arXiv subjects

Jyrko Correa-Morris

Publications and source records attributed to Jyrko Correa-Morris.

4 recordsLinked to original sources

arXiv2026

A Generalized Transform Framework for a Nonlinear Model of Cancer Dynamics

This paper develops a generalized transform framework for a logistic--Allee tumor-growth model. The method combines a generalized Laplace transform, Adomian decomposition, Chebyshev--Padé rational reconstruction, and a $μ$-scaled generalized transform to obtain admissible semi-analytical approximations. Comparisons with experimental tumor-growth data show that the resulting compact representations are stable, admissible, and comparable in error to standard numerical reference solutions.

math.NA↗

arXiv2026

Structural Redundancy in Subspace Network Coding via Atomic Decompositions

Random linear network coding (RLNC) provides a powerful framework for non-coherent communication, where reliable transmission requires correcting errors and erasures induced by network mixing and motivates the use of subspace codes. In this work, we introduce an atomic perspective on subspace coding by formalizing the notion of minimal atomic decompositions in the lattice L(V ) of subspaces of a finite-dimensional vector space over a finite field. We study the function N that assigns to each subspace the number of its minimal atomic decompositions and establish its key structural properties. Leveraging N, we define a new distance metric on L(V ) that refines classical subspace comparisons by capturing atomic-level overlap. We then introduce the Atomic Operator Channel, a transmission model for RLNC in which codewords are conveyed through atomic decompositions and corruption is modeled via atomic insertions and erasures. Within this framework, we prove a minimum-distance decoding guarantee for the induced metric. In the constant-dimension setting, we show that the classical unique-decodability condition under the subspace distance remains sufficient for unique decoding under the atomic metric.

math.CO↗

arXiv2025

Factorizations in Geometric Lattices

This article investigates atomic decompositions in geometric lattices isomorphic to the partition lattice $Π(X)$ of a finite set $X$, a fundamental structure in lattice theory and combinatorics. We explore the role of atomicity in these lattices, building on concepts introduced by D.D. Anderson, D.F. Anderson, and M. Zafrullah within the context of factorization theory in commutative algebra. As part of the study, we first examine the main characteristics of the function $\mathfrak{N}\colon Π(X) \rightarrow \mathbb{N}$, which assigns to each partition $π$ the number of minimal atomic decompositions of $π$. We then consider a distinguished subset of atoms, $\mathcal{R}$, referred to as the set of red atoms, and derive a recursive formula for $\pmbπ(X, j, s, \mathcal{R})$, which enumerates the rank-$j$ partitions expressible as the join of exactly $s$ red atoms.

math.CO↗

arXiv2023

On the additive structure of algebraic valuations of polynomial semirings

In this paper, we study factorizations in the additive monoids of positive algebraic valuations $\mathbb{N}_0[α]$ of the semiring of polynomials $\mathbb{N}_0[X]$ using a methodology introduced by D. D. Anderson, D. F. Anderson, and M. Zafrullah in 1990. A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. We begin by determining when $\mathbb{N}_0[α]$ is atomic, and we give an explicit description of its set of irreducibles. An atomic monoid is a finite factorization monoid (FFM) if every element has only finitely many factorizations (up to order and associates), and it is a bounded factorization monoid (BFM) if for every element there is a bound for the number of irreducibles (counting repetitions) in each of its factorizations. We show that, for the monoid $\mathbb{N}_0[α]$, the property of being a BFM and the property of being an FFM are equivalent to the ascending chain condition on principal ideals (ACCP). Finally, we give various characterizations for $\mathbb{N}_0[α]$ to be a unique factorization monoid (UFM), two of them in terms of the minimal polynomial of $α$. The properties of being finitely generated, half-factorial, and length-factorial are also investigated along the way.

math.NT↗