Publications related to Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham

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

On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

An improvement on the number of simplices in F-q(d)

Van Thang Pham

Let epsilon be a set of points in F-q(d). Bennett et al. (2016) proved that if \epsilon\ >> [GRAHICS] then epsilon determines a positive proportion of all k-simplices. In this paper, we give an improvement of this result in the case when epsilon is the Car ...

Elsevier Science Bv2017

INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

Alfio Quarteroni, Simone Deparis, Davide Forti

We are interested in the approximation of partial differential equations on domains decomposed into two (or several) subdomains featuring non-conforming interfaces. The non-conformity may be due to different meshes and/or different polynomial degrees used ...

Elsevier2016

The Interface Control Domain Decomposition Method For Stokes-Darcy Coupling

Alfio Quarteroni, Marco Discacciati

The interface control domain decomposition (ICDD) method of Discacciati, Gervasio, and Quarteroni [SIAM J. Control Optim., 51 (2013), pp. 3434-3458, doi:10.1137/120890764; J. Coupled Syst. Multiscale Dyn., 1 (2013), pp. 372-392, doi:10.1166/jcsmd.2013.1026 ...

Siam Publications2016

MATHICSE Technical Report : INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutations of PDEs on subdomains featuring non-conforming interfaces

Alfio Quarteroni, Simone Deparis, Davide Forti

We are interested in the approximation of partial differential equations on domains decomposed into two (or several) subdomains featuring non-conforming interfaces. The non-conformity may be due to different meshes and/or different polynomial degrees used ...

MATHICSE2015

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

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

2014

Extensions of a result of Elekes and Rónyai

Frank de Zeeuw

Many problems in combinatorial geometry can be formulated in terms of curves or surfaces containing many points of a cartesian product. In 2000, Elekes and Rónyai proved that if the graph of a polynomial f(x, y) contains cn2 points of an n × n × n cartesia ...

Elsevier2013

Incremental Query Evaluation in a Ring of Databases

Christoph Koch

This article approaches the incremental view maintenance problem from an algebraic perspective. The algebraic structure of a ring of databases is constructed and extended to form a powerful aggregate query calculus. The query calculus inherits the key prop ...

2013

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

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Four-Variable Expanders Over The Prime Fields

On some algebraic and extremal problems in discrete geometry

An improvement on the number of simplices in F-q(d)

INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

The Interface Control Domain Decomposition Method For Stokes-Darcy Coupling

MATHICSE Technical Report : INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutations of PDEs on subdomains featuring non-conforming interfaces

Isometries of quadratic spaces

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Extensions of a result of Elekes and Rónyai

Incremental Query Evaluation in a Ring of Databases

Four-Variable Expanders Over The Prime Fields

On some algebraic and extremal problems in discrete geometry

INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

Incremental Query Evaluation in a Ring of Databases

Isometries of quadratic spaces

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

An improvement on the number of simplices in F-q(d)

The Interface Control Domain Decomposition Method For Stokes-Darcy Coupling

Extensions of a result of Elekes and Rónyai

MATHICSE Technical Report : INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutations of PDEs on subdomains featuring non-conforming interfaces