Tootfinder

This https://arxiv.org/abs/2112.12859 has been replaced.
link: https://scholar.google.com/scholar?q=a

Cardinality of Real Numbers and Set Axiomatization
The cardinality of real numbers depends on the chosen axiomatic system and specific models of set theory. Under the ZF framework, real numbers are nondenumerable, but their exact cardinality remains debated due to possible extensions of the ZF axioms. We explored this issue by analyzing sets within the ZFC model and Wang's $Σ$ model. Set $S'$, within the ZFC framework, includes all pairs of algebraic numbers with a transcendental number inserted between each pair by a function $f$, which inser…

This https://arxiv.org/abs/2110.01673 has been replaced.
link: https://scholar.google.com/scholar?q=a

Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence
We introduce a recursive model-complete theory which completely axiomatizes the structure $Z_α=(Z, +, 0, 1, f)$ where $f : x \to \lfloorα x \rfloor $ is a unary function with $α$ a fixed transcendental number.When α$ is computable, our theory is recursively enumerable, and hence decidable as a result of completeness. Therefore, this result fits into the more general theme of adding traces of multiplication to integers without losing decidability.

This https://arxiv.org/abs/2404.18704 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A geometric approach for stability analysis of delay systems: Applications to network dynamics
Investigating the network stability or synchronization dynamics of multi-agent systems with time delays is of significant importance in numerous real-world applications. Such investigations often rely on solving the transcendental characteristic equations (TCEs) obtained from linearization of the considered systems around specific solutions. While stability results based on the TCEs with real-valued coefficients induced by symmetric networks in time-delayed models have been extensively explored…

This https://arxiv.org/abs/2112.12859 has been replaced.
link: https://scholar.google.com/scholar?q=a

Cardinality of Real Numbers and Set Axiomatization
The cardinality of real numbers depends on the chosen axiomatic system and specific models of set theory. Under the ZF framework, real numbers are nondenumerable, but their exact cardinality remains debated due to possible extensions of the ZF axioms. We explored this issue by analyzing sets within the ZFC model and Wang's $Σ$ model. Set $S'$, within the ZFC framework, includes all pairs of algebraic numbers with a transcendental number inserted between each pair by a function $f$, which inser…

A geometric approach for stability analysis of delay systems: Applications to network dynamics
Shijie Zhou, Wei Lin
https://arxiv.org/abs/2404.18704 https:…

A geometric approach for stability analysis of delay systems: Applications to network dynamics
Investigating the network stability or synchronization dynamics of multi-agent systems with time delays is of significant importance in numerous real-world applications. Such investigations often rely on solving the transcendental characteristic equations (TCEs) obtained from linearization of the considered systems around specific solutions. While stability results based on the TCEs with real-valued coefficients induced by symmetric networks in time-delayed models have been extensively explored…