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32 papers
Faithfulness and fractal (quasi-)equivalence principles for Perron, Engel, and Pierce expansions
Mykola Moroz
We establish several unifying principles that clarify the fractal properties of classical number expansions, which are generalized by the Perron expansions. In particular, we prove…
All-sky, all-frequency directional search for persistent gravitational-waves from Advanced LIGO's and Advanced Virgo's first three observing runs
The LIGO Scientific Collaboration, the Virgo Collaboration, the KAGRA Collaboration +1627
We present the first results from an all-sky all-frequency (ASAF) search for an anisotropic stochastic gravitational-wave background using the data from the first three observing r…
Perfect powers in sequences of polygonal numbers
Andrzej DÄ browski, Salah Eddine Rihane, Gökhan Soydan +1
Let denote the -th -gonal number. Consider the Diophantine equation for integers and . All solutions to this equation are known f…
On the pertubations of E-depth, Ef-depth and sequentially Cohen-Macaulay locus
Doan Trung Cuong, Le Thanh Nhan, Nguyen Xuan Linh
Let (R,m) be a Noetherian local ring, I an ideal of R and M a finitely generated R-module. In this paper, we define and study E-depth and Ef-depth of M in I. We prove that E-depth…
Foundations of Noncommutative Carrollian Geometry via Lie-Rinehart Pairs
Andrew James Bruce
Carrollian manifolds offer an intrinsic geometric framework for the physics in the ultra-relativistic limit. The recently introduced Carrollian Lie algebroids are generalised to th…
Carrollian Lie Algebroids: Taming Singular Carrollian Geometries
Andrew James Bruce
Developments in Carrollian gravity and holography necessitate the use of singular Carroll vector fields, a feature that cannot be accommodated within standard Carrollian geometry.…