3 papers
math.NA2026
Efficient Multi-Precision Computation of Bessel Functions for Real Orders and Complex Arguments with Fortran Implementation -- Part I: The Modified Bessel Function of the First Kind,
Mofreh R. Zaghloul, Steven G. Johnson
This paper is the first in a series devoted to the development of efficient and highly accurate algorithms, with multiprecision \texttt{Fortran} implementations, for the computatio…
cond-mat.other2025
Sufficient conditions for localized vibrational modes in one- and two-dimensional discrete lattices
Jaden Thomas-Markarian, Rodrigo Arrieta, Shu-Ching Yang +2
This paper presents a rigorous proof that arbitrarily weak perturbations produce localized vibrational (phonon) modes in one- and two-dimensional discrete lattices, inspired by ana…
math.HO2025
Matrix Calculus (for Machine Learning and Beyond)
Paige Bright, Alan Edelman, Steven G. Johnson
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector…