Related papers: The Curious Case of Integrator Reach Sets, Part I:…
This PhD thesis aims at combining the framework of noncommutative geometry and supersymmetry. A particular class of non-commutative geometries called almost-commutative geometries can be used to describe particle theories. This thesis…
The present work considers the properties of classes of generally convex sets in the plane known as $1$-semiconvex and weakly $1$-semiconvex. More specifically, the examples of open and closed weakly $1$-semiconvex but non $1$-semiconvex…
The goal of this article is the study of homogeneous Riemannian structure tensors within the framework of reduction under a group $H$ of isometries. In a first result, $H$ is a normal subgroup of the group of symmetries associated to the…
Optimizing an implicational base of a closure system consists in turning this implicational base into an equivalent one with premises and conclusions as small as possible. This task is known to be hard in general but tractable for a number…
We show that any compact connected semialgebraic set is the projection of a connected component of the configuration space of a linkage.
We introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian product, convex hull, intersection, union, and quadratic as well as higher-order maps. We show…
This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial…
The general structure of semi-inclusive polarized electron scattering from polarized spin-1/2 targets is developed for use at all energy scales, from modest-energy nuclear physics applications to use in very high energy particle physics.…
In this work we prove constructively that the complement ${\mathbb R}^n\setminus{\mathcal K}$ of an $n$-dimensional unbounded convex polyhedron ${\mathcal K}\subset{\mathbb R}^n$ and the complement ${\mathbb R}^n\setminus{\rm Int}({\mathcal…
We consider a compact submanifold $M$ of a Riemannian manifold $N$ and we use the second variation formula as a tool to drive some geometric results on reach$(M, N)$ the reach of $M$ in $N$, including some useful relations between the…
This PhD thesis studies the broken ray transform, a generalization of the geodesic X-ray transform where geodesics are replaced with broken rays that reflect on a part of the boundary. The fundamental question is whether this transform is…
We extend the proof in [M.~Crouzeix and C.~Palencia, {\em The numerical range is a $(1 + \sqrt{2})$-spectral set}, SIAM Jour.~Matrix Anal.~Appl., 38 (2017), pp.~649-655] to show that other regions in the complex plane are $K$-spectral sets.…
This paper is the last in a series of three papers which investigate pseudoholomorphic strips in the symplectisation of a three dimensional closed contact manifold with a mixed boundary condition. We will prove a compactness and an…
The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.
We consider the complex cut polytope: the convex hull of Hermitian rank 1 matrices $xx^{\mathrm{H}}$, where the elements of $x \in \mathbb{C}^n$ are $m$th unit roots. These polytopes have applications in ${\text{MAX-3-CUT}}$, digital…
Ellipsoids are a common representation for reachability analysis, because they can be transformed efficiently under affine maps, and allow conservative approximation of Minkowski sums, which let one incorporate uncertainty and linearization…
Convex sets appear in various mathematical theories, and are used to define notions such as convex functions and hulls. As an abstraction from the usual definition of convex sets in vector spaces, we formalize in Coq an intrinsic…
This paper proposes an intrinsic pseudospectral convexification framework for optimal control problems with manifold constraints. While successive pseudospectral convexification combines spectral collocation with successive convexification,…
We study two notions. One is that of spindle convexity. A set of circumradius not greater than one is spindle convex if, for any pair of its points, it contains every short circular arc of radius at least one, connecting them. The other…
This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…