Publications related to Elliptic curve

Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

Fabio Nobile, Daniel Kressner, Francesca Bonizzoni

We study an elliptic equation with stochastic coefficient modeled as a lognormal random field. A perturbation approach is adopted, expanding the solution in Taylor series around the nominal value of the coefficient. The resulting recursive deterministic pr ...

Elsevier2016

On The Number Of Ordinary Conics

Frank de Zeeuw, Adrian Claudiu Valculescu

We prove a lower bound on the number of ordinary conics determined by a finite point set in R-2. An ordinary conic for S subset of R-2 is a conic that is determined by five points of S and contains no other points of S. Wiseman and Wilson proved the Sylves ...

Siam Publications2016

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

János Pach, Gábor Tardos

A long-standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least ...

Cambridge Univ Press2016

MATHICSE Technical Report : Analysis of the internodes method for non-conforming discretizations of elliptic equations

Alfio Quarteroni

INTERNODES is a general method to deal with non-conforming discretizations of second order partial differential equations on regions partitioned into two or several subdomains. It exploits two intergrid interpolation operators, one for transfering the Diri ...

MATHICSE2016

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

Alfio Quarteroni, Gianluigi Rozza, Laura Iapichino

The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to ...

Elsevier2016

Medial axis transformation as a solid modeling representation method for computer aided design software

Paul Xirouchakis, Mihai-Bogdan Lazar, Ian Anthony Stroud, Florian Barras, Guillaume Goualard

A method for achieving a representation of an object within a data structure for a Computer Aided Design system employing a Medial Axis Transformation (MAT), the representation of the object comprising a set of adjacent bounded surface elements called MAT ...

2016

An Inner-Product Calculus for Periodic Functions and Curves

Michaël Unser, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and

L _{ 2 }

distances between such curves. In partic ...

2016

Cloaking using complementary media in the quasistatic regime

Hoài-Minh Nguyên

Cloaking using complementary media was suggested by Lai et al. in [8]. The study of this problem faces two difficulties. Firstly, this problem is unstable since the equations describing the phenomenon have sign changing coefficients, hence the ellipticity ...

2016

Non-autonomous functionals, borderline cases and related function classes

Maria Colombo

The class of non-autonomous functionals under study is characterized by the fact that the energy density changes its ellipticity and growth properties according to the point; some regularity results are proved for related minimizers. These results are the ...

2016

Analytic regularity and collocation approximation for elliptic PDEs with Random domain deformations

Fabio Nobile

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remap ...

2016

Elliptic curve

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Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

On The Number Of Ordinary Conics

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

MATHICSE Technical Report : Analysis of the internodes method for non-conforming discretizations of elliptic equations

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

Medial axis transformation as a solid modeling representation method for computer aided design software

An Inner-Product Calculus for Periodic Functions and Curves

Cloaking using complementary media in the quasistatic regime

Non-autonomous functionals, borderline cases and related function classes

Analytic regularity and collocation approximation for elliptic PDEs with Random domain deformations

Non-autonomous functionals, borderline cases and related function classes

MATHICSE Technical Report : Analysis of the internodes method for non-conforming discretizations of elliptic equations

An Inner-Product Calculus for Periodic Functions and Curves

Analytic regularity and collocation approximation for elliptic PDEs with Random domain deformations

Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

Medial axis transformation as a solid modeling representation method for computer aided design software

On The Number Of Ordinary Conics

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

Cloaking using complementary media in the quasistatic regime