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Formation of multiple Black Holes from Cauchy data
Dawei Shen, Jingbo Wan
https://arxiv.org/abs/2506.16117 https://arxiv.org/pdf/2506…

Formation of multiple Black Holes from Cauchy data
We construct a family of asymptotically flat Cauchy initial data for the Einstein vacuum equations that contain no trapped surfaces, yet whose future development admits multiple causally independent trapped surfaces. Assuming the weak cosmic censorship conjecture, this implies the formation of multiple black holes in finite time. The initial data are obtained by surgically modifying a vacuum geometrostatic manifold equipped with the Brill-Lindquist metric: the data agree exactly with the Brill-…

Reducible Iterated Graph Systems: multiscale-freeness and multifractals
Nero Ziyu Li, Frank Xin Hu, Thomas Britz
https://arxiv.org/abs/2506.18073 https://

Reducible Iterated Graph Systems: multiscale-freeness and multifractals
Iterated Graph Systems (IGS) aims to transplant ideas from fractal geometry into graph theory. Building on this framework, we extend Edge IGS from the primitive to the reducible setting. Within this broader context, we formulate rigorous definitions of multifractality and multiscale-freeness for graph fractals, and we establish conditions that are equivalent to the occurrence of these two phenomena. We further determine the corresponding fractal and degree spectra, proving that both are finite …

On the Sum of Additive Characters and its Applications over Finite Fields
Maithri K., Shivarama K. N., Indira K. P
https://arxiv.org/abs/2506.16081 https:/…

On the Sum of Additive Characters and its Applications over Finite Fields
In this paper, we study the sum of additive characters over finite fields, with a focus on those of specified \(\mathbb{F}_q\)-Order. We establish a general formula for these character sums, providing an additive analogue to classical results previously known for multiplicative characters. As an application, we derive a Möbius function \(μ(g)\) for polynomials \(g \in \mathbb{F}_q[x]\), analogous to the integer Möbius function \(μ(n)\), and develop a characteristic function for \(k\)-normal…

Ahlfors-regularity for minimizers of a multiphase optimal design problem
Luca Esposito, Lorenzo Lamberti, Giovanni Pisante
https://arxiv.org/abs/2506.15861

Ahlfors-regularity for minimizers of a multiphase optimal design problem
We establish an Alhfors-regularity result for minimizers of a multiphase optimal design problem. It is a variant of the classical variational problem which involves a finite number of chambers $\mathcal{E}(i)$ of prescribed volume that partition a given domain $Ω\subset\mathbb{R}^n$. The cost functional associated with a configuration $\left(\{\mathcal{E}(i)\}_i,u\right)$ is made up of the perimeter of the partition interfaces and a Dirichlet energy term, which is discontinuous across the inte…

IRENE: a fluId layeR finitE-elemeNt softwarE
Dennis W\"orthmu\"ller, Gaetano Ferraro, Pierre Sens, Michele Castellana
https://arxiv.org/abs/2506.17827

IRENE: a fluId layeR finitE-elemeNt softwarE
We present a finite-element software library, IRENE, for numerically solving the steady state and dynamics of a two-dimensional viscous fluid layer embedded in three-dimensional space, on multiple physical scales. The library is designed to handle a wide range of physical regimes -- both low-Reynolds-number and turbulent ones -- and geometries, capturing the coupling between in-plane flows, out-of-plane deformations, surface tension, and elastic response. In addition, the software can treat com…

Replaced article(s) found for stat.ME. https://arxiv.org/list/stat.ME/new
[1/2]:
- Simultaneous Inference for Multiple Proportions: A Multivariate Beta-Binomial Model
Max Westphal

Optimization of Flying Ad Hoc Network Topology and Collaborative Path Planning for Multiple UAVs
Ming He, Peizhao Wang, Haihua Chen, Bin Sun, Hongpeng Wang
https://arxiv.org/abs/2506.17945

Optimization of Flying Ad Hoc Network Topology and Collaborative Path Planning for Multiple UAVs
Multiple unmanned aerial vehicles (UAVs) play a vital role in monitoring and data collection in wide area environments with harsh conditions. In most scenarios, issues such as real-time data retrieval and real-time UAV positioning are often disregarded, essentially neglecting the communication constraints. In this paper, we comprehensively address both the coverage of the target area and the data transmission capabilities of the flying ad hoc network (FANET). The data throughput of the network …

Comparison of substructured non-overlapping domain decomposition and overlapping additive Schwarz methods for large-scale Helmholtz problems with multiple sources
Boris Martin, Pierre Jolivet, Christophe Geuzaine
https://arxiv.org/abs/2506.16875

Comparison of substructured non-overlapping domain decomposition and overlapping additive Schwarz methods for large-scale Helmholtz problems with multiple sources
Solving large-scale Helmholtz problems discretized with high-order finite elements is notoriously difficult, especially in 3D where direct factorization of the system matrix is very expensive and memory demanding, and robust convergence of iterative methods is difficult to obtain. Domain decomposition methods (DDM) constitute one of the most promising strategy so far, by combining direct and iterative approaches: using direct solvers on overlapping or non-overlapping subdomains, as a preconditi…

Stability for multiple Lamb dipoles
Ken Abe, In-Jee Jeong, Yao Yao
https://arxiv.org/abs/2507.16474 https://arxiv.org/pdf/2507.16474

Stability for multiple Lamb dipoles
In the class of nonnegative vorticities on the half-plane, we establish the Lyapunov stability of finite sums of Lamb dipoles under the initial assumptions that the dipoles are sufficiently separated and that the faster dipoles are positioned to the right of the slower ones. Our approach combines sharp energy estimates near the Lamb dipoles with a Lagrangian bootstrapping scheme, enabling us to quantify the exchanges of circulation, enstrophy, impulse, and energy between various parts of the so…

New evidence for R\'emond's generalisation of Lehmer's conjecture
Sara Checcoli, Gabriel Andreas Dill
https://arxiv.org/abs/2506.18776 https://…

New evidence for Rémond's generalisation of Lehmer's conjecture
In this article, we generalise a result of Pottmeyer from the multiplicative group of the algebraic numbers to almost split semiabelian varieties defined over number fields. This concerns a consequence of Rémond's generalisation of Lehmer's conjecture. Namely, for a finite rank subgroup $Γ$ of an almost split semiabelian variety $G$, we consider the group of rational points of $G$ over a finite extension of the field generated by the saturated closure of $Γ$, i.e. the division closure of the…