Le Matematiche
type: channel
description: Journal of Pure and Applied Mathematics and Information Science Open Access Journal
publisher: Dipartimento di Matematica e Informatica
language: en
publication name: Le Matematiche
issn: 0373-3505
copyright: The authors retain all rights to the original work without any restrictions. License for Published Contents "Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). Licence scheme | Legal code License for Metadata "Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. Licence scheme | Legal code No Fee Charging No fee is required to complete the submission/review/publishing process of authors paper.
items: Square-mean S-asymptotically (ω,Q)-periodic processes and mild solutions to some neutral fractional stochastic evolution equations
items: Stability of constant equilibria in a diffusive logistic SIR model with saturated treatment and death rates
items: Weak solutions for nonlocal problems in fractional Orlicz-Sobolev spaces
items: On minimum embeddings of Pk(u, λ) into KS(u+w,μ)
items: On the lattice formulation of the union-closed sets conjecture
items: On semi-c-periodic functions of type I and applications
items: Elastic beam qquations with variable coefficients: multiple solutions under mixed nonlinearities
items: Disjoint weak star p-convergent operators on Banach lattices, 1 ≤ p ≤ ∞
items: What is Positive Geometry?
items: On the complements of union of open balls and related set classes
items: Nonnil-Noetherian pairs of the form (R, R[X]) and some related results
items: Moments and (p; q)-Integral Representations of (p; q)-Classical Forms
items: Local and global solvability in attraction-repulsion chemotaxis systems with L2-initial data
items: On all-path convex, gated and Chebyshev sets in graphs
items: On locally factorial Fano fourfolds of Picard number two
items: Voronovskaya-type asymptotic expansions and convergence analysis for neural network operators in complex domains
items: Moduli spaces in positive geometry
items: The two-loop amplituhedron
items: The positive orthogonal grassmannian
items: Points on rational normal curves and the ABCT variety
items: Cyclic polylopes through the lense of iterated integrals
items: Tropicalizing binary geometries
items: Uniqueness of MHV gravity amplitudes
items: The chirotropical grassmannian
items: Proudfoot-Speyer degenerations of scattering equations
items: Logarithmic discriminants of hyperplane arrangements
items: Binary geometries from pellytopes
items: Differential equations for moving hyperplane arrangements
items: Algebraic approaches to cosmological integrals
items: Multiple solutions for a dynamic Sturm-Liouville boundary value problem on time scales with impulsive effects

Square-mean S-asymptotically (ω,Q)-periodic processes and mild solutions to some neutral fractional stochastic evolution equations
type: item
description: Recent results concerning (ω,Q)-periodic functions are extended tore current stochastic processes in the square mean sense, termedS-asymptotic (ω,Q)-periodic processes, where Q denotes a linear isomorphism from a Hilbert space to itself. These quasi-periodic stochastic processes covers S-asymptotic ω-(anti-)periodic processes, Bloch and(ω,c)-periodic stochastic processes in Hilbert spaces. We prove the completeness, convolution and superposition theorems for theS-asymptotic (ω,Q)-periodic process in abstract spaces. We also consider some existence results forS-asymptotically(ω,Q)-periodic mild solutions to stochastically forced fractional evolution equations under some different conditions.Somme examples are given to illustrate the existence results
subject: Articoli
  topic: section
subject: Periodic solutions
  topic: keywords
subject: Stochastic processes
  topic: keywords
subject: stochastic evolution equations
  topic: keywords
creator: Ousmane Touré
creator: Mamadou Moustapha Mbaye
creator: Amadou Diop
rights: Copyright (c) 2026 Ousmane Touré, Mamadou Moustapha Mbaye, Amadou Diop http://creativecommons.org/licenses/by/4.0
date: 2026-07-05
publication date: 2026-07-05
starting page: 109
ending page: 138

