Regular Composition for Slice-Regular Functions of Quaternionic Variable

A regular composition for slice regular function is introduced using a non commutative version of the Faa` di Bruno's Formul

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

Characterization of anomalous diffusion classical statistics powered by deep learning (CONDOR)

Diffusion processes are important in several physical, chemical, biological and human phenomena. Examples include molecular encounters in reactions, cellular signalling, the foraging of animals, the spread of diseases, as well as trends in financial markets and climate records. Deviations from Brownian diffusion, known as anomalous diffusion (AnDi), can often be observed in these processes, when the growth of the mean square displacement in time is not linear. An ever-increasing number of methods has thus appeared to characterize anomalous diffusion trajectories based on classical statistics or machine learning approaches. Yet, characterization of anomalous diffusion remains challenging to date as testified by the launch of the AnDi challenge in March 2020 to assess and compare new and pre-existing methods on three different aspects of the problem: the inference of the anomalous diffusion exponent, the classification of the diffusion model, and the segmentation of trajectories. Here, we introduce a novel method (CONDOR) which combines feature engineering based on classical statistics with supervised deep learning to efficiently identify the underlying anomalous diffusion model with high accuracy and infer its exponent with a small mean absolute error in single 1D, 2D and 3D trajectories corrupted by localization noise. Finally, we extend our method to the segmentation of trajectories where the diffusion model and/or its anomalous exponent vary in time

On Compact Affine Quaternionic Curves and Surfaces

This paper is devoted to the study of affine quaternionic manifolds and to a possible classification of all compact affine quater- nionic curves and surfaces. It is established that on an affine quater- nionic manifold there is one and only one affine quaternionic structure. A direct result, based on the celebrated Kodaira Theorem that classifies all compact complex manifolds in complex dimension 2, states that the only compact affine quaternionic curves are the quaternionic tori. As for compact affine quaternionic surfaces, the study of their fundamental groups, together with the inspection of all nilpotent hypercomplex sim- ply connected 8-dimensional Lie Groups, identifies a path towards their classification

Poles of regular quaternionic functions

This paper studies the singularities of Cullen-regular functions of one quaternionic variable. The quaternionic Laurent series prove to be Cullen-regular. The singularities of Cullen-regular functions are thus classified as removable, essential or poles. The quaternionic analogues of meromorphic complex functions, called semiregular functions, turn out to be quotients of Cullen-regular functions with respect to an appropriate division operation. This allows a detailed study of the poles and their distribution.Comment: 14 page

Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect

We study in detail the zero set of a regular function of a quaternionic or octonionic variable. By means of a division lemma for convergent power series, we find the exact relation existing between the zeros of two octonionic regular functions and those of their product. In the case of octonionic polynomials, we get a strong form of the fundamental theorem of algebra. We prove that the sum of the multiplicities of zeros equals the degree of the polynomial and obtain a factorization in linear polynomials.Comment: Proof of Lemma 7 rewritten (thanks to an anonymous reviewer

Chemical composition and species identification of microalgal biomass grown at pilot-scale with municipal wastewater and CO2 from flue gases

The production potential of a locally isolated Chlorella vulgaris strain and a local green-algae consortium, used in municipal wastewater treatment combined with CO2 sequestration from flue gases, was evaluated for the first time by comparing the elemental and biochemical composition and heating value of the biomass produced. The microalgae were grown in outdoor pilot-scale ponds under subarctic summer conditions. The impact of culti-vation in a greenhouse climate was also tested for the green-algae consortium; additionally, the variation in species composition over time in the three ponds was investigated. Our results showed that the biomass produced in the consortium/outdoor pond had the greatest potential for bioenergy production because both its carbohy-drates and lipids contents were significantly higher than the biomasses from the consortium/greenhouse and C. vulgaris/outdoor ponds. Although greenhouse conditions significantly increased the consortium biomass's monounsaturated fatty acid content, which is ideal for biodiesel production, an undesirable increase in ash and chemical elements, as well as a reduction in heating value, were also observed. Thus, the placement of the pond inside a greenhouse did not improve the production potential of the green-algae consortium biomass in the current study infrastructure and climate conditions.info:eu-repo/semantics/publishedVersio

New Insights on Free Energies and Saint- Venant’s Principle in Viscoelasticity

This work was conceived in 1999 and brought near completion by 2003. Giorgio Gentili was deeply involved in this research until his untimely death. He is greatly missed. Work pressures on the other authors forced a postponement of research on this topic, originally envisaged as lasting a few months but in the event it turned out to be nearly ten years. We now dedicate this work to the memory of Giorgio and to his Family