The noncommutative residue, divergence theorems and the spectral geometry functionalIn this paper, a simple proof of the divergence theorem is given by using the Dirac operator and noncommutative residues. Then we extend the divergence theorem to compact manifolds with boundary by…Jian Wang, Yong Wang·Jun 22, 2025SaveLearn
Changing the discrete spectrum of the half-line matrix Schr\"odinger operatorWe consider the matrix-valued Schr\"odinger operator on the half line with the general selfadjoint boundary condition. When the discrete spectrum is changed without changing the continuous spectrum,…Tuncay Aktosun, Ricardo Weder·Jun 22, 2025SaveLearn
Computation of the masses of the elementary particlesAn approach to gauge theory in the context of locally conformally flat space-time is described. It is discussed how there are a number of natural principal bundles associated with any given locally…John Mashford·Jun 22, 2025SaveLearn
Two-dimensional classical superintegrable systems: polynomial algebra of integralsIn this work, we investigate generic classical two-dimensional (2D) superintegrable Hamiltonian systems H, characterized by the existence of three functionally independent integrals of motion…A. M. Escobar-Ruiz, R. Azuaje, J. C. Gordiano·Jun 20, 2025SaveLearn
On the Relation of Exact Hydrodynamics to the Chapman-Enskog SeriesWe demonstrate that the Chapman-Enskog series is locally equivalent to the exact spectral closure defined on slow kinetic eigenmodes in the limit of vanishing Knudsen number. We further show that the…Florian Kogelbauer, Ilya Karlin·Jun 20, 2025SaveLearn
Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix ModelWe prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve intermediate…László Erdős, Joscha Henheik, Cornelia Vogel·Jun 20, 2025SaveLearn
Skewness-Kurtosis: small samples and power-law behaviorSkewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical…Carlo De Michele, Samuele De Bartolo·Jun 20, 2025SaveLearn
A few notes about viscoplastic rheologiesThe rigorous tools of convex analysis are used to examine various serial and parallel combinations of linear viscosity and perfect plasticity. Nonlinear viscosities are also considered. The general…Tomáš Roubíček·Jun 20, 2025SaveLearn
Leibniz 2-algebras, linear 2-racks and the Zamolodchikov Tetrahedron equationIn this paper, first we show that a central Leibniz 2-algebra naturally gives rise to a solution of the Zamolodchikov Tetrahedron equation. Then we introduce the notion of linear 2-racks and show…Nanyan Xu, Yunhe Sheng·Jun 20, 2025SaveLearn
Generalized Eshelby's inclusion and inhomogeneity problems for transient heat transferEshelby's inclusion problems have been generalized to arbitrary shape of polygonal, polyhedral, and ellipsoidal inclusions embedded in an infinite isotropic domain under transient heat transfer, and…Chunlin Wu, Zhenhua Wei, Huiming Yin·Jun 19, 2025SaveLearn
Existence of Coupled Optical Vortex Solitons Propagating in a Quadratic Nonlinear MediumWe consider the coupled propagation of an optical field and its second harmonic in a quadratic nonlinear medium governed by a coupled system of Schrodinger equations. We prove the existence of…Luciano Medina·Jun 19, 2025SaveLearn
A note on twisted, straight, and sheared waveguideIn this work, we analyze the Dirichlet Laplacian -D in an unbounded waveguide ⊂ R3, where the cross-section is translated in a constant direction and rotated…Diana C. S. Bello·Jun 19, 2025SaveLearn
Measure and integrationThis is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic…Teo Banica·Jun 18, 2025SaveLearn
The large N factorization does not hold for arbitrary multi-trace observables in random tensorsWe consider real tensors of order D, that is D-dimensional arrays of real numbers Ta1a2 … aD, where each index ac can take N values. The tensor entries Ta1a2 … aD…Razvan Gurau, Felix Joos, Benjamin Sudakov·Jun 18, 2025SaveLearn
Dynamical Phase Diagram of the REM under independent spin-flipsWe study the energy landscape of the Random Energy model (REM) integrated along trajectories of the simple random walk on the hypercube. We show that the quenched cumulant generating function of the…Chokri Manai, Simone Warzel·Jun 18, 2025SaveLearn
"Fields" in classical and quantum field theoriesThe challenges posed by the development of field theories, both classical and quantum, force us to question their most basic and foundational ideas like the role and origin of space-time, the meaning…Alberto Ibort, Arnau Mas, Luca Schiavone·Jun 18, 2025SaveLearn
Holographic Mixing and Fock Space Dynamics of Causal Fermion SystemsA limiting case is considered in which the causal action principle for causal fermion systems describing Minkowski space gives rise to the linear Fock space dynamics of quantum electrodynamics. The…Claudio Dappiaggi, Felix Finster, Niky Kamran et al.·Jun 18, 2025SaveLearn
Floquet-like theory and gauge transformations for general smooth dynamical systemsThe classical Floquet theory allows to map a time-periodic system of linear differential equations into an autonomous one. By looking at it in a geometrical way, we extend the theory to a class of…Giuseppe Gaeta, Sebastian Walcher·Jun 17, 2025SaveLearn
Revised identification of strain gradient elastic parametersThe work reported in ``Granular micromechanics-based identification of isotropic strain gradient parameters for elastic geometrically nonlinear deformations" misidentified key terms in the grain-pair…Luca Placidi, Anil Misra, Gabriele La Valle et al.·Jun 17, 2025SaveLearn
First-passage time to capture for diffusion in a 3D harmonic potentialWe determine the survival probability and first-passage time (FPT) to capture for a harmonically trapped particle, diffusing outside an absorbing spherical boundary by directly solving the…Tianyu Yuan, Ivan Surovtsev, Megan C. King et al.·Jun 17, 2025SaveLearn
A general framework for the asymptotic analysis of moist atmospheric flowsWe deal with asymptotic analysis for the derivation of partial differential equation models for geophysical flows in the earth's atmosphere with moist process closures, and we study their…Daniel Bäumer, Rupert Klein, Norbert J. Mauser·Jun 17, 2025SaveLearn
A groupoidal description of elementary particlesIn this work, we show that extending the standard description of space-time symmetries from groups of isometries to the more flexible framework of kinematical groupoids allows for the extension of…Alberto Ibort, Giuseppe Marmo, Arnau Mas et al.·Jun 17, 2025SaveLearn
The angular momentum distribution of electrons in large atoms and its deviation from Madelung's ruleWe show that the angular momentum distribution of neutral atoms, in the sense of occupation numbers, follows the Thomas-Fermi angular momentum distribution in the limit of large atomic number. In…August Bjerg, Søren Fournais, Peter Hearnshaw et al.·Jun 17, 2025SaveLearn
Detecting local topology with the spectral localizerThe spectral localizer is a predictive framework for the computation of topological invariants of natural and artificial materials. Here, three crucial improvements on the criterion for the validity…Alexander Cerjan, Hermann Schulz-Baldes·Jun 17, 2025SaveLearn
A shape optimisation of mutual inductances among coilsThis paper introduces a shape optimisation framework for achieving desired mutual inductances (MIs) among coils in 3D space. Utilising a wire modelling approach, the coils are discretised using…Toru Takahashi, Tatsuya Tokito, Yi Cui et al.·Jun 17, 2025SaveLearn