Tootfinder

Oriented diameter of graphs with given domination number
Xiaolin Wang, Yaojun Chen
https://arxiv.org/abs/2506.15997 https://arxiv.org…

Oriented diameter of graphs with given domination number
Let $G$ be a connected bridgeless graph with domination number $γ$. The oriented diameter (strong diameter) of $G$ is the smallest integer $d$ for which $G$ admits a strong orientation with diameter (strong diameter) $d$. Kurz and Lätsch (2012) conjectured the oriented diameter of $G$ is at most $\lceil \frac{7γ+1}{2}\rceil$ and the bound is sharp. In this paper, we confirm the conjecture by induction on $γ$ through contracting an unavoidable alternative subgraph, which holds potential for …

On the Parameterized Complexity of Semitotal Domination on Graph Classes
Lukas Retschmeier
https://arxiv.org/abs/2506.17485 https://a…

On the Parameterized Complexity of Semitotal Domination on Graph Classes
For a given graph $G = (V, E)$, a subset of the vertices $D\subseteq V$ is called a semitotal dominating set, if $D$ is a dominating set and every vertex $v \in D$ is within distance two to another witness $v' \in D$. We want to find a semitotal dominating set of minimum cardinality. We show that the problem is $\mathrm{W}[2]$-hard on bipartite and split graphs when parameterized by the solution size $k$. On the positive side, we extend the kernelization technique of Alber, Fellows, and Niederm…

On Fragile Power Domination
Beth Bjorkman, Sean English, Johnathan Koch, Amanda Verga
https://arxiv.org/abs/2507.14620 https://arxiv.…

On Fragile Power Domination
Power domination is a graph theoretic model which captures how phasor measurement units (PMUs) can be used to monitor a power grid. Fragile power domination takes into account the fact that PMUs may break or otherwise fail. In this model, each sensor fails independently with probability $q\in [0,1]$ and the surviving sensors monitor the grid according to classical power domination. We study the expected number of observed nodes under the fragile power domination model. We give a characterizat…

Sparse domination for rough multilinear singular integrals
Binwei Dan, Qingying Xue
https://arxiv.org/abs/2506.17905 https://arxiv.or…

Sparse domination for rough multilinear singular integrals
Let $Ω$ be a function on $\mathbb{R}^{mn} $, homogeneous of degree zero, and satisfy a cancellation condition on the unit sphere $\mathbb{S}^{mn-1}$. In this paper, we show that the multilinear singular integral operator \[ \mathcal{T}_Ω(f_1, \ldots, f_m)(x) := \mathrm{p.v.} \int_{\mathbb{R}^{mn}} \frac{Ω(x - y_1, \ldots, x - y_m)}{|x - \vec{y}|^{mn}} \prod_{i=1}^m f_i(y_i) \, d\vec{y}, \] associated with a rough kernel $Ω\in L^r(\mathbb{S}^{mn-1}) $, $r > 1 $, admits a sp…

Queen Domination by SAT Solving
Taha Rostami, Curtis Bright
https://arxiv.org/abs/2508.11945 https://arxiv.org/pdf/2508.11945

Queen Domination by SAT Solving
The queen domination problem asks for the minimum number of queens needed to attack all squares on an $n\times n$ chessboard. Once this optimal number is known, determining the number of distinct solutions up to isomorphism has also attracted considerable attention. Previous work has introduced specialized and highly optimized search procedures to address open instances of the problem. While efficient in terms of runtime, these approaches have not provided proofs that can be independently verif…

https://slate.com/technology/2014/07/a-killer-robots-txt-google-easter-egg.html
see this is wrong, the T-1000’s user agent would actually be
Mozilla/5.0 (T-1000; CPU like T-800) Skynet (KHTML, like Gecko) Terminator version 1000 (like Human)…

Is This a Google Easter Egg or Proof That Skynet Is Actually Plotting World Domination?
It's great to be successful, but sometimes being as huge as Google can make a company lose its sense of humor. Google seems determined not to let that...

Approximations for Fault-Tolerant Total and Partial Positive Influence Domination
Ioannis Lamprou, Ioannis Sigalas, Ioannis Vaxevanakis, Vassilis Zissimopoulos
https://arxiv.org/abs/2506.12828

Approximations for Fault-Tolerant Total and Partial Positive Influence Domination
In $\textit{total domination}$, given a graph $G=(V,E)$, we seek a minimum-size set of nodes $S\subseteq V$, such that every node in $V$ has at least one neighbor in $S$. We define a $\textit{fault-tolerant}$ version of total domination, where we require any node in $V \setminus S$ to have at least $m$ neighbors in $S$. Let $Δ$ denote the maximum degree in $G$. We prove a first $1 + \ln(Δ+ m - 1)$ approximation for fault-tolerant total domination. We also consider fault-tolerant variants of t…

The Domination and Secure Domination Numbers of Direct Product of Cliques with Paths and Cycles
Deepak M. Bakal, S. A. Mane
https://arxiv.org/abs/2506.11865

