Publications associées à Équation du second degré

Hierarchy of quasisymmetries and degeneracies in the CoSi family of chiral crystal materials

Philip Johannes Walter Moll, Chunyu Guo, Yi-Chiang Sun

In materials, certain approximated symmetry operations can exist in a lower-order approximation of the effective model but are good enough to influence the physical responses of the system, and these approximated symmetries were recently dubbed "quasisymme ...

AMER PHYSICAL SOC2023

Simulating supercontinua from mixed and cascaded nonlinearities

Luis Guillermo Villanueva Torrijo, Victor Brasch, Furkan Ayhan, Tobias Herr, Thibault Voumard

Nonlinear optical frequency conversion is of fundamental importance in photonics and underpins countless of its applications: Sum- and difference-frequency generation in media with quadratic nonlinearity permits reaching otherwise inaccessible wavelength r ...

AIP Publishing2023

A finiteness result for p-adic families of Bianchi modular forms

Vlad Serban

We study p-adic families of cohomological automorphic forms for GL(2) over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of classical cuspidal automorphic forms only occur under very restrictive conditions. We show ho ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

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

Apparent diffusion coefficient measured by diffusion MRI of moving and deforming domains

Jan Sickmann Hesthaven

The modeling of the diffusion MRI signal from moving and deforming organs such as the heart is challenging due to significant motion and deformation of the imaged medium during the signal acquisition. Recently, a mathematical formulation of the Bloch-Torre ...

Academic Press Inc - Elsevier Science2020

The fourth moment of individual Dirichlet L-functions on the critical line

Berke Topacogullari

We prove an asymptotic formula for the second moment of a product of two Dirichlet L-functions on the critical line, which has a power saving in the error term and which is uniform with respect to the involved Dirichlet characters. As special cases we give ...

2021

Compact high order finite volume method on unstructured grids IV: Explicit multi-step reconstruction schemes on compact stencil

Qian Wang

In the present paper, a multi-step reconstruction procedure is proposed for high order finite volume schemes on unstructured grids using compact stencil. The procedure is a recursive algorithm that can eventually provide sufficient relations for high order ...

2019

Efficient Verifiable Delay Functions

Benjamin Pierre Charles Wesolowski

We construct a verifiable delay function (VDF). A VDF is a function whose evaluation requires running a given number of sequential steps, yet the result can be efficiently verified. They have applications in decentralised systems, such as the generation of ...

SPRINGER INTERNATIONAL PUBLISHING AG2019

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham, Seyed Hossein Nassajianmojarrad

Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

AMER MATHEMATICAL SOC2018

Statistical physics approaches to subnetwork dynamics in biochemical systems

Barbara Bravi

We apply a Gaussian variational approximation to model reduction in large biochemical networks of unary and binary reactions. We focus on a small subset of variables (subnetwork) of interest, e.g. because they are accessible experimentally, embedded in a l ...

Iop Publishing Ltd2017

A feasible-side globally convergent modifier-adaptation scheme

Dominique Bonvin, Timm Faulwasser, Alejandro Gabriel Marchetti

In the context of static real-time optimization (RTO) of uncertain plants, the standard modifier-adaptation scheme consists in adding first-order correction terms to the cost and constraint functions of a model based optimization problem. If the algorithm ...

Elsevier Sci Ltd2017

Patching And Weak Approximation In Isometry Groups

Eva Bayer Fluckiger

Let R be a semilocal principal ideal domain. Two algebraic objects over R in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all completions of R and its fract ...

Amer Mathematical Soc2017

Quadratic Sieving

Thorsten Kleinjung

We propose an efficient variant for the initialisation step of quadratic sieving, the sieving step of the quadratic sieve and its variants, which is also used in sieving-based algorithms for computing class groups of quadratic fields. As an application we ...

American Mathematical Society2016

Quadratic variance swap models

Damir Filipovic, Loriano Mancini

We introduce a novel class of term structure models for variance swaps. The multivariate state process is characterized by a quadratic diffusion function. The variance swap curve is quadratic in the state variable and available in closed form, greatly faci ...

Elsevier2016

Enumeration of reversible functions and its application to circuit complexity

Giovanni De Micheli, Mathias Soeken, Nabila Abdessaied

We review combinational results to enumerate and classify reversible functions and investigate the application to circuit complexity. In particularly, we consider the effect of negating and permuting input and output variables and the effect of applying li ...

Springer2016

Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains

Alfio Quarteroni, Simone Deparis, Davide Forti

The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid-structure interactions and on the other hand the use of a material ...

Wiley2016

Computational Aspects of Jacobians of Hyperelliptic Curves

Alina Dudeanu

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

EPFL2016

Isometries of quadratic spaces

Eva Bayer Fluckiger

Let k be a global field of characteristic not 2, and let f is an element of k[X] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the compl ...

European Mathematical Soc2015

Producing absorption mode Fourier transform ion cyclotron resonance mass spectra with non-quadratic phase correction functions

Yury Tsybin, Anton Kozhinov, Konstantin Nagornov, Konstantin Zhurov

RATIONALE: Previously described methods for producing absorption mode Fourier transform ion cyclotron resonance (FTICR) mass spectra have all relied on the phase correction function being quadratic. This assumption has been found to be invalid for some ins ...

Wiley-Blackwell2015

Shimura Curves and Special Values of p-adic L-functions

Ernest Hunter Brooks

We construct "generalized Heegner cycles" on a variety fibered over a Shimura curve, defined over a number field. We show that their images under the p-adic Abel-Jacobi map coincide with the values (outside the range of interpolation) of a p-adic L-functio ...

Oxford University Press2015