Tootfinder

Smooth manifolds in $G_{n,2}$ and $\mathbb{C} P^{N}$ defined by symplectic reductions of $T^n$-action
Victor M. Buchstaber, Svjetlana Terzi\'c
https://arxiv.org/abs/2507.04582

Smooth manifolds in $G_{n,2}$ and $\mathbb{C} P^{N}$ defined by symplectic reductions of $T^n$-action
Plücker coordinates define the $T^n$-equivariant embedding $p : G_{n,2}\to \mathbb{C} P^{N}$ of a complex Grassmann manifold $G_{n,2}$ into the complex projective space $\mathbb{C} P^{N}$, $N=\binom{n}{2}-1$ for the canonical $T^n$-action on $G_{n,2}$ and the $T^n$-action on $\mathbb{C} P^{N}$ given by the second symmetric power representation $T^n\to T^{N}$ and the standard $T^{N}$-action. Let $μ: G_{n,2}\to Δ_{n,2}\subset \mathbb{R} ^{n}$ and $\tildeμ: \mathbb{C} P^{N}\to Δ_{n,2}\subset …

$q$-Congruences for Z.-W. Sun's generalized polynomials $w^{(\alpha)}_k(x)$
Lin-Yue Li, Rong-Hua Wang
https://arxiv.org/abs/2507.04653 https://

$q$-Congruences for Z.-W. Sun's generalized polynomials $w^{(α)}_k(x)$
In 2022, Z.-W. Sun defined \begin{equation*} w_k^{(α)}{(x)}=\sum_{j=1}^{k}w(k,j)^αx^{j-1}, \end{equation*} where $k,α$ are positive integers and $w(k,j)=\frac{1}{j}\binom{k-1}{j-1}\binom{k+j}{j-1}$. Let $(x)_{0}=1$ and $(x)_{n}=x(x+1)\cdots(x+n-1)$ for all $n\geq 1$. In this paper, it is proved by $q$-congruences that for any positive integers ${α,β, m,n,r}$, we have \begin{equation*} \frac{(2,n)}{n(n+1)(n+2)}\sum_{k=1}^{n}k^r(k+1)^r(2k+1)w_{k}^{(α)}(x)^{m}\in\mathbb{Z}[x], \end{equation*…

Ramsey goodness of stars and fans for the Haj\'os graph
Jiafu He, Haiyu Zeng, Yanbo Zhang
https://arxiv.org/abs/2506.06724 https://

Ramsey goodness of stars and fans for the Hajós graph
Given two graphs $G_1$ and $G_2$, the Ramsey number $R(G_1,G_2)$ denotes the smallest integer $N$ such that any red-blue coloring of the edges of $K_N$ contains either a red $G_1$ or a blue $G_2$. Let $G_1$ be a graph with chromatic number $χ$ and chromatic surplus $s$, and let $G_2$ be a connected graph with $n$ vertices. The graph $G_2$ is said to be Ramsey-good for the graph $G_1$ (or simply $G_1$-good) if, for $n \ge s$, \[R(G_1,G_2)=(χ-1)(n-1)+s.\] The $G_1$-good property has been exte…

Faster Algorithms for $(2k-1)$-Stretch Distance Oracles
Avi Kadria, Liam Roditty
https://arxiv.org/abs/2507.06721 https://arxiv.org/p…

Faster Algorithms for $(2k-1)$-Stretch Distance Oracles
Let $G=(V, E)$ be an undirected $n$-vertices $m$-edges graph with non-negative edge weights. In this paper, we present three new algorithms for constructing a $(2k-1)$-stretch distance oracle with $O(n^{1+\frac{1}{k}})$ space. The first algorithm runs in $\Ot(\max(n^{1+2/k}, m^{1-\frac{1}{k-1}}n^{\frac{2}{k-1}}))$ time, and improves upon the $\Ot(\min(mn^{\frac{1}{k}},n^2))$ time of Thorup and Zwick [STOC 2001, JACM 2005] and Baswana and Kavitha [FOCS 2006, SICOMP 2010], for every $k > 2$ and $…

Convex real projective structures on Coxeter orbifold $D^2(;n_1,n_2,n_3,n_4)\times \mathbb{R}$
Jaesung Bae
https://arxiv.org/abs/2509.05579 https://arxiv.o…

Convex real projective structures on Coxeter orbifold $D^2(;n_1,n_2,n_3,n_4)\times \mathbb{R}$
The deformation space of real projective structures parametrizes the space of the convex real projective structures on an orbifold. The Coxeter orbifold can be obtained $D^2(;n_1,n_2,n_3,n_4)\times\mathbb{R}$ by embedding the Coxeter quadrilateral from $\mathbb{RP}^2$ to $\mathbb{RP}^3$, and extending the side edges to planes and perturbing these to obtain a convex polytope. This noncompact orbifold can be induced from two combinatorial polytopes. Using this fact, we determine the deformation s…

The volume of marginally trapped submanifolds in a Lorentzian manifold satisfying the null energy condition
Riku Kishida
https://arxiv.org/abs/2506.07093 h…

The volume of marginally trapped submanifolds in a Lorentzian manifold satisfying the null energy condition
In this paper, we focus on a marginally trapped submanifold $f:Σ^n\to M^{n+2}_1$ in a Lorentzian manifold $M^{n+2}_1$. We show that $f$ lies in a certain null hypersurface $\mathcal{N}_f^{n+1}$ in $M^{n+2}_1$ and $f$ has a locally volume-maximizing property in $\mathcal{N}^{n+1}_f$ if $M^{n+2}_1$ satisfies the null energy condition.

2025 NFL preseason, Week 1: What We Learned from Saturday's games https://www.nfl.com/news/2025-nfl-preseason-week-1-what-we-learned-from-saturday-s-games

Bootstrapping the Simplest Deconfined Quantum Critical Point
Shai M. Chester, Alessandro Piazza, Marten Reehorst, Ning Su
https://arxiv.org/abs/2507.06283 …

Bootstrapping the Simplest Deconfined Quantum Critical Point
We study the $N=3$ case of the $CP^{N-1}$ model, which is a field theory of $N$ complex scalars in $3d$ coupled to an Abelian gauge field with $SU(N) \times U(1)$ global symmetry. Recent evidence suggests the $N=2$ theory is not critical, which makes the $N=3$ theory the simplest possibility of deconfined quantum criticality. We apply the conformal bootstrap to correlators of charge $q=0,1,2$ scalar operators under the $U(1)$ symmetry, which gives us access also to $q=3,4$ operators. After impo…

Note on injectivity in second-gradient Nonlinear Elasticity
Stanislav Hencl, Kaushik Mohanta
https://arxiv.org/abs/2507.04938 https://

Note on injectivity in second-gradient Nonlinear Elasticity
Let $q>1$, $(1-\frac{1}{q})a\geq 1$ and let $Ω\subset \mathbb{R}^2$ be Lipschitz domain. We show that planar mappings in the second order Sobolev space $f\in W^{2,q}(Ω,\mathbb{R}^2)$ with $|J_f|^{-a}\in L^1(Ω)$ are homeomorphism if they agree with a homeomorphism on the boundary. The condition $(1-\frac{1}{q})a\geq 1$ is sharp. We also have a new sharp result about the $\mathcal{H}^{n-1}$ measure of the projection of the set $\{J_f=0\}$ in $\mathbb{R}^n$.

Construction of Higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$
Yusuke Nemoto, Ken Sato
https://arxiv.org/abs/2509.05569 https://

Construction of Higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$
In this paper, we construct higher Chow cycles of type $(2, 1)$ on a certain family of surfaces, which are constructed by a product of certain hypergeometric curves of degree $N$. We prove that for a very general member, these cycles are linearly independent over $\mathbb{Z}$ and generate a subgroup of $\operatorname{rank} \ge 36 \cdot φ(N)$, where $φ(N)$ is Euler's totient function, by computing the image of the transcendental regulator map.

On subcodes of the generalized Reed-Solomon codes
Yu Ning
https://arxiv.org/abs/2507.04689 https://arxiv.org/pdf/2507.04689

On subcodes of the generalized Reed-Solomon codes
In this paper, we study a class of subcodes of codimension $1$ in the $[n,k+1]_q$ generalized Reed-Solomon (GRS) codes, whose generator matrix is derived by removing the row of degree $k-r$ from the generator matrix of the $[n,k+1]_q$ GRS codes, where $1 \le r \le k-1$. We show equivalent characterizations for this class of subcodes of the GRS codes being self-dual or near-MDS, which extends the results for $r=1$ in the literature. Along with these characterizations, families of self-dual near-…

Combinatorial results for zero-divisors regarding right zero elements of order-preserving transformations
Emrah Korkmaz, Hayrullah Ay{\i}k
https://arxiv.org/abs/2507.04900

Combinatorial results for zero-divisors regarding right zero elements of order-preserving transformations
For any positive integer $n$, let $\mathcal{O}_{n}$ be the semigroup of all order-preserving full transformations on $X_{n}=\{1<\cdots

On geodesic disks enclosing many points
Prosenjit Bose, Guillermo Esteban, David Orden, Rodrigo Silveira, Tyler Tuttle
https://arxiv.org/abs/2506.06477 htt…

