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Concept

Fraction dyadique

Publications associées (26)

Rational Points in the Noether-Lefschetz Locus of Moduli Spaces of K3 Surfaces

Domenico Valloni

We give a characterization of rational points lying on the Noether-Lefschetz locus of moduli spaces of K3 surfaces by studying their lifting properties under some natural coverings of the ambient space. We then prove that the Bombieri-Lang conjecture impli ...

Oxford Univ Press2024

On rationally connected varieties over C1 fields of characteristic 0

Marta Pieropan

We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequenc ...

MATHEMATICAL SCIENCE PUBL2022

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

Soham Basu

Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...

CAMBRIDGE UNIV PRESS2021

Complements to Mugge and Friedel's Theory of Twinning

Cyril Cayron

The crystallography of twinning is based on the concepts of simple shear and obliquity introduced by Mugge, Mallard and Friedel at the turn of the last century, with tensor mathematics later developed by Bilby, Bevis and Crocker in the 1960s. We propose a ...

2020

Two-dimensional nanochannel membranes for molecular and ionic separations

Guangwei He, Yifan Li, Shaoyu Wang

Two-dimensional (2D) nanosheets have emerged as promising functional materials owing to their atomic thickness and unique physical/chemical properties. By using 2D nanosheets as building blocks, diverse kinds of two-dimensional nanochannel membranes (2DNCM ...

Royal Society of Chemistry2020

Presymplectic convexity and (ir)rational polytopes

Tudor Ratiu

In this paper, we extend the Atiyah-Guillemin-Sternberg convexity theorem and Delzant's classification of symplectic toric manifolds to presymplectic manifolds. We also define and study the Morita equivalence of presymplectic toric manifolds and of their c ...

2019

Moving on: Is Existenzminimum Still Relevant?

Bruno Marchand

In the inter-war period, progressive architects confronted the building of mass housing with an analogy with rational and functional workplaces. At the 2nd CIAM (Congres Internationaux d'Architecture Moderne), held in Frankfurt in 1929, this was tested aga ...

2019

Rationally isomorphic hermitian forms and torsors of some non-reductive groups

Eva Bayer Fluckiger

Let R be a semilocal Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an R-algebra with involution, which are rationally isomorphic and have isomorphic semisimple coradicals, are in fact isomorp ...

Academic Press Inc Elsevier Science2017

Some consequences of Masser's counting theorem on elliptic curves

We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...

Springer Heidelberg2017

Height of rational points on quadratic twists of a given elliptic curve

Pierre Francis André Le Boudec

We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion rational point on a quadratic twist of a given elliptic curve, as the twist varies. This conjecture seems to be very deep and we can prove only partial resul ...

Oxford Univ Press2016

Motivic Classes of Nakajima Quiver Varieties

Dimitri Stelio Wyss

We prove that Hausel’s formula for the number of rational points of a Nakajima quiver variety over a finite field also holds in a suitable localization of the Grothendieck ring of varieties. In order to generalize the arithmetic harmonic analysis in his pr ...

2016

Deductive Synthesis and Repair

Etienne Kneuss

In this thesis, we explore techniques for the development of recursive functional programs over unbounded domains that are proved correct according to their high-level specifications. We present algorithms for automatically synthesizing executable code, st ...

EPFL2016

A Polynomial Regularity Lemma For Semialgebraic Hypergraphs And Its Applications In Geometry And Property Testing

János Pach

In this paper, we prove several extremal results for geometrically defined hypergraphs. In particular, we establish an improved lower bound, single exponentially decreasing in k, on the best constant delta > 0 such that the vertex classes P-1,...,P-k of ev ...

Society for Industrial and Applied Mathematics2016

Density of Rational Points on a Certain Smooth Bihomogeneous Threefold

Pierre Francis André Le Boudec

We establish sharp upper and lower bounds for the number of rational points of bounded anticanonical height on a smooth bihomogeneous threefold defined over Q and of bidegree (1, 2). These bounds are in agreement with Manin's conjecture. ...

Oxford University Press2015

Fast Detection and Refined Scale Estimation Using Complex Isotropic Wavelets

Michaël Unser, Daniel Sage, John Paul Ward, Zsuzsanna Püspöki

The dyadic scaling in the discrete wavelet transform can lead to a loss of precision, in comparison to the computationally unrealistic continuous wavelet transform. To overcome this obstacle, we propose a novel method to locally scale wavelets between dyad ...

IEEE2015

Linear Growth for Certain Elliptic Fibrations

Pierre Francis André Le Boudec

We prove that the number of rational points of bounded height on certain del Pezzo surfaces of degree 1 defined over Q grows linearly, as predicted by Manin's conjecture. ...

Oxford University Press2015

Affine congruences and rational points on a certain cubic surface

Pierre Francis André Le Boudec

We establish estimates for the number of solutions of certain affine congruences. These estimates are then used to prove Manin's conjecture for a cubic surface split over Q whose singularity type is D-4. This improves on a result of Browning and answers a ...

Mathematical Science Publ2014

Density of rational points on del Pezzo surfaces of degree one

We state conditions under which the set S(k) of k-rational points on a del Pezzo surface S of degree 1 over an infinite field k of characteristic not equal to 2 or 3 is Zariski dense. For example, it suffices to require that the elliptic fibration S -> P-1 ...

Academic Press Inc Elsevier Science2014

Time-Domain Implementation of Cooray-Rubinstein Formula via Convolution Integral and Rational Approximation

Farhad Rachidi-Haeri

One of the most popular techniques to take into account the finite ground conductivity in the evaluation of the radial component of the electric field generated by a lightning return stroke is the Cooray-Rubinstein (CR) formula. As this formula is derived ...

2011

Mechanisms for Making Crowds Truthful

Boi Faltings, Radu Jurca

We consider schemes for obtaining truthful reports on a common but hidden signal from large groups of rational, self-interested agents. One example are online feedback mechanisms, where users provide observations about the quality of a product or service s ...

AI Access Foundation2009

Publications associées (26)

Oxford University Press2015