Il Concetto di Numero nei Libri di Testo del Regno d’Italia: Indagini su un Particolare “Numero Complesso” (The Concept of Number in the Textbooks of the Kingdom of Italy: Investigations into a Particular “Complex Number”)

Abstract From the arithmetic books of the schools of the Italian peninsula we can see complex numbers, different from imaginary ones. A complex number is a number accompanied by a unit of measurement, with submultiples not in decimal relation. After the introduction of the new system of weights and measures, the teaching of these numbers remains to help in the conversion. The procedures described by mathematicians who deal with complex numbers find their origin in a fraction described by Fibonacci in Liber Abbaci. It conveys a dynamic meaning of fraction on the number line, which has gradually fallen into disuse. This fraction, unlike complex numbers, was simple to interpret thanks to its symbolic formalism, which disappeared after the invention of printing, but was described in words in the books of subsequent centuries. Complex numbers were taught and learned in Italian schools until the ministerial programs of the 1923 Reform remained in force. Attention will be given to the historical context of the didactic uses of mathematical concepts, with the aim of arousing the epistemological reflections that usually derive from the use of history in mathematics education.Keywords: complex number, graduated multiple fractionSuntoDai libri di aritmetica delle scuole della penisola italiana prima dell'Unità possiamo osservare i numeri complessi, diversi da quelli immaginari. Un numero complesso è un numero accompagnato da un'unità di misura, con sottomultipli non in rapporto decimale. Dopo l'introduzione del nuovo sistema di pesi e misure, l'insegnamento di questi numeri rimane per facilitare la conversione. Le procedure descritte dai matematici che si occupano di numeri complessi trovano la loro origine in una frazione descritta da Fibonacci nel Liber Abbaci. Essa trasmette un significato dinamico di frazione sulla retta numerica, che è gradualmente caduto in disuso. Questa frazione, a differenza dei numeri complessi, era semplice da interpretare grazie al suo formalismo simbolico, scomparso dopo l'invenzione della stampa, ma fu descritta a parole nei libri dei secoli successivi. Dopo l'Unità d'Italia, i numeri complessi furono insegnati e appresi nelle scuole italiane fino a quando i programmi ministeriali della Riforma del 1923 rimasero in vigore. Si darà attenzione al contesto storico degli usi didattici dei concetti matematici, con l'obiettivo di suscitare le riflessioni epistemologiche che solitamente derivano dall'uso della storia nella didattica della matematica.Parole chiave: numero complesso, frazione multipla graduata

η-Ricci solitons in a LP-Sasakian manifolds admitting quarter-symmetric metric connection

The objective of this paper is to investigate the $\eta$-Ricci solitons in a LP-Sasakian manifolds admitting quarter-symmetric metric connection satisfying certain curvature conditions. We study the Ricci solitons in a LP-Sasakian manifolds admitting quarter-symmetric metric connection satisfying certain conditions. Finally, we have given an example of 3-dimensional $\eta$-Ricci solitons in a LP-Sasakian manifolds with respect to quarter-symmetric metric connection

La Macchina Narrativa della Fiction Italiana: Memoria, Storia e Sapere Implicito ne La meglio gioventù, L’amica geniale, 1992 ed Esterno notte (The Narrative Machine of Italian Fiction: Memory, History, and Tacit Knowledge in “La meglio gioventù”, “L’amica geniale”, “1992” and “Esterno notte”)

