Publications associées à Completeness of the real numbers

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

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

The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...

2021

Test and lower bound modeling of keyed shear connections in RC shear walls

Aurelio Muttoni, Cao Linh Hoang, Jesper Harrild Sorensen

This paper presents an investigation into the ultimate behavior of a recently developed design for keyed shear connections. The influence of the key depth on the failure mode and ductility of the connection has been studied by push-off tests. The tests sho ...

Engineering Structures2018

Fréchet means in Wasserstein space : theory and algorithms

Yoav Zemel

This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces,

\mathcal W_2 ( \mathbb R^d )

. This question arises naturally from the problem of separating amplitude and phase variation i ...

EPFL2017

Embeddings of maximal tori in classical groups over local and global fields

Eva Bayer Fluckiger, Ting-Yu Lee

Embeddings of maximal tori in classical groups over fields of characteristic not 2 are the subject matter of several recent papers. The aim of the present paper is to give necessary and sufficient conditions for such an embedding to exist, when the base fi ...

Turpion Ltd2016

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Michaël Unser, Martin Kurt Storath

We consider

L ^{ 1 }

-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is nonconvex for circle-valued data. In this paper, we deriv ...

SIAM2016

Obstacles For Splitting Multidimensional Necklaces

Michal Lason

The well-known "necklace splitting theorem" of Alon (1987) asserts that every k-colored necklace can be fairly split into q parts using at most t cuts, provided k(q - 1)

Amer Mathematical Soc2015

Lower bounds for Pythagoras numbers of function fields

David Maximilian Grimm

We show that the transcendence degree of a real function field over an arbitrary real base field is a strict lower bound for its Pythagoras number and a weak lower bound for all its higher Pythagoras numbers. ...

European Mathematical Soc2015

Modeling and Flatness of Rigid and Flexible Cable Suspended Underactuated Robots

Philippe Müllhaupt, Basile Graf

A modeling framework is proposed for the control of rigid and flexible cable-like systems such as cranes, together with a systematic algorithm for computing flat outputs of mechanical systems for which the flat output is a linear combi- nation of free coor ...

IEEE2010

Modeling and Flatness of Rigid and Flexible Cable Suspended Underactuated Robots

Philippe Müllhaupt, Basile Graf

A modeling framework is proposed for the control of rigid and flexible cable-like systems such as cranes, together with a systematic algorithm for computing flat outputs of mechanical systems for which the flat output is a linear combination of the free co ...

2010

Contribution to the ergodic theory of piecewise monotone continuous maps

Bastien Faller

This thesis is devoted to the ergodic theory of the piecewise monotone continuous maps of the interval. The coding is a classical approach for these maps. Thanks to the coding, we get a symbolic dynamical system which is almost isomorphic to the initial dy ...

EPFL2008

Recent evolution of the simulation tools for computer aided design of electron-optical systems for powerful gyrotrons

Jean-Philippe Hogge, Trach-Minh Tran, Ioannis Pagonakis

Computer aided design of powerful gyrotrons for electron cyclotron resonance heating and current drive of fusion plasmas requires adequate physical models and efficient software packages for analysis, comparison and optimization of their electron-optical s ...

2007