Machiavelli and the Decline of the Classical Notion of the Lessons of History in the Study of War

1988 ◽  
Vol 52 (4) ◽  
pp. 203
Author(s):  
Azar Gat
Keyword(s):  
Classical Notion

A generalization of co-Hopfian abelian groups

2017 ◽  
Vol 27 (04) ◽  
pp. 351-360
Author(s):  
Andrey Chekhlov ◽  
Peter Danchev
Keyword(s):  
Abelian Group ◽  
Representation Theorem ◽  
Abelian Groups ◽  
Classical Notion ◽  
Group A ◽  
Hopfian Group ◽  
Comprehensive Study

We define the concept of an [Formula: see text]-co-Hopfian abelian group, which is a nontrivial generalization of the classical notion of a co-Hopfian group. A systematic and comprehensive study of these groups is given in very different ways. Specifically, a representation theorem for [Formula: see text]-co-Hopfian groups is established as well as it is shown that there exists an [Formula: see text]-co-Hopfian group which is not co-Hopfian.

scholarly journals Asymptotic expansion in measure and strong ergodicity

2021 ◽  
pp. 1-39
Author(s):  
Kang Li ◽  
Federico Vigolo ◽  
Jiawen Zhang
Keyword(s):  
Asymptotic Expansion ◽  
Recent Result ◽  
Spectral Gaps ◽  
Strong Ergodicity ◽  
Classical Notion ◽  
Structure Theorems ◽  
New Perspective

In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalizes expansion in measure and provides a new perspective on the classical notion of strong ergodicity. Moreover, we obtain structure theorems for asymptotically expanding actions, showing that they admit exhaustions by domains of expansion. As an application, we recover a recent result of Marrakchi, characterizing strong ergodicity in terms of local spectral gaps. We also show that homogeneous strongly ergodic actions are always expanding in measure and establish a connection between asymptotic expansion in measure and asymptotic expanders by means of approximating spaces.

James Madison and the Problem of Founding

1996 ◽  
Vol 58 (3) ◽  
pp. 561-596 ◽  
Author(s):  
Gary Rosen
Keyword(s):  
Political Philosophy ◽  
Practical Reason ◽  
Political Thought ◽  
Modern Science ◽  
James Madison ◽  
Social Compact ◽  
Classical Notion ◽  
The Social ◽  
Basic Features

Though indebted to the social compact for the basic features of his political thought, James Madison found the doctrine inadequate in one essential respect: its failure to provide an account of founding. Of course, this is no simple oversight in liberal political philosophy. It reflects deep misgivings about prudence—especially when understood in its “architechtonic” sense as the height of practical reason—and the inequalities that it implies. Madison addresses this problem in Federalist, Nos. 37–40, his fullest treatment of the activities of the Federal Convention. Here he defends the classical notion of prudence, describing its relationship to the modern science of politics and suggesting how it can be reconciled with modern egalitarian principles.

Free Extensions of Chiral Polytopes

1995 ◽  
Vol 47 (3) ◽  
pp. 641-654 ◽  
Author(s):  
Egon Schulte ◽  
Asia Ivić Weiss
Keyword(s):  
Classical Theory ◽  
Convex Polytope ◽  
Regular Polytopes ◽  
Geometric Structures ◽  
Maximal Symmetry ◽  
Abstract Polytopes ◽  
Chiral Polytopes ◽  
Classical Notion ◽  
Extension Result ◽  
Amalgamated Product

AbstractAbstract polytopes are discrete geometric structures which generalize the classical notion of a convex polytope. Chiral polytopes are those abstract polytopes which have maximal symmetry by rotation, in contrast to the abstract regular polytopes which have maximal symmetry by reflection. Chirality is a fascinating phenomenon which does not occur in the classical theory. The paper proves the following general extension result for chiral polytopes. If 𝒦 is a chiral polytope with regular facets 𝓕 then among all chiral polytopes with facets 𝒦 there is a universal such polytope 𝓟, whose group is a certain amalgamated product of the groups of 𝒦 and 𝓕. Finite extensions are also discussed.

scholarly journals MIXED HODGE STRUCTURES WITH MODULUS

2020 ◽  
pp. 1-35
Author(s):  
Florian Ivorra ◽  
Takao Yamazaki
Keyword(s):  
Hodge Structure ◽  
Mixed Hodge Structure ◽  
Hodge Structures ◽  
Classical Notion ◽  
Mixed Hodge Structures

We define a notion of mixed Hodge structure with modulus that generalizes the classical notion of mixed Hodge structure introduced by Deligne and the level one Hodge structures with additive parts introduced by Kato and Russell in their description of Albanese varieties with modulus. With modulus triples of any dimension, we attach mixed Hodge structures with modulus. We combine this construction with an equivalence between the category of level one mixed Hodge structures with modulus and the category of Laumon 1-motives to generalize Kato–Russell’s Albanese varieties with modulus to 1-motives.

scholarly journals Cartan Subalgebras of Jordan Algebras

1966 ◽  
Vol 27 (2) ◽  
pp. 591-609 ◽  
Author(s):  
N. Jacobson
Keyword(s):  
Lie Algebra ◽  
Jordan Algebra ◽  
Cartan Subalgebra ◽  
Jordan Algebras ◽  
Classical Notion ◽  
Cartan Subalgebras ◽  
Definition Of

In this paper we shall give a definition of an analogue for Jordan algebras of the classical notion of a Cartan subalgebra of a Lie algebra. This is based on a notion of associator nilpotency of a Jordan algebra. A Jordan algebra is called associator nilpotent if there exists a positive (odd) integer M such that every associator of order M formed of elements of is 0 (§2).

Representing the Unrepresentable: Making Law Anyway?

Pólemos ◽  
2015 ◽  
Vol 9 (1) ◽  
Author(s):  
François Ost ◽  
Isabelle Ost
Keyword(s):  
Twentieth Century ◽  
Literary Theory ◽  
Human Sciences ◽  
Condensed Form ◽  
Classical Notion ◽  
The Arts ◽  
The Law

Abstract“Representation crisis” is certainly an expression that is too imprecise, clichéd and all-embracing: of little use. However, we have to recognize that the theatrical and literary experiments that shook the classical notion of representation in the twentieth century have been fruitful, not only in the arts, but also in terms of their repercussions in the human sciences. Law is no exception to this. On the contrary, its eminently representative nature benefits from being examined in the mirror of the critical experiments provided by fiction. This is, in a very condensed form, the initial postulate that will underpin our hypothesis, which will consist in showing the usefulness of investigating the notion of representation in law through art and literary theory, as well as through examples drawn from concrete theatrical and fictional works, owing to the light theatre and fiction can shed on the fragile balance, the “representational” razor, on which the law rests.

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