Stability of constant equilibria in a diffusive logistic SIR model with saturated treatment and death rates
type: item
description: This paper is concerned with the Neumann initial-boundary valueproblem for a diffusive logistic SIR model with saturated treatment anddeath rates. The purpose of this paper is to study stability of constant equi-libria under some conditions on parameters. Moreover, several numerical simulations are given
subject: Articoli
  topic: section
subject: SIR epidemic model
  topic: keywords
subject: constant equilibrium
  topic: keywords
subject: saturated treatment rate
  topic: keywords
subject: death rate
  topic: keywords
subject: stability
  topic: keywords
creator: Yutaro Chiyo
creator: Koyuki Yamamoto
creator: Tomomi Yokota
rights: Copyright (c) 2026 Yutaro Chiyo, Koyuki Yamamoto, Tomomi Yokota http://creativecommons.org/licenses/by/4.0
date: 2026-07-05
publication date: 2026-07-05
starting page: 167
ending page: 190

Weak solutions for nonlocal problems in fractional Orlicz-Sobolev spaces
type: item
description: We study a class of nonlocal boundary value problems involving the fractional a(·)-Laplacian operator in fractional Orlicz–Sobolev spaces.The main equation features nonlinear source terms with a nonnegative parameterμand is posed on a bounded domain with homogeneous Dirichlet conditions in the nonlocal sense. Using variational approaches, we establish the existence of at least one nontrivial, non negative weak solution when the parameter μ is sufficiently small. Furthermore, we identify conditions under which the solution is strictly positive. Two examples are included to demonstrate the applicability of the main result
subject: Articoli
  topic: section
subject: Fractional order Sobole spaces, nonlocal problems, weak solutions, critical points.
  topic: keywords
creator: Lingju Kong
rights: Copyright (c) 2026 Lingju Kong http://creativecommons.org/licenses/by/4.0
date: 2026-07-05
publication date: 2026-07-05
starting page: 191
ending page: 206

On minimum embeddings of Pk(u, λ) into KS(u+w,μ)
type: item
description: Let G be a simple finite graph and H be a subgraph of G. We say that an H-design (U,C) of order u and index λ is embedded into a G-design (V,B) of order u+w and index μ, λ ≤ μ, if there is an injective function f : C → B such that C is a subgraph of f (C) for every C ∈ C. The mapping f is called the embedding of (U,C) into (V,B). If w attains the minimum possible value, then f is a minimum embedding. In this paper we study the minimum embedding of a Pk(u,λ) into a KS(u+w,μ), for k = 3,4.
subject: Articoli
  topic: section
subject: graph decomposition, embedding, minimum embedding
  topic: keywords
creator: Giorgio Ragusa
creator: Antoinette Tripodi
rights: Copyright (c) 2026 Giorgio Ragusa, Antoinette Tripodi http://creativecommons.org/licenses/by/4.0
date: 2026-07-05
publication date: 2026-07-05
starting page: 139
ending page: 152

On the lattice formulation of the union-closed sets conjecture
type: item
description: The union-closed sets conjecture, also known as Frankl's conjecture, is a well-studied problem with various formulations. In terms of lattices, the conjecture states that every finite lattice L with more than one element contains a join-irreducible element that is less than or equal to at most half of the elements in L. In this work, we obtain several necessary conditions for any counterexample L of minimum size.
subject: Articoli
  topic: section
subject: union-closed sets conjecture
  topic: keywords
subject: Frankl's conjecture
  topic: keywords
subject: lattice
  topic: keywords
creator: Christopher Bouchard
rights: Copyright (c) 2026 Christopher Bouchard http://creativecommons.org/licenses/by/4.0
date: 2026-07-05
publication date: 2026-07-05
starting page: 153
ending page: 165

