{"paper":{"title":"Decompositions of differential equations from medical imaging","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Benjamin L. Weiss, Douglas Weathers","submitted_at":"2016-10-20T19:49:53Z","abstract_excerpt":"Studying medical imaging, Peter Kuchment and Sergey Lvin encountered an countable family of differential identities for sine, cosine, and the exponential function. Specifically if for a smooth function $u$ and a complex number $\\lambda$ the minimal differential equation $u' = \\lambda u$ held, then $u$ satisfied all of their identities (i). If $u\" = \\lambda^2 u$, then $u$ satisfied all odd-indexed identities (ii). They were unable to determine (iii) if there were some other pattern as well. We realize their $n$-th identity as a polynomial $f_{n,\\lambda}(u)$ in the variable $u$ that turns out to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06555","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}