SuntoSin dalle sue origini la televisione italiana ha rappresentato un medium fondamentale per la costruzione di narrazioni collettive e di un sapere diffuso, contribuendo alla formazione dell’identità culturale nazionale. Lo studio sottolinea l’importanza fondamentale di un’analisi storica della televisione italiana per comprendere appieno le dinamiche narrative che caratterizzano la fiction contemporanea. Attraverso questa lente storica, si evidenzia come la fiction non sia semplicemente un prodotto di intrattenimento, ma un dispositivo culturale complesso che contribuisce attivamente alla formazione del senso pubblico. La capacità delle fiction analizzate — da La meglio gioventù (Rai 1, 2003) a L’amica geniale (Rai 1, 2018) da 1992 (Sky, 2015) a Esterno notte (Rai 1, 2022) — di tradurre eventi storici, tensioni sociali e trasformazioni culturali in narrazioni coinvolgenti e accessibili dimostra il loro ruolo cruciale nella costruzione di una memoria collettiva condivisa.Parole chiave: fiction italiana; storia della televisione; serialità; narrazioni; memoria; cronaca; AbstractSince its inception, Italian television has functioned as a pivotal medium in the construction of collective narratives and the dissemination of culturally embedded knowledge, actively contributing to the shaping of national identity. This study underscores the critical importance of a historically grounded analysis of Italian television as a means to fully apprehend the narrative mechanisms that characterize contemporary serialized fiction. Viewed through this historical framework, television fiction emerges not merely as a vehicle of entertainment, but as a complex cultural apparatus engaged in the ongoing production of public discourse and shared meaning.The selected case studies — La meglio gioventù (Rai 1, 2003), L’amica geniale (Rai 1, 2018), 1992 (Sky, 2015), and Esterno notte (Rai 1, 2022) — exemplify the capacity of contemporary Italian fiction to narrativize historical events, socio-political tensions, and cultural transformations through accessible yet multilayered storytelling. These productions do not merely reflect Italian history but actively participate in the reconfiguration of its public memory, offering narrative frameworks through which audiences engage with the past and negotiate present identities. As such, fiction becomes a privileged site for the elaboration of a shared symbolic repertoire and the circulation of historically resonant imaginaries.Keywords: Italian fiction; television history; seriality; narratives; memory; current event

An introduction to iso-, geno- and hyper-mathematics and their applications in physics, chemistry and biology

In this work, the author reviews recent advances on isomathematics, genomathematics and hypermathematics that were initiated  by the Italian-American scientist Ruggero Maria Santilli for the invariant representation of reversible and irreversible systems of extended constituents in conditions of deep mutual entanglement with conventional linear, local and potential interactions represented by the conventional Hamiltonian H plus non-linear, non-local and non-potential interactions represented by the Santillian S in the axiom-preserving  iso-, geno- and hyper-completion $A\hat \times B = A S B$ of the millenary old associative product of operators $A\times B =  AB$. We then review and present, apparently for the first time, new advances in physics, chemistry  and biology which are permitted by iso-, geno- and hyper-mathematics, but impossible for 20th century applied mathematics

Exploring the Role of Consciousness in the Origin of the Universe and Life: A Hypothesis of a Sentient Creator

This article aims to highlight how consciousness may be interconnected with topics related to the existence of God, physics, and cosmology. Despite the importance of this relationship, academia has studied consciousness in relation to each of these themes separately, neglecting to consider all four within a unified analysis. The notion of a conscious God is defined as a sentient creative consciousness that may have generated a holographic universe, a universe from nothing, a multiverse, or a cyclic universe as to create life and intelligent beings. The discussion addresses how this conception of God can be confirmed or refuted through various means, such as the presence of potential mathematical codes in the spacetime of the universe, the information contained within the universe and planet Earth, the development of artificial intelligence, and contact with extraterrestrial civilizations. This article demonstrates that science and philosophy can work together to solve the great mysteries of the cosmos that humanity has pondered for centuries

Comparison of aggregation methods used in online reviews: a critical analysis

With digitalization, online reviews have become a crucial component of consumer decisions and are an important source of feedback on products and services. Users can make informed choices using online review systems such as e-commerce platforms, social media, and others. However, the collection and analysis of these reviews raises a number of questions regarding reliability, representativeness and accuracy. Since they directly influence users' choices, the methods used to aggregate review scores are extremely important. In this article, we explore the most common aggregation methods for rating online reviews on the Amazon platform, with a particular focus on the arithmetic mean. Although these methods are easy to implement, they do not always accurately reflect the overall quality of a product. We then critically analyze how more sophisticated approaches can minimize some of the limitations of the mean, such as the so-called recent bias; propose more robust solutions and alternative approaches that can provide a more accurate representation of the overall rating, improving the quality of aggregated ratings

Toth e il pensiero trans-euclideo in Aristotele (Toth and trans-euclidean thought in Aristotle)

