{"paper":{"title":"Pareto optimal structures producing resonances of minimal decay under $L^1$-type constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP","physics.optics"],"primary_cat":"math.OC","authors_text":"Illya M. Karabash","submitted_at":"2013-08-08T19:25:57Z","abstract_excerpt":"Optimization of resonances associated with 1-D wave equations in inhomogeneous media is studied under the constraint $\\| B \\|_1 <= m$ on the nonnegative function $B \\in L^1 (0,\\ell)$ that represents the medium's structure. From the Physics and Optimization points of view, it convenient to generalize the problem replacing $B$ by a nonnegative measure $d M$ and imposing on $d M$ the condition that its total mass is $<= m$. The problem is to design for a given frequency $\\alpha \\in R$ a medium that generates a resonance $ \\omega $ on the line $\\alpha + i R$ with a minimal possible decay rate $| I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1943","kind":"arxiv","version":2},"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"}