Rose-Hulman Undergraduate Mathematics

Preprint Sep 2026

Pierce-Birkhoff conjecture is false

We provide a counterexample to the Pierce-Birkhoff conjecture: a continuous function that is piecewise quadratic on a finite collection of semialgebraic sets that partition $\mathbb{R}^n$ but that cannot be expressed as a finite lattice combination of polynomials. The counterexample was found with the assistance of our...

Ze-Hua Lai, Lek-Heng Lim, Jun-Yu Ren · 0 citations

Open access Sep 2026

Some Applications of Fractional Calclus Operator

The aim of this paper is to discuss a new subclass TS(ℏ,σ,ς,ϑ) of univalent functions with negative coefficients related to fractional calclus operator in the unit disk U={z∈C:|z|<1}. We obtain basic properties like coefficient inequality, distortion and covering theorem, radii of starlikeness, convexity and close-to-c...

B. Madhavi · International Journal of Inn... · 0 citations

Open access 2023

On Special Partitions of [0,1] and Lineability within Families of Bounded Variation Functions

We show that there exist large algebraic structures (vector spaces, algebras, closed subspaces, etc.) formed entirely (except for 0), on one hand, by singular, nowhere monotonic functions on [0,1] and, on the other hand, by absolutely continuous nowhere monotonic functions. Several tools, of independent interest, rel...

L. Bernal-González, J. Fernández-Sánchez, J. Seoane-Sepúlveda et al. · Journal of Convex Analysis · 1 citation

Preprint Oct 2026

Counting Bessel zeros and applications

We establish o-minimal definability results and develop point-counting machinery applicable to the zeros of a Bessel function of fixed non-negative real parameter. We also give an Ax-Schanuel theorem for Bessel functions of fixed (complex) parameters and exponential functions. We combine these to prove a sparsity resul...

Gal Binyamini, Avner Kiro, G. Kozma et al. · 0 citations

Open access Oct 2026

Upper Bounds and Fekete–Szegö Problem for Bi-Univalent Functions Involving Bazilevič and λ-Pseudo Functions Related to Lucas-Balancing Polynomials

This work introduces two novel classes of bi-univalent functions, denoted by ℬΣ(μ,γ,λ;r) and ΡΣ(μ,γ,λ;r), linked to Lucas-Balancing polynomials within the open unit disk. For functions pertaining to these newly defined classes, we establish estimates for the early Taylor–Maclaurin coefficients |a2| and |a3|. Furthermor...

Shaymaa Y. Alkufi, A. Wanas, A. Lupaș · Mathematics · 0 citations

Preprint Sep 2026

Splitting the Matroid Determinant

The principal matroid determinant $E_L$ of a linear space $L \subseteq \mathbb{P}^n$ has been introduced in recent work by Matsubara-Heo and Telen. In this paper, we give the complete factorization of this polynomial into its irreducible components, proving a conjecture of the aforementioned authors. Our methods rely o...

Clara Briand, Leonie Kayser, Julian Weigert · 1 citation