Tootfinder

Locally similar distances and equality of the induced intrinsic distances
Erick Lee-Guzm\'an, Egor A. Maximenko, Enrique Abdeel Mu\~noz-de-la-Colina, Marco Iv\'an Ruiz-Carmona
https://arxiv.org/abs/2510.05574

Locally similar distances and equality of the induced intrinsic distances
Let $X$ be a set and $d_1,d_2$ be two distances on $X$. We say that $d_1$ and $d_2$ are locally similar and write $d_1\cong d_2$, if $d_1$ and $d_2$ are topologically equivalent and for every $a$ in $X$, \[ \lim_{x\to a} \frac{d_2(x,a)}{d_1(x,a)}=1. \] We prove that if $d_1\cong d_2$, then the intrinsic distances induced by $d_1$ and $d_2$ are equal. We also provide some sufficient conditions for $d_1\cong d_2$ and consider several examples related to reproducing kernel Hilbert spaces.

Quantum Dynamics of Scalar Particles in a Spinning Cosmic String Background with Topological Defects: A Feshbach-Villars Formalism Perspective
Sarra Garah, Abdelmalek Boumali
https://arxiv.org/abs/2509.25526

Quantum Dynamics of Scalar Particles in a Spinning Cosmic String Background with Topological Defects: A Feshbach-Villars Formalism Perspective
We study the relativistic quantum dynamics of spin-0 particles in the spacetime of a spinning cosmic string that carries both spacelike disclination (conical deficit $α$) and screw dislocation (torsion $J_z$), as well as frame dragging ($J_t$). Using the Feshbach-Villars (FV) reformulation of the Klein-Gordon equation, we obtain a first-order Hamiltonian with a positive-definite density, enabling a clean probabilistic interpretation for bosons in curved or topologically nontrivial backgrounds.…