On geodesic disks enclosing many points
Let $ Π(n) $ be the largest number such that for every set $ S $ of $ n $ points in a polygon~$ P $, there always exist two points $ x, y \in S $, where every geodesic disk containing $ x $ and $ y $ contains $ Π(n) $ points of~$ S $. We establish upper and lower bounds for $ Π(n)$, and show that $ \left\lceil \frac{n}{5}\right\rceil+1 \leq Π(n) \leq \left\lceil \frac{n}{4} \right\rceil +1 $. We also show that there always exist two points $x, y\in S$ such that every geodesic disk with $x$ …

Ballistic Transport for Discrete Multi-Dimensional Schr\"odinger Operators With Decaying Potential
David Damanik (Rice University), Zhiyan Zhao (Universit\'e C\^ote d'Azur)
https://arxiv.org/abs/2507.04988

Ballistic Transport for Discrete Multi-Dimensional Schrödinger Operators With Decaying Potential
We consider the discrete Schrödinger operator $H = -Δ+ V$ on $\ell^2(\mathbb{Z}^d)$ with a decaying potential, in arbitrary lattice dimension $d\in\mathbb{N}^*$, where $Δ$ is the standard discrete Laplacian and $V_n = o(|n|^{-1})$ as $|n| \to \infty$. We prove that the unitary evolution $e^{-i tH}$ exhibits ballistic transport in the sense that, for any $r > 0$, the weighted $\ell^2-$norm $$\|e^{-i tH}u\|_r:=\left(\sum_{n\in\mathbb{Z}^d} (1+|n|^2)^{r} …

House Republicans who voted to pass Donald Trump’s tax bill last week
💥know it’s going to slash the federal Medicaid program by $1 trillion
🔥and kick millions of people off of their health care.
But that sounds bad.
And people already hate this law.
So instead of saying that,
Republicans are trying out a new way of talking about the bill they all voted for:
👉They just pretend they voted to increase Medicaid spending!

The GOP’s New Lie After Cutting $1 Trillion From Medicaid: We Gave It More Money!
“We are increasing Medicaid expenditures by $200 billion,” Rep. Rob Bresnahan (R-Pa.) falsely said of Trump’s tax law, which will strip health care from millions.

A local quantization principle for inclusions of tracial von Neumann algebras
Xinyan Cao, Junsheng Fang, Chunlan Jiang, Zhaolin Yao
https://arxiv.org/abs/2507.04244

A local quantization principle for inclusions of tracial von Neumann algebras
We study the local quantization principle (after Sorin Popa~\cite{popa 94} and \cite{popa 95}) of inclusions of tracial von Neumann algebras. Let $(\mathcal{M},τ)$ be a type ${\rm II}_1$ von Neumann algebra and let $\mathcal{N}\subseteq \mathcal{M}$ be a type ${\rm II}_1$ von Neumann subalgebra. Let $x_1,\ldots, x_m \in \mathcal{M}$ and $ ε> 0$. Then there exists a partition of 1 with projections $p_{1}, \ldots, p_{n}$ in $\mathcal{N}$ such that \[\left\|\sum_{i=1}^n p_{i}\left(x_j-E_{\m…

Galois groups of random integer matrices
Theresa C. Anderson, Evan M. O'Dorney
https://arxiv.org/abs/2506.06463 https://arxiv.org…

Galois groups of random integer matrices
We study the number $M_n(T)$ be the number of integer $n\times n$ matrices $A$ with entries bounded in absolute value by $T$ such that the Galois group of characteristic polynomial of $A$ is not the full symmetric group $S_n$. One knows $M_n(T) \gg T^{n^2 - n + 1} \log T$, which we conjecture is sharp. We first use the large sieve to get $M_n(T) \ll T^{n^2 - 1/2}\log T$. Using Fourier analysis and the geometric sieve, as in Bhargava's proof of van der Waerden's conjecture, we improve this bound…

Compact positive multilinear operators on Banach lattices
Geraldo Botelho, Vinicius C. C. Miranda
https://arxiv.org/abs/2509.04652 https://arxiv.org/pdf/25…

Compact positive multilinear operators on Banach lattices
Let $1 < p_1, \ldots, p_n < \infty, 1\leq q < \infty$ be such that $\sum\limits_{i=1}^n \frac{1}{p_i} < \frac{1}{q}$ and let $μ_1, \ldots, μ_n, ν$ be arbitrary measures. Generalizing known linear and multilinear results, we prove that all positive $n$-linear operators from $\ell_{p_1} \times \cdots \times \ell_{p_n}$ to $L_q(ν)$ and from $L_{p_1}(μ_1) \times \cdots \times L_{p_1}(μ_n)$ to $\ell_{q}$ are compact. This result, along with other related ones concerning free Banach lattices, s…

The GOP's New Lie After Cutting $1 Trillion From Medicaid: We Gave It More Money! (Jennifer Bendery/HuffPost)
https://www.huffpost.com/entry/house-republicans-cut-medicaid-damage-control_n_686d96a0e4b041f69cfd6636
http://www.memeorandum.com/250709/p139#a250709p139

Metric uniform distribution on analytic curves
Vitaly Bergelson, Joel Moreira
https://arxiv.org/abs/2509.06909 https://arxiv.org/pdf/2509.06909

Metric uniform distribution on analytic curves
We obtain multidimensional metric uniform distribution results involving sequences in ${\mathbb R}^k$ parametrized by analytic curves. Our theorems extend the classical theorems of Weyl and Koksma in a variety of ways. One of our main results implies that for any injective sequences $a_1,\dots,a_k:{\mathbb N}\to{\mathbb Z}$ the set $$\Big\{(x_1,\dots,x_k)\in{\mathbb R}^k:\big(a_1(n)x_1,\dots,a_k(n)x_k\big)_{n\in{\mathbb N}}\text{ is uniformly distributed in }{\mathbb T}^k\Big\}$$ has full…

On local large deviations for decoupled random walks
Dariusz Buraczewski, Alexander Iksanov, Alexander Marynych
https://arxiv.org/abs/2508.05178 https://ar…

On local large deviations for decoupled random walks
A decoupled standard random walk is a sequence of independent random variables $(\hat{S}_n)_{n \geq 1}$ such that, for each $n \geq 1$, the distribution of $\hat{S}_n$ is the same as that of $S_n = ξ_1 + \ldots + ξ_n$, where $(ξ_k)_{k \geq 1}$ are independent copies of a nonnegative random variable $ξ$. We consider the counting process $(\hat{N}(t))_{t\geq 0}$ defined as the number of terms $\hat{S}_n$ in the sequence $(\hat{S}_n)_{n \geq 1}$ that lie within the interval $[0, t]$. Under var…

A Note on Deaconescu's Conjecture
Sagar Mandal
https://arxiv.org/abs/2507.02930 https://arxiv.org/pdf/2507.02930

A Note on Deaconescu's Conjecture
Hasanalizade [1] studied Deaconescu's conjecture for positive composite integer $n$. A positive composite integer $n\geq4$ is said to be a Deaconescu number if $S_2(n)\mid ϕ(n)-1$. In this paper, we improve Hasanalizade's result by proving that a Deaconescu number $n$ must have at least seventeen distinct prime divisors, i.e., $ω(n)\geq 17$ and must be strictly larger than $5.86\cdot10^{22}$. Further, we prove that if any Deaconescu number $n$ has all prime divisors greater than or equal to $…

JWST-TST DREAMS: Secondary Atmosphere Constraints for the Habitable Zone Planet TRAPPIST-1 e
Ana Glidden, Sukrit Ranjan, Sara Seager, N\'estor Espinoza, Ryan J. MacDonald, Natalie H. Allen, Caleb I. Ca\~nas, David Grant, Am\'elie Gressier, Kevin B. Stevenson, Natasha E. Batalha, Nikole K. Lewis, Douglas Long, Hannah R. Wakeford, Lili Alderson, Ryan C. Challener, Knicole Col\'on, Jingcheng Huang, Zifan Lin, Dana R. Louie, Elijah Mullens, Kristin S. Sotzen, Jeff A. Valenti, D…

JWST-TST DREAMS: Secondary Atmosphere Constraints for the Habitable Zone Planet TRAPPIST-1 e
The TRAPPIST-1 system offers one of the best opportunities to characterize temperate terrestrial planets beyond our own solar system. Within the TRAPPIST-1 system, planet e stands out as highly likely to sustain surface liquid water if it possesses an atmosphere. Recently, we reported the first JWST/NIRSpec PRISM transmission spectra of TRAPPIST-1 e, revealing significant stellar contamination, which varied between the four visits. Here, we assess the range of planetary atmospheres consistent w…

2025 NFL preseason, Week 1: What We Learned from Friday's tripleheader https://www.nfl.com/news/2025-nfl-preseason-week-1-what-we-learned-from-friday-s-tripleheader

The Molecular Inventory of TMC-1 with GOTHAM Observations
Ci Xue, Alex N. Byrne, Larry Morgan, Gabi Wenzel, P. Bryan Changala, Zachary T. P. Fried, Ryan A. Loomis, Anthony Remijan, Edwin A. Bergin, Ilsa R. Cooke, David Frayer, Andrew M. Burkhardt, Steven B. Charnley, Martin A. Cordiner, Andrew Lipnicky, Michael C. McCarthy, Brett A. McGuire
https://