On semi-c-periodic functions of type I and applications
type: item
description: In this paper, we study the (newly introduced) class of functions called semi-c-periodic functions of type I in a Banach space. We first investigate their basic properties, including a convolution result. Using a suitable norm we prove that the set of such functions is a Banach space. We then study the existence and uniqueness of semi-c-periodic mild solutions for both autonomous and non-autonomous linear evolution equations. We achieve the existence results using the Banach fixed point theorem and the principle of reduction
subject: Articoli
  topic: section
subject: C-periodic; Semi-c-periodic; Uniformly close c-periodic; Volterra integral equation; Banach fixed point principle
  topic: keywords
creator: Ruwaida Aldrsoni
creator: Gaston N'Guerekata
rights: Copyright (c) 2025 R. Aldrsoni, G. N'Guerekata http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 771
ending page: 789

Elastic beam qquations with variable coefficients: multiple solutions under mixed nonlinearities
type: item
description: This paper investigates the existence of multiple solutions for a fourth-order differential equation modelling an elastic beam, where the coefficients are variable, and the nonlinearities exhibit both concave and convex characteristics. Our approach is based on variational methods and critical point theorems, particularly those formulated by Ricceri, which provide a powerful framework for proving the existence of solutions in reflexive Banach spaces. By leveraging these mathematical tools, we establish that the considered problem admits at least three distinct weak solutions under specific conditions. To validate our theoretical findings, we present an illustrative example demonstrating how our results can be applied in practice.
subject: Articoli
  topic: section
creator: Shapour Heidarkhani
creator: Shahin Moradi
creator: Anderson L. A. De Araujo
creator: David Barilla
rights: Copyright (c) 2025 S. Heidarkhani, S. Moradi, A. L. A. De Araujo, D. Barilla http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 749
ending page: 769

Disjoint weak star p-convergent operators on Banach lattices, 1 ≤ p ≤ ∞
type: item
description: We introduce and study the disjoint weak star p-convergent operators on Banach lattices, and we explore some characterizations of them in terms of disjoint sequences in the positive cones. As an application, we examine the domination and the duality properties of the class of positive disjoint weak star p-convergent operators. Next, we investigate the connections between our operators and disjoint p-convergent operators. Finally, we deduce some important results about the positive Schur property of order p.
subject: Articoli
  topic: section
subject: Banach lattice, order continuous norm, p-convergent operator, disjoint p-convergent operator, positive Schur property of order p
  topic: keywords
creator: Abderrahman Retbi
rights: Copyright (c) 2026 Abderrahman Retbi http://creativecommons.org/licenses/by/4.0
date: 2026-07-05
publication date: 2026-07-05
starting page: 253
ending page: 262

What is Positive Geometry?
type: item
description: This article serves as an introduction to the special volume on Positive Geometry in the journal Le Matematiche. We attempt to answer the question in the title by describing the origins and objects of positive geometry at this early stage of its development. We discuss the problems addressed in the volume and report on the progress. We also list some open challenges.
subject: Articoli
  topic: section
subject: Positive Geometry
  topic: keywords
creator: K. Ranestad
creator: B. Sturmfels
creator: S. Telen
rights: Copyright (c) 2025 K. Ranestad, B. Sturmfels, S. Telen http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 3
ending page: 16

On the complements of union of open balls and related set classes
type: item
description: Let a R-body be a closed set, complement of union of open balls of radius R in the Euclidean space. Properties generalizing similar ones for convex sets are proved for the family of R-bodies; properties for the family of sets supported by sphere of radius R (extension of the supporting hyperplane to convex bodies) are investigated. Comparison of that family with the sets of reach R and with the R-rolling sets ( G. Walther, On a generalization of Blachke's Rolling Theorem and the Smoothing Surfaces 1999) are studied. New properties for the previous familes are proved, by using the generalization of the convex cones.
subject: Articoli
  topic: section
subject: generalized convexity, convex hull, rolling bodies, reach positive sets, support cones
  topic: keywords
creator: Marco Longinetti
creator: Paolo Manselli
creator: Adriana Venturi
rights: Copyright (c) 2026 Marco Longinetti, Paolo Manselli, Adriana Venturi http://creativecommons.org/licenses/by/4.0
date: 2026-07-05
publication date: 2026-07-05
starting page: 87
ending page: 108

