Tootfinder

Reading the log canonical threshold of a plane curve singularity from its Newton polyhedron
Erik Paemurru
https://arxiv.org/abs/2404.18238 https://<…

Reading the log canonical threshold of a plane curve singularity from its Newton polyhedron
There is a proposition due to Kollár 1997 on computing log canonical thresholds of certain hypersurface germs using weighted blowups, which we extend to weighted blowups with non-negative weights. Using this, we show that the log canonical threshold of a convergent complex power series is at most $1/c$, where $(c, \ldots, c)$ is a point on a facet of its Newton polyhedron. Moreover, in the case $n = 2$, if the power series is weakly normalised with respect to this facet or the point $(c, c)$ b…

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Welcome to Ubuntu 22.04.3 LTS (GNU/Linux 5.15.0-102-generic x86_64)
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Canonical extensions via fitted sublocales
Tom\'a\v{s} Jakl, Anna Laura Suarez
https://arxiv.org/abs/2404.18325 https://arxiv.org…

Canonical extensions via fitted sublocales
We build on a recent result stating that the frame $\mathsf{SE}(L)$ of strongly exact filters for a frame $L$ is anti-isomorphic to the coframe $\mathsf{S}_o(L)$ of fitted sublocales. The collection $\mathsf{E}(L)$ of exact filters of $L$ is known to be a sublocale of this frame. We consider several other subcollections of $\mathsf{SE}(L)$: the collections $\mathcal{J}(\mathsf{CP}(L))$ and $\mathcal{J}(\mathsf{SO}(L))$ of intersections of completely prime and Scott-open filters, respectively, a…

NEC violation in $f(\bar{R},\bar{T})$ gravity in the context of a non-canonical theory via modified Raychaudhuri equation
Arijit Panda, Debashis Gangopadhyay, Goutam Manna
https://arxiv.org/abs/2402.18431

NEC violation in $f(\bar{R},\bar{T})$ gravity in the context of a non-canonical theory via modified Raychaudhuri equation
In this work, we have developed the Raychaudhuri equation in $f(\bar{R},\bar{T})$ gravity in the setting of a non-canonical theory, namely K-essence theory. We solve the modified Raychaudhuri equation for the additive form of $f(\bar{R},\bar{T})$, which is $f_{1}(\bar{R})+f_{2}(\bar{T})$. For this solution, we employ two different scale factors to give two types of $f(\bar{R},\bar{T})$ solutions. By conducting a viability test and analyzing energy conditions, we have determined that in the firs…

Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement
Andrea Crisanti, Luca Salasnich, Alessandro Sarracino, Marco Zannetti
https://arxiv.org/abs/2404.17300

Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement
We analyze the general relation between canonical and grand canonical ensembles in the thermodynamic limit. We begin our discussion by deriving, with an alternative approach, some standard results first obtained by Kac and coworkers in the late 1970s. Then, motivated by the Bose-Einstein condensation (BEC) of trapped gases with a fixed number of atoms, which is well described by the canonical ensemble and by the recent groundbreaking experimental realization of BEC with photons in a dye-filled …

This https://arxiv.org/abs/2401.02215 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs without AC
In set theory without the Axiom of Choice, we study the set-theoretic strength of a generalized version of the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs introduced by Erdős and Rado, concerning their interrelation with several weak choice forms.

NEC violation in $f(\bar{R},\bar{T})$ gravity in the context of a non-canonical theory via modified Raychaudhuri equation
Arijit Panda, Debashis Gangopadhyay, Goutam Manna
https://arxiv.org/abs/2402.18431

NEC violation in $f(\bar{R},\bar{T})$ gravity in the context of a non-canonical theory via modified Raychaudhuri equation
In this work, we have developed the Raychaudhuri equation in $f(\bar{R},\bar{T})$ gravity in the setting of a non-canonical theory, namely K-essence theory. We solve the modified Raychaudhuri equation for the additive form of $f(\bar{R},\bar{T})$, which is $f_{1}(\bar{R})+f_{2}(\bar{T})$. For this solution, we employ two different scale factors to give two types of $f(\bar{R},\bar{T})$ solutions. By conducting a viability test and analyzing energy conditions, we have determined that in the firs…

Varieties with pseudoeffective canonical divisor and their Kodaira dimension
Gilberto Bini
https://arxiv.org/abs/2402.18055 https://a…

Varieties with pseudoeffective canonical divisor and their Kodaira dimension
Let X be a smooth, projective variety over the field of complex numbers. Here we focus on a conjecture attributed to Shigefumi Mori, which claims that X is uniruled if and only if the Kodaira dimension of X is negative.

Deep generative modelling of canonical ensemble with differentiable thermal properties
Shuo-Hui Li, Yao-Wen Zhang, Ding Pan
https://arxiv.org/abs/2404.18404

Deep generative modelling of canonical ensemble with differentiable thermal properties
We propose a variational modelling method with differentiable temperature for canonical ensembles. Using a deep generative model, the free energy is estimated and minimized simultaneously in a continuous temperature range. At optimal, this generative model is a Boltzmann distribution with temperature dependence. The training process requires no dataset, and works with arbitrary explicit density generative models. We applied our method to study the phase transitions (PT) in the Ising and XY mode…

This https://arxiv.org/abs/2304.11678 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Higher residues and canonical pairing on the twisted de Rham cohomology
We describe an explicit formula of the canonical pairing on the twisted de Rham cohomology associated with the category of local matrix factorizations and by characterizing its relation to Saito's higher residue pairings, we reprove the conjecture of Shklyarov.