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pro vyhledávání: '"Prieto–Martínez, Luis Felipe"'
We provide a complete study of existence and uniqueness (uniqueness up to multiples in the case $\mathbf{d} = \mathbf{0}$) of non-negative and non-trivial solutions $\mathbf{x}$ for the linear system $(\mathbf{I}- \mathbf{A})\mathbf{x} = \mathbf{d}$
Externí odkaz:
http://arxiv.org/abs/2401.15099
Autor:
Prieto-Martínez, Luis Felipe
Several authors have remarked the convenience of understanding the different notions of center appearing in Geometry (centroid of a set of points, incenter of a triangle, center of a conic and many others) as functions. The most general way to do so
Externí odkaz:
http://arxiv.org/abs/2301.09945
In this paper we revisit a result due to Franz Rellich on smoothness of solutions of parametrized linear systems. With this result as a starting point, we obtain finer smoothness results in an elementary fashion and propose an efficient adjoint algor
Externí odkaz:
http://arxiv.org/abs/2301.13164
Autor:
Prieto-Martínez, Luis Felipe
There are several remarkable points, defined for polygons and multisets of points in the plane, called centers (such as the centroid). To make possible their study, there exists a formal definition for the concept of center in both cases. In this pap
Externí odkaz:
http://arxiv.org/abs/2206.13253
In this paper we provide a review of the concept of center of a $n$-gon, generalizing the original idea given by C. Kimberling for triangles. We also generalize the concept of central line for $n$-gons for $n\geq 3$ and establish its basic properties
Externí odkaz:
http://arxiv.org/abs/2204.08342
Autor:
Prieto-Martínez, Luis Felipe
In 1946, J. Rosenbaum proposed a family of problems asking how many power points are needed to ensure that the boundary $c$ of a given convex body is a disk. In this paper, we use Riordan matrices to show that, if this curve $c$ is analytic, then one
Externí odkaz:
http://arxiv.org/abs/2201.07892
We calculate the derived series of the Riordan group. To do that, we study a nested sequence of its subgroups, herein denoted by $\mathcal G_k$. By means of this sequence, we first obtain the n-th commutator subgroup of the Associated subgroup. This
Externí odkaz:
http://arxiv.org/abs/2108.00486
Characteristic curves and the exponentiation in the Riordan Lie group: A connection through examples
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 April 2024 532(1)
Autor:
Prieto-Martínez, Luis Felipe
This article contains a short and entertaining list of unsolved problems in Plane Geometry. Their statement may seem naive and can be understood at an elementary level. But their solutions have refused to appear for forty years in the best case.
Externí odkaz:
http://arxiv.org/abs/2104.09324
Autor:
Prieto-Martínez, Luis Felipe
Around 1930, K. Menger expressed his interest in the concept of abstract angle function. He introduced a general definition of this notion for metric and semi-metric spaces. He also proposed two problems concerning conformal embeddability of spaces e
Externí odkaz:
http://arxiv.org/abs/2011.12152