The Molecular Inventory of TMC-1 with GOTHAM Observations
Spectral line surveys of the Taurus Molecular Cloud-1 (TMC-1) have led to the detection of more than 100 new molecular species, making it the most prolific source of interstellar molecular discoveries. These wide-band, high-sensitivity line surveys have been enabled by advances in telescope and receiver technology, particularly at centimeter and millimeter wavelengths. In this work, we present a statistical analysis of the molecular inventory of TMC-1 as probed by the GOTHAM large program surve…

Twisted conjugacy in $BS(n, 1)$
Oorna Mitra, Mallika Roy, Enric Ventura
https://arxiv.org/abs/2508.04397 https://arxiv.org/pdf/2508.04397

Twisted conjugacy in $BS(n, 1)$
In this article, we solve the twisted conjugacy problem for solvable Baumslag--Solitar groups $BS(n,1)$, i.e., we propose an algorithm which, given two elements $u,v \in BS(n,1)$ and an automorphism $φ\in \Aut(BS(n,1))$, decides whether $v=(wφ)^{-1} u w$ for some $w\in BS(n,1)$. Also we prove that the automorphism group $\Aut(BS(n,1))$ is orbit decidable -- given two words on the generators $u,v\in F(X)$, decide whether the corresponding elements $u,v\in G$ can be mapped to each other by some…

Hey @… – you are complicit in genocide.
Just noting it down for the history books.
#EU #israel

Das Verfahren zum #AfDVerbot muss kommen, bevor uns diese Chancen zum Schutz unseres Landes von der AfD genommen werden kann!
https://mstdn.social/@ntv/115174292597130641

ntv Nachrichten ✅ (@ntv@mstdn.social)
Attached: 1 image RTL/ntv-Trendbarometer: Union hängt hinter AfD fest, SPD im Niemandsland https://www.n-tv.de/mediathek/videos/politik/Union-haengt-hinter-AfD-fest-SPD-im-Niemandsland-article26020651.html?utm_source=dlvr.it&utm_medium=mastodon

Die #Autoindustrie in #Deutschland steht unter Druck. Bis 2030 könnten laut IW-Studie bis zu 90.000 Jobs wegfallen.
Ursachen sind sinkende Gewinne durch das schwache #China-Geschäft, droh…

Schlüsselindustrie in der Krise: Bis zu 90.000 Jobs in deutscher Autoindustrie bis 2030 vor dem Aus
Rund 1,2 Millionen Menschen arbeiten in der deutschen Autoindustrie. Doch das schwächelnde China-Geschäft, US-Zölle und der steinige Weg zur E-Auto-Wende lassen die Gewinne einbrechen. Allein bis Jahresende könnten weitere 18.000 Jobs gestrichen werden. Die Prognose bis 2030 sieht laut IW noch deutlich düsterer aus.

Asymptotically-tight packing and covering with transversal bases in Rota's basis conjecture
Richard Montgomery, Lisa Sauermann
https://arxiv.org/abs/2508.05601 https://

Asymptotically-tight packing and covering with transversal bases in Rota's basis conjecture
In 1989, Rota conjectured that, given any $n$ bases $B_1,\dots,B_n$ of a vector space of dimension $n$, or more generally a matroid of rank $n$, it is possible to rearrange these into $n$ disjoint transversal bases. Here, a transversal basis is a basis consisting of exactly one element from each of the original bases $B_1,\dots,B_n$. Two natural approaches to this conjecture are, to ask in this setting a) how many disjoint transversal bases can we find and b) how few transversal bases do we nee…

Soliton Surfaces and the Geometry of Integrable Deformations of the $\mathbb{CP}^{N-1}$ Model
Christian Ferko, Michele Galli, Zejun Huang, Gabriele Tartaglino-Mazzucchelli
https://arxiv.org/abs/2509.05081

Soliton Surfaces and the Geometry of Integrable Deformations of the $\mathbb{CP}^{N-1}$ Model
The $\mathbb{CP}^{N-1}$ model is an analytically tractable $2d$ quantum field theory which shares several properties with $4d$ Yang-Mills theory. By virtue of its classical integrability, this model also admits a family of integrable higher-spin auxiliary field deformations, including the $T \overline{T}$ deformation as a special case. We study the $\mathbb{CP}^{N-1}$ model and its deformations from a geometrical perspective, constructing their soliton surfaces and recasting physical properties…

TLB-VFI: Temporal-Aware Latent Brownian Bridge Diffusion for Video Frame Interpolation
Zonglin Lyu, Chen Chen
https://arxiv.org/abs/2507.04984 https://

TLB-VFI: Temporal-Aware Latent Brownian Bridge Diffusion for Video Frame Interpolation
Video Frame Interpolation (VFI) aims to predict the intermediate frame $I_n$ (we use n to denote time in videos to avoid notation overload with the timestep $t$ in diffusion models) based on two consecutive neighboring frames $I_0$ and $I_1$. Recent approaches apply diffusion models (both image-based and video-based) in this task and achieve strong performance. However, image-based diffusion models are unable to extract temporal information and are relatively inefficient compared to non-diffusi…

@… @… > Anyway don't bother if you want just to keep this as your personal journal.
More then happy to answer any questions. Also writing blog posts on parts of it once I'm fully happy with them:

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Classification of silted algebras for two quivers of Dynkin type $\mathbb{D}_{n}$
Houjun Zhang

Grandir dans la OKC, ça été quelque chose de différent pour chacun et chacune d'entre nous, mais que ce soit les faits sur l'une ou l'autre génération, les faits sont lŠ, ils n'ont jamais vraiment été jugé dans leur ensemble, ils nous hantent encore, en voici quelques :
1/7

On representations of the multi-virtual braid group $M_kVB_n$ and the multi-welded braid group $M_kWB_n$
Vaibhav Keshari, Mohamad N. Nasser, Madeti Prabhakar
https://arxiv.org/abs/2508.04168

On representations of the multi-virtual braid group $M_kVB_n$ and the multi-welded braid group $M_kWB_n$
This paper classifies complex homogeneous $2$-local representations of the multiple virtual braid group $M_kVB_n$ into $\mathrm{GL}_n(\mathbb{C})$ for $n\geq3$ and $k >1$, showing that such representations fall into exactly $2^{k+1}+1$ distinct types, out of which except three all are unfaithful. In addition, this paper investigates complex homogeneous $2$-local representations of the multiple welded braid group $M_kWB_n$ into $\mathrm{GL}_n(\mathbb{C})$ for $n\geq3$ and $k >1$, identifying $3 …

1/N Tänään on kuulemma Testaajien päivä. Kun nykyään puhutaan paljon ohjelmakoodista ja senkin testaaminen on tärkeää, kannattaa kaikkien hieman meditoida sitä. Tässä muutama pika-ajatus:
Mitä se on:
- Jonkinlaisen logiikan kuvaus tietynlaisella kielellä, syntaksilla ja semantiikalla
- Toiminnallisen systeemielementin perusrakennetta, mutta systeemi on paljon muuta kuin koodinsa

On certain semigroups of finite monotone and order-decreasing partial transformations
Gonca Ay{\i}k, Hayrullah Ay{\i}k, Ilinka Dimitrova, J\"org Koppitz
https://arxiv.org/abs/2507.06047

On certain semigroups of finite monotone and order-decreasing partial transformations
Let $\mathcal{PMD}_{n}$ be the semigroup consisting of all monotone and order-decreasing partial transformations, and let $\mathcal{IMD}_{n}$ be the subsemigroup of $\mathcal{PMD}_{n}$ consisting of all injective monotone and order-decreasing transformations on the finite chain $X_{n}=\{ 1<\cdots

Non-Adaptive Evaluation of $k$-of-$n$ Functions: Tight Gap and a Unit-Cost PTAS
Mads Anker Nielsen, Lars Rohwedder, Kevin Schewior
https://arxiv.org/abs/2507.05877

Non-Adaptive Evaluation of $k$-of-$n$ Functions: Tight Gap and a Unit-Cost PTAS
We consider the Stochastic Boolean Function Evaluation (SBFE) problem in the well-studied case of $k$-of-$n$ functions: There are independent Boolean random variables $x_1,\dots,x_n$ where each variable $i$ has a known probability $p_i$ of taking value $1$, and a known cost $c_i$ that can be paid to find out its value. The value of the function is $1$ iff there are at least $k$ $1$s among the variables. The goal is to efficiently compute a strategy that, at minimum expected cost, tests the vari…

Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
Somnath Gandal, Annunziata Loiudice, Jagmohan Tyagi
https://arxiv.org/abs/2509.06138 https…

Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
We study the following class of quasilinear degenerate elliptic equations with critical nonlinearity \begin{align*} \begin{cases}-Δ_{γ,p} u= λ|u|^{q-2}u+|u|^{p_γ^{*}-2}u & \text{ in } Ω\subset \mathbb{R}^N, \\ u=0 & \text{ on } \partial Ω, \end{cases} \end{align*} where $Δ_{γ, p}v:=\sum_{i=1}^N X_i(|\nabla_γu|^{p-2}X_i u)$ is the Grushin $p$-Laplace operator, $z:=(x, y) \in \mathbb{R}^N$, $N=m+n,$ $m,n \geq 1,$, where $\nabla_γ=(X_1, \ldots, X_N)$ is th…

Bundeswehr will weitere "Patriot"-Luftabwehrraketen kaufen
Die Bundeswehr will Koalitionskreisen zufolge weitere 300 Patriot-Luftabwehrraketen in den USA kaufen. Der Gesamtpreis werde bei 1,5 Milliarden Euro liegen, sagten drei mit den Planungen Vertraute der Nachrichtenagentur Reuters. Norwegen sei aber bereit, sich mit knapp 200 Millionen Euro beteiligen.
Die Bestellung diene teilweise dazu, Bestände nach der Abgabe der Le…
📑

Ukraine-Liveblog: ++ Merz warnt vor "imperialistischen" Plänen Putins ++
Bundeskanzler Merz hat vor einer Ausweitung russischer Machtbestrebungen über die Ukraine hinaus gewarnt. Das russische Militär hat ukrainischen Angaben zufolge bei neuen Luftangriffen ein Wärmekraftwerk in der Region Kiew attackiert.

