Tootfinder

This https://arxiv.org/abs/2208.06684 has been replaced.
link: https://scholar.google.com/scholar?q=a

Extension domains for Hardy spaces
We show that a proper open subset $Ω\subset \rn$ is an extension domain for $\hp$ ($0

This https://arxiv.org/abs/2206.13254 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sample compression schemes for balls in graphs
One of the open problems in machine learning is whether any set-family of VC-dimension $d$ admits a sample compression scheme of size $O(d)$. In this paper, we study this problem for balls in graphs. For a ball $B=B_r(x)$ of a graph $G=(V,E)$, a realizable sample for $B$ is a signed subset $X=(X^+,X^-)$ of $V$ such that $B$ contains $X^+$ and is disjoint from $X^-$. A proper sample compression scheme of size $k$ consists of a compressor and a reconstructor. The compressor maps any realizable sa…

Alexandrov spaces are CS sets
Tadashi Fujioka
https://arxiv.org/abs/2404.14587 https://arxiv.org/pdf/2404.14587

Alexandrov spaces are CS sets
We prove that the extremal stratification of an Alexandrov space by Perelman-Petrunin is a CS stratification in the sense of Siebenmann. We also show that every space of directions of an Alexandrov space without proper extremal subsets is homeomorphic to a sphere. In the appendix we give an example of a primitive extremal subset of codimension 2 that is not an Alexandrov space with respect to the induced intrinsic metric.

Bohr inequalities via proper combinations for a certain class of close-to-convex harmonic mappings
Molla Basir Ahamed, Partha Pratim Roy
https://arxiv.org/abs/2402.11808

Bohr inequalities via proper combinations for a certain class of close-to-convex harmonic mappings
Let $ \mathcal{H}(Ω) $ be the class of complex-valued functions harmonic in $ Ω\subset\mathbb{C} $ and each $f=h+\overline{g}\in \mathcal{H}(Ω)$, where $ h $ and $ g $ are analytic. In the study of Bohr phenomenon for certain class of harmonic mappings, it is to find a constant $ r_f\in (0, 1) $ such that the inequality \begin{align*} M_f(r):=r+\sum_{n=2}^{\infty}\left(|a_n|+|b_n|\right)r^n\leq d\left(f(0), \partialΩ\right) \;\mbox{for}\;|z|=r\leq r_f, \e…

This https://arxiv.org/abs/2310.01793 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On regular sets in Cayley graphs
Let $\Ga = (V, E)$ be a graph and $a, b$ nonnegative integers. An $(a, b)$-regular set in $\Ga$ is a nonempty proper subset $D$ of $V$ such that every vertex in $D$ has exactly $a$ neighbours in $D$ and every vertex in $V \setminus D$ has exactly $b$ neighbours in $D$. A $(0,1)$-regular set is called a perfect code, an efficient dominating set, or an independent perfect dominating set. A subset $D$ of a group $G$ is called an $(a,b)$-regular set of $G$ if it is an $(a, b)$-regular set in some C…

This https://arxiv.org/abs/2401.01979 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Low level definability above large cardinals
We study some connections between definability in generalized descriptive set theory and large cardinals, particularly measurable cardinals and limits thereof, working in ZFC. We show that if $κ$ is a limit of measurable cardinals then there is no $Σ_1(H_κ\cup\mathrm{OR})$ wellorder of a subset of $P(κ)$ of length $\geqκ^+$; this answers a question of Lücke and Müller. However, in $M_1$, the minimal proper class mouse with a Woodin cardinal, for every uncountable cardinal $κ$ which is n…

This https://arxiv.org/abs/2403.10016 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Existence and Regularity for Stationary Boltzmann Equation in a Small Domain
In this article, we study the stationary Boltzmann equation with the incoming boundary condition for the hard potential cases. Assuming the smallness of the domain and a suitable normal curvature condition on the boundary, we find a suitable solution space which is a proper subset of the $W^{1,p}$ space.

Commutative N-polyregular functions
Aliaume Lopez
https://arxiv.org/abs/2404.02232 https://arxiv.org/pdf/2404.02232

Commutative N-polyregular functions
This paper addresses two questions regarding N-polyregular functions, that forms a proper subset of N-rational series. We show that given a Z-rational series, it is decidable whether it is computable via a commutative N-polyregular function, and provide a counter-example to the theorem of Karhumäki that studied the same question in the case of polynomials. We also prove that it is decidable whether a commutative N-polyregular function is star-free, by proving the stronger statement that star-f…

On wen knots
Celeste Damiani, Shin Satoh
https://arxiv.org/abs/2403.03917 https://arxiv.org/pdf/2403.03917

On wen knots
We introduce the notion of wen knots, and prove that the set of wen knots is a proper subset of the set of extended welded knots. Furthermore we prove that the complementary subset consists of welded knots up to horizontal mirror reflections. This allow us to characterise completely extended welded knots by the parity of their number of wens, that we can always reduce to 0 or 1.

