Tootfinder

This https://arxiv.org/abs/2011.02575 has been replaced.
link: https://scholar.google.com/scholar?q=a

The group of affine transformations of homogeneous spaces with discrete isotropy
We present a method to compute the group of affine transformations of a homogeneous $G$-space under specific conditions: when the group $G$ and the homogeneous $G$-space admit linear connections so that the natural projection is affine, and with discrete isotropy group. If $G$ admits a bi-invariant linear connection, we establish conditions under which the homogeneous space admits an invariant linear connection. As a consequence, when the isotropy group is discrete, their respective groups of a…

This https://arxiv.org/abs/2505.04760 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Isotropic Torsors on Smooth Algebras over Prüfer Rings
The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group over a regular semilocal ring is itself trivial. Extending the work of Česnavičius and Fedorov, we prove a non-noetherian analogue of this conjecture for rings $A$ that are semilocalisations of smooth schemes over valuation rings of rank one, and for reductive $A$-group schemes $G$ that are totally isotropic. Roughly speaking, such group schemes are characterised by the existence of a par…

CMB line-of-sight integrators for nearly-isotropic cosmological models
Jo\~ao G. Vicente, Thiago S. Pereira, Cyril Pitrou
https://arxiv.org/abs/2506.07786 …

CMB line-of-sight integrators for nearly-isotropic cosmological models
Homogeneous and nearly-isotropic cosmological models are natural extensions of standard Friedmann cosmologies. Constraining their features is crucial, as any detection of their properties would impact our understanding of inflation and the cosmological principle. Since these models evolve as a set of non-interacting scalar, vector, and tensor modes on top of homogeneous and isotropic spacetimes, their imprints on cosmological observables, particularly the CMB, can be obtained using standard lin…

This https://arxiv.org/abs/2406.16627 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Random Integration Algorithm for High-dimensional Function Spaces
We introduce a novel random integration algorithm that boasts both high convergence order and polynomial tractability for functions characterized by sparse frequencies or rapidly decaying Fourier coefficients. Specifically, for integration in periodic isotropic Sobolev space and the isotropic Sobolev space with compact support, our approach attains a nearly optimal root mean square error (RMSE) bound. In contrast to previous nearly optimal algorithms, our method exhibits polynomial tractability…

Anisotropic quantum polytropes
Hermano Velten, Felipe S. Esc\'orcio, Nadson J. S. Trindade
https://arxiv.org/abs/2506.08135 https://

Anisotropic quantum polytropes
The structure of astrophysical objects is usually modeled under the assumption of hydrostatic equilibrium. However, actual configurations may deviate from perfect spherical or isotropic properties. Consequently, cosmic objects are expected to exhibit some degree of anisotropy. This consideration also extends to hypothetical dark structures, such as dark stars and dark matter halos. Although the nature of dark matter remains unknown, axion-like particles (ALPs) are strong candidates, suggesting …

Revealing Dark Matter's Role in Neutron Stars Anisotropy: A Bayesian Approach Using Multi-messenger Observations
Xue-Zhi Liu, Premachand Mahapatra, Chun Huang, Ayush Hazarika, Chiranjeeb Singha, Prasanta Kumar Das
https://arxiv.org/abs/2506.08376

Revealing Dark Matter's Role in Neutron Stars Anisotropy: A Bayesian Approach Using Multi-messenger Observations
Dark matter (DM) continues to evade direct detection, but neutron stars (NSs) serve as natural laboratories where even a modest DM component can alter their structure. While many studies have examined DM effects on NSs, they often rely on specific choices of equations of state (EOS) models, assume isotropy, and lack a Bayesian statistical framework, limiting their predictive power. In this work, we present a Bayesian framework that couples pressure-anisotropic nuclear EOS to a self-interacting …

A note on isothermic coordinate system for spacelike surfaces with constant mean curvature in Lorentz-Minkowski space
Yu Kawakami, Kaito Satake
https://arxiv.org/abs/2506.07516

A note on isothermic coordinate system for spacelike surfaces with constant mean curvature in Lorentz-Minkowski space
In this note, we present an elementary proof of the existence of isothermic coordinate system and explore its application to global property for space-like surfaces with constant mean curvature in the Lorentz-Minkowski three-space.

This https://arxiv.org/abs/2310.19611 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Exchangeability and irreducible rotational invariance
In this note we prove that a finite family $\{X_1,\dots,X_d\}$ of real r.v.'s that is exchangeable and such that $(X_1,\dots,X_d)$ is invariant with respect to a subgroup of $SO(d)$ acting irreducibly, is actually invariant with respect to the action of the full group $SO(d)$. Three immediate consequences are deduced: a characterization of isotropic spherical random eigenfunctions whose Fourier coefficients are exchangeable, an extension of Bernstein's characterization of the Gaussian and a cha…

On supported deformations and birational isotriviality
Luca Rizzi, Francesco Zucconi
https://arxiv.org/abs/2506.07059 https://arxiv.o…

On supported deformations and birational isotriviality
Let $f\colon X\to B$ be a semistable fibration with fibers of general type. We prove that if the general Kodaira-Spencer class is supported on the divisorial fixed part $D$ of a line bundle in $Ω^k_X$, then, under natural conditions on $D$, the general fibers are birational.

This https://arxiv.org/abs/2412.05110 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Revisiting semiclassical effective dynamics for quantum cosmology
We revise the technique of semiclassical effective dynamics, in particular reexamining the evaluation of Poisson structure of the so-called central moments capturing quantum corrections, providing a systematic, pedagogical, and efficient algorithm for evaluation of said structure. The resulting closed formulae for Poisson brackets involve less summatios than recent results in the literature, thus being more optimal for applications. Found formulae are then applied to a general class of isotropi…