Nonnil-Noetherian pairs of the form (R, R[X]) and some related results
type: item
description: The rings considered in this paper are commutative with identity and are nonzero. Let R be a ring. An ideal I of R is said to be nonnil if it is not contained in the nilradical of R. We say that R is nonnil-Noetherian (resp., nonnil-Laskerian) if each proper nonnil ideal of R is finitely generated (resp., admits a primary decomposition). Whenever T is an extension ring of R, we assume that R contains the identity element of T. Let T be an extension ring of R. We say that (R, T) is a Nonnil-Noetherian pair (resp., Nonnil-Laskerian pair) if f A is nonnil-Noetherian (resp., nonnil-Laskerian) for any intermediate ring A between R and T. This paper aims to characterize R such that (R, R[X]) is a nonnil-Noetherian pair (resp., nonnil-Laskerian pair), where R[X] is the polynomial ring in one variable X over R. Also, this paper aims to characterize R such that each intermediate ring A between R and R[X] posses a property which is related to being nonnil-Noetherian (resp., nonnil-Laskerian).
subject: Articoli
  topic: section
creator: S. Visweswaran
rights: Copyright (c) 2025 S. Visweswaran http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 729
ending page: 747

Moments and (p; q)-Integral Representations of (p; q)-Classical Forms
type: item
description: In [6], the authors introduce a new technical method for studying the Dp,q-classical orthogonal polynomials, where Dp,q is the(p,q)-difference operator, using an algebraic approach. In this paper, we investigate Dp,q-classical orthogonal polynomials associated with the(p,q)-difference op-eratorDp,q. Using Pearson-type functional equations and a suitable de-composition of Dp,q, we simplify the description of the canonical Dp,q-classical forms and clarify their relation with theq-classical framework.We also study the moments and modified moments of the correspondingforms, derive recurrence relations, and establish several explicit (p,q)-integral representations for canonical cases
subject: Articoli
  topic: section
subject: (p; q) calculus; (p; q)-di erence operator; (p; q)-classical polynomial
  topic: keywords
creator: Mabrouk Sghaier
creator: Mohamed Zaatra
rights: Copyright (c) 2026 Mabrouk Sghaier, Mohamed Zaatra http://creativecommons.org/licenses/by/4.0
date: 2026-07-05
publication date: 2026-07-05
starting page: 57
ending page: 86

Local and global solvability in attraction-repulsion chemotaxis systems with L2-initial data
type: item
description: This paper deals with the attraction-repulsion chemotaxis system under homogeneous Neumann initial-boundary conditions, where Ω ⊂ Rn (n ≤ 3) is a smoothly bounded domain and a,b,c,χ,ξ,α,β,γ,δ > 0 and τ ∈ {0, 1} are constants. The purpose of the present paper is to construct a local solution of this system for any L2-initial data without additional conditions on χ and ξ by using the theory for abstract evolution equations and to extend the local solution globally in the repulsion-dominant case by relying on a priori estimates.
subject: Articoli
  topic: section
subject: abstract evolution equations
  topic: keywords
subject: $L^2$-initial data
  topic: keywords
subject: local existence
  topic: keywords
subject: attraction-repulsion chemotaxis systems
  topic: keywords
creator: Yutaro Chiyo
creator: Taisho Saga
creator: Tomomi Yokota
rights: Copyright (c) 2025 Y. Chiyo, T. Saga, T. Yokota http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 701
ending page: 727