The Domination and Secure Domination Numbers of Direct Product of Cliques with Paths and Cycles
In this paper, we obtain the exact values of several domination parameters for the direct product of a complete graph with a path or a cycle. Specifically, we determine the domination number, independent domination number, $[1,2]$-domination number, secure domination number, and 2-domination number for this family of graphs. We show that, in these graphs, the independent domination number and the $[1,2]$-domination number coincide with the domination number, while the secure domination number c…

A profile of Robinhood CEO Vlad Tenev, whose personal fortune has surged 6x over the past year to $6.1B, as the company leans into tokenized stock derivatives (Nina Bambysheva/Forbes)
https://www.forbes.com/sites/ninabambyshev…

Inside Robinhood’s Crypto-Fueled Plan For World Domination
First Vlad Tenev blew up the brokerage industry’s fee model. Now, thanks in part to his full-on crypto embrace, he has increased his fortune sixfold to $6 billion as he embarks on a global financial services takeover with tokenized stocks, AI-powered investing and a bid to own the rails of the looming $124 trillion generational wealth transfer.

A heady throng of tech billionaires, ministers, corporate titans and the king of the Netherlands have convened in Sweden for the 71st Bilderberg meeting
– the publicity-shy annual policy conference that has long sustained conspiracy theorists
– hosted this year by the fabulously wealthy Wallenberg family.
The four days of transatlantic talks are taking place at the swanky Grand hotel,
which is owned, like so much else in Sweden, by the Wallenbergs.
The Swedis…

Equation of state during (p)reheating with trilinear interactions
Stefan Antusch, Kenneth Marschall, Francisco Torrenti
https://arxiv.org/abs/2507.13465 ht…

Equation of state during (p)reheating with trilinear interactions
We characterize the post-inflationary evolution of the equation of state of the universe from the end of inflation until the onset of radiation domination, when the inflaton is coupled to a daughter field through a trilinear interaction. We consider an inflaton potential that is quadratic near the minimum and flattens in the inflationary regime. By simulating the dynamics in 2+1-dimensional lattices, we have tracked the long-term evolution of the equation of state for about ten e-folds of expan…

Primordial Black Hole Formation and Spin in Matter Domination Revisited
Weitao Ye, Yungui Gong, Tomohiro Harada, Zhaofeng Kang, Kazunori Kohri, Daiki Saito, Chul-Moon Yoo
https://arxiv.org/abs/2508.10070

Primordial Black Hole Formation and Spin in Matter Domination Revisited
In this article, we calculate the mass distribution of primordial black holes (PBHs) formed in the matter-dominated (MD) era by the peak theory. We apply the Zel'dovich approximation to track the nonlinear evolution of overdensities and compute the PBH abundance and mass function by incorporating a PBH formation criterion based on the hoop conjecture. We find that the PBH abundance $β$ follows the scaling law $β\simeq A_γσ_h^{*5}$ for $σ_h^*\ll 1$. Here, $σ_h^*$ is the quantity that chara…

One-arm domination time in Cylindrical Hastings-Levitov$(0)$
Guanyi Chen, Eviatar B. Procaccia, Yuxuan Zong
https://arxiv.org/abs/2507.11028 https://

One-arm domination time in Cylindrical Hastings-Levitov$(0)$
The cylindrical Hastings-Levitov$(0)$ admits a single infinite connected tree (arm). For a cylinder of width $N$, and particles of size $λ$, we consider the last time $\upsilon_{N, λ}$, that a finite tree receives a particle. We prove that $\frac{cN^2}{λ^3}<\mathbb{E}[\upsilon_{N, λ}]< \frac{CN^2}{λ^3}$. Furthermore, we establish an exponential tail for $\upsilon_{N, λ}$.

Revisiting $d$-distance (independent) domination in trees and in bipartite graphs
Csilla Bujt\'as, Vesna Ir\v{s}i\v{c} Chenoweth, Sandi Klav\v{z}ar, Gang Zhang
https://arxiv.org/abs/2508.12804

Revisiting $d$-distance (independent) domination in trees and in bipartite graphs
The $d$-distance $p$-packing domination number $γ_d^p(G)$ of $G$ is the minimum size of a set of vertices of $G$ which is both a $d$-distance dominating set and a $p$-packing. In 1994, Beineke and Henning conjectured that if $d\ge 1$ and $T$ is a tree of order $n \geq d+1$, then $γ_d^1(T) \leq \frac{n}{d+1}$. They supported the conjecture by proving it for $d\in \{1,2,3\}$. In this paper, it is proved that $γ_d^1(G) \leq \frac{n}{d+1}$ holds for any bipartite graph $G$ of order $n \geq d+1$,…

I don’t agree in one respect:
Neither OOP nor FP (nor 4GLs nor IDEs nor SOAs nor any of the other new hotnesses past) had anything remotely resembling the current money behind them. None led to companies speculatively laying off tens of thousands of employees for imagined productivity boosts that had not actually arrived yet. None shaped whole election cycles, or led to national proposals for preemptive deregulation. None led to the construction of nuclear power plants or the draining of rivers. None sent oligarchs or fascists into spasmodic wet dreams of world domination. None started quasi-religious cults like EA.
All •that• is the part that feels like blockchain — but even worse, if such a thing is possible.
@…
2/2

