Tootfinder

Nonstandard methods for ultrafilter relation extensions
Leonardo Raffaello Maximilian Gasparro, Lorenzo Luperi Baglini
https://arxiv.org/abs/2506.04692 htt…

Nonstandard methods for ultrafilter relation extensions
We study two types of ultrafilter relation extensions with nonstandard methods and provide characterisations of these extensions in terms of generators of ultrafilters. These characterisations are then used to determine whether various relation properties are preserved by these extensions. Lastly, we study the notion of self-divisible ultrafilter and, with the mentioned characterizations, generalize this notion for a class of relations.

This https://arxiv.org/abs/2503.18789 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Sylvester program and Cayley algorithm for vector partition reduction
A vector partition problem asks for a number of nonnegative integer solutions to a system of several linear Diophantine equations with integer nonnegative coefficients. J.J. Sylvester put forward an idea of reduction of vector partition to a sum of scalar partitions. In the simplest case of two equations with positive coefficients A. Cayley performed a reduction of the corresponding double partition to a sum of scalar partitions using an algorithm subject to a set of conditions on the coefficie…

Estimation of Treatment Effects Under Nonstationarity via Truncated Difference-in-Q's
Ramesh Johari, Tianyi Peng, Wenqian Xing
https://arxiv.org/abs/2506.05308

Estimation of Treatment Effects Under Nonstationarity via Truncated Difference-in-Q's
Randomized controlled experiments (''A/B testing'') are fundamental for assessing interventions in dynamic technology-driven environments, such as recommendation systems, online marketplaces, and digital health interventions. In these systems, interventions typically impact not only the current state of the system, but also future states; therefore, accurate estimation of the global average treatment effect (or GATE) from experiments requires accounting for the dynamic temporal behavior of the …

Have been watching Your Friends and Neighbors on #AppleTVPlus . No masterpiece, and somehow fairly annoying, but still somehow I want to watch all of it. I often find myself fast-forwarding through boring bits, though.

Talousmetsistä voi tehdä luonnolle parempia edullisesti – ”Usein riittää, että jätetään vain jotain tekemättä” #luonto

Metsänomistajat jättävät nyt puuta lahoamaan tarkoituksella – ”50 vuoden päästä talousmetsämaisema on selvästi erinäköinen”
Kun noin 95 prosenttia Suomen metsistä on talousmetsää, vaikuttavat niissä tehdyt toimet merkittävästi luonnon monimuotoisuuteen.

Quantum Hall Andreev Conversion in Graphene Nanostructures
Alexey Bondarev, William H. Klein, Harold U. Baranger
https://arxiv.org/abs/2507.02114 https://

Quantum Hall Andreev Conversion in Graphene Nanostructures
We study Andreev conversion in clean nanostructures containing an interface between graphene in the quantum Hall (QH) state and a superconductor, focusing on the lowest Landau level. First, several graphene nanostructures formed from zigzag edges with sharp corners are considered using a tight-binding model. We find the scattering state for an electron impinging on the interface from the upstream QH edge state, together with the probability of it exiting as a hole in the downstream QH edge stat…

Uncertainty quantification of synchrosqueezing transform under complicated nonstationary noise
Hau-Tieng Wu, Zhou Zhou
https://arxiv.org/abs/2506.00779 htt…

Uncertainty quantification of synchrosqueezing transform under complicated nonstationary noise
We propose a bootstrapping algorithm to quantify the uncertainty of the time-frequency representation (TFR) generated by the short-time Fourier transform (STFT)-based synchrosqueezing transform (SST) when the input signal is oscillatory with time-varying amplitude and frequency and contaminated by complex nonstationary noise. To this end, we leverage a recently developed high-dimensional Gaussian approximation technique to establish a sequential Gaussian approximation for nonstationary random p…

This https://arxiv.org/abs/2411.13818 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Proof of Merca's stronger conjecture on truncated Jacobi triple product series
In the study of theta series and partition functions, Andrews and Merca, Guo and Zeng independently conjectured that a truncated Jacobi triple product series has nonnegative coefficients. This conjecture was proved analytically by Mao and combinatorially by Yee. In 2021, Merca proposed a stronger version of the conjecture, that is, for positive integers $1\leq S

The number of primes not in a numerical semigroup
Yong-Gao Chen, Hui Zhu
https://arxiv.org/abs/2506.03625 https://arxiv.org/pdf/2506.…

The number of primes not in a numerical semigroup
For two coprime positive integers $a,b$, let $π^* (a, b)$ be the number of primes that cannot be represented as $au+bv$, where $u,v$ are nonnegative integers. In this paper, we prove that $π^* (a, b)\ge 0.014 π(ab-a-b)$ and pose following conjecture: $π^* (a, b)\ge \frac 12 π(ab-a-b)$, where $π(x)$ denotes the number of primes not exceeding $x$. This conjecture is confirmed for $1\le a\le 8$.

On the sum of a prime and two Fibonacci numbers
Ji-Zhen Xu, Yong-Gao Chen
https://arxiv.org/abs/2506.03631 https://arxiv.org/pdf/2506…

On the sum of a prime and two Fibonacci numbers
Let $\{f_n\}$ be the Fibonacci sequence. For any positive integer $n$, let $r(n)$ be the number of solutions of $n=p+f_{k_1^{2}} +f_{k_{2}^{2}}$, where $p$ is a prime and $k_1, k_2$ are nonnegative integers with $k_1\le k_2$. In this paper, it is proved that $\{ n : r(n)=0\} $ contains an infinite arithmetic progression, and both sets $\{ n : r(n)=1\} $ and $\{ n : r(n)\ge 2\}$ have positive asymptotic densities.