Comme un air de déjŠ vu... Coucou @… https://mastodon.top/@Haviorig/114819403426671442

Haviorig 🌈, presque Rohirrim (@Haviorig@mastodon.top)
Attaché : 1 image Miam miam #MardiPatisserie

Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits
Mahadi Ddamulira
https://arxiv.org/abs/2509.05984 https://arxiv.org/…

Tribonacci-Lucas numbers that are palindromic concatenations of two distinct repdigits
The Tribonacci-Lucas sequence $\{S_n\}_{n\ge 0}$ is defined by the linear recurrence relation $S_{n+3} = S_{n+2} + S_{n+1} + S_n$, for $ n\ge 0 $, with the initial conditions $S_0 =S_2= 3$ and $S_1 = 1$. A palindromic number is a number that remains the same when its digits are reversed. This paper uses Baker's theory for nozero lower bounds for linear forms in logarithms of algebraic numbers, and reduction methods involving the theory of continued fraction to determine all Tribonacci-Lucas num…

The degree condition in Llarull's theorem on scalar curvature rigidity
Christian Baer, Rudolf Zeidler
https://arxiv.org/abs/2507.05459 https://

The degree condition in Llarull's theorem on scalar curvature rigidity
Llarull's scalar curvature rigidity theorem states that a 1-Lipschitz map $f: M\to S^n$ from a closed connected Riemannian spin manifold $M$ with scalar curvature $\mathrm{scal}\ge n(n-1)$ to the standard sphere $S^n$ is an isometry if the degree of $f$ is nonzero. We investigate if one can replace the condition $\mathrm{deg}(f)\neq0$ by the weaker condition that $f$ is surjective. The answer turns out to be "no" for $n\ge3$ but "yes" for $n=2$. If we replace the scalar curvature by Ricci curva…

P\'olya's conjecture up to $\epsilon$-loss and quantitative estimates for the remainder of Weyl's law
Renjin Jiang, Fanghua Lin
https://arxiv.org/abs/2507.04307

Pólya's conjecture up to $ε$-loss and quantitative estimates for the remainder of Weyl's law
Let $Ω\subset\mathbb{R}^n$ be a bounded Lipschitz domain. For any $ε\in (0,1)$ we show that for any Dirichlet eigenvalue $λ_k(Ω)>Λ(ε,Ω)$, it holds \begin{align*} k&\le (1+ε)\frac{|Ω|ω(n)}{(2π)^n}λ_k(Ω)^{n/2}, \end{align*} where $Λ(ε,Ω)$ is given explicitly. This reduces the $ε$-loss version of Pólya's conjecture to a computational problem. This estimate is based on a uniform estimate on the remainder of the Weyl law on Lipschitz domains, which appears to be the first…

Strongly generalized derivations on C*-algebras
Amin Hosseini
https://arxiv.org/abs/2509.06634 https://arxiv.org/pdf/2509.06634

Strongly generalized derivations on C*-algebras
Let $\mathcal{A}$ and $\mathcal{B}$ be two algebras, let $\mathcal{M}$ be a $\mathcal{B}$-bimodule and let $n$ be a positive integer. A linear mapping $D_n:\mathcal{A} \rightarrow \mathcal{M}$ is called a strongly generalized derivation of order $n$, if there exist the families $\{E_k:\mathcal{A} \rightarrow \mathcal{M}\}_{k = 1}^{n}$, $\{H_k:\mathcal{A} \rightarrow \mathcal{M}\}_{k = 1}^{n}$, $\{F_k:\mathcal{A} \rightarrow \mathcal{B}\}_{k = 1}^{n}$ and $\{G_k:\mathcal{A} \rightarrow \mathcal{…

Criss-Cross Deletion Correcting Codes: Optimal Constructions with Efficient Decoders
Yubo Sun, Gennian Ge
https://arxiv.org/abs/2506.07607 https://

Criss-Cross Deletion Correcting Codes: Optimal Constructions with Efficient Decoders
This paper addresses fundamental challenges in two-dimensional error correction by constructing optimal codes for \emph{criss-cross deletions}. We consider an $ n \times n $ array over a $ q $-ary alphabet $Σ_q := \{0, 1, \ldots, q-1\}$ that is subject to a \emph{$(t_r, t_c)$-criss-cross deletion}, which involves the simultaneous removal of $ t_r $ rows and $ t_c $ columns. A code $\mathcal{C} \subseteq Σ_q^{n \times n}$ is defined as a \emph{$(t_r,t_c)$-criss-cross deletion correcting code} …

A Celestial Soft Symmetry Algebra in the ${\cal N}=8$ Supergravity
Changhyun Ahn, Man Hea Kim
https://arxiv.org/abs/2509.06328 https://arxiv.org/pdf/2509.0…

A Celestial Soft Symmetry Algebra in the ${\cal N}=8$ Supergravity
From the classical $SO({\cal N}=8)$ extended superconformal algebra between the lowest ${\cal N}=8$ multiplet in two dimensions obtained by Ademollo et al. (1976), we generalize it for the arbitrary ${\cal N}=8$ multiplet with manifest $SU(8)$ symmetry containing the bosonic $w_{1+\infty}$ algebra. By modifying this ${\cal N}=8$ supersymmetric $w_{1+\infty}$ algebra, we show that the celestial soft current algebra between the graviton, the gravitinos, the graviphotons, the graviphotinos, and th…

Constructing strong starters of orders $3p$: triplication with SAT solver
Oleg Ogandzhanyants, Sergey Sadov, Margo Kondratieva
https://arxiv.org/abs/2506.06461

Constructing strong starters of orders $3p$: triplication with SAT solver
A novel approach to building strong starters in cyclic groups of orders $n$ divisible by 3 from starters of smaller orders is presented. A strong starter in $Z_n$ ($n$ odd) is a partition of the set $\{1,2,\dots,n-1\}$ into pairs $\{a_i,b_i\}$ such that all pair sums $a_i+b_i$ are distinct and nonzero modulo $n$ and all differences $\pm(a_i-b_i)$ are distinct and nonzero modulo $n$. A special interest to strong starters of odd orders divisible by 3 is motivated by Horton's conjecture which clai…

Mamdani Holds Huge Lead in Mayor's Race, Times/Siena Poll Finds (New York Times)
https://www.nytimes.com/2025/09/09/nyregion/mayor-poll-mamdani-cuomo.html?unlocked_article_code=1.kk8.W-uS.xj_ZeOmF0w2S&smid=url-share
http://www.memeorandum.com/250909/p15#a250909p15

Diophantine tuples and Integral Ideals of $\mathbb{Q}(\sqrt{d})$
Kalyan Chakraborty, Shubham Gupta, Krishnarjun Krishnamoorthy
https://arxiv.org/abs/2509.06522 https://

Diophantine tuples and Integral Ideals of $\mathbb{Q}(\sqrt{d})$
Suppose $n$ is the fundamental discriminant associated with a quadratic extension of $\mathbb{Q}$. We show that for every Diophantine $m$-tuple $ \{t_1, t_2, \ldots, t_m\} $ with the property $ D(n) $, there exists integral ideals $ \mathfrak{t}_1, \mathfrak{t}_2, \ldots, \mathfrak{t}_m $ of $ \mathbb{Q}(\sqrt{n}) $ and $c\in \{1,2\}$ such that $ t_i= c\mathcal{N}(\mathfrak{t}_i) $ for $ i=1,2, \ldots, m $. Here, $ \mathcal{N}(\cdot) $ denotes the norm map from $\mathbb{Q}(\sqrt{n})$ to $\mathb…

On the dynamics of a semigroup and its relation with the Riemann Hypothesis
Carlos F. \'Alvarez, Juan Manzur
https://arxiv.org/abs/2507.03625 https://

On the dynamics of a semigroup and its relation with the Riemann Hypothesis
The semigroup of weighted composition operators $(W_n)_{n\in \mathbb{N}}$, defined by $$W_nf(z)=(1+z+\cdots +z^n)f(z^n),$$ acts on the classical Hardy-Hilbert space $H^{2}(\mathbb{D})$, and exhibits intriguing connections with both the Riemann Hypothesis (RH) and the Invariant Subspace Problem (ISP). In this paper, we prove that the adjoint operators $W^{\ast}_{n}$, for $n\geq 2$, are Devaney chaotic, frequently hypercyclic and mixing. In particular, these operators are hypercyclic and discuss …

On Deterministically Finding an Element of High Order Modulo a Composite
Ziv Oznovich, Ben Lee Volk
https://arxiv.org/abs/2506.07668 https://

