Tootfinder

This https://arxiv.org/abs/2302.06794 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Regge trajectory relations for the universal description of the heavy-light systems: diquarks, mesons, baryons and tetraquarks
Two newly proposed Regge trajectory relations are employed to analyze the heavy-light systems. One of the relations is $M=m_1+m_2+C'+β_x\sqrt{x+c_{0x}}$, $(x=l,\,n_r)$. Another reads $M=m_1+C'+\sqrt{β_x^2(x+c_{0x})+\frac{4}{3}\sqrt{π{β_x}}m^{3/2}_2(x+c_{0x})^{1/4}}$. $M$ is the bound state mass. $m_1$ and $m_2$ are the masses of the heavy constituent and the light constituent, respectively. $l$ is the orbital angular momentum and $n_r$ is the radial quantum number. $β_x$ and $c_{0x}$ are f…

Classification of a class of planar polynomials
Chin Hei Chan, Maosheng Xiong
https://arxiv.org/abs/2404.14291 https://arxiv.org/pdf/…

Classification of a class of planar polynomials
Let $p$ be an odd prime, $k,\ell$ be positive integers, $q=p^k, Q=p^{\ell}$. In this paper we characterise planar functions of the form $f_{\underline{c}}(X)=c_0X^{qQ+q}+c_1X^{qQ+1}+c_2X^{Q+q}+c_3X^{Q+1}$ over $\mathbb{F}_{q^2}$ for any $\underline{c}=(c_0,c_1,c_2,c_3) \in \mathbb{F}_{q^2}^4$ in terms of linear equivalence.

The images of "Aithérios" by @… can appear to show a lift or a fall, can be sparsely populated or tightly packed, but they all convey a sense of translucent weightlessness. Iteration #260 feels special to me in the way it highlights two of its elements in bright white.
Project link:

This https://arxiv.org/abs/2302.06794 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Regge trajectory relations for the universal description of the heavy-light systems: diquarks, mesons, baryons and tetraquarks
Two newly proposed Regge trajectory relations are employed to analyze the heavy-light systems. One of the relations is $M=m_1+m_2+C'+β_x\sqrt{x+c_{0x}}$, $(x=l,\,n_r)$. Another reads $M=m_1+C'+\sqrt{β_x^2(x+c_{0x})+\frac{4}{3}\sqrt{π{β_x}}m^{3/2}_2(x+c_{0x})^{1/4}}$. $M$ is the bound state mass. $m_1$ and $m_2$ are the masses of the heavy constituent and the light constituent, respectively. $l$ is the orbital angular momentum and $n_r$ is the radial quantum number. $β_x$ and $c_{0x}$ are f…

On the Gotzmann threshold of monomials
Vittoria Bonanzinga, Shalom Eliahou
https://arxiv.org/abs/2403.09497 https://arxiv.org/pdf/240…

On the Gotzmann threshold of monomials
Let $R_n=K[x_1,\dots,x_n]$ be the $n$-variable polynomial ring over a field $K$. Let $S_n$ denote the set of monomials in $R_n$. A monomial $u \in S_n$ is a \textit{Gotzmann monomial} if the Borel-stable monomial ideal $\langle u \rangle$ it generates in $R_n$ is a Gotzmann ideal. A longstanding open problem is to determine all Gotzmann monomials in $R_n$. Given $u_0 \in S_{n-1}$, its \textit{Gotzmann threshold} is the unique nonnegative integer $t_0=τ_n(u_0)$ such that $u_0x_n^t$ is a Gotzman…