403 research outputs found
Small points on subvarieties of a torus
Full text linkLet V be a subvariety of a torus defined over the algebraic numbers. We give a qualitative and quantitative description of the set of points of V of height bounded by invariants associated to any variety containing V . Especially, we determine whether such a set is or is not dense in V . We then prove that these sets can always be written as the intersection of V with a finite union of translates of tori of which we control the sum of the degrees. As a consequence, we prove a conjecture by the first author and David up to a logarithmic factor
Concentric Tori in the Three-Spere
Full text linkA torus is the topological product of two circles, while a solid torus is the topological product of a circle and a disk. Two solid tori B1 and B2 in the three-sphere S^3, with B2 interior to B1, are said to be concentric if and only if the closure of B1-B2 (the set of points in B1 but not in B2) is homeomorphic to the topological product of a torus and a closed interval. Two tori in S^3 are concentric if and only if they are respectively the boundaries of two concentric solid tori
Capital in Crisis: Tadeusz Kowalik on the Birth and Development of Capitalism
No full textQuesto capitolo mira a introdurre i temi principali delle due voci scritte da Tadeusz Kowalik per l'Enciclopedia Einaudi. Questi due lunghi saggi rappresentano ulteriori sviluppi dell'interpretazione di Kowalik della natura del capitale e delle cause e delle conseguenze degli sviluppi ciclici nel capitalismo.
Mentre il capitolo è diviso in due sezioni corrispondenti alle due voci, allo stesso tempo cerca di evidenziare il metodo strutturale dell'autore per cui le categorie di capitale e crisi sono storicamente, economicamente e politicamente intrecciate.This chapter aims at introducing the key themes in two entries written by Tadeusz Kowalik for the Encyclopaedia Einaudi. These two long essays represent further developments of Kowalik’s interpretation of the nature of capital and the cause and consequences of cyclical developments in capitalism.
While the chapter is divided into two sections corresponding to the two entries, at the same time it tries to highlight the structural method of the author for which the categories of capital and crisis are historically, economically and politically entangled
On actions of tori and quaternionic tori on products of spheres
Full text linkIn this paper we study the actions of tori (standard compact tori, as well as
their quaternionic analogues) on products of spheres. It is proved that the
orbit space of a specific action of a torus on a product of spheres is
homeomorphic to a sphere. A similar statement for a real torus
was proved by the second author in 2019. We also provide a statement about
arbitrary compact topological groups, generalizing the mentioned results, as
well as the results of the first author about the actions of a compact torus of
complexity one.Comment: 10 page
The Herman invariant tori conjecture
Full text linkWe study a new type of normal form at a critical point of an analytic
Hamiltonian. Under a Bruno condition on the frequency, we prove a convergence
statement to the normal form. Using this result, we prove the Herman invariant
tori conjecture namely the existence of a positive measure set of invariant
tori near the critical point. This paper is an update of the first 2012 proof
of the author. The functional analytic arguments have been simplified using
Banach functors, minor points have been clarified.
A series of videos is available on the webpage
https://www.agtz.mathematik.uni-mainz.de/category/alg-geom
Convergence of Fuzzy Tori and Quantum Tori for the Quantum Gromov-Hausdorff Propinquity: An Explicit Approach
No full textQuantum tori are limits of finite dimensional C*-algebras for the quantum Gromov-Hausdorff propinquity, a metric defined by the author as a strengthening of Rieffel’s quantum Gromov-Hausdorff designed to retain the C*-algebraic structure. In this paper, we propose a proof of the continuity of the family of quantum and fuzzy tori which relies on explicit representations of the C*-algebras rather than on more abstract arguments, in a manner which takes full advantage of the notion of bridge defining the quantum propinquity
Lie tori of rank 1
No full textThis article is based on a talk presented by the first author at the conference on Lie and Jordan Algebras, their Representations and Applications held in Guarujá, Brazil in May 2004. The article surveys some recent progress by a number of authors in the study of extended affine Lie algebras and some closely related Lie algebras called Lie tori
Exploring the Relationship Between the Weight of a Shoulder Purse and Symptoms in the Upper Body
No full textAbstract
Date Presented 3/30/2017
Women (ages 18–79 yr) were surveyed to evaluate their upper-body symptoms associated with carrying a shoulder purse. The significant results will promote awareness of this risk in the field of occupational therapy and prevent further upper-body injuries that may limit occupational performance.
Primary Author and Speaker: Tori Cutshall
Contributing Authors: Edward Mihelcic</jats:p
Minimal periods of holomorphic maps on complex tori
No full textAgraïments: The second author is partially supported by a NSFC grant number 11001172 and by a CUTECH grant number 20100073120067.We study the set of minimal periods of holomorphic self-maps of one and two dimensional complex tori. In particular we characterize when the set of minimal periods of such maps is finite. In fact we have an algorithm for doing this characterization for holomorphic self-maps of an arbitrary dimensional complex tori
Persistence of Hyperbolic Tori in Hamiltonian Systems
No full text1991 Mathematics Subject Classification. 37J40.We generalize the well-known result of Graff and Zehnder on the persistence of hyperbolic invariant tori in Hamiltonian systems by considering non-Floquet, frequency varying normal forms and allowing the degeneracy of
the unperturbed frequencies. The preservation of part or full frequency components associated to the degree of non-degeneracy is considered. As applications, we consider the persistence problem of hyperbolic tori on a submanifold
of a nearly integrable Hamiltonian system and the persistence problem of a fixed invariant hyperbolic torus in a non-integrable Hamiltonian system.The first author is partially supported by NSFC 19971042, National 973 Key Project of China: Nonlinearity, the outstanding young's project of Ministry of Education of China, and National outstanding young's award of China. The second author was partially supported by NSF grant DMS0204119
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