Results 311 to 320 of about 21,501,912 (352)

EQUATIONS IN A FREE GROUP

Mathematics of the USSR-Izvestiya, 1983
An algorithm for recognizing the solvability of arbitrary equations in a free group is constructed. Bibliography: 11 titles.
openaire   +3 more sources

PSEUDOCHARACTERS ON FREE GROUPS

Russian Academy of Sciences. Izvestiya Mathematics, 1995
Let \(G\) be a group. A real function \(\varphi\) from \(G\) is called a pseudocharacter if there exists an \(\varepsilon > 0\) such that \(|\varphi (xy) - \varphi (x) - \varphi (y)|< \varepsilon\) for any \(x, y \in G\) and \(n \varphi (x) = \varphi (x^n)\) for any \(x \in G\) and any integer \(n\).
openaire   +2 more sources

Group Robust Preference Optimization in Reward-free RLHF

Neural Information Processing Systems
Adapting large language models (LLMs) for specific tasks usually involves fine-tuning through reinforcement learning with human feedback (RLHF) on preference data.
S. Ramesh, Yifan Hu, Iason Chaimalas, Viraj Mehta, Pier Giuseppe Sessa, Haitham Bou-Ammar, Ilija Bogunovic   +6 more
semanticscholar   +1 more source

Free Subgroups of Free Topological Groups

1974
It is well known that every subgroup of a free group is a free group. However, it is not true in general that a subgroup of a free topological group is a free topological group.
David C. Hunt, Sidney A. Morris
openaire   +1 more source

Palindromic Length in Free Monoids and Free Groups

Words, 2017
Aleksi Saarela
semanticscholar   +1 more source

On Automorphisms of Free Groups I

Journal of the London Mathematical Society, 1988
Let \(\phi\) be an automorphism of a free group of finite rank. \textit{S. M. Gersten} [Adv. Math. 64, 51-85 (1987; Zbl 0616.20014)] showed that \(\phi\) can be represented by a finite graph. A stronger form of `path surgery' is proved for such a graph. Using this Thurston's uniform boundedness theorem [\textit{D. Cooper}, J. Algebra 111, 453-456 (1987;
openaire   +1 more source

Free random variables : a noncommutative probability approach to free products with applications to random matrices, operator algebras, and harmonic analysis on free groups

, 1992
D. Voiculescu, K. Dykema, A. Nica
semanticscholar   +1 more source

Carrier-free nanomedicines for cancer treatment

Progress in Materials Science, 2022
Li-Han Liu, Xian-Zheng Zhang
exaly  

Moduli of graphs and automorphisms of free groups

, 1986
M. Culler, K. Vogtmann
semanticscholar   +1 more source

Lead-Free Perovskite Materials for Solar Cells

Nano-Micro Letters, 2021
Minghao Wang, Wei Shen, Lihui Liu
exaly