Search results for "Conjecture"

Quantum Mechanics from Periodic Dynamics: the bosonic case

2010

Enforcing the periodicity hypothesis of the "old" formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a Deterministic Field Theory [arXiv:0903.3680]. A novel interpretation of the AdS/CFT conjecture is discussed.

Higher genera Catalan numbers and Hirota equations for extended nonlinear Schrödinger hierarchy

2021

We consider the Dubrovin--Frobenius manifold of rank $2$ whose genus expansion at a special point controls the enumeration of a higher genera generalization of the Catalan numbers, or, equivalently, the enumeration of maps on surfaces, ribbon graphs, Grothendieck's dessins d'enfants, strictly monotone Hurwitz numbers, or lattice points in the moduli spaces of curves. Liu, Zhang, and Zhou conjectured that the full partition function of this Dubrovin--Frobenius manifold is a tau-function of the extended nonlinear Schr\"odinger hierarchy, an extension of a particular rational reduction of the Kadomtsev--Petviashvili hierarchy. We prove a version of their conjecture specializing the Givental--M…

The words of conjecture. Semiotics and epistemology in ancient medicine and rhetoric

2016

This article considers the epistemology of Classical rhetoric and Hippocratic medicine, focusing on two key terms: semeion and tekmerion. Through an analysis of the specific case of ancient Greek medicine and rhetoric, we hope to bring out the conjectural and fallible nature of human knowledge. The paper focuses on the epistemological and methodological affinity between these two ancient technai, and considers the medical uses of semeion and tekmerion in the light of their meaning in the rhetorical sphere. Chronologically, the analysis follows an inverse pathway: it starts from Aristotle and from Rhetorica ad Alexandrum, and then moves on to Antiphon’s texts (chosen as an exemplary case) an…

The cohomology of a variation of polarized Hodge structures over a quasi-compact Kähler manifold

2007

In this article, we consider the cohomologies with coefficients in a variation of polarized Hodge structures on a quasi-compact Kaehler manifold. We show that the L 2 L^2 -Dolbeault cohomology can be identified with the L 2 L^2 cohomology; we also give several direct applications of the result above.

Algebraic de Rham Cohomology

2017

Let k be a field of characteristic zero. We are going to define relative algebraic de Rham cohomology for general varieties over k, not necessarily smooth.

Non-equivalent hyperbolic knots

2002

We construct, for each integer n 3, pairs of non-equivalent hyperbolic knots with the same 2fold and n-fold cyclic branched covers. We also discuss necessary conditions for such pairs of knots to exist.  2001 Elsevier Science B.V. All rights reserved. MSC: primary 57M25; secondary 57M12, 57M50

Steiner configurations ideals: Containment and colouring

2021

Given a homogeneous ideal I&sube

Champs de vecteurs analytiques et champs de gradients

2002

A theorem of Łojasiewicz asserts that any relatively compact solution of a real analytic gradient vector field has finite length. We show here a generalization of this result for relatively compact solutions of an analytic vector field X with a smooth invariant hypersurface, transversally hyperbolic for X, where the restriction of the field is a gradient. This solves some instances of R. Thom's Gradient Conjecture. Furthermore, if the dimension of the ambient space is three, these solutions do not oscillate (in the sense that they cut an analytic set only finitely many times); this can also be applied to some gradient vector fields.

Landis-type conjecture for the half-Laplacian

2023

In this paper, we study the Landis-type conjecture, i.e., unique continuation property from infinity, of the fractional Schrödinger equation with drift and potential terms. We show that if any solution of the equation decays at a certain exponential rate, then it must be trivial. The main ingredients of our proof are the Caffarelli-Silvestre extension and Armitage’s Liouville-type theorem. peerReviewed

Recensione a: Vitae Vergilianae antiquae, ediderunt G. Brugnoli et F. Stok, Romae 1997

2000