Algebraic equation

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A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

Assyr Abdulle, Giacomo Rosilho De Souza

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic problems in high gra ...

EDP SCIENCES S A2019

Generalized Optical Signal Processing Based on Multioperator Metasurfaces Synthesized by Susceptibility Tensors

Karim Achouri, Ali Momeni

This paper theoretically proposes a multichannel nonlocal metasurface computer characterized by generalized sheet transition conditions (GSTCs) and surface susceptibility tensors. The study explores polarization- and angle-multiplexed metasurfaces enabling ...

American Physical Society (APS)2019

The Center of Small Quantum Groups I: The Principal Block in Type A

Anna Lachowska

We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The cases of sl(3) and sl(4) are computed explicitly. This allows us to for ...

OXFORD UNIV PRESS2018

Stable high-order randomized cubature formulae in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

2022

A semi-algebraic version of Zarankiewicz's problem

János Pach

A bipartite graph G is semi-algebraic in R-d if its vertices are represented by point sets P,Q subset of R-d and its edges are defined as pairs of points (p,q) epsilon P x Q that satisfy a Boolean combination of a fixed number of polynomial equations and i ...

European Mathematical Soc2017

Boolean logic optimization in majority-inverter graphs

Giovanni De Micheli, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù

We present a Boolean logic optimization framework based on Majority-Inverter Graph (MIG). An MIG is a directed acyclic graph consisting of three-input majority nodes and regular/complemented edges. Current MIG optimization is supported by a consistent alge ...

2016

Data Reconciliation in Open Reaction Systems using the Concept of Extents

Dominique Bonvin, Julien Léo Billeter, Sriniketh Srinivasan

Kinetic models of chemical reaction systems are typically represented in terms of state variables, such as concentrations, temperature and partial pressures [1]. These state variables in turn depend on the underlying reactions, transfer phenomena, and tran ...

2015

A Decision Procedure for Regular Membership and Length Constraints over Unbounded Strings

Andrew Joseph Reynolds

We prove that the quantifier-free fragment of the theory of character strings with regular language membership constraints and linear integer constraints over string lengths is decidable. We do that by describing a sound, complete and terminating tableaux ...

Springer-Verlag Berlin2015

Enumeration-based approach to solving parametric linear complementarity problems

Colin Neil Jones

This paper presents a solution method for parametric linear complementarity problems (PLCP) that relies on an enumeration technique to discover all feasible bases. The enumeration procedure is based on evaluating all possible combinations of active constra ...

Elsevier2015

Algebraic Nahm transform for parabolic Higgs bundles on P^1

Szilárd Szabó

We formulate the Nahm transform in the context of parabolic Higgs bundles on P^1 and extend its scope in completely algebraic terms. This transform requires parabolic Higgs bundles to satisfy an admissibility condition and allows Higgs fields to have poles ...

2014

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