Anyone here who has got the "Global Domination" achievement in Mindustry by capturing all zones?
I've never gotten it, heck I've never even completed the full game before, before they introduced Erekir...
#Mindustry #Serpulo

On the domination of surface-group representations in $\mathrm{PU}(2,1)$
Pabitra Barman, Krishnendu Gongopadhyay
https://arxiv.org/abs/2506.03838 https://

On the domination of surface-group representations in $\mathrm{PU}(2,1)$
This article explores surface-group representations into the complex hyperbolic group $\mathrm{PU}(2,1)$ and presents domination results for a special class of representations called $T$-bent representations. Let $S_{g,k}$ be a punctured surface of negative Euler characteristic. We prove that for a $T$-bent representation $ρ: π_1(S_{g,k}) \rightarrow \mathrm{PU}(2,1)$, there exists a discrete and faithful representation $ρ_0: π_1(S_{g,k}) \rightarrow \mathrm{PO}(2,1)$ that dominates $ρ$ in…

Pairwise similarity method for majority domination problem
N. I. Shushko, D. V. Lemtyuzhnikova
https://arxiv.org/abs/2506.08886 https://

Pairwise similarity method for majority domination problem
The paper considers the problem of finding the number of dominant voters in two-level voting procedures. At the first stage, voting is conducted among local groups of voters, and at the second stage, the results are aggregated to form a final decision. The goal is to determine the minimum proportion of voters supporting a proposal for it to be accepted. The paper uses the method of pairwise comparisons to analyze the structure of the problem and develop heuristic algorithms with guaranteed accu…

Matrix Weighted $L^p$ Estimates in the Nonhomogeneous Setting
Fernando Benito-de la Cigo\~na, Tainara Borges, Francesco D'Emilio, Marcus Pasquariello, Nathan A. Wagner
https://arxiv.org/abs/2506.15570

Matrix Weighted $L^p$ Estimates in the Nonhomogeneous Setting
We establish a modified pointwise convex body domination for vector-valued Haar shifts in the nonhomogeneous setting, strengthening and extending the scalar case developed in arXiv:2309.13943. Moreover, we identify a subclass of shifts, called $L^1$-normalized, for which the standard convex body domination holds without requiring any regularity assumption on the measure. Finally, we extend the best-known matrix weighted $L^p$ estimates for sparse forms to the nonhomogeneous setting. The key dif…

On 2-Movable Total Domination in the Join and Corona of Graphs
Ariel C. Pedrano, Rolando N. Paluga
https://arxiv.org/abs/2508.10952 https://arxiv.org/pdf/2…

On 2-Movable Total Domination in the Join and Corona of Graphs
Let $G$ be a connected graph. A non-empty $T\subseteq V(G)$ is a $2$-\textit{movable total dominating set} of $G$ if $T$ is a total dominating set and for every pair $x,y \in T$, $T \backslash \{x, y\}$ is a total dominating set in $G$, or there exist $u, v \in V(G) \backslash T$ such that $u$ and $v$ are adjacent to $x$ and $y$, respectively, and $(T \backslash \{x,y\}) \cup \{u,v\}$ is a total dominating set in $G$. The $2$-\textit{movable total domination number} of $G$, denoted by $γ_{mt}^…

Early Growth of Structure in Warm Wave Dark Matter
Mustafa A. Amin, Simon May, Mehrdad Mirbabayi
https://arxiv.org/abs/2506.12131 https://

Early Growth of Structure in Warm Wave Dark Matter
We explore the growth of structure in wave-like dark matter models, where the field and density spectra are peaked at sub-horizon wavenumbers. Starting with the Schrödinger-Poisson system, we derive the scale-dependent evolution of the matter power spectrum during radiation and matter domination. We find a suppression of adiabatic perturbations during radiation domination, controlled by a free-streaming length, and scale-dependent growth of the initially white-noise isocurvature power, control…

Since childhood, I have viewed the family as an inherently authoritarian institution, a primary form of domination that compels obedience and suppresses the individual’s natural freedom to organize themselves, as Rocker made clear in his unyielding critique of all authority.
#Anarchism #Syndicalism

Impact of Non-Thermal Leptogenesis from Early Matter Domination on Gravitational Wave from FOPT
Dilip Kumar Ghosh, Anish Ghoshal, Koustav Mukherjee, Nimmala Narendra, Nobuchika Okada
https://arxiv.org/abs/2508.02619

Impact of Non-Thermal Leptogenesis from Early Matter Domination on Gravitational Wave from FOPT
We study the impact of non-thermal leptogenesis on the spectrum of gravitational waves (GWs) produced by a strong first-order phase transition in the early Universe. We consider a scenario in which a heavy scalar field, $ϕ$, dominates the energy density of the early Universe and decays into heavy right-handed neutrinos (RHNs). The subsequent decay of RHNs generates a lepton asymmetry, which is partially converted into the observed baryon asymmetry via the sphaleron process. The $ϕ$-dominated …

What Trump Told Me About His Complete Domination of Congress (Rachael Bade/Politico)
https://www.politico.com/news/magazine/2025/07/03/trump-interview-megabill-rachael-bade-00438195
http://www.memeorandum.com/250703/p108#a250703p108

The rise of China, along with regional powers such as Turkey, Indonesia and Saudi Arabia, has disrupted the unipolar dominance of the U.S.
These would-be regional hegemons bring with them their own means of imposing influence through economic incentives and coercion.
In China’s case, infrastructure and trade development through the Belt and Road Initiative is counterbalanced with shows of military strength in the South China Sea.
As the global order becomes increasingly fragm…

Are hegemonies a relic of the past? The role of coercion and consent in global domination
From Athens to the British Empire and on to the US – dominant powers have used might and consent to exert influence.

