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

Improvement through process integration using a simulative, dynamic method

The need for globalisation, the saturation and instability of markets, the life-cycle time reduction of products, the growth of item variety, the customer demands have been main factors contributing to a radical change of management conceptions and strategies. This complex environment has induced companies to search the keys to achieve competitiveness, focusing on process integration. The purpose of the paper is to explain how managing the internal functions of a company in an integrated way can lead to an effective improvement. In order to represent the flows and to quantify improvements, a simulative, dynamic and integrated model is developed

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

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

Forecasting SYM-H Index: A Comparison Between LongShort-Term Memory and Convolutional Neural Networks

Forecasting geomagnetic indices represents a key point to develop warning systems for the mitigation of possible effects of severe geomagnetic storms on critical ground infrastructures. Here we focus on SYM‐H index, a proxy of the axially symmetric magnetic field disturbance at low and middle latitudes on the Earth's surface. To forecast SYM‐H, we built two artificial neural network (ANN) models and trained both of them on two different sets of input parameters including interplanetary magnetic field components and magnitude and differing for the presence or not of previous SYM‐H values. These ANN models differ in architecture being based on two conceptually different neural networks: the long short‐term memory (LSTM) and the convolutional neural network (CNN). Both networks are trained, validated, and tested on a total of 42 geomagnetic storms among the most intense that occurred between 1998 and 2018. Performance comparison of the two ANN models shows that (1) both are able to well forecast SYM‐H index 1 h in advance, with an accuracy of more than 95% in terms of the coefficient of determination R2; (2) the model based on LSTM is slightly more accurate than that based on CNN when including SYM‐H index at previous steps among the inputs; and (3) the model based on CNN has interesting potentialities being more accurate than that based on LSTM when not including SYM‐H index among the inputs. Predictions made including SYM‐H index among the inputs provide a root mean squared error on average 42% lower than that of predictions made without SYM‐H

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