On all-path convex, gated and Chebyshev sets in graphs
type: item
description: We present new characterizations for trees, block graphs, and geodetic graphs using all-path convex, gated and Chebyshev sets. Specifically, we prove that trees are exactly the graphs in which all-path convexity is a convex geometry. Block graphs are characterized as graphs in which all balls are all-path convex (equivalently, gated), and geodetic graphs are exactly those graphs where all balls (equivalently, closed neighborhoods) are Chebyshev. Additionally, we prove that almost all graphs have geodesically convex Chebyshev sets, provide a characterization of bipartite graphs with connected Chebyshev sets, and establish a criterion for graphs with trivial Chebyshev sets in the class of graph joins. Finally, we show that graphs of odd order with maximal number of edges under the Seidel switching operation always have trivial Chebyshev sets.
subject: Articoli
  topic: section
subject: all-path convexity
  topic: keywords
subject: geodesic convexity
  topic: keywords
subject: gated set
  topic: keywords
subject: Chebyshev set
  topic: keywords
subject: block graph
  topic: keywords
subject: tree
  topic: keywords
creator: Vladyslav Haponenko
creator: Sergiy Kozerenko
rights: Copyright (c) 2025 V. Haponenko, S. Kozerenko http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 661
ending page: 678

On locally factorial Fano fourfolds of Picard number two
type: item
description: We classify the locally factorial Fano fourfolds of Picard number two with a hypersurface Cox ring that admit an effective action of a three- dimensional torus.
subject: Articoli
  topic: section
creator: Andreas Baeuerle
creator: Christian Mauz
rights: Copyright (c) 2026 Andreas Baeuerle, Christian Mauz http://creativecommons.org/licenses/by/4.0
date: 2026-07-05
publication date: 2026-07-05
starting page: 207
ending page: 252

Voronovskaya-type asymptotic expansions and convergence analysis for neural network operators in complex domains
type: item
description: This paper extends the classical theory of Voronovskaya-type asymptotic expansions to generalized neural network operators defined on non-Euclidean and fractal domains. We introduce and analyze smooth operators activated by modified and generalized hyperbolic tangent functions, extending their applicability to manifold and fractal geometries. Key theoretical results include the preservation of density properties, detailed convergence rates, and asymptotic expansions. Additionally, we explore the role of fractional derivatives in defining neural network operators, which capture non-local behavior and are particularly useful for modeling systems with long-range dependencies or fractal-like structures. Our findings contribute to a deeper understanding of neural network operators in complex, structured spaces, offering robust mathematical tools for applications in signal processing on manifolds and solving partial differential equations on fractals.
subject: Articoli
  topic: section
subject: Neural network operators
  topic: keywords
subject: Voronovskaya-type expansions
  topic: keywords
subject: Non-Euclidean domains
  topic: keywords
subject: Fractional calculus
  topic: keywords
subject: Fractals
  topic: keywords
creator: Romulo D. Chaves dos Santos
creator: Jorge H. O. Sales
rights: Copyright (c) 2026 Romulo D. Chaves dos Santos, Jorge H. O. Sales http://creativecommons.org/licenses/by/4.0
date: 2026-07-05
publication date: 2026-07-05
starting page: 35
ending page: 55

Moduli spaces in positive geometry
type: item
description: These are lecture notes for five lectures given at MPI Leipzig in May 2024. We study the moduli space M0,n of n distinct points on P1 as a positive geometry and a binary geometry. We develop mathematical formalism to study Cachazo-He-Yuan's scattering equations and the associated scalar and Yang-Mills amplitudes. We discuss open superstring amplitudes and relations to tropical geometry.
subject: Articoli
  topic: section
creator: T. Lam
rights: Copyright (c) 2025 T. Lam http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 17
ending page: 101

The two-loop amplituhedron
type: item
description: The loop-Amplituhedron A(L)n is a semialgebraic set in the product of Grassmannians GrR(2,4)L. Recently, many aspects of this geometry for the case of L=1 have been elucidated, such as its algebraic and face stratification, its residual arrangement and the existence and uniqueness of the adjoint. This paper extends this analysis to the simplest higher loop case given by the two-loop four-point Amplituhedron A(2)4$.
subject: Articoli
  topic: section
subject: positive geometry
  topic: keywords
subject: Amplituhedron
  topic: keywords
subject: Amplitudes
  topic: keywords
creator: G. Dian
creator: E. Mazzucchelli
creator: F. Tellander
rights: Copyright (c) 2025 G. Dian, E. Mazzucchelli, F. Tellander http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 255
ending page: 277

