Mathematical preprint links an infinite matrix to two KP systems
The work gives an infinite-matrix system a geometric reading and extends it into a two-component KP framework, with formal links to AKNS and ASDYM.
Scientific publication3 min read
Specialty
Applied Mathematics
19 published articlesPart of Pure & Applied Mathematics
Latest in Applied Mathematics
Mathematical Attractor Shows Patterns Can Fix Its Geometry
A theoretical study of neutral renormalization finds that, in its defined family of cascades and towers, combinatorial data can determine geometric structure.
Scientific publication4 min read
Fractal measures can show gaps and jumps, study finds
A theoretical preprint gives exact descriptions of several spectra linked to planar fractal measures, while identifying special systems where the usual multifractal relationship fails.
Scientific publication4 min read
New Theorem Extends a Classic Dynamical-Systems Result to Group Bundles
An arXiv preprint extends the topological Halmos-von Neumann framework to open abelian group bundles, connecting compactifications with dual sheaves, point spectra and dynamical systems while marking clear limits.
Scientific publication4 min read
Kuramoto study finds selected finite states approach mean-field limits
A theorem-based analysis links finite Kuramoto manifolds with the Ott-Antonsen and continuum descriptions, while restricting the result to a specific model, parameter range and family of trajectories.
Scientific publication4 min read
Preprint finds weak topology can admit chaos in linear maps
A theoretical preprint reports Devaney chaos for some two-dimensional linear maps under weak topology, but a conflict between a Jordan-block theorem and its proof clouds one part of the classification.
Scientific publication5 min read
Preprint links Yang-Mills hierarchy to continuous and lattice systems
The mathematical construction extends Sato-theoretic coordinates to a bi-infinite array, derives exact continuous and discrete flows, and identifies AKNS, GI, and lattice systems as reductions of ASDYM.
Scientific publication4 min read
Preprint finds local and renormalized alternatives to a failed global zeta
A mathematical preprint finds that the model’s global edge-indexed Euler product breaks down coefficient by coefficient, but finite-core determinants and height damping still yield exact local, pressure and spectral results.
Scientific publication4 min read
A function nears Lipschitz regularity; its toral map is not C0-rigid
A mathematical preprint studies a lacunary skew product whose function h is Holder continuous below exponent one but not Lipschitz, while its associated toral map fails bounded mean motion and C0-rigidity for every irrational alpha.
Scientific publication3 min read
Torus Maps Challenge a Link Between Motion and Rigidity
Mathematical constructions on the two-torus preserve area and show weak mixing while meeting a deviation bound without bounded mean motion or a circle-rotation skew-product form.
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Numerical method recovers scattering data from dark solitons
A new numerical direct-scattering method was tested on three modeled dNLSE wave fields, matching analytical scattering quantities in one benchmark and identifying 28 dark solitons in another.
Scientific publication3 min read
Model Links Time-Varying Delays to Intermittent Flocking
A simulation study links time-varying interaction delays with intermittent flocking and fractal changes in collective order; under conservative delays, the same model showed rapid swings between strong and weak order.
Scientific publication6 min read
Preprint finds a recurrence property survives every finite colouring
A new arXiv preprint gives a positive answer to a partition question about sets of nice recurrence. The result is a theorem about abstract mathematical systems, not an experiment or a measured effect.
Scientific publication4 min read
Preprint: Simulations link weak dissipation to dominant solitons in shallow-water waves
A numerical study of a one-dimensional shallow-water model found that a dissipative run produced a dominant soliton in each direction of propagation. The modeled crest-height ratio was about 3, above the study’s reported criterion of greater than 1.25.
Scientific publication6 min read
Preprint Reports Gains From Randomized Reservoir Ensembles in Chaotic-System Tests
A computational study tested ensembles of randomly constructed reservoir computers in three deterministic chaotic systems. It reported a roughly 25-step Hénon-map ensemble horizon and Lorenz 96 ensemble forecasts that remained successful for at least 2.5 Lyapunov times. Performance-weighted averaging outperformed plain averaging.
Scientific publication3 min read
Preprint establishes totally weak-mixing counterparts for free-group actions
A mathematical preprint gives a positive answer to a question in ergodic theory: every free ergodic probability-measure-preserving action of a free group has an orbit-equivalent representative that is totally weak mixing. The result is existential and theoretical; it does not settle whether the representative can be made mixing.
Scientific publication4 min read
Preprint proposes a new way to build wave packets in quantum billiards
A new arXiv preprint presents a mathematical framework for constructing generalized coherent states in quantum billiards. It projects a minimal-dispersion wave packet onto continued eigenstates and develops analytical and numerical routes for studying the result. The work remains a formal construction, with no independent validation of its accuracy or long-term behavior.
Scientific publication3 min read
Preprint suggests flux theory can predict average flips in a chaotic double pendulum
A new arXiv preprint reports that phase-space flux calculations closely tracked average flip rates in a simulated equal-mass, equal-arm double pendulum. The result supports a statistical prediction of event rates within the tested model, while leaving questions about regular motion, broader pendulum designs and higher energies.
Scientific publication4 min read
Preprint shows multiplicity one for two root-of-unity maps
A new arXiv preprint gives arithmetic proofs that the parabolic multiplicity at 0 is 1 for a quadratic polynomial and an entire map at primitive root-of-unity parameters. It extends the polynomial argument to unicritical maps of arbitrary degree, but some valuation patterns remain conjectural and one computer-assisted exceptional case is reported without computational details.
Scientific publication5 min read