Concept

Facet (geometry)

Related publications (19)

Reduced order modelling of nonaffine problems on parameterized NURBS multipatch geometries

Annalisa Buffa, Pablo Antolin Sanchez, Margarita Chasapi

This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework based on a single g ...

2022

Site-selective overgrowth of Ag nanocrystals by Polyvinylpyrrolidone-mediated atom deposition by Ostwald ripening

Francesco Stellacci, Paulo Henrique Jacob Silva, Alejandro Lapresta Fernandez

The growth modulation of metal nanocrystals (NCs) by Ostwald ripening (OR) involves control of the relocation of matter by diffusional mass transfer from the dissolution of small nanocrystals (SNCs) towards large nanocrystals whose surface energy is lower. ...

ELSEVIER2022

Promoting Persistent Superionic Conductivity in Sodium Monocarba-closo-dodecaborate NaCB11H12 via Confinement within Nanoporous Silica

Mirjana Dimitrievska

Superionic phases of bulk anhydrous salts based on large cluster-like polyhedral (carba)borate anions are generally stable only well above room temperature, rendering them unsuitable as solid-state electrolytes in energy-storage devices that typically oper ...

AMER CHEMICAL SOC2021

Complexity of linear relaxations in integer programming

Matthias Schymura

For a set X of integer points in a polyhedron, the smallest number of facets of any polyhedron whose set of integer points coincides with X is called the relaxation complexity rc(X). This parameter was introduced by Kaibel & Weltge (2015) and captures the ...

2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

On 2-Level Polytopes Arising In Combinatorial Settings

Yuri Faenza, Manuel Francesco Aprile, Alfonso Bolívar Cevallos Manzano

2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arisi ...

SIAM PUBLICATIONS2018

On some problems related to 2-level polytopes

Manuel Francesco Aprile

In this thesis we investigate a number of problems related to 2-level polytopes, in particular from the point of view of the combinatorial structure and the extension complexity. 2-level polytopes were introduced as a generalization of stable set polytopes ...

EPFL2018

Extension complexity of stable set polytopes of bipartite graphs

Yuri Faenza, Manuel Francesco Aprile

The extension complexity xc(P) of a polytope P is the minimum number of facets of a polytope that affinely projects to P. Let G be a bipartite graph with n vertices, m edges, and no isolated vertices. Let STAB(G) be the convex hull of the stable sets of G. ...

Springer2017

On vertices and facets of combinatorial 2-level polytopes

Yuri Faenza, Manuel Francesco Aprile, Alfonso Bolívar Cevallos Manzano

2-level polytopes naturally appear in several areas of mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. We investigate upper bounds on the product of the number of facets and the number ...

Springer2016

Differential geometry applied to crystallography

Philippe Kocian

The mathematical facet of modern crystallography is essentially based on analytical geometry, linear algebra as well as group theory. This study endeavours to approach the geometry and symmetry of crystals using the tools furnished by differential geometry ...

EPFL2009

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