Tootfinder

Exponential synchronization of the Kuramoto model with inertia and frustration under locally coupled network
Tingting Zhu, Xiongtao Zhang
https://arxiv.org/abs/2404.18487

Exponential synchronization of the Kuramoto model with inertia and frustration under locally coupled network
We study the collective synchronized behavior of the Kuramoto model with inertia and frustration effects on a connected and symmetric network. We aim to establish sufficient frameworks for achieving complete frequency synchronization, taking into account initial configuration, small inertia and frustration, and large coupling strength. More precisely, we first demonstrate that the phase diameter will be uniformly bounded by a small value after a finite time. Then we prove that the frequency dia…

A class of higher order inverse spectral problems
Ai-Wei Guan, Chuan-Fu Yang, Natalia P. Bondarenko
https://arxiv.org/abs/2402.18343 https://

A class of higher order inverse spectral problems
In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, where these differential operators are endowed with complex-valued distributional coefficients. For the case of multiple spectra, we first establish the relationship between spectra and the Weyl-Yurko matrix. Secondly, we prove the uniqueness theorem for the solution of the inverse problems. Our approach allows us to ob…

On the properties of the set where a generalized function of bounded variation takes infinite value
Alessandro Cucinotta
https://arxiv.org/abs/2402.13078 h…

On the properties of the set where a generalized function of bounded variation takes infinite value
We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new result on strict approximation of sets of finite perimeter from the outside with open sets.

This https://arxiv.org/abs/2403.09534 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Study of measure-valued Markov processes. Explicit bounds for the convergence in distribution of mean-field models
The aim of the paper is to prove that the rates of convergence in distribution for $N$-particle mean-field models are the expected one: $N^{-1}$ in Law of Large Numbers regime, and $N^{-1/2}$ in Central Limit Theorem regime. These proofs require to study empirical measures of McKean-Vlasov particle systems, and conditional laws of McKean-Vlasov processes, as measure-valued Markov processes. In particular, the expressions of the infinitesimal generators of such processes are established for meas…

On groups and fields interpretable in differentially closed valued fields and in various $\mathrm{NTP_2}$ fields
Paul Z. Wang
https://arxiv.org/abs/2402.09143

On groups and fields interpretable in differentially closed valued fields and in various $\mathrm{NTP_2}$ fields
This paper aims at developing model-theoretic tools to study interpretable fields and definably amenable groups, mainly in $\mathrm{NIP}$ or $\mathrm{NTP_2}$ settings. An abstract theorem constructing definable group homomorphisms from generic data is proved. It relies heavily on a stabilizer theorem of Montenegro, Onshuus and Simon. The main application is a structure theorem for definably amenable groups that are interpretable in algebraically bounded perfect $\mathrm{NTP_2}$ fields with boun…

Study of measure-valued Markov processes. Explicit bounds for the convergence in distribution of mean-field models
Xavier Erny
https://arxiv.org/abs/2403.09534

Study of measure-valued Markov processes. Explicit bounds for the convergence in distribution of mean-field models
The aim of the paper is to prove that the rates of convergence in distribution for $N$-particle mean-field models are the expected one: $N^{-1}$ in Law of Large Numbers regime, and $N^{-1/2}$ in Central Limit Theorem regime. These proofs require to study empirical measures of McKean-Vlasov particle systems, and conditional laws of McKean-Vlasov processes, as measure-valued Markov processes. In particular, the expressions of the infinitesimal generators of such processes are established for meas…

This https://arxiv.org/abs/2402.18966 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Vector Valued Gårding Inequality for pseudo-differential operators on compact homogeneous manifolds
We prove sufficient conditions in order to obtain a sharp Gårding inequality for pseudo-differential operators acting on vector-valued functions on compact Lie groups. As a consequence, we obtain a sharp Gårding inequality for compact homogeneous vector bundles and compact homogeneous manifolds. The sharp Gårding inequality is the strongest lower bound estimate known to hold for systems on $\mathbb{R}^n$, and the aim of this paper is to extend this property to systems on compact Lie groups a…