It's always about subtle domination with Casper. Either a surprise attack on Harley's tail or merely looking down on her from above.
#Caturday #CatsOfMastadon #DogsOfMastadon

Fair coalition in graphs
Saeid Alikhani, Abbas Jafari, Maryam Safazadeh
https://arxiv.org/abs/2507.15080 https://arxiv.org/pdf/2507.1…

Fair coalition in graphs
Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The cardinality of a smallest dominating set of $G$, denoted by $γ(G)$, is the domination number of $G$. For $k \geq 1$, a $k$-fair dominating set ($kFD$-set) in $G$, is a dominating set $S$ such that $|N(v) \cap D|=k$ for every vertex $ v \in V\setminus D$. A fair dominating set in $G$ is a $kFD$-set for some integer $k\geq …

On Domination Exponents for Pairs of Graphs
Grigoriy Blekherman, Annie Raymond, Alexander Razborov, Fan Wei
https://arxiv.org/abs/2506.12151 https://

On Domination Exponents for Pairs of Graphs
Understanding graph density profiles is notoriously challenging. Even for pairs of graphs, complete characterizations are known only in very limited cases, such as edges versus cliques. This paper explores a relaxation of the graph density profile problem by examining the homomorphism density domination exponent $C(H_1, H_2)$. This is the smallest real number $c \geq 0$ such that $t(H_1, T) \geq t(H_2, T)^c$ for all target graphs $T$ (if such a $c$ exists) where $t(H,T)$ is the homomorphism den…

I know some of the money is thinking what @… says here. The trouble here is that Tesla is currently wildly, absurdly, comically overvalued wrt its fundamentals, and there are really only two rationalizations for that:
(1) Musk is a brain genius who will innovate the company into magic unicorn fairyland of world domination.
(2) Musk has Trump on a leash and will reap the benefits of kleptocratic plundering of the US Federal budget.
Both of those justifications depend on Musk remaining at Tesla. If he leaves, there’s little reason for the P/E ratio not to correct to normal car company levels — which AIUI would mean a stock price drop of >90%.
https://hachyderm.io/@zzzeek/114637505037473139

Paired Disjunctive Domination Number of Middle Graphs
Hande Tuncel Golpek, Zeliha Kartal Yildiz, Aysun Aytac
https://arxiv.org/abs/2506.19529 https://

Paired Disjunctive Domination Number of Middle Graphs
The concept of domination in graphs plays a central role in understanding structural properties and applications in network theory. In this study, we focus on the paired disjunctive domination number in the context of middle graphs, a transformation that captures both adjacency and incidence relations of the original graph. We begin by investigating this parameter for middle graphs of several special graph classes, including path graphs, cycle graphs, wheel graphs, complete graphs, complete bip…

Domination and Total Domination Numbers in Zero-divisor Graphs of Commutative Rings
Sarah Anderson, Mike Axtell, Brenda Kroschel, Joe Stickles
https://arxiv.org/abs/2506.02953

Domination and Total Domination Numbers in Zero-divisor Graphs of Commutative Rings
Zero-divisor graphs of commutative rings are well-represented in the literature. In this paper, we consider dominating sets, total dominating sets, domination numbers and total domination numbers of zero-divisor graphs. We determine the domination and total domination numbers of zero-divisor graphs are equal for all zero-divisor graphs of commutative rings except for $\mathbb{Z}_2 \times D$ in which $D$ is a domain. In this case, $γ(Γ(\mathbb{Z}_2 \times D)) = 1$ and $γ_t(Γ(\mathbb{Z}_2 \ti…

Recent results on matrix weighted norm inequalities
David Cruz-Uribe
https://arxiv.org/abs/2508.13352 https://arxiv.org/pdf/2508.13352

Recent results on matrix weighted norm inequalities
In this paper we give an overview of recent work on matrix weights, with particular emphasis on convex body sparse domination for singular integrals, Rubio de Francia extrapolation, and Jones factorization. To provide context and motivation, we survey the comparable results in the scalar weighted case.

