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We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume and the dynamics of their geodesic flows.

This volume contains the proceedings of the ICM 2018 satellite school and workshop K-theory conference in Argentina. The school was held from July 16-20, 2018, in La Plata, Argentina, and the workshop was held from July 23-27, 2018, in Buenos Aires, Argentina. The volume showcases current developments in K-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections. Papers cover topics such as K-theory of group rings, Witt groups of real algebraic varieties, coarse homology theories, topological cyclic homology, negative K-groups of monoid algebras, Milnor K-theory and regulators, noncommutative motives, the classification of C^*-algebras via Kasparov's K-theory, the comparison between full and reduced C^*-crossed products, and a proof of Bott periodicity using almost commuting matrices.

By offering a fresh reading of several partially overlooked passages from Aristotle’s Metaphysics Μ and Ν, this article argues that the identification of Forms and ideal numbers in Plato is not presented as Aristotle’s own reconstruction. Instead, Aristotle sets forth what he takes to be Plato’s views. This reading enhances not only our understanding of the Academic debates with which Aristotle engaged but also his status as a historian of philosophy.

\"Theory of Forms\" implies that a genuine version of creatures exists beyond the shapes in this world. Stem cell technology has adopted developmental cues to mimic real life. However, the functionality of the lab-made cells is far from primary ones. Perhaps it is time to switch from analytical to systematic perspective in stem cell science. This may be the way to define new horizons based on the systematic perspective and convergence of science in stem cell biology, bridging the current gap between the shadows of real knowledge in current research and reality in future.

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This paper discusses the teaching of Ancient History in Brazil through the experience of Projeto Vocabulário Político da Antiguidade (Political Vocabulary of Antiquity Project). This project has been developed at the Federal University of Paraíba in João Pessoa, Brazil, since 2016, with a team consisting of professors and students from undergraduate History and Classics programs. The project’s main goal is to create didactical materials that facilitate the teaching of politics and Antiquity to students aged 11 to 17, based on the translation of Greek and Latin texts. This paper will present two educational games developed by this project to teach the theory of forms of government in an engaging and enjoyable way. The positive results of the project highlight the importance of modernizing the teaching of forms of government regbased on the works of authors such as Herodotus, Aristotle, Polybius and Cicero. Furthermore, it demonstrates that the study of Antiquity can effectively contribute to the political awareness of young citizens.

Conceptualism—the view that universals are mental entities without an external, independent, or substantial reality—has enjoyed popularity at various points throughout the history of philosophy. While Plato’s Theory of Forms is not a conceptualist theory of universals, we find at Parmenides 132b–c the startling conceptualist suggestion from a young Socrates that each Form might be a noēma , or a mental entity. This suggestion and Parmenides’ cryptic objections to it have been overshadowed by their placement directly after the notoriously difficult Third Man Argument (132a–b), and before the Likeness Regress (132c–133a). However, in the background of 132b–c, we find illuminating assumptions behind Parmenides’ arguments against the Theory of Forms in the first half of the dialogue. We also find in this text a set of implied criteria for Platonic concepthood. While in the Platonic corpus, Forms are explanantia for many of the phenomena explained by concepts in contemporary philosophy, concepts do seem to have an important epistemic role in Plato’s philosophy. An account of Platonic concepthood therefore opens the door for new ways of understanding the Platonic corpus as a whole. My focus in this paper is to uncover these assumptions and criteria through a close reading of Socrates’ conceptualist suggestion and Parmenides’ truncated objections to it at Parmenides 132b–c.

This volume contains the proceedings of the conference on Formal and Analytic Solutions of Diff. Equations, held from June 28-July 2, 2021, and hosted by University of Alcala, Alcala de Henares, Spain. The manuscripts cover recent advances in the study of formal and analytic solutions of different kinds of equations such as ordinary differential equations, difference equations, $q$-difference equations, partial differential equations, moment differential equations, etc. Also discussed are related topics such as summability of formal solutions and the asymptotic study of their solutions. The volume is intended not only for researchers in this field of knowledge but also for students who aim to acquire new techniques and learn recent results.

The method of transformation is attracting widespread interest in fields such contemporary design. However, in theory of design little attention has been paid to a categorical status of the term \"transformation\". This paper presents the conceptual analysis of transformation based on the theory of form employed in the influential essays by Aristotle and Thomas Aquinas. In the present work the transformation as a method of shaping design has been explored as well as potential application of this term in design has been demonstrated.