On Deterministically Finding an Element of High Order Modulo a Composite
We give a deterministic algorithm that, given a composite number $N$ and a target order $D \ge N^{1/6}$, runs in time $D^{1/2+o(1)}$ and finds either an element $a \in \mathbb{Z}_N^*$ of multiplicative order at least $D$, or a nontrivial factor of $N$. Our algorithm improves upon an algorithm of Hittmeir (arXiv:1608.08766), who designed a similar algorithm under the stronger assumption $D \ge N^{2/5}$. Hittmeir's algorithm played a crucial role in the recent breakthrough deterministic integer f…

JWST-TST DREAMS: NIRSpec/PRISM Transmission Spectroscopy of the Habitable Zone Planet TRAPPIST-1 e
N\'estor Espinoza, Natalie H. Allen, Ana Glidden, Nikole K. Lewis, Sara Seager, Caleb I. Ca\~nas, David Grant, Am\'elie Gressier, Shelby Courreges, Kevin B. Stevenson, Sukrit Ranjan, Knicole Col\'on, Brett M. Morris, Ryan J. MacDonald, Douglas Long, Hannah R. Wakeford, Jeff A. Valenti, Lili Alderson, Natasha E. Batalha, Ryan C. Challener, Jingcheng Huang, Zifan Lin, Dana R. Lo…

JWST-TST DREAMS: NIRSpec/PRISM Transmission Spectroscopy of the Habitable Zone Planet TRAPPIST-1 e
TRAPPIST-1 e is one of the very few rocky exoplanets that is both amenable to atmospheric characterization and that resides in the habitable zone of its star -- located at a distance from its star such that it might, with the right atmosphere, sustain liquid water on its surface. Here, we present a set of 4 JWST/NIRSpec PRISM transmission spectra of TRAPPIST-1 e obtained from mid to late 2023. Our transmission spectra exhibit similar levels of stellar contamination as observed in prior works fo…

Toric geometry of ReLU neural networks
Yaoying Fu
https://arxiv.org/abs/2509.05894 https://arxiv.org/pdf/2509.05894…

Toric geometry of ReLU neural networks
Given a continuous finitely piecewise linear function $f:\mathbb{R}^{n_0} \to \mathbb{R}$ and a fixed architecture $(n_0,\ldots,n_k;1)$ of feedforward ReLU neural networks, the exact function realization problem is to determine when some network with the given architecture realizes $f$. To develop a systematic way to answer these questions, we establish a connection between toric geometry and ReLU neural networks. This approach enables us to utilize numerous structures and tools from algebraic …

A combinatorial approach to the Fourier expansions of powers of cos and sin
Mircea Cimpoeas
https://arxiv.org/abs/2506.06312 https://…

A combinatorial approach to the Fourier expansions of powers of cos and sin
We present a new combinatorial approach to the computation of the (real) Fourier expansions of $\cos^n(t)$ and $\sin^n(t)$, where $n\geq 1$ is an integer. As an application, we compute the Fourier expansions of $f(t)=\frac{1}{a-\cos t}$ and $g(t)=\frac{1}{a-\sin t}$, where $a\in\mathbb R$ with $|a|>1$.

Simple polynomial equations over (mxm)-matrices
Vitalij A. Chatyrko, Alexandre Karassev
https://arxiv.org/abs/2507.07085 https://arxi…

Simple polynomial equations over (mxm)-matrices
Let $m$ be any integer $\geq 3$. We consider the polynomial equation $$X^n + a_{n-1}\cdot X^{n-1} + \dots + a_1 \cdot X + a_0 \cdot I = O,$$ over $(m \times m)$-matrices $X$ with the real entries, where $I$ is the identity matrix, $O$ is the null matrix, $a_i \in \mathbb R$ for each $i$ and $n \geq 1$. We discuss its solution set $S$ supplied with the natural Euclidean topology. In particular, we describe the solution set $S$ for $m=3$ and calculate its dimension.

1/N Tuotteiden läpivalaisusta. Eräässä kirjassa tuli vastaan miten puoli vuosisataa sitten kananmunat läpivalaistiin kaupassa niiden kunnon varmistamiseksi. Nykyään sitä tehdään harvemmin, koska munat myydään _useimmiten_ pahvipakkauksissa. Myös mainittiin, että kenkäkaupassa oli läpivalaisulaite, jolla vanhemmat voivat tarkistaa miten kenkä sopi lapsen jalkaan - sellaista en muista nähneeni. Pitää varmaan olla melkoinen lamppu ja ohutnahkainen kenkä.

X-ray investigation of possible super-Eddington accretion in a radio-loud quasar at $z=6.13$
L. Ighina, A. Caccianiga, T. Connor, A. Moretti, F. Pacucci, C. Reynolds, J. Afonso, B. Arsioli, S. Belladitta, J. W. Broderick, D. Dallacasa, R. Della Ceca, F. Haardt, E. Lambrides, James K. Leung, A. Lupi, I. Matute, F. RIgamonti, P. Severgnini, N. Seymour, F. Tavecchio, C. Vignali

X-ray investigation of possible super-Eddington accretion in a radio-loud quasar at $z=6.13$
We present radio and X-ray observations of the recently discovered $z=6.13$ radio-powerful quasar RACS J032021.44$-$352104.1 using uGMRT, ATCA, LBA, and Chandra. The observed radio properties are in line with what is typically observed in high-$z$ radio quasars ($α_{\rm r}=0.72\pm 0.02$ and L$_{\rm 1.4GHz}=5.8 \pm 0.9 \times 10^{26}$ W Hz$^{-1}$). Despite the relatively low X-ray flux observed $F_{\rm 0.5-7.0 keV}=2.3\pm0.5 \times 10^{-14}$ erg sec$^{-1}$ cm$^{-2}$, the intrinsic luminosity in…

Correcting Bursty/Localized Deletions: A New Error-Position-Estimation Code
Zuo Ye, Yubo Sun, Gennian Ge
https://arxiv.org/abs/2507.04797 https://

Correcting Bursty/Localized Deletions: A New Error-Position-Estimation Code
Codes correcting bursts of deletions and localized deletions have garnered significant research interest in recent years. One of the primary objectives is to construct codes with minimal redundancy. Currently, the best known constructions of $q$-ary codes correcting a burst of at most $t$ deletions ($(\le t)$-burst-deletion correcting codes) achieve redundancy $\log n+8\log\log n+o(\log\log n)$ (for any $q$ and $t$) or $\log n+t\log\log n+O(1)$ (for even $q$). For codes correcting single $t$-lo…

$L^p$ Hardy inequalities with homogeneous weights
Subhajit Roy
https://arxiv.org/abs/2509.05674 https://arxiv.org/pdf/2509.05674

$L^p$ Hardy inequalities with homogeneous weights
For $p\in (1,\infty)$ and $α\in\mathbb{R}$, we consider measurable functions $g$ on $\mathbb{S}^{N-1}$ that satisfy the following weighted Hardy inequality: \begin{equation}\label{abs} \int_{\mathbb{R}^N}\frac{ g (x/|x|)}{|x|^{p+α}}|u(x)|^p dx \leq C\int_{\mathbb{R}^N}\frac{|\nabla u(x)|^p}{|x|^α} dx, \quad\forall\,u\in \mathcal{C}_c^\infty(\mathbb{R}^N), \end{equation} for some constant $C>0$. Depending on $N$, $p$, and $α$, we identify s…

Spectra of high-dimensional sparse random geometric graphs
Yifan Cao, Yizhe Zhu
https://arxiv.org/abs/2507.06556 https://arxiv.org/pd…

Spectra of high-dimensional sparse random geometric graphs
We analyze the spectral properties of the high-dimensional random geometric graph $ G(n, d, p)$, formed by sampling $n$ i.i.d vectors $\{v_i\}_{i=1}^{n}$ uniformly on a $d$-dimensional unit sphere and connecting each pair $\{i,j\}$ whenever $\langle v_i, v_j \rangle \geq τ$ so that $p=\mathbb P(\langle v_i,v_j\rangle \geq τ)$. This model defines a nonlinear random matrix ensemble with dependent entries. We show that if $d =ω( np\log^{2}(1/p))$ and $np\to\infty$, the limiting spectral distrib…

Simple totally disconnected locally compact groups separated by finiteness properties
Laura Bonn, Sebastian Giersbach
https://arxiv.org/abs/2509.05101 https://

Simple totally disconnected locally compact groups separated by finiteness properties
We construct a sequence of simple non-discrete totally disconnected locally compact (tdlc) groups separated by finiteness properties; that is, for every positive integer $n$ there exists a simple non-discrete tdlc group that is of type $F_{n-1}$ but not of type $FP_n$. This generalizes a result of Skipper--Witzel--Zaremsky for discrete groups. Furthermore, we construct a simple non-discrete tdlc group that is of type $FP_2$ but not compactly presented. Our examples arise as Smith groups $\mathc…

2025 NFL preseason, Week 1: What We Learned from Thursday's tripleheader https://www.nfl.com/news/2025-nfl-preseason-week-1-what-we-learned-from-thursday-s-tripleheader

An improved construction for the triangle removal lemma
Zach Hunter
https://arxiv.org/abs/2507.05231 https://arxiv.org/pdf/2507.05231…