Crosslisted article(s) found for astro-ph.CO. https://arxiv.org/list/astro-ph.CO/new
[1/1]:
- Impact of Non-Thermal Leptogenesis from Early Matter Domination on Gravitational Wave from FOPT
Dilip Kumar Ghosh, Anish Ghoshal, Koustav Mukherjee, Nimmala Narendra, Nobuchika Okada

Primordial black hole formation in matter domination
Ehsan Ebrahimian, Ali Akbar Abolhasani, Mehrdad Mirbabayi
https://arxiv.org/abs/2507.18312 https://arx…

Primordial black hole formation in matter domination
We study Primordial Black Holes (PBHs) formed by the collapse of rare primordial fluctuations during an early period of Matter Domination. The collapse threshold strongly depends on the shape of the peaks, decreasing as they become flatter and hence rarer. In the extreme limit of a top-hat perturbation, Harada, Kohri, Sasaki, Terada, and Yoo have argued that the growth of velocity dispersion prevents the formation of black holes unless the initial peak is larger than $ζ_{\rm th} \sim ζ_{\rm r…

Finitary codings and stochastic domination for Poisson representable processes
Yinon Spinka
https://arxiv.org/abs/2506.04797 https://…

Finitary codings and stochastic domination for Poisson representable processes
Construct a random set by independently selecting each finite subset of the integers with some probability depending on the set up to translations and taking the union of the selected sets. We show that when the only sets selected with positive probability are pairs, such a random set is a finitary factor of an IID process, answering a question of Forsström, Gantert and Steif. More generally, we show that this is the case whenever the distribution induced by the size of the selected sets has s…

🇺🇦 #NowPlaying on #BBC6Music's #RileyAndCoe
World Domination Enterprises:
🎵 Go Dominator
#WorldDominationEnterprises
https://worlddominationenterprises.bandcamp.com/album/go-dominator-woke-up-just-in-time
https://open.spotify.com/track/67DUMsx6OiX9kB8hfWzdtc

The reason I’m so fixated on Rudolf Rocker is that he understood authority and centralized control as inherently oppressive structures that suppress individual freedom and the collective ability to self-organize.
He argued that true freedom arises not from legal or political institutions, which often serve to maintain domination, but from the voluntary, free association of people resisting all forms of coercion and hierarchy.
For Rocker, political rights are not granted by govern…

This https://arxiv.org/abs/2505.18811 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Anarchist Approach to the Undergraduate Mathematics Curriculum
Contemporary anarchism centers around three tenets: (1) a constant challenge of and resistance to all forms of domination, (2) so-called "prefigurative politics", in which all decisions are made in a manner that is consistent with a set of non-hierarchical values such as equality, decentralization and voluntary cooperation, (3) a focus on diversity and open-endedness (Gordon, 2008). Within this philosophy the notion of end goals becomes moot; progress, then, is measured by process, in which the…

Recursive spectral relations and the charge versus neutral gap in fractional quantum Hall systems
Marius Lemm, Bruno Nachtergaele, Simone Warzel, Amanda Young
https://arxiv.org/abs/2507.18814

Recursive spectral relations and the charge versus neutral gap in fractional quantum Hall systems
We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge gap dominates the neutral gap. We verify these conditions under a triad of symmetries (translation-invariance, charge and dipole conservation) that are present, e.g., in periodic fractional quantum Hall systems. Thus, this gap domination, previously observed numerically, is a universal feature imposed by symmetry. A se…

This https://arxiv.org/abs/2404.08776 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Complexity of the game connected domination problem
The connected domination game is a variation of the domination game where the played vertices must form a connected subgraph at all stages of the game. In this paper we prove that deciding whether the game connected domination number is smaller than a given integer is PSPACE-complete using log-space reductions for both Dominator- and Staller-start connected domination game.

Weighted inequalities for the Bergman projection involving B\'{e}koll\`{e}--Bonami $B_1$-weights
Chen Jiale
https://arxiv.org/abs/2507.22363 https://ar…

Weighted inequalities for the Bergman projection involving Békollè--Bonami $B_1$-weights
In this paper, we consider weighted inequalities for the Bergman projection via sparse domination. We first establish some quantitative mixed weak-type inequalities, which leads to a weighted weak-type (1,1) bound in terms of Békollè--Bonami $B_1$-weights. We also establish some quantitative weighted $L^p$-estimates in terms of Békollè--Bonami $B_q$-weights for $1\leq q

Towards Industrial Convergence : Understanding the evolution of scientific norms and practices in the field of AI
Antoine Houssard
https://arxiv.org/abs/2505.17945

Towards Industrial Convergence : Understanding the evolution of scientific norms and practices in the field of AI
In the field of artificial intelligence (AI) research, there seems to be a rapprochement between academics and industrial forces. The aim of this study is to assess whether and to what extent industrial domination in the field as well as the ever more frequent switch between academia and industry resulted in the adoption of industrial norms and practices by academics. Using bibliometric information and data on scientific code, we aimed to understand academic and industrial researchers' practice…

Isotope shift for total electron binding energy of atoms
V. A. Dzuba, V. V. Flambaum
https://arxiv.org/abs/2507.21410 https://arxiv.org/pdf/2507.21410 https://arxiv.org/html/2507.21410
arXiv:2507.21410v1 Announce Type: new
Abstract: We compute the isotope shifts of the \emph{total} electron binding energy of neutral atoms and singly charged ions up to element $Z=120$, using relativistic Hartree-Fock method including the Breit interaction. Field shift coefficients are extracted by varying the nuclear charge radius; a small quadratic term is retained to cover large radius changes relevant to superheavy nuclei. We tabulate isotope shift coefficients for closed shell systems from Ne to Og and benchmark selected open shell cases, used to test the interpolation formula. A simple power law interpolation $bZ^k$ reproduces calculated field shifts to within about 1\% across the table, with the effective exponent $k$ growing from roughly 5 near $Z \sim 50$ to about 12 at $Z \sim 118$. Due to the domination of inner shells, differences between neutrals and singly charged ions does not exceed few percent, becoming noticeable mainly when an outer $s$ electron is removed. Therefore, these results may also be used for higher charge ions.
toXiv_bot_toot

Why do I even watch this YouTube spectacle about 20 FRP voters and one Red politician?
No state or party can grasp my needs better than I do. All political systems serve only to chain freedom and divide society.
This is why YouTube is a tool of domination, spreading the lies that keep us enslaved.
https://www.