The positive orthogonal grassmannian
type: item
description: The Plücker positive region OGr+(k,2k) of the orthogonal Grassmannian emerged as the positive geometry behind the ABJM scattering amplitudes. In this paper we initiate the study of the positive orthogonal Grassmannian OGr+(k,n) for general values of k, n. We determine the boundary structure of the quadric OGr+(1,n) in Pn-1+ and show that it is a positive geometry. We show that OGr+(k,2k+1) is isomorphic to OGr+(k+1, 2k+2) and connect its combinatorial structure to matchings on [2k+2]. Finally, we show that in the case n > 2k+1, the positroid cells of Gr+(k,n) do not induce a CW cell decomposition of OGr+(k,n).
subject: Articoli
  topic: section
subject: Orthogonal Grassmannian
  topic: keywords
subject: Flag variety
  topic: keywords
subject: Positive geometry
  topic: keywords
subject: Gröbner bases
  topic: keywords
subject: Straightening laws
  topic: keywords
creator: Y. El Maazouz
creator: Y. Mandelshtam
rights: Copyright (c) 2025 Y. El Maazouz, Y. Mandelshtam http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 279
ending page: 302

Points on rational normal curves and the ABCT variety
type: item
description: The ABCT variety is defined as the closure of the image of G(2, n) under the Veronese map. We realize the ABCT variety V(3,n) as the determinantal variety of a vector bundle morphism. We use this to give a recursive formula for the fundamental class of V(3,n). As an application, we show that special Schubert coefficients of this class are given by Eulerian numbers, matching a formula by Cachazo-He-Yuan. On the way tothis, we prove that the variety of configuration of points on a common divisor on a smooth variety is reduced and irreducible, generalizing a result of Caminata-Moon-Schaffler.
subject: Articoli
  topic: section
subject: rational normal curve, configurations, Grassmannian, positive geometry, spinor helicity, scattering equations
  topic: keywords
creator: D. Agostini
creator: L. Ramesh
creator: D. Shen
rights: Copyright (c) 2025 D. Agostini, L. Ramesh, D. Shen http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 103
ending page: 122

Cyclic polylopes through the lense of iterated integrals
type: item
description: The volume of a cyclic polytope can be obtained by forming an it- erated integral, known as the path signature, along a suitable piecewise linear path running through its edges. Different choices of such a path are related by the action of a subgroup of the combinatorial automorphisms of the polytope. Motivated by this observation, we look for other polyno- mials in the vertices of a cyclic polytope that arise as path signatures and are invariant under the subgroup action. We prove that there are infinitely many such invariants which are algebraically independent in the shuffle algebra.
subject: Articoli
  topic: section
subject: Piecewise linear paths
  topic: keywords
subject: Shuffle algebra
  topic: keywords
subject: Group action
  topic: keywords
subject: Signed volume
  topic: keywords
subject: Invariants
  topic: keywords
subject: Positive Matrices
  topic: keywords
creator: F. Lotter
creator: R. Preiß
rights: Copyright (c) 2025 F. Lotter, R. Preiß http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 365
ending page: 385

Tropicalizing binary geometries
type: item
description: The type A cluster configuration space, commonly known as M0,n, is the very affine part of the binary geometry associated with the associahedron. The tropicalization of M0,n can be realized as the space of phylogenetic trees and its signed tropicalizations as the dual-associahedron subfans. We give a concise overview of this construction and propose an extension to type C. The type C cluster configuration space MCl arises from the binary geometry associated with the cyclohedron. We define a space of axially symmetric phylogenetic trees containing many dual-associahedron and dual-cyclohedron subfans. We conjecturally realize the tropicalization of MCl as the defined space and its signed tropicalizations as the aforementioned subfans.
subject: Articoli
  topic: section
subject: tropical geometry
  topic: keywords
subject: cluster varieties
  topic: keywords
subject: phylogenetic trees
  topic: keywords
subject: associahedra
  topic: keywords
subject: binary geometries
  topic: keywords
creator: S. Cox
creator: I. Makhlin
rights: Copyright (c) 2025 S. Cox, I. Makhlin http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 211
ending page: 231