An improved construction for the triangle removal lemma
We construct $n$-vertex graphs $G$ where $εn^2$ edges must be deleted to become triangle-free, which contain less than $ε^{(C_{\text{new}}-o(1))\log_2 1/ε}n^3$ triangles for $C_{\text{new}}= \frac{1}{4\log_2(4/3)} \approx 1.6601$. Previously, a bound of the same shape was known, but with $C_{\text{new}}$ replaced by $C_{\text{old}} := C_{\text{new}}/2$. Our construction uses ideas from additive combinatorics, drawing especially from the corners problem, but does not yield new bounds for thos…

Gauge Invariants at Arbitrary $N$ and Trace Relations
Pawel Caputa, Robert de Mello Koch
https://arxiv.org/abs/2509.05834 https://arxiv.org/pdf/2509.05834

Gauge Invariants at Arbitrary $N$ and Trace Relations
We investigate conformal field theories with gauge group $U(N)$ at arbitrary rank $N$, focusing on the role of trace relations in determining the structure of the Hilbert space. Working in the free trace algebra without imposing relations, we identify a class of evanescent states that vanish at finite $N$. Using the Koszul complex of [1], we implement trace relations systematically via ghosts and a fermionic charge $Q_b$. This framework allows us to define and compute transition amplitudes betw…

Efficient Computation of Closed Substrings
Samkith K Jain, Neerja Mhaskar
https://arxiv.org/abs/2506.06452 https://arxiv.org/pdf/2506…

Efficient Computation of Closed Substrings
A closed string $u$ is either of length one or contains a border that occurs only as a prefix and as a suffix in $u$ and nowhere else within $u$. In this paper, we present a fast and practical $O(n\log n)$ time algorithm to compute all $Θ(n^2)$ closed substrings by introducing a compact representation for all closed substrings of a string $ w[1..n]$, using only $O(n \log n)$ space. We also present a simple and space-efficient solution to compute all maximal closed substrings (MCSs) using the s…

On the Jacobian polygon and \L ojasiewicz exponent of isolated complex hypersurface singularities
Baldur Sigur{\dh}sson
https://arxiv.org/abs/2509.06150 https://

On the Jacobian polygon and Łojasiewicz exponent of isolated complex hypersurface singularities
Given a hypersurface singularity $(X,0) \subset (\mathbb{C}^{n+1},0)$ defined by a holomorphic function $f:(\mathbb{C}^{n+1},0) \to (\mathbb{C},0)$, we introduce an alternating version of Teissier's Jacobian Newton polygon, associated with a complex isolated hypersurface singularity, and prove formulas for both these invariants in terms of an embedded resolution of $(X,0)$. The formula for the alternating version has an advantage, in that for Newton nondegenerate functions, it can be calculated…

Simple polynomial equations over $(2 \times 2)$-matrices
Vitalij A. Chatyrko, Alexandre Karassev
https://arxiv.org/abs/2506.07689 https://

Simple polynomial equations over $(2 \times 2)$-matrices
We consider the polynomial equation $$X^n + a_{n-1}\cdot X^{n-1} + \dots + a_1 \cdot X + a_0 \cdot I = O,$$ over $(2 \times 2)$-matrices $X$ with the real entries, where $I$ is the identity matrix, $O$ is the null matrix, $a_i \in \mathbb R$ for each $i$ and $n \geq 2$. We discuss its solution set $S$ supplied with the natural Euclidean topology. We completely describe $S$. We also show that $\dim S =2.$

Schwarz-Pick type lemma and Landau type theorem for $\alpha$-harmonic mappings
Vibhuti Arora, Jiaolong Chen, Shankey Kumar, Qianyun Li
https://arxiv.org/abs/2509.06359 https://

Schwarz-Pick type lemma and Landau type theorem for $α$-harmonic mappings
The aim of this paper is twofold. First, we obtain a Schwarz-Pick type lemma for the $α$-harmonic mapping $u=P_α[ϕ]$, where $ϕ\in L^{p}(\mathbb{S}^{n-1},\mathbb{R} )$ and $p\in[1,\infty]$. We get an explicit form of the sharp function $\mathbf{C}_{α, q}(x)$ in the inequality $|\nabla u(x)| \leq \mathbf{C}_{α, q}(x)\|ϕ\|_{L^p(\mathbb{S}^{n-1}, \mathbb{ R} )}$. Second, we prove a Landau type theorem for $u=P_α[ϕ]$, where $ϕ\in L^{\infty}(\mathbb{S}^{n-1},…

On the sum of the largest and smallest eigenvalues of graphs with high odd girth
Fredy Yip
https://arxiv.org/abs/2509.06611 https://arxiv.org/pdf/2509.0661…

On the sum of the largest and smallest eigenvalues of graphs with high odd girth
The sum $λ_1 + λ_n$ of the maximum and minimum eigenvalues, and the odd girth of a graph both measure bipartiteness. We seek to relate these measures. In particular, for an odd integer $k\geq 3$, let $γ_k$ denote the supremum of $\frac{λ_1 + λ_n}{n}$ over graphs without odd cycles of length less than $k$. The example of the $k$-cycle $C_k$ shows that $γ_k\geq Ω(k^{-3})$. In their recent work, Abiad, Taranchuk, and van Veluw showed that $γ_k\leq O(k^{-1})$ and asked to determine the asym…

Average Nikolskii factors for random diffusion polynomials on closed Riemannian manifolds
Yun Ling, Heping Wang
https://arxiv.org/abs/2507.06505 https://…

Average Nikolskii factors for random diffusion polynomials on closed Riemannian manifolds
For $1\le p,q\le \infty$, the Nikolskii factor for a diffusion polynomial $P_{\bf a}$ of degree at most $n$ is defined by $$N_{p,q}(P_{\bf a})=\frac{\|P_{\bf a}\|_{q}}{\|P_{\bf a}\|_{p}},\ \ P_{\bf a}({\bf x})=\sum_{k:λ_{k}\leq n}a_{k}ϕ_{k}({\bf x}),$$ where ${\bf a}=\{a_k\}_{λ_k\le n}$, and $\{(ϕ_k,-λ_k^2)\}_{k=0}^\infty$ are the eigenpairs of the Laplace-Beltrami operator $Δ_{\mathbb M}$ on a closed smooth Riemannian manifold $\mathbb M$ with normalized Riemannian me…

Parallel Batch-Dynamic Algorithms for Spanners, and Extensions
Mohsen Ghaffari, Jaehyun Koo
https://arxiv.org/abs/2507.06338 https://…

Parallel Batch-Dynamic Algorithms for Spanners, and Extensions
This paper presents the first parallel batch-dynamic algorithms for computing spanners and sparsifiers. Our algorithms process any batch of edge insertions and deletions in an $n$-node undirected graph, in $\text{poly}(\log n)$ depth and using amortized work near-linear in the batch size. Our concrete results are as follows: - Our base algorithm maintains a spanner with $(2k-1)$ stretch and $\tilde{O}(n^{1+1/k})$ edges, for any $k\geq 1$. - Our first extension maintains a sparse spanner wit…

A hyperk\"ahler metric on twisted cotangent bundles of the complex projective space
Takashi Hashimoto
https://arxiv.org/abs/2507.06604 https://…

A hyperkähler metric on twisted cotangent bundles of the complex projective space
We construct a hyperkähler metric on twisted cotangent bundles of the complex projective space $\mathbb{CP}^n$ explicitly in terms of local coordinates. Note that the twisted cotangent bundles of $\mathbb{CP}^n$ are holomorphically isomorphic to complex semisimple coadjoint orbits of $\mathrm{SL}_{n+1}(\mathbb{C})$.

Divisibility of the coefficients of modular polynomials
Florian Breuer
https://arxiv.org/abs/2509.06423 https://arxiv.org/pdf/2509.06423

Divisibility of the coefficients of modular polynomials
Let $N>1$ and let $Φ_N(X,Y)\in\mathbb{Z}[X,Y]$ be the modular polynomial which vanishes precisely at pairs of $j$-invariants of elliptic curves linked by a cyclic isogeny of degree $N$. In this note we study the divisibility of the coefficients $Φ_N(X+J, Y+J)$ for certain algebraic numbers $J$, in particular $J=0$ and $J=1728$. It turns out that these coefficients are highly divisible by small primes at which $J$ is supersingular.

