L’œuvre mathématique de Leibniz a ceci d’intéressant qu’au travers des innombrables manuscrits de travail dont nous disposons dans ses archives à Hanovre, le philosophe nous a confié le matériel nécessaire pour rétablir ses divers cheminements de recherche ainsi que ses méthodes de découvertes à l’origine de ses créations mathématiques. L’exemple des exposants que nous allons traiter permet d’éclairer utilement la façon dont Leibniz apprend les mathématiques et change progressivement de posture et de démarche. Ainsi, dans sa première année parisienne, la (...) primauté est-elle donnée aux relations tabulaires, plutôt qu’aux formes et aux similitudes. Ces enjeux épistémologiques expliquent la manière dont Leibniz généralise partiellement la notion d’exposant. (shrink)

The purpose of the study is to introduce a new economic index, the "relative productivity exponent in the global economy g", which characterizes the deviation of the economic productivity index of a given country from some ideal productivity determined by the shape of the axial line of the swarm of the global economy in the three-dimensional space of economic indices EPI, BLI, CPI. To determine the values of the relative productivity exponent g, the shape of the axial line of the (...) global economy of 2019, established earlier by the authors, is used. The article examines the distribution of countries according to the exponent g and the index of socio-economic equilibrium of countries, and also investigates the relationship between the exponent g and the index of economic productivity EPI. The scientific novelty of the research lies in the introduction of a new economic index g and the calculation of its values for countries based on economic data from 2019. The distribution of countries according to the value of g allows us to reveal, as a result, a certain range of the exponent g, indicating a balanced state of the economy. (shrink)

The experimental results reported in Clahsen's target article clearly distinguish regular from irregular processes and suggest a basic difference between items that are productively formed and items which are stored in the lexicon. However, these results do not directly implicate any particular combinatory operation (such as affixation), nor do they distinguish inflectional items from other productive formations.

On September 24, 787, the works of the VII Ecumenical Synod were opened in the 'Saint Sophia' Church in Nicaea, after the first attempt, on August 7, 786, had failed. Although the nominal presidency was held by the legates of Pope Adrian I, the effective presidency was exercised by Patriarch Tarasios of Constantinople. A skilful church diplomat, with experience, gained as an imperial secretary and a remarkable theologian whose authority was imposed even during his election as a patriarch amongst the (...) laity, Tarasios meticulously and clairvoyantly prepared for the deployment of the Nicene synod. This is noticeable from the agreement made with the papal legates regarding the reading of the letters of Pope Adrian I whose content directly concerned the persona of the patriarch, agreeing to omit those compromising paragraphs, from the procedure of re-welcoming in the communion of the church of some former iconoclastic bishops, by correctly managing the resistance of the monks to whom he gave satisfaction regarding the patristic and traditional argumentation of the cult of the holy icons and by rejecting point-by-point the dogmatic decision of the iconoclastic synod of Hieria, a rejection of which the patriarch Tarasie is in all probability the author. Satisfied with the success of the synod, whose craftsman he indeed was, Patriarch Tarasios was able to communicate to both Pope Adrian I and the emperors and clergy of Constantinople that the unity of the Church residing in Christ had been restored and that the place in the church and due honour of the holy icons had been restored through the synodal decision of 302 participants. The success of the Seventh Ecumenical Council is unequivocally because of the tactful and competent preparation and management of Patriarch Tarasios. CONTRIBUTION: The perspective we promote on the events highlighted in the study, could contribute to unblocking the theological dialogue between Orthodox and Catholics on the issue of papal primacy, the study thus promotes HTS as an important forum for mediating interfaith dialogue. (shrink)

Let p be an odd prime. A method is described which given a structure M of finite similarity type produces a nilpotent group of class 2 and exponent p which is in the same stability class as M. Theorem. There are nilpotent groups of class 2 and exponent p in all stability classes. Theorem. The problem of characterizing a stability class is equivalent to characterizing the (nilpotent, class 2, exponent p) groups in that class.

In this text I shall explore the meaning of the concept “exponent” in the first Critique by resorting to its provenience. Beginning with a brief analysis of the two meanings Kant ascribes to it the Critique, the exponent of a series and the exponent of a rule, I intend to point out that by means of Kant’s concept of analogy, intimately linked with proportion, we can find a route into some of the mathematics textbooks of the 18 th century, which (...) shed great light in the matter. Thereafter, as a transition for returning to the Critique, we shall see how, in the Duisburgscher Nachlass, the exponent plays a central role for Kant as he thinks the emergency and necessity of rules in Philosophy, in comparison to Mathematics. In this way I hope to show how the “exponent” is taken up by Kant and made fruitful, especially for the Analogies of experience. (shrink)

Let L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}$$\end{document} be the language of group theory with n additional new constant symbols c1,…,cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c_1,\ldots,c_n}$$\end{document}. In L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}$$\end{document} we consider the class K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb{K}}}$$\end{document} of all finite groups G of exponent p>2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${p > 2}$$\end{document}, where G′⊆⟨c1G,…,cnG⟩⊆Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G'\subseteq\langle c_1^G,\ldots,c_n^G\rangle \subseteq Z}$$\end{document} and c1G,…,cnG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c_1^G,\ldots,c_n^G}$$\end{document} are linearly independent. Using amalgamation we show the existence of Fraïssé limits D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}$$\end{document} of K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb{K}}}$$\end{document}. D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}$$\end{document} is Felgner’s extra special p-group. The elementary theories of the D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}$$\end{document} are supersimple of SU-rank 1. They have the independence property. (shrink)

We introduce the set of definable restricted complex powers for expansions of the real field and calculate it explicitly for expansions of the real field itself by collections of restricted complex powers. We apply this computation to establish a classification theorem for expansions of the real field by families of locally closed trajectories of linear vector fields.

The label ‘Frankfurt School’ became popular in the ‘positivism dispute’ in the mid-1960s, but this article shows that it is wrong to describe Jürgen Habermas as representing a ‘second generation’ of exponents of critical theory. His communication theory of society is intended not as a transformation of, but as an alternative to, the older tradition of thought represented by Adorno and Horkheimer. The novel and innovative character of Habermas’s approach is demonstrated in relation to three thematic complexes: (1) the (...) public sphere and language; (2) democracy and the constitutional state; and (3) system and lifeworld as categories for a theory of modernity. (shrink)

Gracias a unas intervenciones de recuperación que se presentaban casi imposibles, dentro del amplio plan de restauración, precedido de investigaciones y estudios, de todo el conjunto de las edificaciones que bajo Augusto fueron realizadas en la colina del Palatino, se han abierto al público en Roma las puertas de la casa que Octaviano mandó edificar en el año 36 a.C., antes de convertirse en Augusto (27 a.C.-14d.C.).

In his interesting paper on babeo and aueo published in CQ 66 , 388–98, Dr. A.S. Gratwick raised a number of questions bearing on my own discussion of the origin and development of the babeo+infinitive construction in CQ 65 , 215–31. First the collapse of the earlier future-tense system. As I said, this was ‘the product of a number of different linguistic events’, phonetic, grammatical, and semantic, which were summarized and illustrated on pp. 220–1 of my paper. Even so Dr. (...) Gratwick believes that I assigned too much weight to ‘phonetic attrition of the future simple’. (shrink)