13 papers
Diffeologies on Locally Convex Spaces and Smooth Multiplication of Distributions
Alireza Ahmadi, Bijan Davvaz, Jean-Pierre Magnot
We investigate the canonical and -diffeologies on Hausdorff locally convex spaces and their applications to Schwartz distributions. We prove that a Hausdorff locally conv…
Pairwise-comparison-valued cosurfaces: a projective framework for multi-scale relational structures
Jean-Pierre Magnot
We introduce cosurfaces with values in the group \(\PC_n(H)\) of \(H\)-valued reciprocal pairwise comparison matrices. The composition law is covariant on upper triangular coeffici…
Noisy Nonreciprocal Pairwise Comparisons: Scale Variation, Noise Calibration, and Admissible Ranking Regions
Jean-Pierre Magnot
Pairwise comparisons are widely used in decision analysis, preference modeling, and evaluation problems. In many practical situations, the observed comparison matrix is not recipro…
Effective dynamics and defect expansions for polynomial PDEs on thin annuli
Jean-Pierre Magnot
We develop a geometric and analytic framework for polynomial partial differential equations posed on thin annuli in the plane. Using renormalized Sobolev inner products, we constru…
A Lorentzian SU(3)-covariant noncommutative KP hierarchy and hypercomplex gauge fields
Jean-Pierre Magnot
We propose a formal framework for a noncommutative Kadomtsev--Petviashvili (KP) hierarchy which is covariant under the action of and compatible with a Lorentzian structure…
Preliminaries on Pre-Hilbert Structures on Polynomial Spaces and Associated Laplacians
Jean-Pierre Magnot
We study orthogonal polynomial systems arising from general pre-Hilbert inner products on polynomial spaces, beyond the classical framework of measures. To each such inner product…