) and a complete ammonium (NH4+) removal after 9 days. The switch to semi-continuous caused an increase in NH4+ concentration and a consistent decrease in biomass concentration. Biomass production reached the steady-state, with a concentration of 1.9 and 1.2 g L-1 for the UC pre-treated and untreated digestate, respectively (+55.6 % biomass production obtained with UC pre-treated digestate). Moreover, an NH4+ removal of 93.5 % and 92.3 % was reached for UC pre-treated and untreated conditions, respectively

Regular Moebius transformations of the space of quaternions

Let H be the real algebra of quaternions. The notion of regular function of a quaternionic variable recently presented by G. Gentili and D. C. Struppa developed into a quite rich theory. Several properties of regular quaternionic functions are analogous to those of holomorphic functions of one complex variable, although the diversity of the quaternionic setting introduces new phenomena. This paper studies regular quaternionic transformations. We first find a quaternionic analog to the Casorati-Weierstrass theorem and prove that all regular injective functions from H to itself are affine. In particular, the group Aut(H) of biregular functions on H coincides with the group of regular affine transformations. Inspired by the classical quaternionic linear fractional transformations, we define the regular fractional transformations. We then show that each regular injective function from the Alexandroff compactification of H to itself is a regular fractional transformation. Finally, we study regular Moebius transformations, which map the unit ball B onto itself. All regular bijections from B to itself prove to be regular Moebius transformations.Comment: 12 page

The Huygens Atmospheric Structure Instrument (HASI): Expected Results at Titan and Performance Verification in Terrestrial Atmosphere

The Huygens ASI is a multi-sensor package resulting from an international cooperation, it has been designed to measure the physical quantities characterizing Titan's atmosphere during the Huygens probe mission. On 14th January, 2005, HASI will measure acceleration, pressure, temperature and electrical properties all along the Huygens probe descent on Titan in order to study Titan s atmospheric structure, dynamics and electric properties. Monitoring axial and normal accelerations and providing direct pressure and temperature measurements during the descent, HASI will mainly contribute to the Huygens probe entry and trajectory reconstruction. In order to simulate the Huygens probe descent and verify HASI sensors performance in terrestrial environment, stratospheric balloon flight experiment campaigns have been performed, in collaboration with the Italian Space Agency (ASI). The results of flight experiments have allowed to determine the atmospheric vertical profiles and to obtain a set of data for the analysis of probe trajectory and attitude reconstruction

Serum Deprivation of Mesenchymal Stem Cells Improves Exosome Activity and Alters Lipid and Protein Composition

Exosomes can serve as delivery vehicles for advanced therapeutics. The components necessary and sufficient to support exosomal delivery have not been established. Here we connect biochemical composition and activity of exosomes to optimize exosome-mediated delivery of small interfering RNAs (siRNAs). This information is used to create effective artificial exosomes. We show that serum-deprived mesenchymal stem cells produce exosomes up to 22-fold more effective at delivering siRNAs to neurons than exosomes derived from control cells. Proteinase treatment of exosomes stops siRNA transfer, indicating that surface proteins on exosomes are involved in trafficking. Proteomic and lipidomic analyses show that exosomes derived in serum-deprived conditions are enriched in six protein pathways and one lipid class, dilysocardiolipin. Inspired by these findings, we engineer an artificial exosome, in which the incorporation of one lipid (dilysocardiolipin) and three proteins (Rab7, Desmoplakin, and AHSG) into conventional neutral liposomes produces vesicles that mimic cargo delivering activity of natural exosomes