Uniqueness of MHV gravity amplitudes
type: item
description: We investigate MHV tree-level gravity amplitudes as defined on the spinor-helicity variety. Unlike their gluon counterparts, the gravity amplitudes do not have logarithmic singularities and do not admit Amplituhedron-like construction. Importantly, they are not determined just by their singularities, but rather their numerators have interesting zeroes. We make a conjecture about the uniqueness of the numerator and explore this feature from a more mathematical perspective. This leads us to a new approach for examining adjoints. We outline steps of our proposed proof and provide computational evidence for its validity in specific cases.
subject: Articoli
  topic: section
subject: scattering amplitudes, adjoints, commutative algebra
  topic: keywords
creator: J. Koefler
creator: U. Oktem
creator: S. Paranjape
creator: J. Trnka
creator: B. Zacovic
rights: Copyright (c) 2025 J. Koefler, U. Oktem, S. Paranjape, J. Trnka, B. Zacovic http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 347
ending page: 364

The chirotropical grassmannian
type: item
description: Recent developments in particle physics have revealed deep connections between scattering amplitudes and tropical geometry. From the heart of this relationship emerged the chirotropical Grassmannian TropχG(k,n) and the chirotropical Dressian Drχ(k,n), polyhedral fans built from uniform realizable chirotopes that encode the combinatorial structure of Generalized Feynman Diagrams. We prove that TropχG(3,n) = Drχ(3,n) for $n = 6,7,8$, and develop algorithms to compute these objects from their rays modulo lineality. Using these algorithms, we compute all chirotropical Grassmannians TropχG(3,n) for n = 6,7,8 across all isomorphism classes of chirotopes. We prove that each chirotopal configuration space Xχ(3,6) is diffeomorphic to a polytope and propose an associated canonical logarithmic differential form. Finally, we show that the equality between chirotropical Grassmannian and Dressian fails for (k,n) = (4,8).
subject: Articoli
  topic: section
subject: tropical geometry
  topic: keywords
subject: configuration space
  topic: keywords
subject: matroids
  topic: keywords
subject: scattering amplitudes
  topic: keywords
creator: D. Antolini
creator: N. Early
rights: Copyright (c) 2025 D. Antolini, N. Early http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 123
ending page: 142

Proudfoot-Speyer degenerations of scattering equations
type: item
description: We study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as linear equations on a reciprocal linear space and develop a degeneration-based homotopy algorithm for solving them. We investigate the Hilbert regularity of the corresponding homogeneous ideal and apply our methods to CHY scattering equations.
subject: Articoli
  topic: section
subject: hyperplane arrangements
  topic: keywords
subject: scattering equations
  topic: keywords
subject: maximum likelihood estimation
  topic: keywords
subject: homotopy continuation
  topic: keywords
subject: Hilbert regularity
  topic: keywords
creator: B. Betti
creator: V. Borovik
creator: S. Telen
rights: Copyright (c) 2025 B. Betti, V. Borovik, S. Telen http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 143
ending page: 165

Logarithmic discriminants of hyperplane arrangements
type: item
description: A recurring task in particle physics and statistics is to compute the complex critical points of a product of powers of affine-linear functions. The logarithmic discriminant characterizes exponents for which such a function has a degenerate critical point in the corresponding hyperplane arrangement complement. We study properties of this discriminant, exploiting its connection with the Hurwitz form of a reciprocal linear space.
subject: Articoli
  topic: section
subject: discriminant
  topic: keywords
subject: hyperplane arrangement
  topic: keywords
subject: scattering equations
  topic: keywords
subject: likelihood equations
  topic: keywords
creator: L. Kayser
creator: A. Kretschmer
creator: S. Telen
rights: Copyright (c) 2025 L. Kayser, A. Kretschmer, S. Telen http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 325
ending page: 346