Israel is accelerating its efforts to cement its permanent control over the West Bank
through a number of sweeping legal and institutional changes,
according to a new report from Adalah, The Legal Center for Arab Minority Rights in Israel.
The 87-page report, 
"Legal Structures of Distinction, Separation, and Territorial Domination", describes the ways in which the Netanyahu government is rapidly building on a long-standing legal matrix that further threatens…

Israel is changing the legal system governing the West Bank to accelerate annexation: report
Netanyahu’s government is building on a long-standing legal matrix to accelerate Israel’s de facto annexation in the West Bank

The Price of Being Partial: Complexity of Partial Generalized Dominating Set on Bounded-Treewidth Graphs
Jakob Greilhuber, D\'aniel Marx
https://arxiv.org/abs/2506.01645

The Price of Being Partial: Complexity of Partial Generalized Dominating Set on Bounded-Treewidth Graphs
The $(σ, ρ)$-domination framework introduced by Telle [Nord. J. Comput.'94] captures many classical graph problems. For fixed sets $σ, ρ$ of non-negative integers, a $(σ,ρ)$-set of a graph $G$ is a set $S$ such that for every $v\in V(G)$, we have (1) if $v \in S$, then $|N(v) \cap S| \in σ$, and (2) if $v \not\in S$, then $|N(v) \cap S| \in ρ$. We initiate the study of a natural partial variant of the problem, in which the constraints given by $σ, ρ$ need not be fu…

Crosslisted article(s) found for astro-ph.CO. https://arxiv.org/list/astro-ph.CO/new
[1/1]:
- Primordial Black Hole Formation and Spin in Matter Domination Revisited
Weitao Ye, Yungui Gong, Tomohiro Harada, Zhaofeng Kang, Kazunori Kohri, Daiki Saito, Chul-Moon Yoo

Induced subgraphs and tree decompositions XIX. Bags of bounded domination
Maria Chudnovsky, Sepehr Hajebi, Sophie Spirkl
https://arxiv.org/abs/2506.05602 h…

Induced subgraphs and tree decompositions XIX. Bags of bounded domination
We prove that every graph of sufficiently large treewidth has an induced subgraph $H$ of large treewidth such that either $H$ is a subdivided wall or the line graph of a subdivided wall, or every induced subgraph of $H$ admits a tree decomposition where each bag induces a subgraph of small domination number. This is best possible as subdivided walls and their line graphs do not admit such tree decompositions. As a corollary, we deduce that if a graph $G$ has maximum degree at most $Δ\in \mat…

This https://arxiv.org/abs/2410.12801 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qfi…

Exploring the Interplay of Skewness and Kurtosis: Dynamics in Cryptocurrency Markets Amid the COVID-19 Pandemic
We examine how skewness interacts with kurtosis within the cryptocurrency market. We show that during the COVID-19 pandemic there are more clusters of observations around the two flanks, highlighting the presence of a volatile behavior. Moreover, we document the evolvement of the interrelationship as the pandemic progresses, identifying the domination of the extremes. Our findings advance the thinking that by exploiting the interrelationship between the two higher moments of cryptocurrencies, i…

Grundy double domination number: bounds, graph operations, and efficient computation for $P_4$-tidy graphs
Pablo Torres
https://arxiv.org/abs/2506.21235 ht…

Grundy double domination number: bounds, graph operations, and efficient computation for $P_4$-tidy graphs
Inspired by graph domination games, various domination-type vertex sequences have been introduced, including the Grundy double dominating sequence (GDDS) of a graph and its associated parameter, the Grundy double domination number (GDDN). The decision version of the problem of computing the GDDN is known to be NP-complete, even when restricted to split graphs and bipartite graphs. In this paper, we establish general tight bounds for the GDDN. We also describe GDDSs for vertex-removed graphs and…

Stability of $2$-domination number of a graph
Mazharuddin Mehraban, Saeid Alikhani
https://arxiv.org/abs/2507.18535 https://arxiv.org/pdf/2507.18535…

Stability of $2$-domination number of a graph
This paper delves into the stability of the $2$-domination number in simple undirected graphs. The $2$-domination number of a graph $G$, $γ_2(G)$, represents the minimum size of a vertex subset where every other vertex in the graph is adjacent to at least two members of the subset. We define the $2$-domination stability, $st_{γ_2}(G)$, as the smallest number of vertices whose removal causes a change in $γ_2(G)$. Our primary contributions include computing this parameter for specific graphs, …