Serrin's overdetermined theorem within Lipschitz domains
Hongjie Dong, Yi Ru-Ya Zhang
https://arxiv.org/abs/2509.05155 https://arxiv.org/pdf/2509.05155…

Serrin's overdetermined theorem within Lipschitz domains
Let $Ω\subset\mathbb R^n$ be a Lipschitz domain, $K$ be a (bounded) ellipsoid centered at the origin and $H$ be the associated Wulff potential. We prove that, % under a $L^2$-Dini-VMO condition and a non-degeneracy condition on $|Du|$ near the boundary, $Ω$ satisfies the following Serrin-type overdetermined system $$u \in W^{1,2}(\mathbb R^n), \quad u=0\ \text{ a.e. in }\R^n\setminus Ω,\quad Δ_H u=\mathbf{c}\mathscr{H}^{n-1}|_{\partial^*Ω} - \mathbf{1}_Ω\,dx,$$ in the w…

Using dense graph limit theory to count cocycles of random simplicial complexes
Andr\'as M\'esz\'aros
https://arxiv.org/abs/2509.06559 https://…

Using dense graph limit theory to count cocycles of random simplicial complexes
We develop a limit theory for $1$-cochains of complete graphs with coefficients from a finite abelian group. We prove an analogue of the large deviation principle of Chatterjee and Varadhan for random cochains. We use these new tools to prove results about the homology of random $2$-dimensional simplicial complexes. More specifically, we prove that if $T_n$ is a random $2$-dimensional determinantal hypertree on $n$ vertices and $p$ is any prime, then \[\frac{\dim H_1(T_n,\mathbb{F}_p)}{n^2}\]…

Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties
Yohsuke Matsuzawa
https://arxiv.org/abs/2507.05027

Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties
Consider a dominant rational self-map $f$ on a smooth projective variety $X$ defined over $\overline{\mathbb{Q}}$. We prove that \begin{align} \lim_{n \to \infty} \frac{h_{Y}(f^{n}(x))}{h_{H}(f^{n}(x)) } = 0, \end{align} where $h_{Y}$ is a height associated with a closed subscheme $Y \subset X$ of codimension $c$, $h_{H}$ is any ample height on $X$, and $x \in X(\overline{\mathbb{Q}})$ is a point with well-defined orbit, under the following assumptions: (1) either $f$ is a morphism, or $Y$ is p…

Massless higher-spin supermultiplets in 5D harmonic superspace
Evgeny I. Buchbinder, Sergei M. Kuzenko, Igor B. Samsonov
https://arxiv.org/abs/2509.06604 https://

Massless higher-spin supermultiplets in 5D harmonic superspace
Off-shell actions for massless higher-spin $\mathcal{N}=1$ supermultiplets in five dimensions (5D) are constructed in harmonic superspace in terms of unconstrained prepotentials. Cubic couplings of these supermultiplets to the $q$-hypermultiplet are derived. We also provide a detailed derivation of the unconstrained prepotential for the 5D Weyl supermultiplet which has been used within the conformal superspace approach to $\mathcal{N}=1$ supergravity-matter systems.

Planar Tur\'{a}n numbers of three configurations
Xuqing Bai, Zhipeng Gao, Ping Li
https://arxiv.org/abs/2509.06131 https://arxiv.org/pdf/2509.06131

Planar Turán numbers of three configurations
The planar Tuán number of $H$, denoted by $ex_{\mathcal{P}}(n,H)$, is defined as the maximum number of edges in an $n$-vertex $H$-free planar graph. The exact value of $ex_{\mathcal{P}}(n,H)$ remains a mystery when $H$ is large (for example, $H$ is a long path or a long cycle), while tight bounds have been established for many small planar graphs such as cycles, paths, $Θ$-graphs and other small graphs formed by a union of them. One representative graph among such union graphs is $K_1+L$ wh…

The $L^p$ regularity problem for parabolic operators with transversally independent coefficients
Martin Dindo\v{s}, Jill Pipher, Martin Ulmer
https://arxiv.org/abs/2509.06627 ht…

The $L^p$ regularity problem for parabolic operators with transversally independent coefficients
In this paper, we fully resolve the question of whether the Regularity problem for the parabolic PDE $\partial_tu - \mbox{div}(A\nabla u)=0$ on the domain $\mathbb R^{n+1}_+\times\mathbb R$ is solvable for some $p\in (1,\infty)$ under the assumption that the matrix $A$ is elliptic, has bounded and measurable coefficients and its coefficients are independent of the spatial variable $x_{n+1}$ (which is transversal to the boundary). We prove that for some $p_0>1$ the Regularity problem is solvable…

Additive, Near-Additive, and Multiplicative Approximations for APSP in Weighted Undirected Graphs: Trade-offs and Algorithms
Liam Roditty, Ariel Sapir
https://arxiv.org/abs/2509.04640

Additive, Near-Additive, and Multiplicative Approximations for APSP in Weighted Undirected Graphs: Trade-offs and Algorithms
We present a $+2\sum_{i=1}^{k+1}{W_i}$-APASP algorithm for dense weighted graphs with runtime $\tilde O\left(n^{2+\frac{1}{3k+2}}\right)$, where $W_{i}$ is the weight of an $i^\textnormal{th}$ heaviest edge on a shortest path. Dor, Halperin and Zwick [FOCS'96, SICOMP'00] had two algorithms for the commensurate unweighted $+2\cdot\left( k+1\right)$-APASP: $\tilde O\left(n^{2-\frac{1}{k+2}}m^{\frac{1}{k+2}}\right)$ runtime for sparse graphs and $\tilde O\left(n^{2+\frac{1}{3k+2}}\right)$ runtime …

On certain root number $1$ cases of the cube sum problem
Shamik Das, Somnath Jha
https://arxiv.org/abs/2508.05361 https://arxiv.org/pdf/2508.05361

On certain root number $1$ cases of the cube sum problem
We consider certain families of integers $n$ determined by some congruence condition, such that the global root number of the elliptic curve $E_{-432n^2}: Y^2=X^3-432n^2$ is $1$ for every $n$, however a given $n$ may or may not be a sum of two rational cubes. We give explicit criteria in terms of the $2$-parts and $3$-parts of the ideal class groups of certain cubic number fields to determine whether such an $n$ is a cube sum. In particular, we study integers $n$ divisible by $3$ such that the …

Almost all graphs have no cospectral mate with fixed level
Wei Wang, Da Zhao
https://arxiv.org/abs/2509.05781 https://arxiv.org/pdf/2509.05781

Almost all graphs have no cospectral mate with fixed level
Haemers conjectures that almost all graphs are determined by their spectra. Suppose $G \sim \mathcal{G}(n, p)$ is a random graph with each edge chosen independently with probability $p$ with $0 < p < 1$. Then $$\Pr(G \text{ is not controllable}) + \sum_{\ell = 2}^{n^{n^2}} \Pr(G \text{ has a generalized copsectral mate with level } \ell) \to 0$$ as $n \to \infty$ implies that almost all graphs are determined by their generalized spectra. It is known that almost all graphs are controllable. We s…

Entanglement Asymmetry and Quantum Mpemba Effect for Non-Abelian Global Symmetry
Harunobu Fujimura, Soichiro Shimamori
https://arxiv.org/abs/2509.05597 https://

Entanglement Asymmetry and Quantum Mpemba Effect for Non-Abelian Global Symmetry
Entanglement asymmetry is a measure that quantifies the degree of symmetry breaking at the level of a subsystem. In this work, we investigate the entanglement asymmetry in $\widehat{su}(N)_k$ Wess-Zumino-Witten model and discuss the quantum Mpemba effect for SU$(N)$ symmetry, the phenomenon that the more symmetry is initially broken, the faster it is restored. Due to the Coleman-Mermin-Wagner theorem, spontaneous breaking of continuous global symmetries is forbidden in $1+1$ dimensions. To circ…

Counting linear congruence systems with a fixed number of solutions
Marcus Nilsson
https://arxiv.org/abs/2507.04688 https://arxiv.org…

Counting linear congruence systems with a fixed number of solutions
For a prime p and a positive integer s consider a homogeneous linear system over the ring Z_p^s (the ring of integers modulo p^s) described by an n x m-matrix. The possible number of solutions to such a system is p^j, where j=0,1,..., sm. We study the problem of how many n x m -matrices over Z_p^s there are given that we have exactly p^j homogeneous solutions. For the case s=1 (when Z_p^s is a field) George von Landsberg proved a general formula in 1893. However, there seems to be few published…

Capillary $L_p$ Minkowski Flows
Jinrong Hu, Yingxiang Hu, Mohammad N. Ivaki
https://arxiv.org/abs/2509.06110 https://arxiv.org/pdf/2509.06110

Capillary $L_p$ Minkowski Flows
We study the long-time existence and asymptotic behavior of a class of anisotropic capillary Gauss curvature flows. As an application, we provide a flow approach to the existence of smooth solutions to the capillary even $L_p$ Minkowski problem in the Euclidean half-space for all $p \in (-n-1, \infty)$ and capillary $L_p$ Minkowski problem for $p > n+1$.