Binary geometries from pellytopes
type: item
description: Binary geometries have recently been introduced in particle physics in connection with stringy integrals. In this work, we study a class of simple polytopes, called \emph{pellytopes}, whose number of vertices are given by Pell's numbers. We provide a new family of binary geometries determined by pellytopes as conjectured by He--Li--Raman--Zhang. We relate this family to the moduli space of curves by comparing the pellytope to the ABHY associahedron.
subject: Articoli
  topic: section
subject: binary geometry
  topic: keywords
subject: Pell's number
  topic: keywords
subject: moduli space of curves
  topic: keywords
creator: L. Bossinger
creator: M.L. Telek
creator: H. Tillmann-Morris
rights: Copyright (c) 2025 L. Bossinger, M.L. Telek, H. Tillmann-Morris http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 189
ending page: 209

Differential equations for moving hyperplane arrangements
type: item
description: We investigate Mellin integrals of products of hyperplanes, raised to an individual power each. We refer to the resulting functions as combinatorial correlators. We investigate their behavior when moving the hyperplanes individually. To encode these functions as holonomic functions in the constant terms of the hyperplanes, we aim to construct a holonomic annihilating D-ideal purely in terms of the hyperplane arrangement.
subject: Articoli
  topic: section
subject: Algebraic Analysis
  topic: keywords
subject: Holonomic Function
  topic: keywords
subject: Combinatorial Correlator
  topic: keywords
subject: Hyperplane Arrangement
  topic: keywords
creator: A. Pfister
creator: A.-L. Sattelberger
rights: Copyright (c) 2025 A. Pfister, A.-L. Sattelberger http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 409
ending page: 429

Algebraic approaches to cosmological integrals
type: item
description: Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space wavefunction. The singularities of these cosmological integrals are parameterized by binary hyperplane arrangements. Using different algebraic tools, we shed light on the differential and difference equations satisfied by these integrals. Moreover, we study a multivariate version of partial fractioning of the flat space wavefunction, and propose a graph-based algorithm to compute this decomposition.
subject: Articoli
  topic: section
subject: Cosmological correlators
  topic: keywords
subject: D-modules
  topic: keywords
subject: Wavefunction
  topic: keywords
subject: restricted GKZ systems
  topic: keywords
subject: multivariate partial fraction
  topic: keywords
creator: C. Fevola
creator: G. L. Pimentel
creator: A.-L. Sattelberger
creator: T. Westerdijk
rights: Copyright (c) 2025 C. Fevola, G. L. Pimentel, A.-L. Sattelberger , T. Westerdijk http://creativecommons.org/licenses/by/4.0
date: 2025-05-23
publication date: 2025-05-23
starting page: 303
ending page: 324

Multiple solutions for a dynamic Sturm-Liouville boundary value problem on time scales with impulsive effects
type: item
description: In this study, we explore the existence of multiple solutions for a dynamic Sturm-Liouville boundary value problem on time scales that incorporate impulsive effects. Utilizing variational methods and applying certain critical point theorems from Ricceri for smooth functionals, we demonstrate the existence of at least three solutions to the problem. To illustrate the practical relevance of our findings, we provide an example at the end.
subject: Articoli
  topic: section
creator: Massimiliano Ferrara
creator: Shapour Heidarkhani
creator: Shahin Moradi
creator: Anderson L.A. de Araujo
rights: Copyright (c) 2025 M. Ferrara, S. Heidarkhani, S. Moradi, A.L.A. de Araujo http://creativecommons.org/licenses/by/4.0
date: 2025-12-05
publication date: 2025-12-05
starting page: 679
ending page: 700