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

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

Six Sigma methodology: an effective tool for quality management.

The quality standards of the output, the features of delivery and the introduction of new services are becoming the most important factors to success in business performance. In this context, the application of new methodologies is essential to increase the business performance. Six Sigma can give an important solution for those companies that intend to highlight the customer satisfaction focusing on the continuous improvement of the processes. The purpose of this paper is to show the power of the Six Sigma methodology in increasing the performance level of industrial processes and systems. The paper shows a Six Sigma case study applied to the automotive market

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

Hepatotoxicity induced by greater celandine (Chelidonium majus L.): a review of the literature

The available literature assessing Chelidonium majus L. (CM) hepatotoxicity potential, and its risk to benefit assessment has been reviewed in this paper. Identification of significant scientific literature was performed via the following research databases: Cochrane Central, Google Scholar, EMBASE, Medline, Science Direct, Scopus, Web of Science, using the following keywords: "Chelidonium majus", "greater celandine", "Hepatotoxicity", "Liver" "Injury", "Toxicity" individually investigated and then again in association. CM named also greater celandine, swallow-wort, or bai-qu-cai (Chinese), has been used for a long time in traditional Chinese medicine and phytotherapy. Its extracts have been claimed to display a wide variety of biological activities: antimicrobial, anti-inflammatory, spasmolytic, antineoplastic, hepatoprotective, and analgesic. Moreover, herbal medicine suggests this plant have numerous additional effects which have not yet been scientifically evaluated, such as antitussive, diuretic, and eye-regenerative. However, despite its claimed hepatoprotective effects, several hepatotoxicity cases have been reported to be probably or highly probably connected with CM exposure, after their evaluation through liver-targeted causality assessment methods. CM hepatotoxicity has been defined as a distinct form of herb-induced liver injury (HILI), due to an idiosyncratic reaction of the metabolic type. This evidence has to be considered in relationship with the absence of considerable benefits of CM therapy. Therefore, the risk to benefit ratio of the use of herbal products containing greater celandine can actually be considered as negative

A TE11 Dual-Mode Monoblock Dielectric Resonator Filter

A novel TE11 monoblock dual-mode dielectric resonator filter is presented in this paper. The proposed filter is made of a single piece of ceramic with silver plated external surfaces and metallic lids for hosting tuning elements. The dominant TE11 dual-mode is supported by H-shape dielectric resonator having r =45. The resonator is ultra-compact in size and offers a maximized space utilization since no metallic housing is required. In addition, the proposed resonator offers a high unloaded quality factor, reasonably wide spurious window and lend itself to implement tunability. One prototype filter operating at 1.96 GHz with 50-MHz bandwidth is designed

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