2025-12-05
Keiju Sono
The main purpose of this paper is to clarify the numerical value of the constant cLG such that the above in- equality holds. We see that c LG is determined by several factors related to analytic number theory, for example, the ratio of integrals of functions in the multidimensional sieve of Maynard [14], the distribution of primes in arithmetic progressions to large moduli, and the coefficient of upper bound sieve of Selberg. We prove that the above inequality is valid at least for some c LG ≥ 2.0 × 10 −17 .
2025-12-05
Yutaro Chiyo, Taisho Saga, Tomomi Yokota
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.
2025-12-05
Shapour Heidarkhani, Shahin Moradi, Anderson L. A. De Araujo, David Barilla
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.
2025-05-23
D. Agostini, L. Ramesh, D. Shen
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.
2025-05-23
L. Bossinger, M.L. Telek, H. Tillmann-Morris
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.
2025-05-23
M. Borinsky, C. Meroni, M. Wiesmann
We show that specific exponential bivariate integrals serve as generating functions of labeled edge-bicolored graphs. Based on this, we prove an asymptotic formula for the number of regular edge-bicolored graphs with arbitrary weights assigned to different vertex incidence structures. The asymptotic behavior is governed by the critical points of a polynomial. As an application, we discuss the Ising model on a random 4-regular graph and show how its phase transitions arise from our formula.
2025-05-23
K. Ranestad, B. Sturmfels, S. Telen
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.
2025-05-23
L. Kayser, A. Kretschmer, S. Telen
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.
2025-05-23
S. Cox, I. Makhlin
The type A cluster configuration space, commonly known as M 0,n , is the very affine part of the binary geometry associated with the associahedron. The tropicalization of M 0,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 M Cl 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 M Cl as the defined space and its signed tropicalizations as the aforementioned subfans.
2025-05-23
F. Lotter, R. Preiß
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.