This https://arxiv.org/abs/2408.00277 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stochastic Domination of Exit Times for Random Walks and Brownian Motion with Drift
In this note, by an elementary use of Girsanov's transform we show that the exit time for either a biased random walk or a drifted Brownian motion on a symmetric interval is stochastically monotone with respect to the drift parameter. In the random walk case, this gives an alternative proof of a recent result of E. Peköz and R. Righter in 2024. Our arguments in both discrete and continuous cases are parallel to each other. We also outline a simple SDE proof for the Brownian case based on a sta…

An Anarchist Approach to the Undergraduate Mathematics Curriculum
Asia Matthews, Vincent Bouchard
https://arxiv.org/abs/2505.18811 https://

An Anarchist Approach to the Undergraduate Mathematics Curriculum
Contemporary anarchism centers around three tenets: (1) a constant challenge of and resistance to all forms of domination, (2) so-called "prefigurative politics", in which all decisions are made in a manner that is consistent with a set of non-hierarchical values such as equality, decentralization and voluntary cooperation, (3) a focus on diversity and open-endedness (Gordon, 2008). Within this philosophy the notion of end goals becomes moot; progress, then, is measured by process, in which the…

The multilinear fractional bounded mean oscillation operator theory I: sparse domination, sparse $T1$ theorem, off-diagonal extrapolation, quantitative weighted estimate -- for generalized commutators
Xi Cen, Zichen Song
https://arxiv.org/abs/2506.23486

The multilinear fractional bounded mean oscillation operator theory I: sparse domination, sparse $T1$ theorem, off-diagonal extrapolation, quantitative weighted estimate -- for generalized commutators
This paper introduces and studies a class of multilinear fractional bounded mean oscillation operators (denoted {\rm $m$-FBMOOs}) defined on ball-basis measure spaces $(X, μ, \mathcal{B})$. These operators serve as a generalization of canonical classes, such as the multilinear fractional maximal operators, the multilinear fractional Ahlfors-Beurling operators, the multilinear pseudo-differential operators with multi-parameter Hörmander symbol, and some multilinear operators admitting $\mathbb…

Proof of a conjecture on isolation of graphs with a universal vertex
Peter Borg, Alastair Farrugia
https://arxiv.org/abs/2506.09290 https://

Proof of a conjecture on isolation of graphs with a universal vertex
A copy of a graph $F$ is called an $F$-copy. For any graph $G$, the $F$-isolation number of $G$, denoted by $ι(G,F)$, is the size of a smallest subset $D$ of the vertex set of $G$ such that the closed neighbourhood $N[D]$ of $D$ in $G$ intersects the vertex sets of the $F$-copies contained by $G$ (equivalently, $G-N[D]$ contains no $F$-copy). Thus, $ι(G,K_1)$ is the domination number $γ(G)$ of $G$, and $ι(G,K_2)$ is the vertex-edge domination number of $G$. Settling a conjecture of Zhang an…

Domination, matching and transversal numbers for Berge-$G$ hypergraphs
Mar\'ia Jos\'e Ch\'avez de Diego, Pablo Montero Moreno, Mar\'ia Trinidad Villar-Li\~n\'an
https://arxiv.org/abs/2507.22957

Domination, matching and transversal numbers for Berge-$G$ hypergraphs
Let $G=(V(G),E(G))$ be a graph and $H=(V(H),E(H))$ be a hypergraph. The hypergraph $H$ is a {\it Berge-G} if there is a bijection $f : E(G) \mapsto E(H)$ such that for each $e \in E(G)$ we have $e \subseteq f(e)$. We define {\it dilations of $G$} as a particular subfamily of not necessarily uniform Berge-$G$ hypergraphs. We examine domination, matching and transversal numbers and some relation between these parameters in that family of hypergraphs. Our work generalizes previous results concer…

Liar's vertex-edge domination in subclasses of chordal graphs
Debojyoti Bhattacharya, Subhabrata Paul
https://arxiv.org/abs/2507.04721 https://

Liar's vertex-edge domination in subclasses of chordal graphs
Let $G=(V, E)$ be an undirected graph. The set $N_G[x]=\{y\in V|xy\in E\}\cup \{x\}$ is called the closed neighbourhood of a vertex $x\in V$ and for an edge $e=xy\in E$, the closed neighbourhood of $e$ is the set $N_G[x]\cup N_G[y]$, which is denoted by $N_G[e]$ or $N_G[xy]$. A set $L\subseteq V$ is called \emph{liar's vertex-edge dominating set} of a graph $G=(V,E)$ if for every $e_i\in E$, $|N_G[e_i]\cap L|\geq 2$ and for every pair of distinct edges $e_i,e_j\in E$, $|(N_G…

The $k$-Total Bondage Number of a Graph
Jean-Pierre Appel, Gabby Fischberg, Kyle Kelley, Nathan Shank, Eliel Sosis
https://arxiv.org/abs/2506.07000 https:/…

The $k$-Total Bondage Number of a Graph
Let $G=(V,E)$ be a connected, finite undirected graph. A set $S \subseteq V$ is said to be a total dominating set of $G$ if every vertex in $V$ is adjacent to some vertex in $S$. The total domination number, $γ_{t}(G)$, is the minimum cardinality of a total dominating set in $G$. We define the $k$-total bondage of $G$ to be the minimum number of edges to remove from $G$ so that the resulting graph has a total domination number at least $k$ more than $γ_{t}(G)$. We establish general properties…