Abstract For about 2000 years the postulate of parallels, enunciated by Euclid, was a source of doubts (postulate or theorem?) clarified with the birth of non-Euclidean geometry.In the light of this new knowledge of geometry, Toth, a Greek scholar and historian of mathematics, glimpses typical properties of geometry today defined as non-Euclidean in some writings of Aristotle. To clearly highlight free will, the Stagirite uses geometric examples partly taken from the geometry known at the time, partly uses its negation, that is, he shows, involuntarily, the presuppositions of the geometry that we know today as non-Euclidean, without delving into the possible logical coexistence of antithetical statements.This short note is an invitation to read Aristotle in a re-interpretative way.Keywords: Toth, Aristotle, free will, non-euclidean geometry.SuntoPer cica 2000 anni il postulato delle parallele, enunciato da Euclide, è stato fucina di dubbi (postulato o teorema?) chiariti con la nascita dela Geometria Non-Euclidea. Alla luce d queste nuove conoscenze di geometria, Toth, grecista e storico della matematica, in alcuni scritti di Aristotele intravede proprietà tipiche di geometria non euclidea. Lo Stagirita, per descrivere con rigore il libero arbitrio, usa esempi geometrici, in parte prelevati dalla geometria all’epoca nota, in parte ponendo la sua negazione, ovvero mostra, involontariamente, i presupposti della geometria, oggi definita non euclidea, senza approfondire la possibile coesistenza logica di affermazioni antitetiche. Questa breve nota è un invito alla lettura d’Aristotele in chiave re-interpretativa.Parole chiave: Toth, Aristotele, libero arbitrio, geometria non-euclidea

Intersex and Healthcare: A Narrative Review of Social Sciences Perspectives

Intersex individuals—those whose physical sex characteristics do not align with conventional male or female categories—encounter considerable challenges within healthcare systems, which often medicalize their bodies through invasive treatments aimed at “normalizing” their traits. This narrative review synthesizes key contributions from medical sociology, medical anthropology, and gender studies to examine the social processes that define, regulate, and often marginalize intersex identities in clinical contexts. Drawing on theoretical frameworks such as medicalization, biopower, stigma theory, intersectionality, and structural violence, the paper situates intersex healthcare within broader systems of normativity and control. It critiques the historical and contemporary role of healthcare institutions in reinforcing binary understandings of sex and gender, often at the cost of individual autonomy and psychosocial well-being. Comparative analyses with transgender healthcare reveal both shared and divergent mechanisms of institutional gatekeeping, underscoring the need for a justice-oriented, intersectional approach to care. This work ultimately advocates for systemic change in both healthcare delivery and policy, informed by sociological insight and intersex-led activism, emphasizing dignity, self-determination, and epistemic inclusion

Lie-admissible irreversible biological entanglements and their apparent initiation of hadronic medicine

In a preceding paper, two of us (R. M. S. and Th. V.) initiated the mathematical representation of life intended as the difference between organic and inorganic molecules, via the Lie-admissible hyperstructural branch of hadronic mechanics representing the size of biological entities, their contact interactions and their irreversibility over time. In this paper, we review the time reversal Lie-isotopic branch of hadronic mechanics, as well as its Lie-admissible covering, by showing that 20th century reversible Lie theories can be extended to an irreversible form by adding symmetric Jordan algebra brackets to antisymmetric Lie brackets. We then introduce, apparently for the first time: a Lie and Jordan admissible axiomatic formulation of the two directions of time; the Lie and Jordan admissible irreversible formulation of biological entanglements; their lack of visible use of energy; and a smooth connection between hadronic uncertainties at small distances and full determinism at classical distances. We then show that biological entanglements can provide a quantitative representation of the behavior by biological entities beyond our sensory perception, with expected diagnostic and curative values suggesting the apparent initiation of the novel hadronic medicine.

Data Mining Meets Logic: Situation-Based Modal Logic and Metadata Veracity

Logic and theoretical computer science are deeply interconnected, with logic forming a foundational pillar in the emergence of computer science. This connection has grown stronger over time, driven by advancements in symbolic systems within artificial intelligence, formal verification methods, and automated reasoning techniques. However, within the vast landscape of computer science, data science remains an area where the link to logic is relatively underdeveloped. In this paper, I apply algebraic logic to address an urgent challenge for data scientists: metadata veracity. Inspired byWillard Van Orman Quine’s well-known slogan, “No entity without identity”, I propose, “No data without metadata”, underscoring the importance of descriptive metadata in scientific articles. The central idea of my framework is that the geometric zones of a scientific article – with its atomic metadata – , correspond to an algebraic situation space. Consequently, I develop a situation-based semantics grounded on the idea that situations are portions of a possible world, a possible world is a PDF document and that sentences point to situations and describe what is going on in them. Applying mathematical logic tools to data mining enables a rigorous framework for defining metadata veracity, offering a structured approach to assess the accuracy and reliability of extracted information