Bohr inequalities via proper combinations for a certain class of close-to-convex harmonic mappings
Molla Basir Ahamed, Partha Pratim Roy
https://arxiv.org/abs/2402.11808

Bohr inequalities via proper combinations for a certain class of close-to-convex harmonic mappings
Let $ \mathcal{H}(Ω) $ be the class of complex-valued functions harmonic in $ Ω\subset\mathbb{C} $ and each $f=h+\overline{g}\in \mathcal{H}(Ω)$, where $ h $ and $ g $ are analytic. In the study of Bohr phenomenon for certain class of harmonic mappings, it is to find a constant $ r_f\in (0, 1) $ such that the inequality \begin{align*} M_f(r):=r+\sum_{n=2}^{\infty}\left(|a_n|+|b_n|\right)r^n\leq d\left(f(0), \partialΩ\right) \;\mbox{for}\;|z|=r\leq r_f, \e…

This https://arxiv.org/abs/2401.01979 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Low level definability above large cardinals
We study some connections between definability in generalized descriptive set theory and large cardinals, particularly measurable cardinals and limits thereof, working in ZFC. We show that if $κ$ is a limit of measurable cardinals then there is no $Σ_1(H_κ\cup\mathrm{OR})$ wellorder of a subset of $P(κ)$ of length $\geqκ^+$; this answers a question of Lücke and Müller. However, in $M_1$, the minimal proper class mouse with a Woodin cardinal, for every uncountable cardinal $κ$ which is n…

This https://arxiv.org/abs/2401.14062 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Minimal doubling for small subsets in compact Lie groups
We prove a sharp bound for the minimal doubling of a small measurable subset of a compact connected Lie group. Namely, let $G$ be a compact connected Lie group of dimension $d_G$, we show that for for all measurable subsets $A$, we have $$μ_G(A^2) \geq \left(2^{d_G-d_H} - Cμ_G(A)^{\frac{2}{d_G-d_H}}\right)μ_G(A)$$ where $d_H$ is the maximal dimension of a proper closed subgroup $H$ and $C > 0$ is a dimensional constant. This settles a conjecture of Breuillard and Green, and recovers and impr…

This https://arxiv.org/abs/2311.18337 has been replaced.
initial toot: https://mastoxiv.page/@arX…

From isolated polyelectrolytes to star-like assemblies: The role of sequence heterogeneity on the statistical structure of the intrinsically disordered Neurofilament-low tail domain
Intrinsically disordered proteins (IDPs) are a subset of proteins that lack stable secondary structure. Given their polymeric nature, previous mean-field approximations have been used to describe the statistical structure of IDPs. However, the amino-acid sequence heterogeneity and complex intermolecular interaction network have significantly impeded the ability to get proper approximations. One such case is the intrinsically disordered tail domain of Neurofilament low (NFLt), which comprises a …

On the number of minimal forts of a graph
Paul Becker, Thomas R. Cameron, Derek Hanely, Boon Ong, Joseph P. Previte
https://arxiv.org/abs/2404.05963 https:…

On the number of minimal forts of a graph
In 2018, a fort of a graph was introduced as a non-empty subset of vertices in which no vertex outside of the set has exactly one neighbor in the set. Since then, forts have been used to characterize zero forcing sets, model the zero forcing number as an integer program, and generate lower bounds on the zero forcing number of a Cartesian product. In this article, we investigate the number of minimal forts of a graph, where a fort is minimal if every proper subset is not a fort. In particular, w…

On the Existence and Regularity for Stationary Boltzmann Equation in a Small Domain
I-Kun Chen, Chun-Hsiung Hsia, Daisuke Kawagoe, Jhe-Kuan Su
https://arxiv.org/abs/2403.10016

On the Existence and Regularity for Stationary Boltzmann Equation in a Small Domain
In this article, we study the stationary Boltzmann equation with the incoming boundary condition for the hard potential cases. Assuming the smallness of the domain and a suitable normal curvature condition on the boundary, we find a suitable solution space which is a proper subset of the $W^{1,p}$ space.

The $X$-semiprimeness of Rings
Grigore C\u{a}lug\u{a}reanu, Tsiu-Kwen Lee, Jerzy Matczuk
https://arxiv.org/abs/2402.19374 https://arx…

The $X$-semiprimeness of Rings
For a subset $X$ of a ring $R$, the ring $R$ is called $X$-semiprime if, given $a\in R$, $aXa=0$ implies $a=0$. This provides with a proper class of semiprime rings. If $\mathit{Id}(R)$ denotes the set of all idempotents of $ R $, and $U(R)$ denotes the set of all units of $R$, $R$ is also called idempotent semiprime (resp. unit-semiprime) if $R$ is $\mathit{Id}(R)$ -semiprime (resp. $U(R)$-semiprime). It is proved that every idempotent semiprime ring is unit-semiprime. This gives a close link …

This https://arxiv.org/abs/2401.14062 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Minimal doubling for small subsets in compact Lie groups
We prove a sharp bound for the minimal doubling of a small measurable subset of a compact connected Lie group. Namely, let $G$ be a compact connected Lie group of dimension $d_G$, we show that for every $ε> 0$ and for all measurable subsets $A$ of small enough Haar measure, we have $$ μ_G(A^2) > \left(2^{d_G - d_H}-ε\right)μ_G(A)$$ where $d_H$ is the maximal dimension of a proper closed subgroup $H$. This settles a conjecture of Breuillard and Green and recovers - with completely differ…

This https://arxiv.org/abs/2401.14062 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Minimal doubling for small subsets in compact Lie groups
We prove a sharp bound for the minimal doubling of a small measurable subset of a compact connected Lie group. Namely, let $G$ be a compact connected Lie group of dimension $d_G$, we show that for every $ε> 0$ and for all measurable subsets $A$ of small enough Haar measure, we have $$ μ_G(A^2) > \left(2^{d_G - d_H}-ε\right)μ_G(A)$$ where $d_H$ is the maximal dimension of a proper closed subgroup $H$. This settles a conjecture of Breuillard and Green and recovers - with completely differ…