Tootfinder

Bounds on the game isolation number and exact values for paths and cycles
Csilla Bujt\'as, Tanja Dravec, Michael A. Henning, Sandi Klav\v{z}ar
https://arxiv.org/abs/2507.08503

Bounds on the game isolation number and exact values for paths and cycles
The isolation game is played on a graph $G$ by two players who take turns playing a vertex such that if $X$ is the set of already played vertices, then a vertex can be selected only if it dominates a vertex from a nontrivial component of $G \setminus N_G[X]$, where $N_G[X]$ is the set of vertices in $X$ or adjacent to a vertex in $X$. Dominator wishes to finish the game with the minimum number of played vertices, while Staller has the opposite goal. The game isolation number $ι_{\rm g}(G)$ is …

Upper cluster structure on Kac--Moody Richardson varieties
Huanchen Bao, Jeff York Ye
https://arxiv.org/abs/2506.10382 https://arxiv.…

Upper cluster structure on Kac--Moody Richardson varieties
We show coordinate rings of open Richardson varieties are upper cluster algebras for any symmetrizable Kac--Moody type. We further show the coordinate rings of (generalized) open Richardson varieties on the twisted product of flag varieties are upper cluster algebras for any symmetrizable Kac--Moody type. This includes, as special cases, reduced double Bruhat cells, Bott-Samelson varieties, braid varieties. Our results generalize various results by Casals--Gorsky--Gorsky--Le--Shen--Simental and…

The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisors
Masataka Iwai, Satoshi Jinnouchi, Shiyu Zhang
https://arxiv.org/abs/2507.08522

The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisors
We establish the Miyaoka-Yau inequality for $n$-dimensional projective klt varieties with big canonical divisor $K_X$: \[ (2(n+1)\widehat{c}_2(X) - n \widehat{c}_1(X)^2) \cdot \langle c_1(K_X)^{n-2} \rangle \ge 0. \] We also prove the Miyaoka-Yau inequality for K-semistable projective klt varieties with big anticanonical divisor $-K_X$. As part of our approach, we define the non-pluripolar product $\langle α_1 \cdots α_p \rangle$ on singular varieties, and establish the Bogomolov-Gieseker typ…

Active flow control of vertical-axis wind turbines: Insights from large-eddy simulation and finite-time resolvent analysis
Lucas Feitosa de Souza, Renato Fuzaro Miotto, William Roberto Wolf
https://arxiv.org/abs/2507.08625

Active flow control of vertical-axis wind turbines: Insights from large-eddy simulation and finite-time resolvent analysis
Active flow control is applied to improve the aerodynamic performance of a NACA0018 airfoil operating as a single-bladed vertical axis wind turbine (VAWT). Results computed by wall-resolved large-eddy simulations (LES) highlight the detrimental effects of the dynamic stall vortex (DSV) and trailing-edge vortex (TEV) on turbine efficiency, primarily through increased drag and energy loss. The proposed flow control strategy effectively delays flow separation and suppresses large-scale vortex form…

📢 Drei Festnahmen im Zusammenhang mit mutmaßlichen Sabotageanschlägen
Die Bundesanwaltschaft hat drei ukrainische Staatsbürger wegen des Verdachts der Agententätigkeit festnehmen lassen. Ihnen werde "Agententätigkeit zu Sabotagezwecken" vorgeworfen, teilte die Behörde mit.
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Drei Festnahmen im Zusammenhang mit mutmaßlichen Sabotageanschlägen
Die Bundesanwaltschaft hat drei ukrainische Staatsbürger wegen des Verdachts der Agententätigkeit festnehmen lassen. Ihnen werde "Agententätigkeit zu Sabotagezwecken" vorgeworfen, teilte die Behörde mit.

Spin-Orbit Structure and Helicity Anomaly in Relativistic Electron Vortex Beams
Zhongze Guo, Bei Xu, Qiang Gu
https://arxiv.org/abs/2507.08493 https://

Spin-Orbit Structure and Helicity Anomaly in Relativistic Electron Vortex Beams
The relativistic electron vortex beam (REVB) has attracted increasing attention due to its nontrivial spin-orbit structure recently. As relativistic electrons are governed by the Dirac equation, exact solutions to this equation provide the most reliable starting point for understanding angular momentum characteristics of REVBs. In this work, a set of exact eigensolutions of the Dirac equation are derived in a complex cylindrical coordinate system using a generalized series expansion method. We …

Virasoro constraints for Hodge integrals
Xin Wang
https://arxiv.org/abs/2506.10033 https://arxiv.org/pdf/2506.10033

Virasoro constraints for Hodge integrals
The purpose of this paper is to study Virasoro constraints for Hodge integrals in Gromov-Witten theory of any target varieties. Results consist of the following: Firstly, we propose Virasoro conjecture for Hodge integrals in Gromov-Witten theory of any target varieties; Secondly, we prove Virasoro constraints for Hodge integrals in genus zero of any target varieties; Thirdly, we prove the genus-1 $L_1^{\mathbb{E}}$ constraint with one Hodge character class insertion for any target varieties; La…

Non-augmented velocity-vorticity-pressure formulation for the Navier--Stokes--Brinkman--Forchheimer problem
Santiago Badia, Carsten Carstensen, Alberto F. Martin, Ricardo Ruiz-Baier, Segundo Villa-Fuentes
https://arxiv.org/abs/2506.10533

Non-augmented velocity-vorticity-pressure formulation for the Navier--Stokes--Brinkman--Forchheimer problem
The flow of incompressible fluid in highly permeable porous media in vorticity - velocity - Bernoulli pressure form leads to a double saddle-point problem in the Navier--Stokes--Brinkman--Forchheimer equations. The paper establishes, for small sources, the existence of solutions on the continuous and discrete level of lowest-order piecewise divergence-free Crouzeix--Raviart finite elements. The vorticity employs a vector version of the pressure space with normal and tangential velocity jump pen…

Vortex-magnetic competition and regime transitions in antiparallel flux tubes
Weiyu Shen, Rodolfo Ostilla-M\'onico, Xiaojue Zhu
https://arxiv.org/abs/2506.10648

Vortex-magnetic competition and regime transitions in antiparallel flux tubes
Vortex-magnetic interactions shape magnetohydrodynamic (MHD) turbulence, influencing energy transfer in astrophysical, geophysical, and industrial systems. On the Sun, granular-scale vortex flows couple strongly with magnetic fields, channelling energy into the corona. At high Reynolds numbers, vorticity and magnetic fields are nearly frozen into the charged fluid, and MHD flows emerge from the interplay between vortex dynamics and Lorentz forces. To probe this competition in a controlled setti…

The Classification of Graphs on $8$ vertices with Coinciding Zero Forcing number and Maximum Nullity
Wayne Barrett, Mark Hunnell, John Hutchens, John Sinkovic
https://arxiv.org/abs/2506.10726

The Classification of Graphs on $8$ vertices with Coinciding Zero Forcing number and Maximum Nullity
We study the minimum rank of a (simple, undirected) graph, which is the minimum rank among all matrices in a space determined by the graph. We determine the exact set of graphs on eight vertices for which the nullity of a minimum rank matrix does not coincide with a bound determined by the zero forcing number of a graph. Although our goal was to determine which eight-vertex graphs satisfy maximum nullity equal to the zero forcing number, we also established several additional methods to assist …