Large N Chern-Simons-matter fixed points with multiple flavors
Ofer Aharony, Ronny Frumkin, Jonathan Mehl
https://arxiv.org/abs/2509.04565 https://arxiv.or…

Large N Chern-Simons-matter fixed points with multiple flavors
In this paper we analyze the $2+1$d conformal fixed points arising from $SU(N_c)$ Chern-Simons-matter theories with multiple flavors $N_f > 1$ in the 't Hooft large $N_c$ limit. The multi-flavor generalization of quasi-fermionic theories (fermions or critical scalars coupled to Chern-Simons gauge fields) is straightforward, but this is not true for quasi-bosonic theories (scalars or critical fermions coupled to Chern-Simons gauge fields). The latter theories have three flavor-singlet relevant o…

Notes and computations on forbidden differences
Christian Dean, Haley Havard, Elizabeth Hawkins, Patch Heard, Andrew Lott, Alex Rice
https://arxiv.org/abs/2508.03650 https://

Notes and computations on forbidden differences
We explore from several perspectives the following question: given $X\subseteq \mathbb{Z}$ and $N\in \mathbb{N}$, what is the maximum size $D(X,N)$ of $A\subseteq \{1,2,\dots,N\}$ before $A$ is forced to contain two distinct elements that differ by an element of $X$? The set of forbidden differences, $X$, is called \textit{intersective} if $D(X,N)=o(N)$, with the most well-studied examples being $X=S=\{n^2: n\in \mathbb{N}\}$ and $X=\mathcal{P}-1=\{p-1: p\text{ prime}\}$. In addition to some ne…

Descent sets of cyclic permutations in types B and D
Kevin Liu
https://arxiv.org/abs/2508.02432 https://arxiv.org/pdf/2508.02432

Descent sets of cyclic permutations in types B and D
Elizalde constructed a bijection $ϕ$ from the cyclic permutations $π\in S_{n+1}$ to the symmetric group $S_n$ satisfying $\operatorname{Des}(π)\cap \{1,2,\ldots,n-1\}=\operatorname{Des}(ϕ(π))$. We give a corresponding result on the signed symmetric group $B_n$ by constructing a function $Φ$ from the cyclic signed permutations $π\in B_{n+1}$ to $B_n$ satisfying $\operatorname{Des}(π)\cap \{0,1,\ldots,n-1\}=\operatorname{Des}(Φ(π))$. Moreover, letting $D_{n+1}\subseteq B_{n+1}$ be the s…

Chemotaxis Models with Nonlinear/Porous Medium Diffusion, Consumption, and Logistic source on $\mathbb{R}^N$: I. Global Solvability and Boundedness
Zulaihat Hassan, Wenxian Shen, Yuming Paul Zhang
https://arxiv.org/abs/2509.05494

Chemotaxis Models with Nonlinear/Porous Medium Diffusion, Consumption, and Logistic source on $\mathbb{R}^N$: I. Global Solvability and Boundedness
This series of papers is concerned with the global solvability, boundedness, regularity, and uniqueness of weak solutions to the following parabolic-parabolic chemotaxis system with a logistic source and chemical consumption: \begin{equation*} \begin{cases} u_t = m\nabla\cdot \left((\eps+u)^{m-1}\nabla u\right) - χ\nabla \cdot (u \nabla v) + u(a - b u), & \text{ in } (0,\infty)\times\mathbb{R}^N, \\ v_t = Δv - uv, & \text{ in } (0,\infty)\times\mathbb{R}^N, \end{cases} \end{equation*} where $…

Narayana numbers that are products of two Fibonacci numbers
Japhet Odjoumani
https://arxiv.org/abs/2508.02688 https://arxiv.org/pdf/2508.02688

Narayana numbers that are products of two Fibonacci numbers
Let $\{N_m\}_{m\ge0}$ be the Narayana's cows sequence given by $N_0=0$, $N_1=1=N_2=1$ and \[ N_{m+3}=N_{m+2}+N_m,\quad \text{ for }\; m\geq 0 \] and let $\{F_n\}_{n\ge0}$ be the Fibonacci sequence. In this paper we solve explicitely the Diophantine equation \[ N_m=F_nF_k, \] in positive unknowns $m,\,n$ and $k$. That is, we find the non-zero narayana numbers that are products of two Fibonacci numbers.

H\"older regularity of weak solutions to nonlocal doubly degenerate parabolic equations
Qifan Li
https://arxiv.org/abs/2509.05914 https://arxiv.org/pd…

Hölder regularity of weak solutions to nonlocal doubly degenerate parabolic equations
We study local regularity for nonlocal doubly degenerate parabolic equations. The model equation is \begin{equation*}\begin{split} \partial_t(|u|^{q-1}u)+\mathrm{P}.\mathrm{V}.\int_{\mathbb{R}^n}\frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{n+sp}}\,\mathrm{d}y=0, \end{split} \end{equation*} where $02$ and $0

The Saturation Number for the Diamond is Linear
Maria-Romina Ivan, Sean Jaffe
https://arxiv.org/abs/2507.05122 https://arxiv.org/pdf/…

The Saturation Number for the Diamond is Linear
For a fixed poset $\mathcal P$ we say that a family $\mathcal F\subseteq\mathcal P([n])$ is $\mathcal P$-saturated if it does not contain an induced copy of $\mathcal P$, but whenever we add a new set to $\mathcal F$, we form an induced copy of $\mathcal P$. The size of the smallest such family is denoted by $\text{sat}^*(n, \mathcal P)$.\par For the diamond poset $\mathcal D_2$ (the two-dimensional Boolean lattice), while it is easy to see that the saturation number is at most $n+1$, the best …

Triple convolution sums of the generalised divisor functions
Bikram Misra, Biswajyoti Saha
https://arxiv.org/abs/2509.04610 https://arxiv.org/pdf/2509.0461…

Triple convolution sums of the generalised divisor functions
We study the triple convolution sum of the generalised divisor functions given by $$\sum_{n\leq x} d_k(n+h)d_l(n)d_m(n-h),$$ where $h \le x^{1-ε}$ for any $ε>0$ and $d_k(n)$ denotes the generalised divisor function which counts the number of ways $n$ can be written as product of $k$ many positive integers. The purpose of this paper is two-fold. Firstly, we note a predicted asymptotic estimate for the above sum, where the constant appearing in the estimate can be obtained from the theory of Di…

Hypergraph Tur\'an problem of the generalized triangle with bounded matching number
Jian Wang, Wenbin Wang, Weihua Yang
https://arxiv.org/abs/2507.04579

Hypergraph Turán problem of the generalized triangle with bounded matching number
Let $\mathcal{H}$ be a 3-graph on $n$ vertices. The matching number $ν(\mathcal{H})$ is defined as the maximum number of disjoint edges in $\mathcal{H}$. The generalized triangle $F_5$ is a 3-graph on the vertex set $\{a,b,c,d,e\}$ with the edge set $\{abc, abd,cde\}$. In this paper, we showed that an $F_5$-free 3-graph $\mathcal{H}$ with matching number at most $s$ has at most $s\lfloor (n-s)^2/4\rfloor$ edges for $n\geq 30(s+1)$ and $s\geq 3$. For the proof, we establish a 2-colored version …

A non-face characterization of spheres on few vertices
Shuai Huang, Jasper Miller, Daniel Rose-Levine, Steven Simon
https://arxiv.org/abs/2507.06120 https:…

A non-face characterization of spheres on few vertices
We give a relatively simple characterization of simplicial $d$-spheres on $d+4$ vertices; our criteria are in terms of the intersection patterns of a simplicial complex's minimal non-faces. Namely, let $Σ$ be a simplicial complex with vertex set $[d+4]$ and let $\mathcal{F}=\{A_0,\ldots, A_{n-1}\}$ be its family of minimal non-faces, indices taken in $\mathbb{Z}_n$. Then $Σ$ is a $d$-sphere if and only if the following hold: $n\geq 3$ is odd, successive $A_i$ are disjoint, and the alternating…

Extendability of $1$-decomposable complexes
Rhea Ghosal, Melody Han, Benjamin Keller, Scarlett Kerr, Justin Liu, SuHo Oh, Ryan Tang, Chloe Weng
https://arxiv.org/abs/2508.04555 …

Extendability of $1$-decomposable complexes
A well-known conjecture of Simon (1994) states that any pure $d$-dimensional shellable complex on $n$ vertices can be extended to $Δ_{n-1}^{(d)}$, the $d$-skeleton of the $(n-1)$-dimensional simplex, by attaching one facet at a time while maintaining shellability. The notion of $k$-decomposability for simplicial complexes, which generalizes shellability, was introduced by Provan and Billera (1980). Coleman, Dochtermann, Geist, and Oh (2022) showed that any pure $d$-dimensional $0$-decomposab…

Partitioning set $[n] = \{1, \dots, n\}$ into subsets of size at most $m$ such that all sums are powers of $m$
Vladimir Gurvich, Mariya Naumova
https://arxiv.org/abs/2508.00946 …

Partitioning set $[n] = \{1, \dots, n\}$ into subsets of size at most $m$ such that all sums are powers of $m$
Given integer $n > 0$ and $m > 1$, we call a partition of set $[n] = \{1, \dots, n\}$ {\em $m$-good} if each of the partitioning sets is of size at most $m$ and the sum of numbers in it is a power of $m$, that is, $m^t$ for some $t \geq 0$. It is easily seen that a unique 2-good partition exists for each $n$ and, in contrast, for each fixed $m>3$, for infinitely many $n$, no $m$-good partition exists. Case $m=3$ is more difficult. We conjecture that 3-good partitions exist for each $n$ and pr…

Sums of Laplacian eigenvalues and sums of degrees
Alan Lew
https://arxiv.org/abs/2508.04209 https://arxiv.org/pdf/2508.04209…

Sums of Laplacian eigenvalues and sums of degrees
Let $X$ be a simplicial complex. For $1\le i\le\dim(X)$, let $X(i)$ be the set of $i$-dimensional faces of $X$, and let $f_i(X)=|X(i)|$. For $0\le i\le \dim(X)-1$, let $L_i^+(X)$ be the $i$-th upper Laplacian operator of $X$. For $σ\in X$ and $1\le r\le \dim(X)$, we denote by $\text{deg}_X^{(r)}(σ)$ the number of $r$-dimensional faces of $X$ containing $σ$. For a symmetric matrix $M\in \mathbb{R}^{n\times n}$ and $1\le i\le n$, let $λ_i(M)$ be the $i$-th largest eigenvalue of $M$.…