Locating-dominating partitions for some classes of graphs
Florent Foucaud, Paras Vinubhai Maniya, Kaustav Paul, Dinabandhu Pradhan
https://arxiv.org/abs/2506.12933

Locating-dominating partitions for some classes of graphs
A dominating set of a graph $G$ is a set $D \subseteq V(G)$ such that every vertex in $V(G) \setminus D$ is adjacent to at least one vertex in $D$. A set $L\subseteq V(G)$ is a locating set of $G$ if every vertex in $V(G) \setminus L$ has pairwise distinct open neighborhoods in $L$. A set $D\subseteq V(G)$ is a locating-dominating set of $G$ if $D$ is a dominating set and a locating set of $G$. The location-domination number of $G$, denoted by $γ_{LD}(G)$, is the minimum cardinality among all …

Domination numbers and homotopy in certain ternary graphs
Taehyun Eom, Jinha Kim, Minki Kim
https://arxiv.org/abs/2508.00699 https://arxiv.org/pdf/2508.006…

Domination numbers and homotopy in certain ternary graphs
A ternary graph is a graph with no induced cycles of length $0$ modulo $3$. It was recently shown that, if the independence complex of a ternary graph is not contractible, then it is homotopy equivalent to a sphere. When a ternary graph also does not contain induced cycles of length $1$ modulo $3$, we prove that the dimension of the sphere is equal to the dimension of a minimum maximal simplex of the independence complex, or equivalently, to the value obtained by subtracting $1$ from the indepe…

The $d$-distance $p$-packing domination number: complexity and trees
Csilla Bujt\'as, Vesna Ir\v{s}i\v{c} Chenoweth, Sandi Klav\v{z}ar, Gang Zhang
https://arxiv.org/abs/2507.18272

The $d$-distance $p$-packing domination number: complexity and trees
A set of vertices $X\subseteq V(G)$ is a $d$-distance dominating set if for every $u\in V(G)\setminus X$ there exists $x\in X$ such that $d(u,x) \le d$, and $X$ is a $p$-packing if $d(u,v) \ge p+1$ for every different $u,v\in X$. The $d$-distance $p$-packing domination number $γ_d^p(G)$ of $G$ is the minimum size of a set of vertices of $G$ which is both a $d$-distance dominating set and a $p$-packing. It is proved that for every two fixed integers $d$ and $p$ with $2 \le d$ and $0 \le p \leq …

Replaced article(s) found for astro-ph.CO. https://arxiv.org/list/astro-ph.CO/new
[1/1]:
- Limits on Early Matter Domination from the Isotropic Gamma-Ray Background
Himanish Ganjoo, M. Sten Delos

Refinement of a conjecture on positive square energy of graphs
Saieed Akbari, Hitesh Kumar, Bojan Mohar, Shivaramakrishna Pragada, Shengtong Zhang
https://arxiv.org/abs/2506.07264

Refinement of a conjecture on positive square energy of graphs
Let $G$ be a simple graph of order $n$ with eigenvalues $λ_1(G)\geq \cdots \geq λ_n(G)$. Define \[s^+(G)=\sum_{λ_i >0} λ_i^2(G), \quad s^-(G)=\sum_{λ_i<0} λ_i^2(G).\] It was conjectured by Elphick, Farber, Goldberg and Wocjan that for every connected graph $G$ of order $n$, $s^+(G) \ge n-1.$ We verify this conjecture for graphs with domination number at most 2. We then strengthen the conjecture as follows: if $G$ is a connected graph of order $n$ and size $m \geq n+1$, then $s^+(G) \geq n…

Thresholds of Queen covers
Tirthankar Adhikari, Harman Agrawal, Anjali Bhagat, Ankita Dargad, Sahana Jahagirdar, Prem Kant, Urban Larsson, Sahil Wagh
https://arxiv.org/abs/2508.02545

Thresholds of Queen covers
We study optimal configurations of Queens on a square chessboard, defined as those covering the maximum number of squares. For a fixed number of Queens, $q$, we prove the existence of two thresholds in board size: a non-attacking threshold beyond which all optimal configurations are pairwise non-attacking, and a stabilizing threshold beyond which the set of optimal configurations becomes constant. Related studies on Queen domination, such as Tarnai and Gáspár (2007), focus on minimizing the n…

Multipacking in Hypercubes
Deepak Rajendraprasad, Varun Sani, Birenjith Sasidharan, Jishnu Sen
https://arxiv.org/abs/2507.01565 https://

Multipacking in Hypercubes
For an undirected graph $G$, a dominating broadcast on $G$ is a function $f : V(G) \rightarrow \mathbb{N}$ such that for any vertex $u \in V(G)$, there exists a vertex $v \in V(G)$ with $f(v) \geqslant 1$ and $d(u,v) \leqslant f(v)$. The cost of $f$ is $\sum_{v \in V} f(v)$. The minimum cost over all the dominating broadcasts on $G$ is defined as the broadcast domination number $γ_b(G)$ of $G$. A multipacking in $G$ is a subset $M \subseteq V(G)$ such that, for every vertex $v \in V(G)$ and ev…