Publications related to Diophantine equation

Spectral methods for multiscale stochastic differential equations

This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free method, which rely o ...

2017

MATHICSE Technical Report : Spectral methods for multiscale stochastic differential equations

Assyr Abdulle, Grigorios A. Pavliotis

This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free method, which rely o ...

MATHICSE2016

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Afsaneh Asaei, Mohammadjavad Taghizadeh, Saeid Haghighatshoar

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation

Ax=b

, where

A

is an

m\times n

full-rank matrix,

b

is a column-vector of dimension

m

, and

m

(the number of equations) is larger tha ...

2015

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Afsaneh Asaei, Mohammadjavad Taghizadeh, Saeid Haghighatshoar

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation

Ax=b

, where

A

is an

m\times n

full-rank matrix,

b

is a column-vector of dimension

m

, and

m

(the number of equations) is larger tha ...

Idiap2015

Diophantine properties of nilpotent Lie groups

A finitely generated subgroup F of a real Lie group G is said to be Diophantine if there is beta > 0 such that non-trivial elements in the word ball B-Gamma(n) centered at 1 is an element of F never approach the identity of G closer than broken vertical ba ...

London Mathematical Society, Cambridge2015

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

Jean-Christophe Mourrat

The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For s ...

Springer Heidelberg2014

Nonlinear Analysis of a Coaxial Microhelicopter with a Bell Stabilizer Bar

Philippe Müllhaupt, Basile Graf

Nonlinear modeling of coaxial microhelicopters is studied. All equations are derived using a Lagrangian approach and simplified aerodynamics assumptions so that all parameters have a physical meaning; there is no “black box.” The model is constructed with ...

Amer Helicopter Soc Inc2014

Coupled equations for Kahler metrics and Yang-Mills connections

Mario Garcia Fernandez

We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kahler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kahler metric and Hermite-Yang-Mi ...

Geometry & Topology Publications2013

ElimLin Algorithm Revisited

Serge Vaudenay, Pouyan Sepehrdad, Petr Susil

ElimLin is a simple algorithm for solving polynomial systems of multivariate equations over small finite fields. It was initially proposed as a single tool by Courtois to attack DES. It can reveal some hidden linear equations existing in the ideal generate ...

Springer2012

Le "Fragmentum de inventionibus scientiarum" de Diego Palomino

Nouara Chekhar

The objective of this PhD thesis is the translation of, and the mathematical commentary on, a 16th-century Latin book. Its author, Diego Palomino is not well known. With a background in theology, he was a prior. In order to obtain his PhD at the University ...

EPFL2012

Diophantine equation

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Spectral methods for multiscale stochastic differential equations

MATHICSE Technical Report : Spectral methods for multiscale stochastic differential equations

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Diophantine properties of nilpotent Lie groups

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

Nonlinear Analysis of a Coaxial Microhelicopter with a Bell Stabilizer Bar

Coupled equations for Kahler metrics and Yang-Mills connections

ElimLin Algorithm Revisited

Le "Fragmentum de inventionibus scientiarum" de Diego Palomino

Diophantine properties of nilpotent Lie groups

ElimLin Algorithm Revisited

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Spectral methods for multiscale stochastic differential equations

MATHICSE Technical Report : Spectral methods for multiscale stochastic differential equations

Nonlinear Analysis of a Coaxial Microhelicopter with a Bell Stabilizer Bar

Le "Fragmentum de inventionibus scientiarum" de Diego Palomino

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

Coupled equations for Kahler metrics and Yang-Mills connections