Related papers: Linear Geometry: flats, ranks, regularity, paralle…
The Centre Symmetry Set of a planar curve $M$ is the envelope of affine chords of $M$, i.e. the lines joining points on $M$ with parallel tangent lines. In this paper we study global geometrical properties of this set including the number…
In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.
We first establish several general properties of modality of algebraic group actions. In particular, we introduce the notion of a modality-regular action and prove that every visible action is modality-regular. Then, using these results, we…
Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By a proper subset one understands a set included in A,…
In this paper, we define a new type of ruled surface called ruled surface by using the alternative frame of a base curve. Then, we study its differential geometric properties such as striction line, distribution parameter, fundamental…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…
The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the…
The space ML(F) of measured geodesic laminations on a given closed hyperbolic surface F has a canonical linear structure arising in fact from different sources in 2-dimensional hyperbolic (earthquake theory) or complex projective (grafting)…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Inspired by the classical theory of modules over a monoid, we give a first account of the natural notion of module over a monad. The associated notion of morphism of left modules ("Linear" natural transformations) captures an important…
Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view…
In this paper, we investigate the continuity of linear and sublinear correspondences defined on cones in normed spaces. We also generalize some known results for sublinear correspondences.
In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold $\mathbb{L}$, there exists a global trivialization of the tangent bundle, which defines a map…
The initial techniques developed in Euclid's Elements, well before the use of the parallel postulate, are reexamined in order to clarify even the most obscure details, particularly those related to equality, superposition and angle…
We describe a notion of (abstract) projective line over a field as a set equipped with a certain first order structure, and a projectivity between projective lines as a bijection preserving this structure. The structure in question is that…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…